Contents - انجمن مهندسين برق و الکترونيک ايران

‫ﻓﺼﻞ ﻧﺎﻣﻪ ﻋﻠﻤﯽ ﭘﮋوﻫﺸﯽ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ ‫ﺳﺎل ﭼﻬﺎرم – ﺷﻤﺎره دوم – ﭘﺎﯾﯿﺰ و زﻣﺴﺘﺎن ‪1386‬‬ ‫ﻣﺠﻮز اﻋﻄﺎي درﺟﻪ ﻋﻠﻤﯽ ﭘﮋوﻫﺸﯽ‪:‬‬ ‫ﻃﯽ ﻧﺎﻣﻪ ﺷﻤﺎره ‪ 6/2910/3‬ﻣﻮرخ ‪83/1/16‬‬ ‫از وزارت ﻋﻠﻮم‪ ،‬ﺗﺤﻘﯿﻘﺎت و ﻓﻨﺎوري‬ ‫ﺷﺎﭘﺎ‪ISSN 1735-7152 :‬‬ ‫ﺻﻔﺤﻪآراﯾﯽ و وﯾﺮاﯾﺶ ‪:‬‬ ‫ﺧﺎﻧﻢ زﻫﺮا ﺣﻖﺷﻨﻮ‬ ‫ﭼﺎپ‪:‬‬ ‫اﻧﺘﺸﺎرات داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫ﺷﻤﺎرﮔﺎن‪ 500:‬ﺟﻠﺪ‬ ‫ﺑﻬﺎ‪:‬‬ ‫آدرس‪ :‬ﺗﻬﺮان‪ -‬ﺧﯿﺎﺑﺎن ﻓﻠﺴﻄﯿﻦ ﺷﻤﺎﻟﯽ –‬ ‫ﭘﻼك ‪ –39‬ﺳﺎﺧﺘﻤﺎن ‪ – 55‬ﻃﺒﻘﻪ دوم‪-‬‬ ‫ﮐﺪ ﭘﺴﺘﯽ‪14158 :‬‬ ‫ﻣﺠﻠﻪ ﻋﻠﻤﯽ ﭘﮋوﻫﺸﯽ اﻧﺠﻤﻦ‬ ‫ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ ‫ﺗﻠﻔﻦ‪64543504 :‬‬ ‫دور ﻧﮕﺎر‪66406469 :‬‬ ‫ﭘﺴﺖ اﻟﮑﺘﺮوﻧﯿﮑﯽ‪grptian@aut.ac.ir :‬‬ ‫ﺳﺎﯾﺖ‪http://www.iaeee-iran.org :‬‬ ‫ﺻﺎﺣﺐ اﻣﺘﯿﺎز‪ :‬دﮐﺘﺮ ﺣﺴﻦ ﻏﻔﻮري ﻓﺮد‬ ‫ﻣﺪﯾﺮ ﻣﺴﺌﻮل‪ :‬ﻣﻬﻨﺪس ﻣﺴﻌﻮد ﺣﺠﺖ‬ ‫ﺳﺮدﺑﯿﺮ‪ :‬دﮐﺘﺮ ﮔﺌﻮرگ ﻗﺮه ﭘﺘﯿﺎن‬ ‫ﻣﺪﯾﺮ اﺟﺮاﯾﯽ‪ :‬ﻣﻬﻨﺪس اﻣﯿﺮ ﺣﺴﯿﻦ رﻧﺠﺒﺮ‬ ‫ﻣﺴﺌﻮل دﺑﯿﺮﺧﺎﻧﻪ‪ :‬ﺧﺎﻧﻢ زﻫﺮا ﺣﻖﺷﻨﻮ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان ﻓﺼﻞ ﻧﺎﻣﻪ ﻋﻠﻤﯽ ﭘﮋوﻫﺸﯽ‬ ‫دو زﺑﺎﻧﻪ ﻓﺎرﺳﯽ‪ -‬اﻧﮕﻠﯿ ﺴﯽ اﺳﺖ و در آن ﻣﻘﺎﻻﺗﯽ ﭘﺬﯾﺮﻓﺘﻪ و ﭼـﺎپ ﺧﻮاﻫﻨـﺪ‬ ‫ﺷﺪ ﮐﻪ ﺣﺎﺻﻞ ﭘﮋوﻫﺶ ﻫﺎي اﺻﯿﻞ و ﺣﺎوي ﻧﺘﺎﯾﺞ ﻧﻮ در زﻣﯿﻨﻪ ﻫﺎي ﮔﻮﻧـﺎﮔﻮن‬ ‫ﻣﻬﻨﺪﺳﯽ ﺑﺮق از ﺟﻤﻠﻪ اﻟﮑﺘﺮوﻧﯿﮏ‪ ،‬ﻗـﺪرت‪ ،‬ﮐﻨﺘـﺮل‪ ،‬ﮐـﺎﻣﭙﯿﻮﺗﺮ‪ ،‬ﻣﺨـﺎﺑﺮات و‬ ‫ﻣﻬﻨﺪﺳﯽ ﭘﺰﺷﮑﯽ ﺑﺎﺷﻨﺪ‪ .‬از ﮐﻠﯿﻪ ﻣﺤﻘﻘﺎﻧﯽ ﮐﻪ ﺑﺮاي اﯾﻦ ﻣﺠﻠـﻪ ﻣﻘﺎﻟـﻪ ﺗﻬﯿـﻪ‬ ‫ﻣﯽ ﮐﻨﻨﺪ درﺧﻮاﺳﺖ ﻣﯽ ﺷﻮد ﮐﻪ ﻣﻘﺎﻻت ﺧﻮد را ﺑﻪ ﭘﺴﺖ اﻟﮑﺘﺮوﻧﯿﮑﯽ ﺳـﺮدﺑﯿﺮ‬ ‫ارﺳﺎل ﻧﻤﺎﯾﻨﺪ‪ .‬ﻣﻘﺎﻻت ﺟﻬﺖ ﭘﺬﯾﺮش ﺑﺎﯾﺪ ﻋﻼوه ﺑﺮ ﺗﺎﯾﯿﺪ ﺗﻮﺳﻂ داوران ﻗـﺒﻼ‬ ‫در ﻫﯿﭻ ﻧﺸﺮﯾﻪ‪ ،‬ﮐﺘﺎب و ﯾﺎ رﺳﺎﻧﻪ ﮔﺮوﻫﯽ دﯾﮕﺮي اراﺋﻪ ﻧـﺸﺪه ﺑﺎﺷـﻨﺪ‪ .‬ﻓﺮﻣـﺖ‬ ‫اﻧﮕﻠﯿﺴﯽ و ﻓﺎرﺳﯽ ﻣﻘﺎﻻت در وب ﺳﺎﯾﺖ ﻣﺠﻠﻪ ﻣﻮﺟﻮد ﻣﯽ ﺑﺎﺷﺪ‪.‬‬ ‫ﺑــﺪﯾﻬﯽ اﺳــﺖ ﻣﻄﺎﻟــﺐ ﻣﻨــﺪرج در ﻣﻘــﺎﻻت ﺻــﺮﻓﺎً ﺑﯿــﺎﻧﮕﺮ ﻧﻘﻄــﻪ ﻧﻈــﺮات‬ ‫ﻧﻮﯾﺴﻨﺪﮔﺎن ﺑﻮده و اﯾﻦ آرا ﻟﺰوﻣﺎً ﻧﻈﺮ ﻣﺴﺌﻮﻟﯿﻦ ﻣﺠﻠﻪ ﯾﺎ اﻧﺠﻤﻦ ﻧﻤﯽ ﺑﺎﺷﻨﺪ‪.‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ PDF created with pdfFactory Pro trial version www.pdffactory.com ‫اﻋﻀﺎي ﮔﺮوه ﺗﺨﺼﺼﯽ اﻟﮑﺘﺮوﻧﯿﮏ‬ ‫دﮐﺘﺮ ﻋﻠﯽ رﺳﺘﻤﯽ‬ ‫دﮐﺘﺮ ﺣﺴﻦ ﻏﻔﻮريﻓﺮد‬ ‫دﮐﺘﺮ ﮐﺮﯾﻢ ﻓﺎﺋﺰ‬ ‫دﮐﺘﺮ ﺧﻠﯿﻞ ﻣﺎﻓﯽﻧﮋاد‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪﮐﺎﻇﻢ ﻣﺮوجﻓﺮﺷﯽ‬ ‫دﮐﺘﺮ ﺷﻤﺲاﻟﺪﯾﻦ ﻣﻬﺎﺟﺮزاده‬ ‫اﻋﻀﺎي ﻫﯿﺌﺖ ﺗﺤﺮﯾﺮﯾﻪ‬ ‫اﻋﻀﺎي ﮔﺮوه ﺗﺨﺼﺼﯽ ﮐﻨﺘﺮل‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﺗﺒﺮﯾﺰ‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﻓﺮدوﺳﯽ ﻣﺸﻬﺪ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﺮﺑﯿﺖﻣﺪرس‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫دﮐﺘﺮ ﭘﺮوﯾﺰ ﺟﺒﻪدار ﻣﺎراﻻﻧﯽ‬ ‫دﮐﺘﺮ ﻋﻠﯽ ﺧﺎﮐﯽﺻﺪﯾﻖ‬ ‫دﮐﺘﺮ ﺳﻬﺮاب ﺧﺎﻧﻤﺤﻤﺪي‬ ‫دﮐﺘﺮ ﻧﺎﺻﺮ ﺳﺎداﺗﯽ‬ ‫دﮐﺘﺮ ﻣﺴﻌﻮد ﺷﻔﯿﻌﯽ‬ ‫دﮐﺘﺮ ﮐﺎروﻟﻮﮐﺲ‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪﺑﺎﻗﺮ ﻣﻨﻬﺎج‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺧﻮاﺟﻪ ﻧﺼﺮاﻟﺪﯾﻦ ﻃﻮﺳﯽ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﺒﺮﯾﺰ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ ﺷﺮﯾﻒ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪ اﺣﻤﺪﯾﺎن‬ ‫دﮐﺘﺮ ﻫﺎﺷﻢ اورﻋﯽ‬ ‫اﺳﺘﺎدﯾﺎر داﻧﺸﮕﺎه ﺻﻨﻌﺖ آبوﺑﺮق‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ ﺷﺮﯾﻒ‬ ‫دﮐﺘﺮ ﺳﯿﺪ ﮐﻤﺎلاﻟﺪﯾﻦ ﻧﯿﮑﺮوش‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫ﻣﻬﻨﺪس ﻣﺴﻌﻮد ﺣﺠﺖ‬ ‫ﻣﺤﻘﻖ وزارت ﻧﯿﺮو‬ ‫دﮐﺘﺮ ﺳﯿﺪ ﺣﺴﯿﻦ ﺣﺴﯿﻨﯽ‬ ‫دﮐﺘﺮ ﻗﺪرتاﻟﻪ ﺣﯿﺪري‬ ‫دﮐﺘﺮ ﺣﯿﺪرﻋﻠﯽ ﺷﺎﯾﺎﻧﻔﺮ‬ ‫دﮐﺘﺮ ﻣﻬﺮداد ﻋﺎﺑﺪي‬ ‫دﮐﺘﺮ ﺣﺴﯿﻦ ﻋﺴﮑﺮﯾﺎن اﺑﯿﺎﻧﻪ‬ ‫دﮐﺘﺮ ﺟﻮاد ﻓﯿﺾ‬ ‫دﮐﺘﺮ ﮔﺌﻮرگ ﻗﺮهﭘﺘﯿﺎن‬ ‫دﮐﺘﺮ ﺣﺴﯿﻦ ﻣﺤﺴﻨﯽ‬ ‫دﮐﺘﺮ ﻣﻬﺪي ﻣﻌﻠﻢ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﺒﺮﯾﺰ‬ ‫ﻣﺤﻘﻖ ﻣﺮﮐﺰ ﺗﺤﻘﯿﻘﺎت ﻧﯿﺮو‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﻋﻠﻢ و ﺻﻨﻌﺖ اﯾﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﺻﻔﻬﺎن‬ ‫اﻋﻀﺎي ﮔﺮوه ﺗﺨﺼﺼﯽ ﻗﺪرت‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪ اﺑﻄﺤﯽ‬ ‫ﻣﻬﻨﺪس ﻣﺤﻤﻮد اﺣﻤﺪيﭘﻮر‬ ‫ﻣﻬﻨﺪس ﺣﺴﯿﻦ ﺑﺨﺘﯿﺎري زاده‬ ‫دﮐﺘﺮ ﺣﺴﯿﻦ ﺑﺮﺳﯽ‬ ‫ﻣﻬﻨﺪس ﻣﺤﻤﺪ ﭘﺎرﺳﺎ‬ ‫دﮐﺘﺮ ﻣﺤﺴﻦ ﭘﻮر رﻓﯿﻊ ﻋﺮﺑﺎﻧﯽ‬ ‫دﮐﺘﺮ ﻏﻼﻣﻌﻠﯽ ﺣﺴﻨﯽ ﺻﺪر‬ ‫دﮐﺘﺮ اﺣﻤﺪ ﺧﺎدمزاده‬ ‫دﮐﺘﺮ ﻋﺒﺪاﻟﻪ ﺧﻮﯾﯽ‬ ‫دﮐﺘﺮ ﻓﺮﻫﺎد رﺷﯿﺪي‬ ‫دﮐﺘﺮ ﻏﻼﻣﺤﺴﯿﻦ روﯾﯿﻦ ﺗﻦ‬ ‫اﻋﻀﺎي ﮔﺮوه ﺗﺨﺼﺼﯽ ﻣﺨﺎﺑﺮات‬ ‫دﮐﺘﺮ ﻋﻠﯽ آﻗﺎﮔﻠﺰاده‬ ‫دﮐﺘﺮ ﻓﺮخ ﺣﺠﺖ ﮐﺎﺷﺎﻧﯽ‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪ ﺣﮑﺎك‬ ‫دﮐﺘﺮ ﺟﻮاد ﺻﺎﻟﺤﯽ‬ ‫دﮐﺘﺮ ﻫﻤﺎﯾﻮن ﻋﺮﯾﻀﯽ‬ ‫دﮐﺘﺮ ﻣﺤﻤﻮد ﮐﻤﺮهاي‬ ‫اﻋﻀﺎي ﻫﯿﺌﺖ ﻣﺸﺎوران‬ ‫ﻣﺤﻘﻖ ﻣﺮﮐﺰ ﺗﺤﻘﯿﻘﺎت ﻣﺨﺎﺑﺮات اﯾﺮان‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﻣﺸﺎﻧﯿﺮ‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﻗﺪس ﻧﯿﺮو‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ ﻫﺎﻧﻮور آﻟﻤﺎن‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﭘﺎرس ﺗﺎﺑﻠﻮ‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﻣﺸﺎﻧﯿﺮ‬ ‫ﻣﺤﻘﻖ ﻣﺮﮐﺰ آﻣﻮزش ﻣﺨﺎﺑﺮات‬ ‫ﻣﺤﻘﻖ ﻣﺮﮐﺰ ﺗﺤﻘﯿﻘﺎت ﻣﺨﺎﺑﺮات اﯾﺮان‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه اروﻣﯿﻪ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﻟﻮزان ﺳﻮﯾﯿﺲ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﻣﯿﺸﯿﮕﺎن آﻣﺮﯾﮑﺎ‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﺗﺒﺮﯾﺰ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﻋﻠﻢ و ﺻﻨﻌﺖ اﯾﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﺮﺑﯿﺖ ﻣﺪرس‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ ﺷﺮﯾﻒ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﻋﻠﻢ و ﺻﻨﻌﺖ اﯾﺮان‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫دﮐﺘﺮ ﻓﺮاﻣﺮز رﻫﺒﺮ‬ ‫دﮐﺘﺮ ﺣﻤﯿﺪ ﺳﻠﻄﺎﻧﯿﺎنزاده‬ ‫ﻣﻬﻨﺪس ﻋﻠﯿﺮﺿﺎ ﺷﯿﺮاﻧﯽ‬ ‫دﮐﺘﺮ ﺳﯿﺪ ﺣﺴﯿﻦ ﺣﺴﺎماﻟﺪﯾﻦ ﺻﺎدﻗﯽ‬ ‫دﮐﺘﺮ رﺿﺎ ﺻﻔﺎﺑﺨﺶ‬ ‫دﮐﺘﺮ ﻣﻌﺼﻮم ﻓﺮدﯾﺲ‬ ‫دﮐﺘﺮ ﻋﺒﺎس ﻓﺮﺷﭽﯽ‬ ‫دﮐﺘﺮ ﻣﺴﻌﻮد ﻓﺮزاﻧﻪ‬ ‫دﮐﺘﺮ ﻣﺤﻤﺪ ﺻﺎدق ﻗﺎﺿﯽزاده‬ ‫دﮐﺘﺮ ﻋﻠﯽ ﻗﻨﺒﺮي‬ ‫دﮐﺘﺮ ﺣﻤﯿﺪ ﻋﺒﺎﭼﯽ‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﻣﻬﻨﺪﺳﯿﻦ ﻣﺸﺎور ﻧﯿﺮو‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺗﻬﺮان‬ ‫ﻣﺤﻘﻖ ﺷﺮﮐﺖ ﻣﻮﻧﻨﮑﻮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ اﻣﯿﺮﮐﺒﯿﺮ‬ ‫ﻣﺤﻘﻖ وزارت ارﺗﺒﺎﻃﺎت و ﻓﻨﺎوري اﻃﻼﻋﺎت‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﺻﻨﻌﺘﯽ ﮐﻤﻨﯿﺘﺰ آﻟﻤﺎن‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه ﮐﺒﮏ ﮐﺎﻧﺎدا‬ ‫اﺳﺘﺎدﯾﺎر داﻧﺸﮕﺎه ﺻﻨﻌﺖ آب و ﺑﺮق‬ ‫اﺳﺘﺎد داﻧﺸﮕﺎه اﺳﮑﺲ اﻧﮕﻠﺴﺘﺎن‬ ‫داﻧﺸﯿﺎر داﻧﺸﮕﺎه ﻣﻮﻧﺎش اﺳﺘﺮاﻟﯿﺎ‬ ‫‪١‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺍﻋﻀﺎﺀ ﻫﻴﺌﺖ ﺩﺍﻭﺭﺍﻥ ﺟﻠﺪ ﭼﻬﺎﺭﻡ‬ ‫ﺩﻛﺘﺮ ﺷﻔﻴﻌﻲ‬ ‫ﺧﺎﻧﻢ ﺩﻛﺘﺮ ﺷﺎﻳﺴﺘﻪ‬ ‫ﺩﻛﺘﺮ ﺻﺎﻣﺘﻲ‬ ‫ﺩﻛﺘﺮ ﺻﻨﺎﻳﻊﭘﺴﻨﺪ‬ ‫ﺩﻛﺘﺮ ﻃﺮﻓﺪﺍﺭ ﺣﻖ‬ ‫ﺩﻛﺘﺮ ﻋﺒﺎﭼﻲ‬ ‫ﺩﻛﺘﺮ ﻋﺴﻜﺮﻳﺎﻥ‬ ‫ﺩﻛﺘﺮ ﻋﺎﺑﺪﻱ‬ ‫ﺩﻛﺘﺮ ﻓﺎﺗﺤﻲ‬ ‫ﻣﻬﻨﺪﺱ ﻗﺎﺳﻢﺯﺍﺩﻩ‬ ‫ﺩﻛﺘﺮ ﻗﺮﻩﭘﺘﻴﺎﻥ‬ ‫ﻣﻬﻨﺪﺱ ﻛﺎﻇﻤﻲ‬ ‫ﺩﻛﺘﺮ ﻋﻠﻮﻣﻲ‬ ‫ﺩﻛﺘﺮ ﻟﺴﺎﻧﻲ‬ ‫ﺩﻛﺘﺮ ﻣﻌﻴﻦ‬ ‫ﺩﻛﺘﺮ ﻧﺒﻮﻱ‬ ‫ﺩﻛﺘﺮ ﻫﻤﺎﻳﻮﻥﭘﻮﺭ‬ ‫ﺩﻛﺘﺮ ﺁﻗﺎﮔﻠﺰﺍﺩﻩ‬ ‫ﺩﻛﺘﺮ ﺁﻧﺎﻟﻮﻳﻲ‬ ‫ﺩﻛﺘﺮ ﺍﻓﺸﺎﺭﻧﻴﺎ‬ ‫ﺩﻛﺘﺮ ﺍﺣﺴﺎﻥ‬ ‫ﺩﻛﺘﺮ ﺍﻛﺒﺮﻱ‬ ‫ﺩﻛﺘﺮ ﺑﻄﺤﺎﺋﻲ‬ ‫ﺩﻛﺘﺮ ﭘﺮﻳﺰ‬ ‫ﺩﻛﺘﺮ ﭘﺎﺭﺳﺎ ﻣﻘﺪﻡ‬ ‫ﺩﻛﺘﺮ ﺗﻤﺪﻥ‬ ‫ﺩﻛﺘﺮ ﺟﺎﻭﻳﺪﻱ‬ ‫ﺩﻛﺘﺮ ﺣﺴﻴﻨﻲ‬ ‫ﺩﻛﺘﺮ ﺣﺴﻴﻦﺯﺍﺩﻩ‬ ‫ﺩﻛﺘﺮ ﺣﺎﺋﺮﻱ‬ ‫ﺩﻛﺘﺮ ﺧﺎﻥﻣﺤﻤﺪﻱ‬ ‫ﺩﻛﺘﺮ ﺭﺍﺷﺪ ﻣﺤﺼﻞ‬ ‫ﺩﻛﺘﺮ ﺭﺣﻴﻢﭘﻮﺭ‬ ‫ﺩﻛﺘﺮ ﺭﺍﺩﺍﻥ‬ ‫‪٢‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﻣﻌﺮﻓﻲ ﻳﻚ ﺭﻭﺵ ﺟﺪﻳﺪ ﺑﺮﺍﻱ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺩﺭ ﺷﺒﻜﻪ‬ ‫ﻫﺎﻱ ﻗﺪﺭﺕ ﺑﺮ ﻣﺒﻨﺎﻱ ﺣﻔﺎﻇﺖ ﮔﺴﺘﺮﺩﻩ ﺷﺒﻜﻪ‬ ‫ ﻣﻬﺪﯼ ﺩﺍﻭﺭﭘﻨﺎﻩ‬،‫ ﻣﺠﻴﺪ ﺻﻨﺎﻳﻊ ﭘﺴﻨﺪ‬،‫ﺣﺎﻣﺪ ﺍﺳﺪﯼ‬ ‫ ﺩﺍﻧﺸﮕﺎﻩ ﺗﻬﺮﺍﻥ‬-‫ ﭘﺮﺩﻳﺲ ﺩﺍﻧﺸﮑﺪﻩ ﻫﺎﻱ ﻓﻨﻲ‬-‫ ﺩﺍﻧﺸﮑﺪﻩ ﻣﻬﻨﺪﺳﻲ ﺑﺮﻕ ﻭ ﮐﺎﻣﭙﻴﻮﺗﺮ‬-‫ﻗﻄﺐ ﻋﻠﻤﻲ ﮐﻨﺘﺮﻝ ﻭ ﭘﺮﺩﺍﺯﺵ ﻫﻮﺷﻤﻨﺪ‬ ‫ ﺍﻳﺮﺍﻥ‬-‫ﺗﻬﺮﺍﻥ‬ ‫ ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺷﺒﻜﻪ‬،‫ ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﺑﺎﺭﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ ﺩﺭ ﺑﺮﺍﺑﺮ ﺍﻏﺘﺸﺎﺷﺎﺕ ﻭﻟﺘﺎﮊﻱ‬:‫ﭼﻜﻴﺪﻩ‬ ۲ ‫ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﻭ ﺭﻓﺘﺎﺭ ﺷﺒﻜﻪ ﺩﺭ‬،‫ ﻣﺤﺪﻭﺩ ﻛﻨﻨﺪﻩ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﻭ ﺑﺎﺭﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ‬،‫ ﮔﺎﻭﺭﻧﺮ‬،AVR ،‫ﺧﺮﺍﺳﺎﻥ ﺷﺎﻣﻞ ﻣﺪﻟﺴﺎﺯﻱ ﮊﻧﺮﺍﺗﻮﺭ‬ ‫ ﺑﺮﺍﻱ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﻭﺿﻌﻴﺖ‬VCI ‫ ﺳﭙﺲ ﺭﻭﺵ ﺟﺪﻳﺪ‬.‫ ﺑﺮﺭﺳﻲ ﻣﻲ ﮔﺮﺩﺩ‬،‫ﺍﻏﺘﺸﺎﺵ ﺑﺰﺭﮒ ﻭ ﻳﻚ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ ﻭﻟﺘﺎﮊ ﻧﻮﻋﻲ‬ .‫ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺩﺭ ﺷﺒﻜﻪ ﻫﺎﻱ ﻗﺪﺭﺕ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﻭ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻣﻲ ﮔﺮﺩﺩ‬ ‫ ﺗﺨﻤﻴﻦ ﺑﻪ‬،‫ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺑﻠﻨﺪ ﻣﺪﺕ‬،‫ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ‬،‫ ﻣﺪﻝ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺑﺎﺭ‬،P.M.U. ،‫ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ‬ :‫ﻭﺍﮊﻩ ﻫﺎﻱ ﻛﻠﻴﺪﻱ‬ ‫ﻫﻨﮕﺎﻡ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Introducing a Novel Method for Real Time Estimation of Power System Voltage Instability Based on Wide Area Protection Hamed Asadi, Majid Sanaye-Pasand, Mahdi Davarpanah School of Electrical & Computer Engineering, College of Engineering University of Tehran, Tehran, Iran Abstract : In this paper, the behavior of dynamic loads of a power system against voltage disturbances is investigated. Then a real electric grid, Khorasan electric grid in North-East of Iran, is modeled by dynamic model of generators, AVRs, governors, field current limiting systems and electric loads. The paper is continued by introducing a novel method, called VCI, for real time voltage instability detection. Mentioned method is simulated on Khorasan electric grid and results are analyzed. Keywords: Dynamic modeling, P.M.U., Dynamic load modeling, Transient voltage collapse, Longer term voltage collapse, Real time voltage instability estimation 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ ۳ PDF created with pdfFactory Pro trial version www.pdffactory.com ‫ﺍﺳﺖ ﻛﻪ ﺣﺠﻢ ﺍﻃﻼﻋﺎﺗﻲ ﻛﻪ ﺩﺭ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ﺍﺯ ﻃﺮﻳﻖ ﺍﺭﺗﺒﺎﻁ ﻣﺨﺎﺑﺮﺍﺗﻲ‬ ‫ﻣﻨﺘﻘﻞ ﻣﻲ ﮔﺮﺩﺩ ﺑﺴﻴﺎﺭ ﭘﺎﻳﻴﻦ ﺍﺳﺖ ﻭ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻨﻜﻪ ﺍﺯ ﻣﺤﻴﻄﻬﺎﻱ‬ ‫ﻣﺨﺎﺑﺮﺍﺗﻲ ﺳﺮﻳﻊ ﻣﺎﻧﻨﺪ ﻓﻴﺒﺮ ﻧﻮﺭﻱ ﺍﺳﺘﻔﺎﺩﻩ ﻛﺮﺩﻩ ﻭ ﻧﻴﺎﺯ ﺑﻪ ﻣﺤﺎﺳﺒﺎﺕ ﺳﺮﻳﻊ ﻭ‬ ‫ﺳﺎﺩﻩﺍﻱ ﺩﺍﺭﻧﺪ‪ ،‬ﻛﺎﺭ ﺑﺮﺩ ﻫﻤﺰﻣﺎﻥ ﺁﻧﻬﺎ ﺑﺮﺍﻱ ﺗﻌﻴﻴﻦ ﻧﻮﺍﺣﻲ ﻧﺰﺩﻳﻚ ﺑﻪ‬ ‫ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻭ ﺣﻔﺎﻇﺖ ﺷﺒﻜﻪﺍﻱ ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ ﺩﺭ ﺑﺮﺍﺑﺮ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ‬ ‫ﭼﻪ ﺩﺭ ﺣﺎﻟﺖ ﮔﺬﺭﺍ ﻭ ﭼﻪ ﺩﺭ ﺣﺎﻟﺖ ﺑﻠﻨﺪﻣﺪﺕ‪ ،‬ﻣﻴﺴﺮ ﻣﻲ ﺑﺎﺷﺪ‪.‬‬ ‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﭘﺲ ﺍﺯ ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﻳﻚ ﺭﻭﺵ ﺟﺪﻳﺪ‬ ‫ﺑﺮﺍﻱ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻣﻌﺮﻓﻲ ﻭ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﻣﻲ‬ ‫ﮔﺮﺩﺩ‪.‬‬ ‫‪ -۱‬ﻣﻘﺪﻣﻪ‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫ﺍﻓﺰﺍﻳﺶ ﺑﻴﺶ ﺍﺭ ﭘﻴﺶ ﺗﻘﺎﺿﺎﻱ ﻣﺼﺮﻑ ﺑﺮﻕ ﺍﺯ ﻳﻚ ﻃﺮﻑ ﻭ ﻫﺰﻳﻨﻪ ﺑﺎﻻﻱ‬ ‫ﺍﺣﺪﺍﺙ ﻧﻴﺮﻭﮔﺎﻫﺎ ﻭ ﺧﻄﻮﻁ ﺍﻧﺘﻘﺎﻝ ﻭ ﻫﻤﭽﻨﻴﻦ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺳﻴﺴﺘﻢ ﻫﺎﻱ‬ ‫ﻛﻨﺘﺮﻟﻲ ﻭ ﺣﻔﺎﻇﺘﻲ ﭘﻴﺸﺮﻓﺘﻪ‪ ،‬ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭﺍﻥ ﺳﻴﺴﺘﻢ ﻫﺎﻱ ﻗﺪﺭﺕ ﺭﺍ ﺑﺮ ﺁﻥ‬ ‫ﺩﺍﺷﺖ ﺗﺎ ﺣﺪﺍﻛﺜﺮ ﺍﺳﺘﻔﺎﺩﻩ ﺭﺍ ﺍﺯ ﻇﺮﻓﻴﺖ ﺍﻧﺘﻘﺎﻝ ﺧﻄﻮﻁ ﻣﻮﺟﻮﺩ ﺑﻪ ﻋﻤﻞ‬ ‫ﺁﻭﺭﺩﻧﺪ‪.‬‬ ‫ﺩﺭ ﺷﺮﺍﻳﻂ ﺟﺪﻳﺪ‪ ،‬ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﻜﻲ ﺍﺯ ﻣﺤﺪﻭﺩﻳﺘﻬﺎﻱ ﺍﺻﻠﻲ ﺩﺭ‬ ‫ﺍﻧﺘﻘﺎﻝ ﺗﻮﺍﻥ ﺑﻪ ﻣﺼﺮﻑ ﻛﻨﻨﺪﻩ ﻣﻲ ﺑﺎﺷﺪ ﻛﻪ ﺑﺎﻳﺴﺘﻲ ﺩﺭ ﻣﺮﺣﻠﻪ ﻃﺮﺍﺣﻲ ﻭ‬ ‫ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭﻱ ﺑﻪ ﺁﻥ ﺗﻮﺟﻪ ﺷﻮﺩ ]‪ .[۱‬ﺯﻣﺎﻧﻲ ﺍﻳﻦ ﻣﻮﺿﻮﻉ ﻋﻤﺪﺗﺎ ﺑﺎ ﺳﻴﺴﺘﻢ‬ ‫ﻫﺎﻱ ﺿﻌﻴﻒ ﻭ ﺧﻄﻮﻁ ﻃﻮﻻﻧﻲ ﻣﺮﺗﺒﻂ ﺑﻮﺩ‪ ،‬ﺍﻣﺎ ﺍﻛﻨﻮﻥ ﺩﺭ ﻧﺘﻴﺠﻪ ﺑﺎﺭ ﮔﺬﺍﺭﻱ‬ ‫ﺷﺪﻳﺪﺗﺮ ﺧﻄﻮﻁ‪ ،‬ﺩﺭ ﺷﺒﻜﻪ ﻫﺎﻱ ﺑﺴﻴﺎﺭ ﺗﻮﺳﻌﻪ ﻳﺎﻓﺘﻪ ﻧﻴﺰ ﺑﺎﻳﺴﺘﻲ ﺍﻳﻦ ﻣﺴﺎﻟﻪ‬ ‫ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ ﻗﺮﺍﺭ ﮔﻴﺮﺩ ]‪ .[۲‬ﻭﻗﻮﻉ ﻓﺮﻭﭘﺎﺷﻴﻬﺎﻱ ﮔﺴﺘﺮﺩﻩ ﺩﺭ ﺷﺒﮑﻪ ﻫﺎﻱ‬ ‫ﺍﺭﻭﭘﺎ ﻭ ﺁﻣﺮﻳﮑﺎ ﺩﺭ ﺳﺎﻟﻬﺎﻱ ﺍﺧﻴﺮ ﺩﺭ ﺍﺛﺮ ﻫﻤﻴﻦ ﭘﺪﻳﺪﻩ ﺧﻮﺩ ﺷﺎﻫﺪ ﺍﻳﻦ‬ ‫ﻣﺪﻋﺎﺳﺖ ]‪ [۳‬ﻭ ]‪ .[۴‬ﻟﺬﺍ ﻟﺰﻭﻡ ﺑﺮﺭﺳﻲ ﻭ ﺷﻨﺎﺧﺖ ﺑﻴﺸﺘﺮ ﺭﻭﻱ ﺍﻳﻦ ﭘﺪﻳﺪﻩ ﻭ‬ ‫ﻋﻼﺋﻢ ﺁﻥ ﻭ ﺗﺪﻭﻳﻦ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﻣﻨﺎﺳﺐ ﺑﺮﺍﻱ ﺗﺸﺨﻴﺺ ﺍﻳﻦ ﭘﺪﻳﺪﻩ ﻭ‬ ‫ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﺁﻥ ﺿﺮﻭﺭﻱ ﺑﻪ ﻧﻈﺮ ﻣﻲ ﺭﺳﺪ‪ .‬ﺭﻭﺷﻬﺎﻱ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﺑﺎﻳﺪ ﺑﺎ ﺑﻪ‬ ‫ﮐﺎﺭ ﮔﻴﺮﻱ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺷﺒﮑﻪ ﻧﻈﻴﺮ ﻭﻟﺘﺎﮊ‪ ،‬ﺟﺮﻳﺎﻥ ﻭ ﺗﻮﭘﻮﻟﻮﮊﻱ ﺷﺒﮑﻪ ﺑﻪ ﻃﻮﺭ‬ ‫ﻣﺪﺍﻭﻡ ﻭ ﭘﻴﺎﭘﻲ ﻭﺿﻌﻴﺖ ﺷﺒﮑﻪ ﺭﺍ ﺑﻪ ﻟﺤﺎﻅ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻣﺸﺨﺺ ﮐﻨﻨﺪ‪.‬‬ ‫ﺑﻴﺸﺘﺮ ﺭﻭﺷﻬﺎﻳﻲ ﻛﻪ ﺗﺎ ﺍﻣﺮﻭﺯ ﺑﺮﺍﻱ ﺗﺤﻠﻴﻞ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﻪ ﻛﺎﺭ ﺑﺮﺩﻩ ﺷﺪﻩﺍﻧﺪ‬ ‫ﺑﺮ ﻣﺒﻨﺎﻱ ﺗﺤﻠﻴﻠﻬﺎﻱ ﺍﺳﺘﺎﺗﻴﻜﻲ ﻭ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺎﺗﺮﻳﺲ ﮊﺍﻛﻮﺑﻴﻦ ﺳﻴﺴﺘﻢ‬ ‫ﻗﺪﺭﺕ ﺑﻮﺩﻩﺍﻧﺪ‪ .‬ﺩﺭ ﻭﺍﻗﻊ ﺑﺎ ﺑﻪﻛﺎﺭﮔﻴﺮﻱ ﺿﺮﺍﻳﺐ ﺣﺴﺎﺳﻴﺖ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ‬ ‫ﻣﺎﺗﺮﻳﺲ ﮊﺍﻛﻮﺑﻴﻦ ﻭ ﺭﻓﺘﺎﺭ ﻣﻘﺎﺩﻳﺮ ﻭﻳﮋﻩ ﺁﻥ ﻣﻴﺰﺍﻥ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ ‫ﺳﻴﺴﺘﻢ ﺑﺪﺳﺖ ﻣﻲﺁﻳﺪ‪ .‬ﻳﻚ ﺍﺷﻜﺎﻝ ﻣﻬﻢ ﺍﻳﻦ ﺗﺤﻠﻴﻠﻬﺎ‪ ،‬ﺣﺠﻢ ﺯﻳﺎﺩ ﻭ‬ ‫ﭘﻴﭽﻴﺪﮔﻲ ﻣﺤﺎﺳﺒﺎﺕ ﺁﻧﻬﺎﺳﺖ ]‪ .[۵‬ﺑﺮﺍﻱ ﻳﻚ ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ ﺑﺰﺭﮒ‪ ،‬ﺍﺑﻌﺎﺩ‬ ‫ﻣﺎﺗﺮﻳﺲ ﮊﺍﻛﻮﺑﻴﻦ ﺑﺴﻴﺎﺭ ﺑﺰﺭﮒ ﺷﺪﻩ ﻭ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺮﺑﻮﻁ ﺑﻪ ﻣﻘﺎﺩﻳﺮ ﻭﻳﮋﻩ ﻭ‬ ‫ﺿﺮﺍﻳﺐ ﺣﺴﺎﺳﻴﺖ ﺁﻥ‪ ،‬ﺑﺴﻴﺎﺭ ﺯﻳﺎﺩ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﺍﺯ ﻃﺮﻓﻲ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﺔ‬ ‫ﻣﺎﺗﺮﻳﺲ ﮊﺍﻛﻮﺑﻴﻦ ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ‪ ،‬ﻧﻴﺎﺯ ﺑﻪ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﻫﺮ ﺑﺎﺱ‬ ‫ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ ﻭ ﺗﻮﭘﻮﻟﻮﮊﻱ ﺷﺒﻜﻪ ﻣﻲﺑﺎﺷﺪ‪ .‬ﺑﺮﺍﻱ ﺍﺟﺮﺍﻱ ﺑﻪ ﻫﻨﮕﺎﻡ ﺍﻳﻦ ﺭﻭﺷﻬﺎ‪،‬‬ ‫ﻻﺯﻡ ﺍﺳﺖ ﺍﻳﻦ ﺍﻃﻼﻋﺎﺕ ﺑﻪ ﺻﻮﺭﺕ ‪ on-line‬ﺍﺯ ﻃﺮﻳﻖ ﻭﺍﺣﺪﻫﺎﻱ‬ ‫ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻱ ﻓﺎﺯﻭﺭ‪ ١‬ﻛﻪ ﺩﺭ ﻫﺮ ﺑﺎﺱ ﺷﺒﻜﻪ ﻧﺼﺐ ﻫﺴﺘﻨﺪ ﻭ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ‬ ‫ﺍﺭﺗﺒﺎﻁ ﻣﺨﺎﺑﺮﺍﺗﻲ‪ ،‬ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﺍﺭﺳﺎﻝ ﺷﻮﺩ‪ .‬ﺩﺭ ﺷﺒﻜﻪﻫﺎﻱ ﺑﺰﺭﮒ‪ ،‬ﺍﺭﺳﺎﻝ‬ ‫ﺍﻳﻦ ﺍﻃﻼﻋﺎﺕ ﺑﺮﺍﻱ ﻣﺤﺎﺳﺒﺎﺕ ‪ on-line‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻓﻮﺍﺻﻞ ﺯﻳﺎﺩ ﻭ ﺣﺠﻢ‬ ‫ﺯﻳﺎﺩ ﺍﻃﻼﻋﺎﺕ ﺑﺎ ﺗﺄﺧﻴﺮ ﺯﻳﺎﺩﻱ ﻫﻤﺮﺍﻩ ﺑﻮﺩﻩ ﻭ ﺍﻣﻜﺎﻥ ﭘﺬﻳﺮ ﻧﻴﺴﺖ‪.‬‬ ‫ﺩﻻﻳﻞ ﻓﻮﻕﺍﻟﺬﻛﺮ‪ ،‬ﺳﺒﺐ ﺷﺪﻩﺍﻧﺪ ﻛﻪ ﻣﺘﺨﺼﺼﺎﻥ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺑﻪ ﺳﻤﺖ‬ ‫ﻣﻌﻴﺎﺭﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺗﺨﻤﻴﻦ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﻪ ﺻﻮﺭﺕ ﻫﻤﺰﻣﺎﻥ ﺑﺎ‬ ‫ﺑﻬﺮﻩﺑﺮﺩﺍﺭﻱ ﺍﺯ ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ‪ ،‬ﭘﻴﺶ ﺑﺮﻭﻧﺪ‪ .‬ﺍﻳﻦ ﺭﻭﺷﻬﺎ‪ ،‬ﻋﻤﺪﺗﺎﹰ ﺑﺮ ﻣﺒﻨﺎﻱ‬ ‫ﺍﻧﺪﺍﺯﻩﮔﻴﺮﻳﻬﺎﻱ ﻓﺎﺯﻭﺭﻫﺎﻱ ﻭﻟﺘﺎﮊ ﻭ ﺟﺮﻳﺎﻥ ﺑﻪ ﺻﻮﺭﺕ ﻣﺤﻠﻲ ﻫﺴﺘﻨﺪ ]‪[ ۶] ،[۵‬‬ ‫ﻭ ]‪ .[۷‬ﻟﻴﻜﻦ ﺗﻔﺎﻭﺕ ﺍﻳﻦ ﺭﻭﺷﻬﺎ ﺑﺎ ﺭﻭﺷﻬﺎﻱ ﻣﺒﺘﻨﻲ ﺑﺮ ﻣﺎﺗﺮﻳﺲ ﮊﺍﻛﻮﺑﻴﻦ ﺍﻳﻦ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪ -۲‬ﺍﻧﺘﺨﺎﺏ ﺷﺒﮑﻪ ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ‬ ‫ﻳﻜﻲ ﺍﺯ ﺍﻫﺪﺍﻑ ﺍﻳﻦ ﻣﻘﺎﻟﻪ‪ ،‬ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻭ ﻣﻄﺎﻟﻌﻪ ﺑﺮ ﺭﻭﻱ ﻳﻚ ﺷﺒﻜﻪ ﻗﺪﺭﺕ‬ ‫ﻭﺍﻗﻌﻲ ﺑﻮﺩﻩ ﺍﺳﺖ‪ .‬ﺷﺒﻜﻪ ﺑﺮﻕ ﻣﻨﻄﻘﻪ ﺍﻱ ﺧﺮﺍﺳﺎﻥ ﺑﺎ ‪ ۸۶‬ﺑﺎﺱ‪ ۱۱ ،‬ﻭﺍﺣﺪ‬ ‫ﻧﻴﺮﻭﮔﺎﻫﯽ‪ ۷ ،‬ﺧﻂ ‪ ۴۰۰‬ﮐﻴﻠﻮﻭﻟﺖ ﻭ ‪ ۱۱۶‬ﺧﻂ ‪ ۱۳۲‬ﮐﻴﻠﻮﻭﻟﺖ ﺑﻪ ﺩﻻﻳﻞ‬ ‫ﺫﻳﻞ ﺟﻬﺖ ﻣﻄﺎﻟﻌﻪ ﺍﻧﺘﺨﺎﺏ ﺷﺪﻩ ﺍﺳﺖ‪:‬‬ ‫ ﺩﺭ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﺧﺮﺍﺳﺎﻥ ﻛﻪ ﺍﺯ ﻧﻈﺮ ﻭﺳﻌﺖ ﺑﺰﺭﮔﺘﺮﻳﻦ ﺑﺮﻕ ﻣﻨﻄﻘﻪﺍﻱ‬‫ﺍﻳﺮﺍﻥ ﻣﺤﺴﻮﺏ ﻣﻲﮔﺮﺩﺩ‪ ،‬ﺑﻪ ﻟﺤﺎﻅ ﻃﻮﻻﻧﻲ ﺑﻮﺩﻥ ﻓﻮﺍﺻﻞ ﻭ ﭼﮕﺎﻟﻲ ﺑﺎﺭ ﻛﻢ ﺍﺯ‬ ‫ﺧﻄﻮﻁ ‪ ۱۳۲‬ﻛﻴﻠﻮﻭﻟﺖ ﻭ ‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﺑﺮﺍﻱ ﺍﻧﺘﻘﺎﻝ ﻗﺪﺭﺕ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ‬ ‫ﺍﺳﺖ‪ .‬ﻃﻮﻝ ﺧﻄﻮﻁ ‪ ۱۳۲‬ﻛﻴﻠﻮﻭﻟﺖ ﺑﻌﻀﺎﹰ ﺑﻪ ‪ ۱۴۰‬ﻛﻴﻠﻮﻣﺘﺮ ﻫﻢ ﻣﻲﺭﺳﺪ‪.‬‬ ‫ ﺍﻳﻦ ﺷﺒﻜﻪ ﺩﺭ ﺣﺎﻝ ﺣﺎﺿﺮ ﺗﻨﻬﺎ ﺍﺯ ﻃﺮﻳﻖ ﺧﻂ ‪ ۲۷۰‬ﻛﻴﻠﻮﻣﺘﺮﻱ ‪۴۰۰‬‬‫ﻛﻴﻠﻮﻭﻟﺖ ﻋﻠﻲﺁﺑﺎﺩ ‪ -‬ﺍﺳﻔﺮﺍﻳﻦ ﺑﻪ ﺷﺒﻜﻪ ﺳﺮﺍﺳﺮﻱ ﻣﺘﺼﻞ ﺍﺳﺖ‪.‬‬ ‫ ﺑﻪ ﺩﻟﻴﻞ ﺗﺮﺍﻛﻢ ﺑﺎﺭ ﺩﺭ ﻧﺎﺣﻴﻪ ﺷﻤﺎﻝ ﻏﺮﺏ ﺧﺮﺍﺳﺎﻥ ﺑﻴﺶ ﺍﺯ ‪ ۹۰‬ﺩﺭﺻﺪ‬‫ﻧﻴﺮﻭﮔﺎﻫﻬﺎﻱ ﺑﺮﻕ ﻣﻨﻄﻘﻪﺍﻱ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﺍﻳﻦ ﻧﺎﺣﻴﻪ‪ ،‬ﻣﺘﻤﺮﻛﺰ ﺑﻮﺩﻩ ﻭ ﺑﺮﺍﻱ‬ ‫ﺍﻧﺘﻘﺎﻝ ﺗﻮﺍﻥ ﺑﻪ ﻧﻮﺍﺣﻲ ﺩﻳﮕﺮ ﺍﺯ ﺧﻄﻮﻁ ﻃﻮﻻﻧﻲ ‪ ۴۰۰‬ﻭ ‪ ۱۳۲‬ﻛﻴﻠﻮﻭﻟﺖ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺩﻻﻳﻞ ﻓﻮﻕ‪ ،‬ﺳﺒﺐ ﺷﺪﻩﺍﻧﺪ ﻛﻪ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﺧﺮﺍﺳﺎﻥ ﺑﺎ ﻭﺟﻮﺩ ﺁﻧﻜﻪ ﺗﻨﻬﺎ ‪۱۰‬‬ ‫ﺩﺭﺻﺪ ﺑﺎﺭ ﻛﻞ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﺍﻳﺮﺍﻥ ﺭﺍ ﺩﺍﺭﺍ ﻣﻲﺑﺎﺷﺪ‪ ،‬ﺩﺭ ﺑﺮﺧﻲ ﻧﻮﺍﺣﻲ ﻭ ﺑﻌﻀﺎﹰ‬ ‫ﺩﺭ ﻛﻞ ﺷﺒﻜﻪ ﺑﻪ ﻟﺤﺎﻅ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺁﺳﻴﺐ ﭘﺬﻳﺮ ﺑﺎﺷﺪ‪ .‬ﺩﺭ ﻧﺘﻴﺠﻪ‪ ،‬ﺍﻳﻦ‬ ‫ﺷﺒﻜﻪ ﺟﻬﺖ ﻣﻄﺎﻟﻌﻪ ﻣﻌﻴﺎﺭﻫﺎﻱ ﻣﺨﺘﻠﻒ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻭ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ‬ ‫ﺭﻭﺷﻬﺎﻱ ﻣﺨﺘﻠﻒ ﭘﻴﺶ ﺑﻴﻨﻲ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺍﻧﺘﺨﺎﺏ ﮔﺮﺩﻳﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺩﺭ ﻣﺪﻟﺴﺎﺯﻱ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﺧﺮﺍﺳﺎﻥ ﻣﻮﺍﺭﺩ ﺫﻳﻞ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﻗﺮﺍﺭ‬ ‫ﮔﺮﻓﺘﻪﺍﻧﺪ‪:‬‬ ‫ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺁﻧﻜﻪ ﻧﻴﺮﻭﮔﺎﻩ ﺁﺑﻲ ﺩﺭ ﺍﻳﻦ ﺷﺒﻜﻪ ﻣﻮﺟﻮﺩ ﻧﻤﻲﺑﺎﺷﺪ‪ ،‬ﻟﺬﺍ ﻻﺯﻡ‬‫ﺍﺳﺖ ﻳﻚ ﻧﻴﺮﻭﮔﺎﻩ ﮔﺎﺯﻱ ﺑﻪ ﻋﻨﻮﺍﻥ ﺑﺎﺱ ﻣﺒﻨﺎ‪ ،‬ﺍﻧﺘﺨﺎﺏ ﮔﺮﺩﺩ‪ .‬ﺩﺭ ﺍﻳﻦ ﺭﺍﺳﺘﺎ‪،‬‬ ‫ﻭﺍﺣﺪﻫﺎﻱ ﮔﺎﺯﻱ ﻧﻴﺮﻭﮔﺎﻩ ﻧﻴﺸﺎﺑﻮﺭ‪ ،‬ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺒﻨﺎ ﺍﻧﺘﺨﺎﺏ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺍﻳﻦ‬ ‫ﻧﻴﺮﻭﮔﺎﻩ‪ ،‬ﻧﻴﺮﻭﮔﺎﻫﻲ ﺟﺪﻳﺪ ﻭ ﺳﺮﻳﻊ ﺑﻮﺩﻩ ﻭ ﺩﺭ ﺣﺎﻟﺖ ﺑﻬﺮﻩﺑﺮﺩﺍﺭﻱ ﻭﺍﻗﻌﻲ ﺍﺯ‬ ‫ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺩﺭ ﺻﻮﺭﺕ ﻗﻄﻊ ﺑﻮﺩﻥ ﺧﻂ ﻋﻠﻲﺁﺑﺎﺩ ‪ -‬ﺍﺳﻔﺮﺍﻳﻦ‪ ،‬ﺍﻳﻦ ﻧﻴﺮﻭﮔﺎﻩ‬ ‫ﻣﺒﻨﺎ ﻣﻲﺑﺎﺷﺪ‪.‬‬ ‫‪۴‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ ﻣﻄﺎﺑﻖ ﺑﺎ ﭘﺨﺶ ﺑﺎﺭ ﻭﺍﻗﻌﻲ ﺷﺒﻜﻪ ﺩﺭ ﻓﺼﻮﻝ ﺑﻬﺎﺭ ﻭ ﺗﺎﺑﺴﺘﺎﻥ ﺳﺎﻝ ‪ ،۸۵‬ﺧﻂ‬‫‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﻋﻠﻲﺁﺑﺎﺩ – ﺍﺳﻔﺮﺍﻳﻦ ﺩﺭ ﻫﺮ ﺩﻭ ﺣﺎﻟﺖ ﺩﺭ ﻣﺪﺍﺭ ﺑﻮﺩﻩ ﻭ ﺩﺭ‬ ‫ﺣﺎﻟﺖ ﺑﺎﺭ ﭘﻴﻚ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﺗﺎﺑﺴﺘﺎﻥ ‪ ،۸۵‬ﺑﺎﺭﻱ ﻣﻌﺎﺩﻝ ‪ ۶۰‬ﻣﮕﺎﻭﺍﺕ ﺍﺯ ﺷﺒﻜﻪ‬ ‫ﺍﻳﺮﺍﻥ ﺑﻪ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﻣﻨﺘﻘﻞ ﻣﻲ ﻛﺮﺩﻩ ﺍﺳﺖ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺩﺭﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ‬ ‫ﺩﺭ ﻣﺪﺍﺭ ﻗﺮﺍﺭ ﺩﺍﺩﻥ ﺧﻂ ﻣﺬﻛﻮﺭ‪ ،‬ﺗﻮﻟﻴﺪ ﻧﻴﺮﻭﮔﺎﻫﻬﺎﻱ ﺧﺮﺍﺳﺎﻥ ﻃﻮﺭﻱ ﺗﻨﻈﻴﻢ‬ ‫ﮔﺮﺩﻳﺪﻩ ﻛﻪ ﺗﻮﺍﻥ ﺍﻧﺘﻘﺎﻟﻲ ﺍﺯ ﺍﻳﻦ ﺧﻂ ﻣﻌﺎﺩﻝ ﻣﻘﺪﺍﺭ ﻭﺍﻗﻌﻲ ﺗﺎﺑﺴﺘﺎﻥ ‪ ،۸۵‬ﻳﻌﻨﻲ‬ ‫‪ ۶۰‬ﻣﮕﺎﻭﺍﺕ ﺑﺎﺷﺪ‪.‬‬ ‫ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﻼﺣﻈﺎﺕ ﭘﺎﻳﺪﺍﺭﻱ ﻧﻮﺳﺎﻧﻲ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺩﺭ ﺷﺮﺍﻳﻂ ﺑﻬﺮﻩ‬‫ﺑﺮﺩﺍﺭﻱ ﻭﺍﻗﻌﻲ ﺷﺒﻜﻪ ﺣﺪ ﻣﺎﻛﺰﻳﻤﻢ ﺍﻧﺘﻘﺎﻝ ﺗﻮﺍﻥ ﺧﻂ ‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﻋﻠﻲﺁﺑﺎﺩ‬ ‫– ﺍﺳﻔﺮﺍﻳﻦ ﺑﺮﺍﺑﺮ ‪ ۳۰۰‬ﻣﮕﺎﻭﺍﺕ ﺍﺳﺖ‪ .‬ﻟﺬﺍ ﺷﺒﻜﻪ ﺍﻳﺮﺍﻥ ﺩﺭ ﺍﻳﻦ ﻣﻄﺎﻟﻌﻪ ﺑﺎ ﻳﻚ‬ ‫ﮊﻧﺮﺍﺗﻮﺭ ﺑﺎ ﺗﻮﺍﻥ ﻣﺎﻛﺰﻳﻤﻢ ‪ ۳۰۰‬ﻭ ﻣﻴﻨﻴﻤﻢ ‪ -۳۰۰‬ﻣﮕﺎﻭﺍﺕ ﻭ ﺑﺎ ﺩﺭﻭﭖ ﺑﺎﻻ ﻣﺪﻝ‬ ‫ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ ﭘﺨﺶ ﺑﺎﺭ ﺑﻴﻦ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ ﺑﺮ ﺍﺳﺎﺱ ﺩﺭﻭﭖ ﺁﻧﻬﺎ ﭘﻴﺮﺍﻣﻮﻥ ﻧﻘﻄﻪ ﻛﺎﺭﻱ ﻣﻌﻴﻦ‬‫ﺷﺪﻩ ﺑﺮﺍﻱ ﻫﺮ ﮊﻧﺮﺍﺗﻮﺭ ﺍﻧﺠﺎﻡ ﻣﻲ ﮔﺮﺩﺩ‪ .‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺤﺪﻭﺩﻳﺖ ﮊﻧﺮﺍﺗﻮﺭ ﺷﺒﻜﻪ‬ ‫ﺍﻳﺮﺍﻥ ﺩﺭ ﺣﺎﻟﺖ ﻭﺻﻞ ﺑﻮﺩﻥ ﺧﻂ ﻋﻠﻲﺁﺑﺎﺩ – ﺍﺳﻔﺮﺍﻳﻦ‪ ،‬ﺍﺑﺘﺪﺍ ﺍﻳﻦ ﮊﻧﺮﺍﺗﻮﺭ ﺑﺎ‬ ‫ﺗﻮﺟﻪ ﺑﻪ ﺩﺭﻭﭖ ﺑﺎﻻﻱ ﺁﻥ ﺑﻪ ﺗﻐﻴﻴﺮﺍﺕ ﺷﺒﻜﻪ ﭘﺎﺳﺦ ﺩﺍﺩﻩ ﻭ ﭘﺲ ﺍﺯ ﺁﻧﻜﻪ ﺑﻪ‬ ‫ﺣﺪﻭﺩ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺗﻮﻟﻴﺪ ﺧﻮﺩ ﺭﺳﻴﺪ‪ ،‬ﻭﺍﺣﺪﻫﺎﻱ ﮔﺎﺯﻱ ﻧﻴﺮﻭﮔﺎﻩ ﻧﻴﺸﺎﺑﻮﺭ ﺑﻪ‬ ‫ﻋﻨﻮﺍﻥ ﮊﻧﺮﺍﺗﻮﺭ ﻣﺒﻨﺎ‪ ،‬ﻛﻤﺒﻮﺩ ﻭ ﻳﺎ ﺍﺿﺎﻓﺔ ﺗﻮﻟﻴﺪ ﺷﺒﻜﻪ ﺭﺍ ﺟﺒﺮﺍﻥ ﻣﻲ ﻧﻤﺎﻳﻨﺪ‪.‬‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺩﺭ ﺍﺧﺘﻴﺎﺭ ﻧﺪﺍﺷﺘﻦ ﺍﻃﻼﻋﺎﺕ ﻭﺍﻗﻌﻲ ﺗﻮﺭﺑﻴﻦ ﻭ ﮔﺎﻭﺭﻧﺮﻫﺎﻱ ﺷﺒﻜﻪ‬ ‫ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺍﺯ ﺩﻭ ﻣﺪﻝ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ‪ GAST‬ﺑﺮﺍﻱ ﺗﻮﺭﺑﻴﻦﻫﺎﻱ ﮔﺎﺯﻱ ﻭ ‪IEEE-‬‬ ‫‪ G1‬ﺑﺮﺍﻱ ﺗﻮﺭﺑﻴﻦﻫﺎﻱ ﺑﺨﺎﺭﻱ ﻛﻪ ﺩﺭ ﻛﺘﺎﺑﺨﺎﻧﻪ ﻧﺮﻡﺍﻓﺰﺍﺭ ‪ Digsilent‬ﻣﻮﺟﻮﺩ‬ ‫ﻣﻲﺑﺎﺷﻨﺪ‪ ،‬ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ]‪.[۸‬‬ ‫ﺑﺮﺍﻱ ﻣﺪﻟﺴﺎﺯﻱ ﻣﺤﺪﻭﺩﻛﻨﻨﺪﻩ ﺗﺤﺮﻳﻚ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ ﺍﺯ ﻣﺪﻝ ﺷﻜﻞ )‪ (۱‬ﺍﺯ ﻣﺮﺟﻊ‬ ‫]‪ [۹‬ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺷﺮﺍﻳﻂ ﻃﺒﻴﻌﻲ‪ ،‬ﭼﻨﺎﻧﭽﻪ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﺍﺯ‬ ‫ﻣﻘﺪﺍﺭ ﻣﺎﻛﺰﻳﻤﻢ ﺗﻨﻈﻴﻢ ﺷﺪﻩ )ﻣﺜﻼﹰ ‪ ۱۰۵‬ﺩﺭﺻﺪ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﻧﺎﻣﻲ( ﻛﻤﺘﺮ‬ ‫ﺑﺎﺷﺪ‪ ،‬ﺍﺯ ﻃﺮﻳﻖ ﺩﻭ ﻣﺴﻴﺮ ‪ ۱‬ﻭ ‪ ،۲‬ﺍﻧﺘﮕﺮﺍﻝﮔﻴﺮ ﺑﻪ ﺳﻤﺖ ﺣﺪ ﭘﺎﻳﻴﻦ ﺁﻥ )‪(-A‬‬ ‫ﺳﻮﻕ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻭﻟﺘﺎﮊ ﺍﺿﺎﻓﻪ ﺷﺪﻩ ﺑﻪ ﻭﺭﻭﺩﻱ ﻣﺮﺟﻊ‬ ‫‪ ،AVR‬ﺻﻔﺮ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﺍﮔﺮ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﺑﺎ ﻻﺗﺮ ﺍﺯ ﺣﺪ ﺗﻨﻈﻴﻢ ﺑﺎﺷﺪ‪،‬‬ ‫ﻣﺴﻴﺮ ‪ ،۲‬ﺍﻧﺘﮕﺮﺍﻟﮕﻴﺮ ﺭﺍ ﺑﻪ ﻳﻚ ﻣﻘﺪﺍﺭ ﻣﺜﺒﺖ ﺳﻮﻕ ﺩﺍﺩﻩ ﻭ ﻟﺬﺍ ﻳﻚ ﺳﻴﮕﻨﺎﻝ‬ ‫ﻭﻟﺘﺎﮊ ﻣﺜﺒﺖ ﺍﺯ ﻭﻟﺘﺎﮊ ﻭﺭﻭﺩﻱ ﻣﺮﺟﻊ ‪ ،AVR‬ﻛﻢ ﺷﺪﻩ ﻭ ﺩﺭ ﻧﺘﻴﺠﻪ ﺧﺮﻭﺟﻲ‬ ‫‪ AVR‬ﻛﻪ ﻫﻤﺎﻥ ﻭﻟﺘﺎﮊ ﺗﺤﺮﻳﻚ ﻛﻨﻨﺪﺓ ﮊﻧﺮﺍﺗﻮﺭ ﺍﺳﺖ‪ ،‬ﻛﺎﻫﺶ ﻣﻲﻳﺎﺑﺪ ﻭ ﻟﺬﺍ‬ ‫ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﺭﺍ ﺑﻪ ﺯﻳﺮ ﻣﻘﺪﺍﺭ ﺣﺪ ﺗﻨﻈﻴﻢ ﺑﺮﻣﻲﮔﺮﺩﺍﻧﺪ‪.‬‬ ‫ﺑﺮﺍﻱ ﻳﻚ ﺍﻓﺰﺍﻳﺶ ﭘﻠﻪﺍﻱ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﻧﺴﺒﺖ ﺑﻪ ﺣﺪ ﺗﻨﻈﻴﻢ ‪ ۱۰۵‬ﺩﺭﺻﺪ‪،‬‬ ‫ﺯﻣﺎﻥ ﻻﺯﻡ ﺑﺮﺍﻱ ﻋﻤﻞ ﻣﺤﺪﻭﺩ ﻛﻨﻨﺪﺓ ﺟﺮﻳﺎﻥ ﺑﺮﺍﺑﺮ ﺧﻮﺍﻫﺪ ﺑﻮﺩ ﺑﺎ‪:‬‬ ‫ﺑﻪ ﻣﻨﻈﻮﺭ ﻣﺪﻟﺴﺎﺯﻱ ﺧﻄﻮﻁ ﺍﻧﺘﻘﺎﻝ ﻭ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎ‪ ،‬ﺍﺯ ﻣﺪﻝ ‪ π‬ﺍﺳﺘﻔﺎﺩﻩ‬ ‫ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﻻﺯﻡ ﺑﻪ ﺫﮐﺮ ﺍﺳﺖ ﮐﻞ ﻇﺮﻓﻴﺖ ﻧﺼﺐ ﺷﺪﻩ ﺩﺭ ﺍﻳـﻦ ﺷـﺒﮑﻪ ﺗـﺎ ﺳـﺎﻝ ‪۱۳۸۵‬‬ ‫ﺣﺪﻭﺩ ‪ ۲۷۰۰‬ﻣﮕﺎﻭﺍﺕ ﻭ ‪ ۱۸۰۰‬ﻣﮕﺎﻭﺍﺭ ﻭ ﮐﻞ ﺑﺎﺭ ﭘﻴﮏ ﺗﺎ ﻫﻤﻴﻦ ﺳـﺎﻝ ﺣـﺪﻭﺩ‬ ‫‪ ۲۳۰۰‬ﻣﮕﺎﻭﺍﺕ ﻭ ‪ ۹۰۰‬ﻣﮕﺎﻭﺍﺭ ﻣﯽ ﺑﺎﺷﺪ‪.‬‬ ‫ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ‪ k2 ،k1‬ﻭ ‪ k3‬ﻃﻮﺭﻱ ﺗﻨﻈﻴﻢ ﺷﺪﻩ ﺍﻧﺪ ﻛﻪ ﺍﻳﻦ ﺯﻣﺎﻥ ﻣﻄﺎﺑﻖ‬ ‫ﻣﻨﺤﻨﻲ ﺍﺿﺎﻓﻪ ﺑﺎﺭ ـ ﺯﻣﺎﻥ ﺷﻜﻞ )‪ (۲‬ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﻣﻨﺤﻨﻲ ﻣﺮﺑﻮﻁ ﺑﻪ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ‬ ‫‪ ANSI C50.13-1972‬ﻣﻲﺑﺎﺷﺪ ]‪ .[۲‬ﺑﺪﻳﻦ ﺗﺮﺗﻴﺐ ﺗﺤﺮﻳﻚ ﮊﻧﺮﺍﺗﻮﺭ‪،‬‬ ‫ﻣﺸﺎﺑﻪ ﮊﻧﺮﺍﺗﻮﺭﻫﺎﻱ ﻭﺍﻗﻌﻲ ﺑﻪ ﮔﻮﻧﻪ ﺍﻱ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺷﺪﻩ ﺍﺳﺖ ﻛﻪ ﺑﺘﻮﺍﻥ ﻣﺜﻼﹰ‬ ‫ﺑﻪ ﻣﺪﺕ ‪ ۲‬ﺩﻗﻴﻘﻪ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﺭﺍ ﺍﺯ ﻣﻘﺪﺍﺭ ﻧﺎﻣﻲ ﺣﺪﻭﺩ ‪ ۲۰‬ﺩﺭﺻﺪ ﺍﻓﺰﺍﻳﺶ‬ ‫ﺩﺍﺩ‪.‬‬ ‫ﺩﺭ ﻣﺪﻟﺴﺎﺯﻱ ﺑﺎﺭ‪ ،‬ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﻣﻮﺗﻮﺭﻫﺎﻱ ﺍﻟﻘﺎﻳﻲ ﺩﺭ ﻭﻟﺘﺎﮊﻫﺎﻱ ﭘﺎﻳﻴﻦ‪ ،‬ﺩﺭ‬ ‫ﻣﻄﺎﻟﻌﺎﺕ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺑﺴﻴﺎﺭ ﺣﺎﺋﺰ ﺍﻫﻤﻴﺖ ﺍﺳﺖ‪ .‬ﺷﻜﻞ )‪ (۳‬ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ‬ ‫ﻳﻚ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪.‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻦ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺑﻪ ﺩﻧﺒﺎﻝ‬ ‫ﺑﺮﻭﺯ ﻳﻚ ﺍﻏﺘﺸﺎﺵ‪،‬ﻣﻮﺗﻮﺭ ﺩﺭ ﺍﺑﺘﺪﺍ ﺑﻪ ﺻﻮﺭﺕ ﺍﻣﭙﺪﺍﻧﺲ ﺛﺎﺑﺖ ﻛﺎﺭ ﻣﻲﻛﻨﺪ‪ .‬ﭼﺮﺍ‬ ‫ﻛﻪ ﻟﻐﺰﺵ ﺑﻪ ﻃﻮﺭ ﺁﻧﻲ ﻧﻤﻲﺗﻮﺍﻧﺪ ﺗﻐﻴﻴﺮ ﻛﻨﺪ‪ .‬ﺍﻳﻦ ﻣﺴﺄﻟﻪ ﺑﻪ ﺧﺎﻃﺮ ﻟﺨﺘﻲ‬ ‫ﻣﻮﺗﻮﺭ ﻭ ﺑﺎﺭ ﻣﻲﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﺑﺎﺭ ﺍﻣﭙﺪﺍﻧﺴﻲ ﺑﻪ ﺗﻐﻴﻴﺮﺍﺕ ﭘﻠﻪﺍﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺑﻪ ﺳﺮﻋﺖ‬ ‫ﭘﺎﺳﺦ ﻣﻲﺩﻫﺪ ﻭ ﻟﺬﺍ ﺗﻮﺍﻥ ﺍﻛﺘﻴﻮ ﻭ ﺭﺍﻛﺘﻴﻮ ﻣﻮﺗﻮﺭ ﺩﺭ ﺍﺑﺘﺪﺍ‪ ،‬ﺑﻪ ﺳﺮﻋﺖ ﻛﻢ‬ ‫ﻣﻲﺷﻮﺩ‪ .‬ﺩﺭ ﺍﺩﺍﻣﻪ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺸﺨﺼﺔ ﮔﺸﺘﺎﻭﺭ ـ ﺳﺮﻋﺖ ﻣﻄﺎﺑﻖ ﺷﻜﻞ )‪(۴‬‬ ‫ﻛﻪ ﺑﺮﺍﻱ ﻳﻚ ﻣﻮﺗﻮﺭ ﻧﻤﻮﻧﻪ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺳﺮﻋﺖ ﻣﻮﺗﻮﺭ ﻛﻢ ﻭ ﺑﻪ‬ ‫ﺩﻧﺒﺎﻝ ﺁﻥ ﻟﻐﺰﺵ ﻣﻮﺗﻮﺭ ﺯﻳﺎﺩ ﻣﻲﮔﺮﺩﺩ‪ .‬ﻣﺴﻴﺮ ﺣﺮﻛﺖ ﻧﻘﻄﻪ ﻛﺎﺭ ﻣﺎﺷﻴﻦ ﺩﺭ‬ ‫ﺍﻳﻦ ﺷﻜﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ‪،‬‬ ‫ﻧﺴﺒﺖ ‪ X/R‬ﺩﻳﺪﻩ ﺷﺪﻩ ﺍﺯ ﺳﺮ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻮﺗﻮﺭ ﺑﻪ ﺩﻟﻴﻞ ﻛﺎﻫﺶ ‪ Rr/s‬ﺯﻳﺎﺩ‬ ‫ﺷﺪﻩ ﻭ ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ ﻣﻮﺗﻮﺭ ﺷﺮﻭﻉ ﺑﻪ ﺍﻓﺰﺍﻳﺶ ﻣﻲﻛﻨﺪ‪ .‬ﺍﺯ ﻃﺮﻓﻲ ﺑﺴﺘﻪ ﺑﻪ ﺍﻳﻨﻜﻪ‬ ‫ﻣﺸﺨﺼﻪ ﺑﺎﺭ ﻣﻄﺎﺑﻖ ﺷﻜﻞ )‪ (۴‬ﺛﺎﺑﺖ ﻳﺎ ﻣﺘﻐﻴﺮ ﺑﺎﺷﺪ‪ ،‬ﮔﺸﺘﺎﻭﺭ ﻣﻜﺎﻧﻴﻜﻲ ﺑﺎ‬ ‫‪ -۳‬ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‬ ‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﻪ ﻣﻨﻈﻮﺭ ﻣﻄﺎﻟﻌﺎﺕ ﭘﺎﻳﺪﺍﺭﻱ ﮔﺬﺭﺍ ﻭ ﺑﻠﻨﺪﻣﺪﺕ ﺷﺒﻜﻪ ﻗﺪﺭﺕ‬ ‫ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺿﻤﻦ ﻣﺪﻟﺴﺎﺯﻱ ﻛﺎﻣﻞ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ‪ ،‬ﻣﺪﻝ ﻣﺆﺛﺮﺗﺮﻳﻦ ﺍﺩﻭﺍﺕ ﺗﺄﺛﻴﺮﮔﺬﺍﺭ‬ ‫ﺩﺭ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺷﺎﻣﻞ ‪ AVR‬ﻭ ﮔﺎﻭﺭﻧﺮ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ‪ ،‬ﻣﺪﻝ ﻣﺤﺪﻭﺩﻛﻨﻨﺪﺓ‬ ‫ﺗﺤﺮﻳﻚ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ ﻭ ﻣﺪﻟﻬﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺑﺎﺭ ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﺳﺖ‪.‬‬ ‫ﺩﺭ ﺍﺩﺍﻣﻪ ﺑﻪ ﺗﻔﺼﻴﻞ ﺑﻪ ﺍﻳﻦ ﺑﺮﺭﺳﻲ ﺍﻳﻦ ﻣﺪﻟﻬﺎ ﻣﻲﭘﺮﺩﺍﺯﻳﻢ‪ .‬ﻧﺮﻡ ﺍﻓﺰﺍﺭ ﻣﻮﺭﺩ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ‪ ،‬ﻧﺮﻡ ﺍﻓﺰﺍﺯ ‪ Digsilent Power Factory 13.1‬ﻣﻲ ﺑﺎﺷﺪ ]‪.[۸‬‬ ‫ﺑﺮﺍﻱ ﻣﺪﻟﺴﺎﺯﻱ ﮊﻧﺮﺍﺗﻮﺭ ﺍﺯ ﻣﺪﻝ ﻣﺮﺗﺒﻪ ‪ ۸‬ﮊﻧﺮﺍﺗﻮﺭ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﻛﻪ ﺷﺎﻣﻞ‬ ‫ﻣﺪﻝ ﻣﺮﺗﺒﻪ ‪ ۶‬ﺍﻟﻜﺘﺮﻳﻜﻲ ﺑﺎ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﻛﻠﻴﻪ ﺍﻣﭙﺪﺍﻧﺴﻬﺎﻱ ﮔﺬﺭﺍ ﻭ ﺯﻳﺮ‬ ‫ﮔﺬﺭﺍ ﻭ ﻣﺪﻝ ﻣﺮﺗﺒﻪ ‪ ۲‬ﻣﻜﺎﻧﻴﻜﻲ ﺍﺳﺖ‪ .‬ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺳﻴﺴﺘﻢ ﺗﺎ ﺣﺪ‬ ‫ﺍﻣﻜﺎﻥ ﻣﻘﺎﺩﻳﺮ ﻭﺍﻗﻌﻲ ﺷﺒﻜﻪ ﻫﺴﺘﻨﺪ ﻭ ﺩﺭ ﺟﺎﻳﻲ ﻛﻪ ﻣﻘﺎﺩﻳﺮ ﻭﺍﻗﻌﻲ ﺩﺭ ﺍﺧﺘﻴﺎﺭ‬ ‫ﻧﺒﻮﺩﻩ ﺍﻧﺪ ﺍﺯ ﻣﻘﺎﺩﻳﺮ ﻧﻮﻋﻲ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺑﺮﺍﻱ ﻣﺪﻟﺴﺎﺯﻱ ‪ AVR‬ﮊﻧﺮﺍﺗﻮﺭﻫﺎﻱ ﺷﺒﻜﺔ ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺩﺭ ﺩﺳﺖ‬ ‫ﻧﺒﻮﺩﻥ ﺍﻃﻼﻋﺎﺕ ﻭﺍﻗﻌﻲ‪ ،‬ﺍﺯ ﻣﺪﻝ ﺍﺳﺘﺎﻧﺪﺍﺭﺩ ‪ IEEE-DC1A‬ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ‬ ‫ﺍﺳﺖ‪.‬‬ ‫‪۵‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫)‪(۱‬‬ ‫‪A‬‬ ‫) ‪k2 k3 ( I fd − 1.05I fd rated‬‬ ‫=‪t‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﻛﺎﻫﺶ ﺳﺮﻋﺖ ﻣﻲﺗﻮﺍﻧﺪ ﺛﺎﺑﺖ ﺑﺎﺷﺪ ﻳﺎ ﻛﺎﻫﺶ ﭘﻴﺪﺍ ﻧﻤﺎﻳﺪ‪ .‬ﺩﺭ ﻫﺮ ﺩﻭﻱ ﺍﻳﻦ‬ ‫ﭘﺎﻳﺪﺍﺭ ﻣﻮﺗﻮﺭ ﻧﻴﺴﺖ‪ .‬ﭼﺮﺍ ﻛﻪ ﺑﺎ ﻛﻮﭼﻜﺘﺮﻳﻦ ﺍﻏﺘﺸﺎﺵ‪ ،‬ﻣﻮﺗﻮﺭ ﺍﻳﻦ ﻧﻘﻄﺔ ﻛﺎﺭ‬ ‫ﺧﻮﺩ ﺭﺍ ﺍﺯ ﺩﺳﺖ ﻣﻲﺩﻫﺪ ﻭ ﻣﻲﺍﻳﺴﺘﺪ‪ .‬ﺑﻪ ﻫﺮ ﺣﺎﻝ ﻣﻮﺗﻮﺭ ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ‬ ‫ﻣﺠﺪﺩﺍﹰ ﺷﻜﻞ ﺍﻣﭙﺪﺍﻧﺲ ﺛﺎﺑﺖ ﭘﻴﺪﺍ ﻛﺮﺩﻩ ﻭ ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ ﺁﻥ ﺑﺎ ﻛﺎﻫﺶ ﺑﻴﺸﺘﺮ‬ ‫ﻭﻟﺘﺎﮊ ﻣﺠﺪﺩﺍﹰ ﻛﺎﻫﺶ ﻣﻲﻳﺎﺑﺪ ﺗﺎ ﺳﺮﺍﻧﺠﺎﻡ ﻣﻮﺗﻮﺭ ﺍﺯ ﺷﺒﻜﻪ ﺟﺪﺍ ﮔﺮﺩﺩ‪ .‬ﭘﺲ‬ ‫ﺗﻮﺍﻥ ﺍﻛﺘﻴﻮ ﻣﻮﺗﻮﺭﻫﺎﻱ ﺍﻟﻘﺎﻳﻲ ﺩﺭ ﺑﺮﺍﺑﺮ ﻛﺎﻫﺶ ﻭﻟﺘﺎﮊ‪ ،‬ﻫﻤﻮﺍﺭﻩ ﻛﻢ ﻣﻲﺷﻮﺩ ﻭ‬ ‫ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ ﺁﻧﻬﺎ‪ ،‬ﺍﺑﺘﺪﺍ ﻛﻢ‪ ،‬ﺳﭙﺲ ﺯﻳﺎﺩ ﻣﻲﺷﻮﺩ ﻭ ﺑﺎ ﻛﺎﻫﺶ ﺑﻴﺸﺘﺮ ﻭﻟﺘﺎﮊ ﻭ ﺍﺯ‬ ‫ﺩﺳﺖ ﺭﻓﺘﻦ ﻧﻘﻄﺔ ﻛﺎﺭ ﭘﺎﻳﺪﺍﺭ ﻣﻮﺗﻮﺭ‪ ،‬ﻣﺠﺪﺩﺍﹰ ﻛﻢ ﻣﻲﮔﺮﺩﺩ‪.‬‬ ‫ﺣﺎﻟﺘﻬﺎ‪ ،‬ﺗﻮﺍﻥ ﻣﻜﺎﻧﻴﻜﻲ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺭﺍﺑﻄﺔ ‪ Pm = Tωω m‬ﻛﺎﻫﺶ ﻳﺎﻓﺘﻪ ﻭ ﺑﻪ‬ ‫ﺩﻧﺒﺎﻝ ﺁﻥ ﺗﻮﺍﻥ ﺍﻛﺘﻴﻮ ﺷﺒﻜﻪ ﺑﻪ ﻣﻘﺪﺍﺭﻱ ﻛﻤﺘﺮ ﺍﺯ ﻣﻘﺪﺍﺭ ﻧﺎﻣﻲ‪ ،‬ﻛﺎﻫﺶ ﻣﻲﻳﺎﺑﺪ‪.‬‬ ‫ﺷﻜﻞ ‪ -۱‬ﻣﺪﻝ ﻣﺤﺪﻭﺩ ﻛﻨﻨﺪﻩ ﺟﺮﻳﺎﻥ ﺗﺤﺮﻳﻚ ﮊﻧﺮﺍﺗﻮﺭ‬ ‫ﺷﻜﻞ ‪ -۴‬ﻣﻨﺤﻨﻲ ﮔﺸﺘﺎﻭﺭ‪-‬ﺳﺮﻋﺖ ﻳﻚ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ ﻧﻤﻮﻧﻪ ﻭ ﻣﺸﺨﺼﻪ ﻫﺎﻱ‬ ‫ﺑﺎﺭ ﻣﻜﺎﻧﻴﻜﻲ‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫ﺩﺭ ﺷﺒﻜﻪﻫﺎﻱ ﻗﺪﺭﺕ‪ ،‬ﻏﻴﺮ ﺍﺯ ﻣﻮﺗﻮﺭﻫﺎﻱ ﺑﺰﺭﮒ ﻛﻪ ﺑﺎ ﻛﻠﻴﺪﻫﺎﻱ ﻗﺪﺭﺕ ﺑﻪ‬ ‫ﺷﺒﻜﻪ ﻭﺻﻞ ﻣﻲﮔﺮﺩﻧﺪ‪ ،‬ﺑﻴﺸﺘﺮ ﻣﻮﺗﻮﺭﻫﺎ ﺑﻮﺳﻴﻠﺔ ﻛﻨﺘﺎﻛﺘﻮﺭ ﻭ ﻓﻴﻮﺯ ﺑﻪ ﺷﺒﻜﻪ‬ ‫ﻣﺘﺼﻞ ﻣﻲﺷﻮﻧﺪ‪ .‬ﺷﻜﻞ )‪ (۵‬ﻣﺪﺍﺭ ﺍﺗﺼﺎﻝ ﺍﻳﻦ ﻣﻮﺗﻮﺭﻫﺎ ﺑﻪ ﺷﺒﻜﻪ ﺭﺍ ﻧﺸﺎﻥ‬ ‫ﻣﻲﺩﻫﺪ‪ .‬ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺭﻓﺘﺎﺭ ﻛﻨﺘﺎﻛﺘﻮﺭﻫﺎ ﺩﺭ ﻭﻟﺘﺎﮊﻫﺎﻱ ﭘﺎﻳﻴﻦ ﻧﻴﺰ ﺑﺴﻴﺎﺭ‬ ‫ﺍﻫﻤﻴﺖ ﺩﺍﺭﺩ‪ .‬ﻣﻌﻤﻮﻻﹰ ﺯﻣﺎﻧﻲ ﻛﻪ ﻭﻟﺘﺎﮊ ﻓﺎﺯ ﺑﻪ ﻓﺎﺯ ﺗﺮﻣﻴﻨﺎﻝ ﻣﻮﺗﻮﺭﻫﺎ‪ ،‬ﺑﻪ ‪ ۳۰‬ﺗﺎ‬ ‫‪ ۶۰‬ﺩﺭﺻﺪ ﻣﻘﺪﺍﺭ ﻧﺎﻣﻲ ﺭﺳﻴﺪ‪ ،‬ﺭﻟﻪ ﻋﻤﻠﮕﺮ ‪ ،M‬ﺗﺮﻳﭗ ﺩﺍﺩﻩ ﻭ ﻛﻨﺘﺎﻛﺘﻮﺭ ﺑﺎﺯ‬ ‫ﻣﻲﺷﻮﺩ‪ .‬ﺯﻣﺎﻥ ﺑﺎﺯ ﺷﺪﻥ ﻛﻨﺘﺎﻛﺘﻮﺭ ﻣﺎﺑﻴﻦ ﻳﻚ ﺳﻴﻜﻞ ﺗﺎ ‪ ۱۰‬ﺳﻴﻜﻞ ﻣﻲﺑﺎﺷﺪ‬ ‫]‪ .[۲‬ﺍﻳﻦ ﻣﻄﻠﺐ ﺩﺭ ﺧﺼﻮﺹ ﺩﻭ ﻛﻨﺘﺎﻛﺘﻮﺭ ‪ ۲۲۰‬ﻭﻟﺘﻲ ﺩﺭ ﺁﺯﻣﺎﻳﺸﮕﺎﻩ‬ ‫ﻣﺎﺷﻴﻦﻫﺎﻱ ﺍﻟﻜﺘﺮﻳﻜﻲ ﺩﺍﻧﺸﻜﺪﺓ ﻣﻬﻨﺪﺳﻲ ﺑﺮﻕ ﻣﻮﺭﺩ ﺗﺴﺖ ﻗﺮﺍﺭ ﮔﺮﻓﺖ‪.‬‬ ‫ﻣﺸﺎﻫﺪﻩ ﺷﺪ ﻛﻪ ﺩﺭ ﻭﻟﺘﺎﮊﻫﺎﻱ ﺯﻳﺮ ‪ ۱۰۰-۱۱۰‬ﻭﻟﺖ‪ ،‬ﻫﺮ ﺩﻭ ﻛﻨﺘﺎﻛﺘﻮﺭ‪ ،‬ﺑﺎﺯ‬ ‫ﺷﺪﻧﺪ‪.‬‬ ‫ﺷﻜﻞ ‪ -۲‬ﻣﻨﺤﻨﻲ ﺍﺿﺎﻓﻪ ﺑﺎﺭ ـ ﺯﻣﺎﻥ ﺑﺮﺍﻱ ﺗﺤﺮﻳﻚ ﮊﻧﺮﺍﺗﻮﺭ‬ ‫ﺷﻜﻞ ‪ -۳‬ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﻳﻚ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ‬ ‫ﺑﺎ ﻛﺎﻫﺶ ﺑﻴﺸﺘﺮ ﻭﻟﺘﺎﮊ‪ ،‬ﻣﻘﺪﺍﺭ ﮔﺸﺘﺎﻭﺭ ﻣﺎﻛﺰﻳﻤﻢ ﺩﺭ ﻣﺸﺨﺼﻪ ﮔﺸﺘﺎﻭﺭ ـ‬ ‫ﺳﺮﻋﺖ ﻛﻢﻛﻢ ﺑﻪ ﺯﻳﺮ ﻣﺸﺨﺼﺔ ﺑﺎﺭ ﺁﻣﺪﻩ ﻭ ﻟﺬﺍ ﻣﻮﺗﻮﺭ ﻧﻘﻄﺔ ﻛﺎﺭ ﺧﻮﺩ ﺭﺍ ﺩﺭ‬ ‫ﻗﺴﻤﺖ ﭘﺎﻳﺪﺍﺭ ﻛﺎﺭﻱ ﻣﻮﺗﻮﺭ ﺍﺯ ﺩﺳﺖ ﻣﻲﺩﻫﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﺳﺮﻋﺖ ﺑﻪ ﺳﻤﺖ‬ ‫ﺻﻔﺮ ﺭﻓﺘﻪ ﻭ ﻣﻮﺗﻮﺭ ﻣﻲﺍﻳﺴﺘﺪ ﻳﺎ ﺩﺭ ﺳﺮﻋﺖ ﺑﺴﻴﺎﺭ ﭘﺎﻳﻴﻦ ﻭ ﺛﺎﺑﺘﻲ ﺩﺭ ﻗﺴﻤﺖ‬ ‫ﺷﻴﺐ‪-‬ﻣﺜﺒﺖ ﻣﺸﺨﺼﻪ ﮔﺸﺘﺎﻭﺭ ـ ﺳﺮﻋﺖ ﻛﺎﺭ ﻣﻲﻛﻨﺪ‪ .‬ﺍﻳﻦ ﻗﺴﻤﺖ‪ ،‬ﻧﻘﻄﻪ ﻛﺎﺭ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪۶‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺷﻜﻞ ‪ -۵‬ﻳﻚ ﻧﻤﻮﻧﻪ ﻣﺪﺍﺭ ﺍﺗﺼﺎﻝ ﻳﻚ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ ﺑﻪ ﺷﺒﻜﻪ ﺍﺯ ﻃﺮﻳﻖ‬ ‫‪1.2‬‬ ‫ﻛﻨﺘﺎﻛﺘﻮﺭ‬ ‫‪nehbandan‬‬ ‫‪tabas‬‬ ‫‪istgah azadvar‬‬ ‫‪ghaenat-400‬‬ ‫‪aliabad-400‬‬ ‫‪kohsangi‬‬ ‫‪0.8‬‬ ‫‪0.6‬‬ ‫)‪Voltage (p.u.‬‬ ‫ﻓﺮﻭﭘﺎﺷﻲ ﻋﻤﻠﻜﺮﺩ ﻣﻮﺗﻮﺭﻫﺎ ﻣﻌﻤﻮﻻﹰ ﺩﺭ ﻭﻟﺘﺎﮊﻫﺎﻱ ﻣﺎﺑﻴﻦ ‪ ۵۰‬ﺗﺎ ‪ ۷۰‬ﺩﺭﺻﺪ‬ ‫ﻭﻟﺘﺎﮊ ﻧﺎﻣﻲ ﺑﺴﺘﻪ ﺑﻪ ﻣﺸﺨﺼﺔ ﻣﻮﺗﻮﺭ‪ ،‬ﻣﻲﺗﻮﺍﻧﺪ ﺭﺥ ﺩﻫﺪ‪ .‬ﺩﺭ ﺁﺯﻣﺎﻳﺸﮕﺎﻩ‬ ‫ﻣﺎﺷﻴﻦﻫﺎﻱ ﺍﻟﻜﺘﺮﻳﻜﻲ ﺩﺍﻧﺸﻜﺪﺓ ﻣﻬﻨﺪﺳﻲ ﺑﺮﻕ ﺑﻪ ﺍﺯﺍﻱ ﺷﺮﺍﻳﻂ ﻣﺨﺘﻠﻒ‬ ‫ﮔﺸﺘﺎﻭﺭ ﺛﺎﺑﺖ ﻭ ﺗﻮﺍﻥ ﺛﺎﺑﺖ‪ ،‬ﻭﻟﺘﺎﮊ ﻣﻮﺗﻮﺭ ﻛﺎﻫﺶ ﺩﺍﺩﻩ ﺷﺪﻩ ﻭ ﺩﻳﺪﻩ ﺷﺪ ﻛﻪ ﺩﺭ‬ ‫ﺷﺮﺍﻳﻂ ﺑﺎﺭ ﻧﺎﻣﻲ‪ ،‬ﻣﻌﻤﻮﻻﹰ ﻭﻟﺘﺎﮊﻫﺎﻱ ﺯﻳﺮ ‪ ۶۰‬ﺩﺭﺻﺪ ﻭ ﺩﺭ ﺷﺮﺍﻳﻂ ﻧﺼﻒ ﺑﺎﺭ‬ ‫ﻭﻟﺘﺎﮊﻫﺎﻱ ﺯﻳﺮ ‪ ۵۰‬ﺩﺭﺻﺪ‪ ،‬ﻣﻮﺗﻮﺭ ﺭﺍ ﺑﻪ ﺳﻤﺖ ﻓﺮﻭﭘﺎﺷﻲ ﻣﻲﺑﺮﻧﺪ‪ .‬ﻟﺬﺍ ﻗﺒﻞ ﺍﺯ‬ ‫ﺁﻧﻜﻪ ﻣﻮﺗﻮﺭ ﺗﻮﺳﻂ ﺣﻔﺎﻇﺘﻬﺎﻱ ﺧﻮﺩ‪ ،‬ﺍﺯ ﻣﺪﺍﺭ ﺟﺪﺍ ﮔﺮﺩﺩ‪ ،‬ﻣﻲﺗﻮﺍﻧﺪ ﺷﺒﻜﻪ ﺭﺍ ﺩﺭ‬ ‫ﻭﻟﺘﺎﮊﻫﺎﻱ ﭘﺎﻳﻴﻦ ﺁﺯﺍﺭ ﺩﺍﺩﻩ ﻭ ﺍﺯ ﺍﻳﻦ ﺟﻬﺖ ﻣﺪﻟﺴﺎﺯﻱ ﺁﻥ ﺩﺭ ﻣﻄﺎﻟﻌﺎﺕ‬ ‫ﺩﻳﻨﺎﻣﻴﻚ ﻭ ﺣﺘﻲ ﻣﻄﺎﻟﻌﺎﺕ ﺍﺳﺘﺎﺗﻴﻚ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﺴﻴﺎﺭ ﺍﻫﻤﻴﺖ ﺩﺍﺭﺩ؛ ﺍﮔﺮ‬ ‫ﭼﻪ ﺍﻳﻦ ﻣﺴﺄﻟﻪ ﺑﺮﺍﻱ ﻣﻄﺎﻟﻌﺎﺕ ﺍﺳﺘﺎﺗﻴﻚ ﻣﺘﺪﺍﻭﻝ ﻧﻴﺴﺖ ﻛﻪ ﺷﺎﻳﺪ ﺑﻪ ﺧﺎﻃﺮ‬ ‫ﭘﻴﭽﻴﺪﮔﻲ ﺯﻳﺎﺩ ﺁﻥ ﺑﺎﺷﺪ‪.‬‬ ‫ﺑﺮﺍﻱ ﻣﺪﻟﺴﺎﺯﻱ ﺑﺎﺭﻫﺎﻱ ﺷﺒﻜﺔ ﺧﺮﺍﺳﺎﻥ‪ ،‬ﻣﺪﻟﺴﺎﺯﻱ ﻋﻤﻮﻣﻲ ﺍﺳﺘﺎﺗﻴﻜﻲ ـ‬ ‫ﺩﻳﻨﺎﻣﻴﻜﻲ )ﺗﻚ ﻣﻮﺗﻮﺭﻩ( ﺑﻪ ﻛﺎﺭ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺳﻬﻢ ﻋﻤﺪﻩ ﺑﺎﺭﻫﺎﻱ‬ ‫ﺳﻴﺴﺘﻢ ﻗﺪﺭﺕ ﺑﺮ ﺍﺳﺎﺱ ﺑﺮﺭﺳﻴﻬﺎﻱ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﻣﺮﺑﻮﻁ ﺑﻪ ﺑﺎﺭﻫﺎﻱ ﻣﻮﺗﻮﺭﻱ‬ ‫ﺍﺳﺖ ﻛﻪ ﺩﺭ ﻣﻮﺗﻮﺭﻫﺎﻱ ﺻﻨﻌﺘﻲ‪ ،‬ﻳﺨﭽﺎﻝ ﻭ ﻓﺮﻳﺰﺭ‪ ،‬ﺳﻴﺴﺘﻤﻬﺎﻱ ﺗﻬﻮﻳﻪ ﻫﻮﺍ‪،‬‬ ‫ﺳﻴﺴﺘﻤﻬﺎﻱ ﮔﺮﻣﺎﻳﺸﻲ ﺑﺎ ﺳﺮﻣﺎﻳﺸﻲ ﻭ ﻟﻮﺍﺯﻡ ﺷﺴﺘﺸﻮ‪-‬ﺍﻋﻢ ﺍﺯ ﻣﺎﺷﻴﻦ‬ ‫ﻇﺮﻓﺸﻮﻳﻲ ﻭ ﻳﺎ ﻟﺒﺎﺱ ﺷﻮﻳﻲ‪ ،‬ﺧﻼﺻﻪ ﻣﻲ ﺷﻮﻧﺪ ]‪ .[۲‬ﺳﺎﻳﺮ ﺍﺟﺰﺍﻱ ﺑﺎﺭ ﺭﺍ ﺑﻪ‬ ‫ﻃﻮﺭ ﻋﻤﺪﻩ ﺑﺎﺭﻫﺎﻱ ﺍﻣﭙﺪﺍﻧﺴﻲ ﺩﺭ ﺑﺮ ﻣﻲ ﮔﻴﺮﻧﺪ‪ .‬ﺑﺎﺭﻫﺎﻱ ﺭﻭﺷﻨﺎﻳﻲ‪ -‬ﺑﻪ ﺟﺰ‬ ‫ﻻﻣﭙﻬﺎﻱ ﺗﺨﻠﻴﻪ ﺍﻱ ﻭ ﻓﻠﻮﺭﺳﻨﺖ‪ -‬ﺑﺨﺶ ﻋﻤﺪﻩ ﺑﺎﺭﻫﺎﻱ ﺍﻣﭙﺪﺍﻧﺴﻲ ﺭﺍ ﺷﺎﻣﻞ‬ ‫ﻣﻲ ﺷﻮﻧﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﺮﺍﻱ ﺑﺨﺶ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺍﺯ ﻣﺪﻝ ﺍﻣﭙﺪﺍﻧﺲ ﺛﺎﺑﺖ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺳﻬﻢ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺑﺎﺭﻫﺎﻱ ﺧﺮﺍﺳﺎﻥ ﺑﺎ ﻳﻚ ﻣﻮﺗﻮﺭ ﺍﻟﻘﺎﻳﻲ ﺗﻠﻔﻴﻘﻲ ﺩﺭ ﻫﺮ ﺑﺎﺱ‬ ‫ﻣﺪﻝ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻧﺤﻮﺓ ﻣﺪﻟﺴﺎﺯﻱ ﺗﻠﻔﻴﻘﻲ ﻣﻮﺗﻮﺭﻫﺎﻱ ﺍﻟﻘﺎﻳﻲ ﻭ ﻫﻤﭽﻨﻴﻦ‬ ‫ﻣﺪﻟﺴﺎﺯﻱ ﺗﻠﻔﻴﻘﻲ ﺑﺎﺭﻫﺎﻱ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺷﺒﻜﺔ ﺧﺮﺍﺳﺎﻥ‪ ،‬ﺑﻪ ﻃﻮﺭ ﻛﺎﻣﻞ ﺩﺭ ﻣﺮﺟﻊ‬ ‫]‪ [۱۰‬ﺑﻴﺎﻥ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫‪1‬‬ ‫‪0.4‬‬ ‫‪0.2‬‬ ‫‪0‬‬ ‫‪2‬‬ ‫‪2.5‬‬ ‫‪1.5‬‬ ‫)‪Time (Sec.‬‬ ‫‪1‬‬ ‫‪0.5‬‬ ‫‪0‬‬ ‫ﺷﻜﻞ ‪ -۷‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ ‪۱‬‬ ‫‪ -۴‬ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ‬ ‫ﺩﺭ ﺍﻳﻦ ﺑﺨﺶ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ ﺩﺭ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺍﺯ ﻃﺮﻳﻖ ﺍﻋﻤﺎﻝ ‪۲‬‬ ‫ﺍﻏﺘﺸﺎﺵ ﻣﻄﺎﺑﻖ ﺟﺪﻭﻝ )‪ (۱‬ﺍﻧﺠﺎﻡ ﻣﻲ ﮔﻴﺮﺩ‪ .‬ﻣﻌﻴﺎﺭ ﺍﻧﺘﺨﺎﺏ ﺍﻳﻦ ﺍﻏﺘﺸﺎﺷﺎﺕ‬ ‫ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﺍﺳﺘﺎﺗﻴﻚ ﺑﻪ ﺩﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﺭﺳﻢ ﻣﻨﺤﻨﻴﻬﺎﻱ ‪ P-V‬ﺍﻳﻦ‬ ‫ﺷﺒﻜﻪ‪ ،‬ﺩﺭ ﺷﺮﺍﻳﻂ ﻗﺒﻞ ﻭ ﺑﻌﺪ ﺍﺯ ﺍﻏﺘﺸﺎﺵ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺑﺮﺍﻱ ﺗﻮﺿﻴﺢ ﺍﻳﻦ ﻣﻄﻠﺐ‬ ‫ﻻﺯﻡ ﺍﺳﺖ ﺑﻪ ﺷﻜﻞ )‪ (۶‬ﺗﻮﺟﻪ ﮔﺮﺩﺩ‪ g1 .‬ﻣﻨﺤﻨﻲ ‪ P-V‬ﻗﺒﻞ ﺍﺯ ﺣﺎﺩﺛﻪ ﻭ ‪g2‬‬ ‫ﻣﻨﺤﻨﻲ ﺑﻌﺪ ﺍﺯ ﺣﺎﺩﺛﻪ ﺍﺳﺖ‪ .‬ﺑﻼﻓﺎﺻﻠﻪ ﭘﺲ ﺍﺯ ﺣﺎﺩﺛﻪ ﺑﻪ ﺩﻟﻴﻞ ﺭﻓﺘﺎﺭ ﺑﺎﺭﻫﺎﻱ‬ ‫ﻭﺍﺑﺴﺘﻪ ﺑﻪ ﻭﻟﺘﺎﮊ ﻭ ﺑﺎﺭﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ‪ ،‬ﺗﻮﺍﻥ ﻭ ﻭﻟﺘﺎﮊ ﺷﺒﻜﻪ ﺑﻪ ﻳﻜﺒﺎﺭﻩ ﻛﻢ ﻣﻲ‬ ‫ﺷﻮﺩ ]‪ .[۱۱‬ﺳﭙﺲ ﺷﺒﻜﻪ ﺑﺮﺍﻱ ﺑﺎﺯﻳﺎﺑﻲ ﺗﻮﺍﻥ ﺑﺎﺭﻫﺎﻱ ﺧﻮﺩ ﺣﻮﻝ ﻧﻘﻄﻪ ﻛﺎﺭ ‪-‬‬ ‫ﺗﻮﺍﻥ ‪ -PInitial‬ﻧﻮﺳﺎﻥ ﻣﻲ ﻛﻨﺪ‪ .‬ﭼﻨﺎﻧﭽﻪ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﺍﺳﺘﺎﺗﻴﻚ ﺩﺭ‬ ‫ﻣﻨﺤﻨﻲ ‪ g2‬ﻧﺎﻛﺎﻓﻲ ﺑﺎﺷﺪ‪ -‬ﻫﻤﭽﻮﻥ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ ‪ ۱‬ﺍﺯ ﺟﺪﻭﻝ )‪ -(۱‬ﺩﺭ ﺣﻴﻦ‬ ‫ﻧﻮﺳﺎﻧﺎﺕ ﺷﺒﻜﻪ ﺣﻮﻝ ﻧﻘﻄﻪ ﻛﺎﺭ ‪ PInitial‬ﺷﺒﻜﻪ ﺑﻪ ﺑﻴﻨﻲ ﻣﻨﺤﻨﻲ ﻳﻌﻨﻲ ﻧﻘﻄﻪ‬ ‫ﻣﺎﻛﺰﻳﻤﻢ ﺗﻮﺍﻥ ﺍﻧﺘﻘﺎﻟﻲ ﺭﺳﻴﺪﻩ ﻭ ﺩﭼﺎﺭ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﻣﻲ ﮔﺮﺩﺩ‪ .‬ﺩﺭ ﺣﺎﺩﺛﻪ‬ ‫ﺷﻤﺎﺭﻩ ‪ ،۲‬ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﺩﺭ ﻣﻨﺤﻨﻲ ﺑﻌﺪ ﺍﺯ ﺍﻏﺘﺸﺎﺵ ﺑﻴﺸﺘﺮ ﺍﺯ ﺣﺎﺩﺛﻪ‬ ‫ﺷﻤﺎﺭﻩ ‪ ۱‬ﺑﻮﺩﻩ ﻭ ﺷﺎﻧﺲ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺷﺒﻜﻪ ﺑﻴﺸﺘﺮ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺷﻜﻠﻬﺎﻱ‬ ‫)‪ (۷‬ﻭ )‪ ،(۸‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺷﺒﻜﻪ ﺭﺍ ﺩﺭ ﺍﻳﻦ ‪ ۲‬ﺣﺎﺩﺛﻪ ﺑﺰﺭﮒ ﺍﻋﻤﺎﻝ‬ ‫ﺷﺪﻩ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﻨﺪ‪ .‬ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺩﺭ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ ‪ ۱‬ﺩﺭ ﻛﻤﺘﺮ ﺍﺯ ‪۲‬‬ ‫ﺛﺎﻧﻴﻪ ﻭ ﭘﺎﻳﺪﺍﺭﻱ ﺳﻴﺴﺘﻢ ﺩﺭ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ ‪ ۲‬ﭘﺲ ﺍﺯ ﻃﻲ ﻧﻮﺳﺎﻧﺎﺕ ﺳﻴﺴﺘﻢ‪،‬‬ ‫ﻗﺎﺑﻞ ﻣﺸﺎﻫﺪﻩ ﺍﺳﺖ‪.‬‬ ‫‪ -۵‬ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﻠﻨﺪ ﻣﺪﺕ ﺑﺮ ﺭﻭﻱ‬ ‫ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‬ ‫ﺑﺮﺍﻱ ﻣﻄﺎﻟﻌﻪ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺑﻠﻨﺪ ﻣﺪﺕ‪ ،‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻋﺪﻡ ﺍﻣﻜﺎﻥ ﺷﺒﻴﻪﺳﺎﺯﻱ‬ ‫ﺑﻠﻨﺪ ﻣﺪﺕ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺑﺎ ﺑﺎﺭﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺑﻪ ﺩﻟﻴﻞ ﺣﺠﻢ ﺑﺴﻴﺎﺭ ﺑﺎﻻﻱ‬ ‫ﻣﺤﺎﺳﺒﺎﺕ ﻣﻌﺎﺩﻻﺕ ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﻭ ﺯﻣﺎﻥ ﺑﺴﻴﺎﺭ ﺯﻳﺎﺩ ﺁﻥ‪ ،‬ﺷﺒﻴﻪﺳﺎﺯﻱ‬ ‫ﺷﻜﻞ ‪ -۶‬ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ ﺩﺭ ﻳﻚ ﺍﻏﺘﺸﺎﺵ ﺑﺰﺭﮒ ﻧﻮﻋﻲ‬ ‫‪۷‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫ﺧﺮﺍﺳﺎﻥ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺩﻳﻨﺎﻣﻴﻜﻲ ﺩﺭ ﺣﻮﺯﺓ ﺯﻣﺎﻥ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺑﺎﺭ ﺷﺎﻣﻞ ﺗﺮﻛﻴﺐ‬ ‫ﻣﺪﻝ ﺍﻣﭙﺪﺍﻧﺲ ﺛﺎﺑﺖ ﻭ ﻣﺪﻝ ﺗﻮﺍﻥ ﺛﺎﺑﺖ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺷﺮﺍﻳﻄﻲ ﻛﻪ ‪۲‬‬ ‫ﻭﺍﺣﺪ ﻧﻴﺮﻭﮔﺎﻩ ﮔﺎﺯﻱ ﺷﺮﻳﻌﺘﻲ ﺩﺭ ﻣﺪﺍﺭ ﻧﻴﺴﺘﻨﺪ‪ ،‬ﺩﺭ ﺑﺎﺯﺓ ﺯﻣﺎﻧﻲ ﺻﻔﺮ ﺗﺎ ‪۴۵‬‬ ‫ﺩﻗﻴﻘﻪ‪ ،‬ﺩﺭ ﻫﺮ ‪ ۳۰‬ﺛﺎﻧﻴﻪ ﻳﻜﻲ ﺍﺯ ﺑﺎﺭﻫﺎﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺭﺍ ﺑﻪ ﻣﻴﺰﺍﻥ ‪ ۲۰‬ﺗﺎ‬ ‫‪ ۳۰‬ﺩﺭﺻﺪ ﺑﺎ ﺣﻔﻆ ﺿﺮﻳﺐ ﻗﺪﺭﺕ ﺍﺿﺎﻓﻪ ﻣﻲﻛﻨﻴﻢ‪ .‬ﺩﺭ ﺩﻗﻴﻘﻪ ‪ ،۲۰‬ﮊﻧﺮﺍﺗﻮﺭ‬ ‫ﻭﺍﺣﺪ ﺑﺨﺎﺭﻱ ﻧﻴﺮﻭﮔﺎﻩ ﺷﺮﻳﻌﺘﻲ ﺍﺯ ﻣﺪﺍﺭ ﺧﺎﺭﺝ ﻣﻲ ﮔﺮﺩﺩ‪ .‬ﺩﺭ ﺍﺛﺮ ﺍﻓﺰﺍﻳﺶ ﺑﺎﺭ‪،‬‬ ‫ﺣﺎﺷﻴﻪ ﺍﻃﻤﻴﻨﺎﻥ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺷﺒﻜﻪ ﻛﻢ ﺷﺪﻩ ﻭ ﺩﺭ ﺯﻣﺎﻥ ‪ ۴۱‬ﺩﻗﻴﻘﻪ ﻭ ‪۲۰‬‬ ‫ﺛﺎﻧﻴﻪ‪ ،‬ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ‪ ۴۰۰/۱۳۲‬ﻛﻴﻠﻮﻭﻟﺖ ﺗﺮﺑﺖ ﺟﺎﻡ ﺑﺮ ﺍﺛﺮ ﺍﺿﺎﻓﻪ ﺑﺎﺭ ﺗﺮﻳﭗ‬ ‫ﻣﻲ ﺩﻫﺪ‪ .‬ﺩﺭ ﻧﻬﺎﻳﺖ ﺩﺭ ﺩﺭ ﺩﻗﻴﻘﻪ ‪ ،۴۳‬ﺷﺒﻜﻪ ﺩﭼﺎﺭ ﻓﺮﻭﭘﺎﺷﻲ ﻛﺎﻣﻞ ﻭﻟﺘﺎﮊ ﻣﻲ‬ ‫ﮔﺮﺩﺩ‪ .‬ﺷﻜﻞ )‪ (۹‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺷﺒﻜﻪ ﻭ ﺷﻜﻞ )‪ (۱۰‬ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ‬ ‫ﺗﻮﻟﻴﺪﻱ ﺑﺮﺧﻲ ﺍﺯ ﮊﻧﺮﺍﺗﻮﺭﻫﺎﻱ ﻣﻬﻢ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲﺩﻫﻨﺪ‪ .‬ﻣﺤﺪﻭﺩ ﺷﺪﻥ ﺗﻮﺍﻥ‬ ‫ﺭﺍﻛﺘﻴﻮ ﮊﻧﺮﺍﺗﻮﺭﻫﺎ ﺩﺭ ﺷﻜﻞ )‪ (۱۰‬ﻣﺸﺨﺺ ﺍﺳﺖ‪ .‬ﺩﺭ ﺷﻜﻞ )‪ (۹‬ﺑﺎﺱ ﻋﻠﻲ‬ ‫ﺁﺑﺎﺩ‪ ،‬ﻣﺘﺼﻞ ﺑﻪ ﺷﺒﻜﻪ ﺍﻳﺮﺍﻥ ﺍﺳﺖ ﻛﻪ ﻭﻟﺘﺎﮊ ﺁﻥ ﺑﻪ ﺩﻟﻴﻞ ﻗﻮﻱ ﺑﻮﺩﻥ ﺷﺒﻜﻪ‬ ‫ﺍﻳﺮﺍﻥ ﭘﺎﻳﺪﺍﺭ ﻣﺎﻧﺪﻩ ﺍﺳﺖ‪.‬‬ ‫‪1.05‬‬ ‫‪1‬‬ ‫‪0.95‬‬ ‫‪0.9‬‬ ‫‪0.8‬‬ ‫‪nehbandan‬‬ ‫‪tabas‬‬ ‫‪istgah azadvar‬‬ ‫‪ghaenat-400‬‬ ‫‪aliabad-400‬‬ ‫‪kohsangi‬‬ ‫‪0.75‬‬ ‫‪0.7‬‬ ‫‪0.65‬‬ ‫‪0.6‬‬ ‫‪3000‬‬ ‫‪2000‬‬ ‫‪2500‬‬ ‫‪1500‬‬ ‫)‪Time (Sec.‬‬ ‫‪1000‬‬ ‫‪0‬‬ ‫‪500‬‬ ‫ﺷﻜﻞ ‪ -۹‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ ﻭﻟﺘﺎﮊ‬ ‫‪600‬‬ ‫‪shariatiG2‬‬ ‫‪500‬‬ ‫‪shariatiG6‬‬ ‫‪Reactive Power Limitation‬‬ ‫‪1.2‬‬ ‫‪400‬‬ ‫‪mashhadG1‬‬ ‫‪300‬‬ ‫‪mashhadS1‬‬ ‫‪1‬‬ ‫‪neishaburSG‬‬ ‫‪200‬‬ ‫‪0.8‬‬ ‫)‪Voltage (p.u.‬‬ ‫‪tousS‬‬ ‫‪0‬‬ ‫‪0.4‬‬ ‫‪3000‬‬ ‫‪0.2‬‬ ‫‪9‬‬ ‫‪7‬‬ ‫‪6‬‬ ‫‪4‬‬ ‫‪5‬‬ ‫)‪Tiem (Sec.‬‬ ‫‪3‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫ﻭﻟﺘﺎﮊ‬ ‫ﺷﻜﻞ ‪ -۸‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ‪۲‬‬ ‫‪ -۶‬ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ ‫ﻫﻤﭽﻨﺎﻥ ﻛﻪ ﺩﺭ ﻣﻘﺪﻣﻪ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﻴﺎﻥ ﺷﺪ‪ ،‬ﺩﺭ ﺳﺎﻟﻬﺎﻱ ﺍﺧﻴﺮ ﺭﻭﺷﻬﺎﻱ‬ ‫ﻣﺘﻌﺪﺩﻱ ﺑﺮ ﺍﺳﺎﺱ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﻱ ﻓﺎﺯﻭﺭﻫﺎﻱ ﻣﺤﻠﻲ ﻭﻟﺘﺎﮊ ﻭ ﺟﺮﻳﺎﻥ ﺑﺮﺍﻱ‬ ‫ﺗﺨﻤﻴﻦ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻫﻤﺰﻣﺎﻥ ﺑﺎ ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭﻱ ﺍﺯ ﺷﺒﻜﻪ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﻣﻌﻴﺎﺭ ‪ VCPI‬ﻣﻌﺮﻓﻲ ﺷﺪﻩ ﺗﻮﺳﻂ ﻣﺮﺟﻊ ]‪ [۱۲‬ﺩﺍﺭﺍﻱ ﻣﻘﺪﺍﺭ ﻧﺰﺩﻳﻚ ﺑﻪ ‪۱‬‬ ‫ﺩﺭ ﻧﻘﻄﻪ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﻭ ﻣﻘﺪﺍﺭ ﻧﺰﺩﻳﻚ ﺑﻪ ﺻﻔﺮﺩﺭ ﺣﺎﻟﺖ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ ‫ﺻﻔﺮ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﺭﻭﺵ ﺩﺭ ﻣﺮﺟﻊ ]‪ [۱۲‬ﺗﻨﻬﺎ ﺑﺮﺍﻱ ﺍﻓﺰﺍﻳﺶ ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ‬ ‫ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺷﺒﻜﻪ ﺩﺭ ﺣﺎﻟﺖ ‪ off-line‬ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺩﺭ ﻭﺍﻗﻊ ﺍﻟﮕﻮﻳﻲ ﻣﺸﺎﺑﻪ ﺁﻧﭽﻪ ﻛﻪ ﺩﺭ ﺭﺳﻢ ﻣﻨﺤﻨﻴﻬﺎﻱ ‪ V-Q‬ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ‬ ‫ﻣﻲ ﺷﻮﺩ ﻣﻮﺭﺩ ﺗﺴﺖ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﻛﻪ ﺍﻟﮕﻮﻱ ﻭﺍﻗﻌﻲ ﻳﻚ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﻧﻤﻲ‬ ‫ﺑﺎﺷﺪ‪ .‬ﺩﺭ ﻭﺍﻗﻊ ﺭﻭﺵ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺑﻴﺸﺘﺮ ﺩﺭ ﻣﺤﺎﺳﺒﺎﺕ ‪ Off-Line‬ﺑﺮﺍﻱ‬ ‫ﺗﻌﻴﻴﻦ ﺣﺎﺷﻴﻪ ﺍﺳﺘﺎﺗﻴﻜﻲ ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ ﺑﺎﺱ ﻧﺘﻴﺠﻪ ﻗﺎﺑﻞ ﺗﻮﺟﻪ ﺩﺍﺭﺩ ﻭ ﺩﺭ ﺑﻬﺮﻩ‬ ‫ﺑﺮﺩﺍﺭﻱ ﻭﺍﻗﻌﻲ ﺷﺒﻜﻪ ﺍﺯ ﻣﻘﺪﺍﺭ ﻣﻄﻠﻖ ﺁﻥ ﻧﻤﻲ ﺗﻮﺍﻥ ﺗﺨﻤﻴﻦ ﻗﺎﺑﻞ ﺗﻮﺟﻬﻲ‬ ‫ﺑﺮﺍﻱ ﻭﺿﻌﻴﺖ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺩﺭ ﺑﺎﺳﻬﺎﻱ ﻣﺨﺘﻠﻒ ﺷﺒﻜﻪ ﺍﺭﺍﺋﻪ ﺩﺍﺩ‪.‬‬ ‫‪1.05‬‬ ‫‪1‬‬ ‫‪0.95‬‬ ‫‪0.9‬‬ ‫‪0.85‬‬ ‫‪0.8‬‬ ‫‪0.75‬‬ ‫‪0.7‬‬ ‫‪0.65‬‬ ‫‪0.6‬‬ ‫‪3000‬‬ ‫‪2500‬‬ ‫‪2000‬‬ ‫‪1500‬‬ ‫)‪Time (Sec.‬‬ ‫‪1000‬‬ ‫‪500‬‬ ‫‪2000‬‬ ‫ﺷﻜﻞ ‪ -۱۰‬ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ ﮊﻧﺮﺍﺗﻮﺭﻫﺎﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ‬ ‫‪0‬‬ ‫‪nehbandan‬‬ ‫‪tabas‬‬ ‫‪istgah azadvar‬‬ ‫‪ghaenat-400‬‬ ‫‪aliabad-400‬‬ ‫‪kohsangi‬‬ ‫‪2500‬‬ ‫‪1500‬‬ ‫‪1000‬‬ ‫‪500‬‬ ‫‪0‬‬ ‫)‪Time (Sec.‬‬ ‫‪0‬‬ ‫‪8‬‬ ‫‪100‬‬ ‫‪shirvanG‬‬ ‫)‪Voltage (p.u.‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫‪nehbandan‬‬ ‫‪tabas‬‬ ‫‪aliabad400‬‬ ‫‪ghaenat-400‬‬ ‫‪kohsangi‬‬ ‫‪istgah azadvar‬‬ ‫‪neishaburG‬‬ ‫)‪Reactive Power (MVAR‬‬ ‫‪ghaenG‬‬ ‫‪0.6‬‬ ‫)‪Voltage (p.u.‬‬ ‫‪0.85‬‬ ‫‪0‬‬ ‫ﺷﻜﻞ ‪ -۹‬ﻭﻟﺘﺎﮊ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎﻱ ﺧﺮﺍﺳﺎﻥ ﺩﺭ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ ﻭﻟﺘﺎﮊ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪۸‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﻣﺮﺟﻊ ]‪ [۶‬ﻣﻌﻴﺎﺭ ‪ VSI‬ﺭﺍ ﻣﻌﺮﻓﻲ ﻛﺮﺩﻩ ﻛﻪ ﺑﺮﺍﻱ ﺣﺎﻟﺖ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻋﺪﺩ‬ ‫ﺑﺰﺭﮔﻲ ﺍﺳﺖ ﻭ ﺩﺭ ﻧﻘﻄﻪ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺑﻪ ﻋﺪﺩ ‪ ۱‬ﻣﻲ ﺭﺳﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺭﻭﺵ ﺑﺎ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻓﺎﺯﻭﺭﻫﺎﻱ ﻭﻟﺘﺎﮊ ﻭ ﺟﺮﻳﺎﻥ ﺩﺭ ﻣﺤﻞ ﻫﺮ ﺷﻴﻦ ﺑﺎﺭ ﺷﺒﻜﻪ ﺩﺭ ﻫﺮ‬ ‫ﻟﺤﻈﻪ‪ ،‬ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺩﻳﺪﻩ ﺷﺪﻩ ﺍﺯ ﻣﺤﻞ ﺁﻥ ﺑﺎﺱ ﺗﺨﻤﻴﻦ ﺯﺩﻩ ﻣﻲ ﺷﻮﺩ ‪.‬‬ ‫‪ VSI‬ﺑﺮﺍﺑﺮ ﻧﺴﺒﺖ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺷﻴﻦ ﺑﺎﺭ ﻣﻮﺭﺩ ﻧﻈﺮ ﺑﻪ ﺗﻔﺎﺿﻞ ﻓﺎﺯﻭﺭ ﻫﺎﻱ ﻭﻟﺘﺎﮊ‬ ‫ﺷﻴﻦ ﺑﺎﺭ ﻭ ﺷﻴﻦ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺗﻮﻧﻦ ﺍﺳﺖ‪ .‬ﻣﺸﻜﻞ ﺍﻳﻦ ﺭﻭﺵ ﺁﻥ ﺍﺳﺖ ﻛﻪ‬ ‫ﺗﺨﻤﻴﻦ ﭘﺎﺭﺍﻣﺘﺮ ﻫﺎﻱ ﻣﺪﺍﺭ ﻣﻌﺎﺩﻝ ﺑﺎ ﺗﺄﺧﻴﺮ ﻭ ﺩﺭ ﺑﺮﺧﻲ ﻣﻮﺍﺭﺩ ﻫﻤﭽﻮﻥ‬ ‫ﺣﻮﺍﺩﺙ ﺑﺰﺭﮒ ﺑﺎ ﻧﻮﺳﺎﻧﺎﺕ ﺗﻮﺍﻥ ﺷﺒﻜﻪ‪ ،‬ﺩﭼﺎﺭ ﺧﻄﺎ ﺷﺪﻩ ﻛﻪ ﮔﺎﻩ ﺩﺭ ﺗﺼﻤﻴﻢ‬ ‫ﮔﻴﺮﻳﻬﺎﻱ ﺣﻔﺎﻇﺘﻲ ﻣﺸﻜﻞ ﺍﻳﺠﺎﺩ ﻣﻲ ﻛﻨﺪ‪.‬‬ ‫ﻣﺮﺟﻊ ]‪ [۵‬ﻣﻌﻴﺎﺭ ‪ SDC‬ﺭﺍ ﻣﻌﺮﻓﻲ ﻧﻤﻮﺩﻩ ﺍﺳﺖ ﻛﻪ ﺩﺍﺭﺍﻱ ﻣﻘﺪﺍﺭ ‪ ۱‬ﻳﺎ ﺑﺎﻻﺗﺮ‬ ‫ﺩﺭ ﺣﺎﻟﺖ ﭘﺎﻳﺪﺍﺭ ﻭ ﻣﻘﺪﺍﺭ ﺻﻔﺮ ﺩﺭ ﻧﻘﻄﻪ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﻣﻌﻴﺎﺭ ﺍﺯ‬ ‫ﺁﻧﺠﺎ ﺑﻪ ﺩﺳﺖ ﺁﻣﺪﻩ ﻛﻪ ﺩﺭ ﻧﻘﻄﻪ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﻫﺮ ﺗﻐﻴﻴﺮ ﺗﻮﺍﻥ ﻇﺎﻫﺮﻱ ﺩﺭ‬ ‫ﺍﺑﺘﺪﺍﻱ ﻳﻚ ﺧﻂ ﺍﻧﺘﻘﺎﻝ ﺑﻪ ﻣﺼﺮﻑ ﺧﻮﺩ ﺧﻂ ﺭﺳﻴﺪﻩ ﻭ ﺩﺭ ﺍﻧﺘﻬﺎﻱ ﺧﻂ ﺗﻐﻴﻴﺮ‬ ‫ﺗﻮﺍﻥ ﻇﺎﻫﺮﻱ ﺑﺮﺍﺑﺮ ﺻﻔﺮ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﺭﻭﺵ ﻫﺮ ﭼﻨﺪ ﺍﺯ ﻧﻈﺮ ﺭﻳﺎﺿﻲ ﺻﺤﻴﺢ‬ ‫ﺍﺳﺖ ﻭﻟﻲ ﺑﻪ ﺗﺮﺗﻴﺒﻲ ﻛﻪ ﺗﻮﺳﻂ ﻣﺮﺟﻊ ]‪ [۵‬ﺑﻴﺎﻥ ﺷﺪﻩ ﺍﺳﺖ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ‬ ‫ﺳﺎﺯﻱ ﺑﺮ ﺭﻭﻱ ﻳﻚ ﺷﺒﻜﻪ ﻗﺪﺭﺕ ﺑﻪ ﺻﻮﺭﺕ ﺑﻪ ﻫﻨﮕﺎﻡ ﻧﻴﺴﺖ ﻭ ﻧﺮﺥ ﻧﻤﻮﻧﻪ‬ ‫ﺑﺮﺩﺍﺭﻱ ﺍﺯ ﻭﻟﺘﺎﮊﻫﺎ ﻭ ﺟﺮﻳﺎﻧﻬﺎﻱ ﺷﺒﻜﻪ ﺩﺭ ﺻﺤﺖ ﻋﻤﻠﻜﺮﺩ ﺁﻥ ﺑﺴﻴﺎﺭ ﻣﺆﺛﺮ‬ ‫ﺍﺳﺖ‪ .‬ﭼﻨﺎﭼﻪ ﺑﺎ ﺗﻨﻈﻴﻤﺎﺕ ﻣﺸﺨﺺ ﺍﻣﻜﺎﻥ ﺍﺟﺮﺍﻱ ﺁﻥ ﺑﺮﺍﻱ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ‬ ‫ﻣﺪﺕ ﻭﻟﺘﺎﮊ ﻓﺮﺍﻫﻢ ﮔﺮﺩﺩ ﺩﺭ ﺣﻮﺍﺩﺙ ﺑﺰﺭﮒ ﻗﻄﻌﺎﹰ ﺑﺎ ﻣﺸﻜﻞ ﺭﻭﺑﺮ ﻣﻲ ﮔﺮﺩﺩ‪.‬‬ ‫ﻻﺯﻡ ﺑﻪ ﺫﻛﺮ ﺍﺳﺖ ﻛﻪ ﺩﺭ ﻣﺮﺟﻊ ]‪ [۵‬ﻫﻴﭻ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺯﻣﺎﻧﻲ ﺍﺭﺍﺋﻪ ﻧﺸﺪﻩ ﻭ‬ ‫ﺍﻓﺰﺍﻳﺶ ﺗﻮﺍﻥ ﺑﺮﺧﻲ ﺍﺯ ﺑﺎﺳﻬﺎ ﻳﺎ ﻛﻞ ﺷﺒﻜﻪ ﺩﺭ ﺣﺎﻟﺖ ‪ off-line‬ﻣﺸﺎﺑﻪ ﺁﻧﭽﻪ‬ ‫ﻛﻪ ﺩﺭ ﻣﻨﺤﻨﻴﻬﺎﻱ ‪ P-V‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ ،‬ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﺳﺖ‪.‬‬ ‫ﺭﻭﺷﻬﺎﻱ ﺩﻳﮕﺮﻱ ﻧﻴﺰ ﻛﻪ ﺩﺭ ﻣﺮﺍﺟﻊ ]‪ [۱۳‬ﻭ ]‪ [۱۴‬ﭘﻴﺸﻨﻬﺎﺩ ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﻧﻴﺰ‬ ‫ﻣﻄﺎﻟﻌﻪ ﻭ ﺩﺭ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﻣﻮﺭﺩ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﺍﻧﺪ‪ .‬ﺍﻳﻦ ﺭﻭﺷﻬﺎ‬ ‫ﺑﺮﺍﻱ ﺗﺸﺨﻴﺺ ﻭﺿﻌﻴﺖ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺧﻂ ﺑﻪ ﻛﺎﺭ ﺭﻓﺘﻪ ﻭ ﺩﺭ ﺷﺒﻴﻪ ﺳﺎﺯﻳﻬﺎ‬ ‫ﺭﻭﺷﻬﺎﻱ ﻣﻨﺎﺳﺒﻲ ﺑﻪ ﻧﻈﺮ ﺁﻣﺪﻧﺪ ﻟﻴﻜﻦ ﺷﻨﺎﺧﺖ ﺩﻗﻴﻖ ﻧﻮﺍﺣﻲ ﻧﺎﭘﺎﻳﺪﺍﺭ ﺍﺯ ﺭﻭﻱ‬ ‫ﺁﻧﻬﺎ ﺑﺮﺍﻱ ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭ ﻣﻤﻜﻦ ﺍﺳﺖ ﭼﻨﺪﺍﻥ ﺳﺎﺩﻩ ﻧﺒﺎﺷﺪ‪.‬‬ ‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﺎ ﻣﻄﺎﻟﻌﻪ ﺭﻭﺷﻬﺎﻱ ﺍﺷﺎﺭﻩ ﺷﺪﻩ ﻭ ﺭﻭﺷﻬﺎﻱ ﺗﺤﻠﻴﻞ ﺍﺳﺘﺎﺗﻴﻚ ‪-‬‬ ‫ﻫﻤﭽﻮﻥ ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ‪ -‬ﺭﻭﺷﻲ ﺟﺪﻳﺪ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ ﻛﻪ ﺑﺎ ﺑﻪ ﻛﺎﺭ ﮔﻴﺮﻱ‬ ‫ﺍﻣﻜﺎﻧﺎﺕ ﻣﺨﺎﺑﺮﺍﺗﻲ ﺑﺘﻮﺍﻧﺪ ﺗﺨﻤﻴﻦ ﻣﻨﺎﺳﺒﻲ ﺑﺮﺍﻱ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺷﺒﻜﻪ‬ ‫ﺩﺭ ﻧﻮﺍﺣﻲ ﻣﺨﺘﻠﻒ ﺑﺎﺭ ﺍﺭﺍﺋﻪ ﻛﻨﺪ‪ .‬ﺑﺨﺶ ) ‪ (۱-۵‬ﻭ )‪ (۲-۵‬ﺑﻪ ﻣﻌﺮﻓﻲ ﻭ ﭘﻴﺎﺩﻩ‬ ‫ﺳﺎﺯﻱ ﺍﻳﻦ ﺭﻭﺵ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﻣﻲ ﭘﺮﺩﺍﺯﺩ‪.‬‬ ‫ﺷﻤﺎﺭﻩ‬ ‫ﺣﺎﺩﺛﻪ‬ ‫ﺗﻮﺍﻥ ﺍﻛﺘﻴﻮ‬ ‫ﺍﻧﺘﻘﺎﻟﻲ ﺧﻂ‬ ‫)ﻣﮕﺎﻭﺍﺕ(‬ ‫ﺗﻮﺍﻥ ﺭﺍﻛﺘﻴﻮ‬ ‫ﺍﻧﺘﻘﺎﻟﻲ ﺧﻂ‬ ‫)ﻣﮕﺎﻭﺍﺭ(‬ ‫ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ ‫ﺍﺳﺘﺎﺗﻴﻜﻲ ﺷﺒﻜﻪ ﻗﺒﻞ ﺍﺯ‬ ‫ﺧﺮﻭﺝ ﺧﻂ )ﺩﺭﺻﺪ(‬ ‫ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ‬ ‫ﻭﻟﺘﺎﮊ ﺍﺳﺘﺎﺗﻴﻜﻲ‬ ‫ﺷﺒﻜﻪ ﺑﻌﺪ ﺍﺯ ﺧﺮﻭﺝ‬ ‫ﺧﻂ )ﺩﺭﺻﺪ(‬ ‫‪۱‬‬ ‫ﺧﺮﻭﺝ ﺧﻂ ‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﻧﻴﺸﺎﺑﻮﺭ‪ -‬ﺷﺎﺩﻣﻬﺮ ﺩﺭ‬ ‫ﺣﺎﻟﺖ ﺩﺭ ﻣﺪﺍﺭ ﻧﺒﻮﺩﻥ ﻧﻴﺮﻭﮔﺎﻩ ﺗﻮﺱ‬ ‫‪۳۵۱‬‬ ‫‪۴۱‬‬ ‫‪۷/۵۶‬‬ ‫‪۰/۶۸‬‬ ‫‪۲‬‬ ‫ﺧﺮﻭﺝ ﺧﻂ ‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﻧﻴﺸﺎﺑﻮﺭ‪ -‬ﺗﻮﺱ ﺑﺮ ﺍﺛﺮ‬ ‫ﺧﻄﺎ ﺩﺭ ﺣﺎﻟﺖ ﺩﺭ ﻣﺪﺍﺭ ﻧﺒﻮﺩﻥ ﻧﻴﺮﻭﮔﺎﻩ ﺷﺮﻳﻌﺘﻲ‬ ‫‪۳۴۶‬‬ ‫‪۲۲‬‬ ‫‪۷/۹۵‬‬ ‫‪۳/۴۷‬‬ ‫ﺳﭙﺲ ﺩﺭ ﻫﺮ ﻧﺎﺣﻴﻪ ﺑﺎﺭ‪ ،‬ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ ﻫﻤﺰﻣﺎﻥ ﺑﺎ ﺑﻬﺮﻩﺑﺮﺩﺍﺭﻱ ﺍﺯ ﺷﺒﻜﻪ ﺩﺭ‬ ‫ﺩﻭﺭﻩﻫﺎﻱ ﺯﻣﺎﻧﻲ ﺗﻌﺮﻳﻒ ﺷﺪﻩ ﻛﻪ ﺑﺮﺍﻱ ﺟﻤﻊ ﺁﻭﺭﻱ ﺍﻃﻼﻋﺎﺕ ﻭ ﻣﺤﺎﺳﺒﺎﺕ‬ ‫ﻣﺪﺍﻝ ﻛﺎﻓﻲ ﺑﺎﺷﺪ‪ ،‬ﺻﻮﺭﺕ ﻣﻲﮔﻴﺮﺩ ]‪ .[۱‬ﺑﺮﺍﻱ ﻣﺜﺎﻝ ﺩﺭ ﻫﺮ ﭼﻨﺪ ﺩﻗﻴﻘﻪ‪ ،‬ﺍﻳﻦ‬ ‫ﺗﺤﻠﻴﻞ ﺑﺮﺍﻱ ﻫﺮ ﻧﺎﺣﻴﻪ ﺍﺯ ﺑﺎﺭ‪ ،‬ﺍﻧﺠﺎﻡ ﻣﻲﮔﻴﺮﺩ‪ .‬ﻣﺮﻛﺰ ﺍﻧﺠﺎﻡ ﺍﻳﻦ ﻣﺤﺎﺳﺒﺎﺕ‪،‬‬ ‫ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﻭﻟﺘﺎﮊ ﻫﺮ ﻧﺎﺣﻴﻪ ﺍﺳﺖ ﻛﻪ ﻣﻲﺗﻮﺍﻧﺪ ﻳﻜﻲ ﺍﺯ ﭘﺴﺘﻬﺎﻱ ﻣﻬﻢ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﺑﺎﺷﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﺍﻧﺘﻘﺎﻝ ﺍﻃﻼﻋﺎﺕ ﻓﺎﺯﻭﺭﻫﺎﻱ ﻭﻟﺘﺎﮊ ﻭ ﺗﻮﭘﻮﻟﻮﮊﻱ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﻭﻟﺘﺎﮊ ﺁﻥ ﻧﺎﺣﻴﻪ‪ ،‬ﺑﻪ ﺩﻟﻴﻞ ﺗﻌﺪﺍﺩ ﺑﺎﺳﻬﺎﻱ ﻛﻢ ﻭ ﻓﻮﺍﺻﻞ‬ ‫ﻛﻮﭼﻚ‪ ،‬ﺍﻣﻜﺎﻥﭘﺬﻳﺮ ﻭ ﺳﺮﻳﻊ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﺩﺭ ﻫﺮ ﺩﻭﺭﺓ ﺯﻣﺎﻧﻲ ﭼﻨﺪ ﺩﻗﻴﻘﻪﺍﻱ‪،‬‬ ‫ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ ﺑﺮ ﺭﻭﻱ ﻧﻮﺍﺣﻲ ﻛﻮﭼﻚ ﺍﻧﺠﺎﻡ ﮔﺮﻓﺘﻪ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﻭﻳﮋﻩ ﻭ ﺑﻪ ﺩﻧﺒﺎﻝ‬ ‫ﺁﻥ ﺑﺎﺳﻬﺎﻱ ﺑﺤﺮﺍﻧﻲ ﺁﻥ ﻧﺎﺣﻴﻪ ﺩﺭ ﺁﻥ ﺩﻭﺭﻩ ﻣﺸﺨﺺ ﻣﻲﮔﺮﺩﺩ‪.‬‬ ‫ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﺑﺎﺱ ﻗﻮﻱ ﺑﻪ ﻳﻚ ﻧﺎﺣﻴﻪ ﺑﺎﺭ‪ ،‬ﻣﻲ ﺗﻮﺍﻧﺪ ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﺑﺎﺱ ﮊﻧﺮﺍﺗﻮﺭﻱ‬ ‫ﻭ ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﺑﺎﺳﻲ ﺑﺎﺷﺪ ﻛﻪ ﺩﺍﺭﺍﻱ ﺳﻄﺢ ﺍﺗﺼﺎﻝ ﻛﻮﺗﺎﻩ ﺯﻳﺎﺩﻱ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ‬ ‫ﺑﺎﺳﻬﺎﻱ ﺁﻥ ﻧﺎﺣﻴﻪ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﺑﺎﺱ ﺑﻪ ﻋﻨﻮﺍﻥ ﻣﺮﺟﻊ ﻭﻟﺘﺎﮊ ﻫﺮ ﻧﺎﺣﻴﻪ ﺷﻨﺎﺧﺘﻪ‬ ‫‪ -۷‬ﻣﻌﺮﻓﻲ ﺭﻭﺵ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ‪VCI‬‬ ‫ﻣﻌﻴﺎﺭ ‪ VCI‬ﻧﺴﺒﺖ ﺗﻔﺎﺿﻞ ﺑﺮﺩﺍﺭ ﻭﻟﺘﺎﮊ ﺿﻌﻴﻒ ﺗﺮﻳﻦ ﺑﺎﺱ ﻫﺮ ﻧﺎﺣﻴﻪ ﺑﻪ‬ ‫ﺗﻔﺎﺿﻞ ﺁﻥ ﺍﺯ ﺑﺮﺩﺍﺭﻫﺎﻱ ﻭﻟﺘﺎﮊ ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﺑﺎﺱ ﻗﻮﻱ ﺑﻪ ﺁﻥ ﻧﺎﺣﻴﻪ ﺍﺯ‬ ‫ﺑﺎﺭﻣﻲﺑﺎﺷﺪ‪ .‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻨﻜﻪ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺍﻏﻠﺐ ﺑﻪ ﺻﻮﺭﺕ ﻧﺎﺣﻴﻪ ﺍﻳﺴﺖ‪،‬‬ ‫ﺩﺭ ﺍﻳﻦ ﺭﻭﺵ‪،‬ﺷﺒﻜﻪﻫﺎﻱ ﺑﺰﺭﮒ ﺭﺍ ﺑﻪ ﭼﻨﺪﻳﻦ ﻧﺎﺣﻴﻪ ﻛﻮﭼﻜﺘﺮ ﺑﺎﺭ ﺗﻘﺴﻴﻢﺑﻨﺪﻱ‬ ‫ﻣﻲﻛﻨﻴﻢ‪ .‬ﺩﺭ ﺍﻧﺘﺨﺎﺏ ﻧﻮﺍﺣﻲ ﺑﺎﺭ ﺳﻪ ﻧﻜﺘﻪ ﺭﺍ ﺑﺎﻳﺴﺘﻲ ﻟﺤﺎﻅ ﻧﻤﻮﺩ‪:‬‬ ‫ﺍﻟﻒ( ﻣﻴﺰﺍﻥ ﺗﻤﺮﻛﺰ ﺑﺎﺭ ﺩﺭ ﻫﺮ ﻧﺎﺣﻴﻪ‬ ‫ﺏ( ﻃﻮﻝ ﺧﻄﻮﻁ ﺍﺭﺗﺒﺎﻃﻲ ﺑﻴﻦ ﻧﻮﺍﺣﻲ ﺑﻪ ﻟﺤﺎﻅ ﺍﻧﺘﺨﺎﺏ ﻣﺪﻳﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ‬ ‫ﺝ( ﺗﻌﺪﺍﺩ ﺑﺎﺳﻬﺎﻱ ﻫﺮ ﻧﺎﺣﻴﻪ‪ .‬ﺍﻳﻦ ﻋﺪﺩ ﺑﺴﺘﻪ ﺑﻪ ﺣﺠﻢ ﻣﺤﺎﺳﺒﺎﺕ ﻭ ﺳﺮﻋﺖ‬ ‫ﺁﻧﻬﺎ ﺩﺍﺭﺩ ﻭ ﻫﺮ ﭼﻪ ﻛﻤﺘﺮ ﺑﺎﺷﺪ‪ ،‬ﭘﻴﺎﺩﻩﺳﺎﺯﻱ ﺍﻳﻦ ﺭﻭﺵ ﺳﺎﺩﻩﺗﺮ ﻭ ﻋﻤﻠﻲﺗﺮ‬ ‫ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬ ‫‪۹‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫ﺟﺪﻭﻝ ‪ -۱‬ﺣﻮﺍﺩﺙ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺷﺪﻩ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺗﻮﺿﻴﺤﺎﺕ ﺩﺍﺩﻩ ﺷﺪﻩ‪ ،‬ﺩﺭ ﺍﻳﻦ ﺭﻭﺵ ﺩﻭ ﻣﺮﺣﻠﻪ ﺍﺭﺳﺎﻝ ﺍﻃﻼﻋﺎﺕ‬ ‫ﺩﺭ ﻃﻮﻝ ﺷﺒﻜﻪ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪:‬‬ ‫ﺍﻟﻒ( ﺍﺭﺳﺎﻝ ﺍﻃﻼﻋﺎﺕ ﻓﺎﺯﻭﺭﻱ ﻫﺮ ﭘﺴﺖ ﺑﺤﺮﺍﻧﻲ ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﻭﻟﺘﺎﮊ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﺩﺭ ﻫﺮ ﭘﺮﻳﻮﺩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ‪ .‬ﺍﻳﻦ ﻣﺮﺣﻠﻪ ﭼﻮﻥ ﺑﻪ ﺻﻮﺭﺕ ﻧﺎﺣﻴﻪ ﺍﻱ ﻭ‬ ‫ﺩﺭ ﺍﺑﻌﺎﺩ ﻛﻮﭼﻚ‪ ،‬ﺳﺎﺩﻩ ﻭ ﻋﻤﻠﻲ ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﮔﺎﻡ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺑﺴﺘﻪ ﺑﻪ‬ ‫ﺗﺄﺧﻴﺮ ﻣﺪﻳﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ ﻭ ﺳﺮﻋﺖ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ‪ P.M.U.‬ﻫﺎ ﺍﺯ ‪ ۵۰‬ﻣﻴﻠﻲ‬ ‫ﺛﺎﻧﻴﻪ ﺑﻪ ﺑﺎﻻ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﺎﺷﺪ‪.‬‬ ‫ﺏ( ﺍﺭﺳﺎﻝ ﺍﻃﻼﻋﺎﺕ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺑﺎﺱ ﻣﺮﺟﻊ ﻫﺮ ﻧﺎﺣﻴﻪ ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﻭﻟﺘﺎﮊ‬ ‫ﻫﺮ ﻧﺎﺣﻴﻪ ﺩﺭ ﻫﺮ ﭘﺮﻳﻮﺩ ﻧﻤﻮﻧﻪﺑﺮﺩﺍﺭﻱ ﻛﻪ ﻧﻴﺎﺯ ﺑﻪ ﻣﺤﻴﻂ ﻣﺨﺎﺑﺮﺍﺗﻲ ﺳﺮﻳﻊ ﺑﺎ‬ ‫ﺳﺮﻋﺖ ﺍﻧﺘﻘﺎﻝ ﺩﺍﺩﻩ ﺑﺎﻻ ﺩﺍﺭﺩ‪ .‬ﺑﺴﺘﻪ ﺑﻪ ﺳﺮﻋﺖ ﻣﺤﻴﻂ ﻣﺨﺎﺑﺮﺍﺗﻲ ﻭ ﻃﻮﻝ‬ ‫ﻣﺴﻴﺮﻫﺎﻱ ﺍﻧﺘﻘﺎﻝ ﺩﺍﺩﻩ ﻫﺎ‪ ،‬ﭘﺮﻳﻮﺩ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻣﻲ ﺗﻮﺍﻧﺪ ﺍﺯ ‪ ۵۰‬ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ‬ ‫ﺗﺎ ‪ ۱‬ﺛﺎﻧﻴﻪ ﺑﺎﺷﺪ‪.‬‬ ‫ﺷﻜﻞ )‪ (۱۱‬ﺍﻳﻦ ﺳﺎﺧﺘﺎﺭ ﺍﻧﺘﻘﺎﻝ ﺍﻃﻼﻋﺎﺕ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺷﻜﻞ‬ ‫ﻓﺮﺽ ﺷﺪﻩ ﻛﻪ ﺑﺎﺱ ﻗﻮﻱ ﻣﺮﺟﻊ ﺗﻤﺎﻣﻲ ﻧﻮﺍﺣﻲ ﻳﻚ ﺑﺎﺱ ﺍﺳﺖ‪ .‬ﺩﺭ ﺻﻮﺭﺕ‬ ‫ﺗﻔﺎﻭﺕ ﺍﻳﻦ ﺑﺎﺱ ﺑﺮﺍﻱ ﻧﻮﺍﺣﻲ ﻣﺨﺘﻠﻒ‪ ،‬ﺳﺎﺧﺘﺎﺭﻱ ﻣﺸﺎﺑﻪ ﻭﻟﻲ ﻣﺨﺘﺺ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ‪.‬‬ ‫ﺍﮔﺮ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺑﺎﺱ ﻗﻮﻱ ﻭ ﺍﺭﺳﺎﻝ ﺁﻥ ﺑﻪ ﻫﺮ ﻧﺎﺣﻴﻪ ‪۵۰۰‬‬ ‫ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﻮﺩ ﻭ ﻧﺮﺥ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺍﺯ ﺑﺎﺳﻬﺎﻱ‬ ‫ﻫﺮ ﻧﺎﺣﻴﻪ ﻭ ﺍﺭﺳﺎﻝ ﺁﻥ ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﺁﻥ ﻧﺎﺣﻴﻪ ‪ ۵۰‬ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﺑﺎﺷﺪ‪ ،‬ﺩﺭ‬ ‫ﺍﻳﻦ ﺻﻮﺭﺕ ﺑﺮﺍﻱ ﻫﺮ ‪ ۱۰‬ﻧﻤﻮﻧﻪ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﻧﺎﺣﻴﻪ ﺍﻱ‪ ،‬ﻳﻚ ﻧﻤﻮﻧﻪ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ‬ ‫ﻗﻮﻱ ﺗﺮﻳﻦ ﺑﺎﺱ ﺷﺒﻜﻪ‪ ،‬ﺑﻪ ﻛﺎﺭ ﮔﺮﻓﺘﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﺭﺷﻜﻞ )‪ (۱۳‬ﻓﻠﻮﭼﺎﺭﺕ‬ ‫ﺍﻟﮕﻮﺭﻳﺘﻢ ‪ VCI‬ﺑﺎ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺍﻳﻦ ﻧﺮﺥ ﻫﺎﻱ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺭﺳﻢ ﺷﺪﻩ‬ ‫ﺍﺳﺖ‪.‬‬ ‫ﻣﻲ ﮔﺮﺩﺩ‪ .‬ﺩﺭ ﺷﺒﻜﻪ ﻫﺎﻱ ﻛﻮﭼﻚ ﻣﻲ ﺗﻮﺍﻥ ﺍﻳﻦ ﺑﺎﺱ ﺭﺍ ﺑﺮﺍﻱ ﻫﻤﻪ ﻧﻮﺍﺣﻲ‬ ‫ﻳﻜﺴﺎﻥ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ‪ .‬ﻟﻴﻜﻦ ﺩﺭ ﺷﺒﻜﻪ ﻫﺎﻱ ﺑﺰﺭﮒ‪ ،‬ﺑﻪ ﺩﻟﻴﻞ ﻣﺤﺪﻭﺩﻳﺘﻬﺎﻱ‬ ‫ﻣﺨﺎﺑﺮﺍﺗﻲ ﻭ ﺗﺄﺧﻴﺮ ﺯﻳﺎﺩﺗﺮ ﺍﻧﺘﻘﺎﻝ ﺩﺍﺩﻩ ﻫﺎ ﺩﺭ ﻓﻮﺍﺻﻞ‬ ‫ﺯﻳﺎﺩ‪ ،‬ﻣﻨﺎﺳﺐ ﺍﺳﺖ ﻛﻪ ﺑﺮﺍﻱ ﻧﻮﺍﺣﻲ ﻣﺨﺘﻠﻒ ﺑﺎﺱ ﻣﺮﺟﻊ ﺭﺍ ﻧﺰﺩﻳﻚ ﺑﻪ ﺁﻥ‬ ‫ﻧﻮﺍﺣﻲ ﺭﺍ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﺣﺎﻟﺖ ﻣﻤﻜﻦ ﺍﺳﺖ ﺑﺎﺱ ﻣﺮﺟﻊ ﺑﺮﺍﻱ ﺩﻭ ﻳﺎ‬ ‫ﭼﻨﺪ ﻧﺎﺣﻴﻪ ﻣﺸﺘﺮﻙ ﺑﺎﺷﺪ‪.‬‬ ‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﻮﺍﺭﺩ ﻓﻮﻕ‪ ،‬ﻣﻌﻴﺎﺭ ‪ VCI‬ﺭﺍ ﺑﺮﺍﻱ ﻫﺮ ﻧﺎﺣﻴﻪ ﻣﻲﺗﻮﺍﻥ ﺑﻪ ﺻﻮﺭﺕ‬ ‫ﺯﻳﺮ ﻣﺤﺎﺳﺒﻪ ﻧﻤﻮﺩ‪:‬‬ ‫)‪(۲‬‬ ‫‪Vk ,i‬‬ ‫‪Vk ,i − VSBk ,i‬‬ ‫= ‪VCI k ,i‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫ﻛﻪ ‪ ،Vk,i‬ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺿﻌﻴﻒﺗﺮﻳﻦ ﺑﺎﺱ ﻧﺎﺣﻴﻪ ‪i‬ﺍﻡ ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ ﻭ ‪،VSB,k,i‬‬ ‫ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﻧﺰﺩﻳﻜﺘﺮﻳﻦ ﺑﺎﺱ ﻗﻮﻱ ﺑﻪ ﻧﺎﺣﻴﻪ ‪i‬ﺍﻡ ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ ﻣﻲﺑﺎﺷﺪ‪ .‬ﺑﺎ‬ ‫ﺗﻮﺟﻪ ﺑﻪ ﺁﻧﻜﻪ ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ ﺩﺭﻫﺮ ﺩﻭﺭﺓ ﭼﻨﺪ ﺩﻗﻴﻘﻪﺍﻱ ﺩﺭ ﻫﺮ ﻧﺎﺣﻴﻪ‪ ،‬ﺍﻧﺠﺎﻡ‬ ‫ﻣﻲﺷﻮﺩ‪ ،‬ﻟﺬﺍ ﺑﺤﺮﺍﻧﻲﺗﺮﻳﻦ ﺑﺎﺱ ﻧﺎﺣﻴﻪ ﺩﺭ ﻫﺮ ﺑﺎﺯﺓ ﭼﻨﺪ ﺩﻗﻴﻘﻪﺍﻱ ﺗﻌﻴﻴﻦ‬ ‫ﻣﻲﮔﺮﺩﺩ‪ .‬ﺩﺭ ﻃﻮﻝ ﺍﻳﻦ ﺑﺎﺯﻩ‪ ،‬ﻓﺎﺯﻭﺭ ﺍﻳﻦ ﺑﺎﺱ ﺑﺎ ﺩﻭﺭﻩ ‪ ۵۰‬ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﻳﺎ ﺑﺎﻻﺗﺮ‬ ‫ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﻱ ﺷﺪﻩ ﻭ ﺩﺭ ﻣﺤﺎﺳﺒﺎﺕ ﺑﻪ ﻫﻨﮕﺎﻡ‪ ،‬ﻭﺍﺭﺩ ﺧﻮﺍﻫﺪ ﺷﺪ‪ .‬ﭼﻨﺎﻧﭽﻪ‬ ‫ﺑﺮﺍﻱ ﺍﻳﻦ ﺑﺎﺱ ﺩﺭ ﺍﻳﻦ ﻓﺎﺻﻠﻪ ﭼﻨﺪ ﺩﻗﻴﻘﻪﺍﻱ‪ ،‬ﺣﺎﺩﺛﻪﺍﻱ ﭘﻴﺶ ﺑﻴﺎﻳﺪ‪ ،‬ﺩﺭ ﺍﻳﻦ‬ ‫ﺻﻮﺭﺕ ﺑﺎﺱ ﺩﻭﻡ ﺑﺤﺮﺍﻧﻲ‪ ،‬ﺟﺎﻳﮕﺰﻳﻦ ﺁﻥ ﺧﻮﺍﻫﺪ ﺷﺪ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺩﺭ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﻭ ﺩﺭ ﻫﺮ ﺩﻭﺭﻩ ﻣﺜﻼﹰ ﻳﻚ ﺩﻗﻴﻘﻪ ﺍﻱ‪ ،‬ﺗﻨﻬﺎ ﺍﻃﻼﻋﺎﺕ ﻓﺎﺯﻭﺭ ﻳﻚ ﺑﺎﺱ ﺩﺭ‬ ‫ﻫﺮ ‪ ۵۰‬ﻣﻴﻠﻲ ﺛﺎﻧﻴﻪ ﻳﺎ ﺑﺎﻻﺗﺮ ﺑﻪ ﻣﺮﻛﺰ ﻛﻨﺘﺮﻝ ﺁﻥ ﻧﺎﺣﻴﻪ ﺍﺭﺳﺎﻝ ﻣﻲ ﮔﺮﺩﺩ‪ .‬ﺑﺎ‬ ‫ﺗﻮﺟﻪ ﺑﻪ ﺍﻳﻦ ﻧﻜﺘﻪ ﻭ ﻫﻤﭽﻨﻴﻦ ﺳﺮﻋﺖ ﺑﺎﻻﻱ ﺍﻧﺘﻘﺎﻝ ﻣﺤﻴﻄﻬﺎﻱ ﻣﺨﺎﺑﺮﺍﺗﻲ‬ ‫ﻣﻮﺟﻮﺩ ﻭ ﻓﻮﺍﺻﻞ ﻛﻢ ﺩﺭ ﻫﺮ ﻧﺎﺣﻴﻪ‪ ،‬ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﻳﻦ ﻃﺮﺡ ﻛﺎﻣﻼﹰ ﻋﻤﻠﻲ‬ ‫ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬ ‫ﻣﻘﺪﺍﺭ ‪ VCIk,i‬ﺩﺭ ﺷﺮﺍﻳﻂ ﻧﺰﺩﻳﻚ ﺑﻪ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺑﻪ ﻋﺪﺩ ﻳﻚ ﻧﺰﺩﻳﻚ‬ ‫ﻣﻲﮔﺮﺩﺩ ﻭ ﻣﻲ ﺗﻮﺍﻧﺪ ﻣﻌﻴﺎﺭ ﺗﺸﺨﻴﺺ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻫﺮ ﻧﺎﺣﻴﻪ ﻗﺮﺍﺭ‬ ‫ﮔﻴﺮﺩ‪.‬‬ ‫‪ -۱-۷‬ﺷﺒﻴﻪﺳﺎﺯﻱ ﺭﻭﺵ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ‪ VCI‬ﺑﺮ‬ ‫ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‬ ‫ﺑﺮﺍﻱ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﻳﻦ ﺭﻭﺵ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺭﺍ ﺑﻪ ‪ ۶‬ﻧﺎﺣﻴﻪ ﺑﺎﺭ ﻣﻄﺎﺑﻖ ﺷﻜﻞ‬ ‫)‪ (۱۲‬ﺗﻘﺴﻴﻢ ﺑﻨﺪﻱ ﻣﻲ ﻛﻨﻴﻢ‪ .‬ﺩﺭ ﺿﻤﻴﻤﻪ ﻣﻘﺎﻟﻪ‪ ،‬ﺑﺎﺳﻬﺎﯼ ﻣﺮﺑﻮﻁ ﺑﻪ ﻫﺮ‬ ‫ﻧﺎﺣﻴﻪ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﻧﺪ‪ .‬ﻻﺯﻡ ﺑﻪ ﺫﮐﺮ ﺍﺳﺖ ﮐﻪ ﺍﻳﻦ ﺍﻃﻼﻋﺎﺕ‪ ،‬ﻣﺮﺑﻮﻁ ﺑﻪ‬ ‫ﭘﻴﺸﺒﻴﻨﯽ ﺑﺎﺭ ﺳﺎﻝ ‪ ۸۵‬ﻣﯽ ﺑﺎﺷﻨﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺗﻘﺴﻴﻢ ﺑﻨﺪﻱ‪ ،‬ﺳﻪ ﻧﻜﺘﻪ ﺍﺷﺎﺭﻩ‬ ‫ﺷﺪﻩ ﺩﺭ ﺑﺨﺶ ) ‪ (۱-۶‬ﻟﺤﺎﻅ ﮔﺮﺩﻳﺪﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﺷﺒﻴﻪ ﺳﺎﺯﻳﻬﺎ ﺑﺎﺱ‬ ‫ﻗﻮﻱ ﻣﺮﺟﻊ ﺑﺮﺍﻱ ﺗﻤﺎﻣﻲ ﻧﻮﺍﺣﻲ‪ ،‬ﺑﺎﺱ ﺷﺒﻜﻪ ﺍﻳﺮﺍﻥ ﻳﺎ ﻫﻤﺎﻥ ﺑﺎﺱ ﻋﻠﻲ ﺁﺑﺎﺩ‬ ‫ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺷﻜﻞ )‪ (۱۴‬ﻧﺘﺎﻳﺞ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺍﻳﻦ ﺭﻭﺵ ﺭﺍ ﺑﺮﺍﻱ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ ﻭﻟﺘﺎﮊ‬ ‫ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﻛﺎﻫﺶ ﻣﻘﺪﺍﺭ ‪ VCI‬ﺩﺭ ‪ ۶‬ﻧﺎﺣﻴﻪ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺩﺭ ﺷﻜﻞ‬ ‫)‪ ،(۱۴‬ﺣﺮﻛﺖ ﺳﻴﺴﺘﻢ ﺑﻪ ﺳﻤﺖ ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﻧﻮﺍﺣﻲ ‪۱‬‬ ‫ﻭ ‪ ۲‬ﻣﻄﺎﺑﻖ ﺍﻳﻦ ﺷﻜﻞ ﺩﺍﺭﺍﻱ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻧﺴﺒﺖ ﺑﻪ ﺳﺎﻳﺮ ﻧﻮﺍﺣﻲ ﻫﺴﺘﻨﺪ‬ ‫ﻛﻪ ﺍﻳﻦ ﻣﻄﻠﺐ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻧﺘﺎﻳﺞ ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ ﻛﻪ ﺑﺮ ﺭﻭﻱ ﻛﻞ ﺷﺒﻜﻪ‬ ‫ﺧﺮﺍﺳﺎﻥ ﻭ ﺩﺭ ﺣﺎﻟﺖ ‪ off-line‬ﻭ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻃﻼﻋﺎﺕ ﻣﻮﺟﻮﺩ ﺍﻧﺠﺎﻡ ﮔﺮﻓﺘﻪ‪،‬‬ ‫ﺷﻜﻞ ‪ -۱۱‬ﺳﺎﺧﺘﺎﺭ ﻣﺨﺎﺑﺮﺍﺗﻲ ﭘﻴﺸﻨﻬﺎﺩﻱ ﺩﺭ ﺭﻭﺵ ‪VCI‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪۱۰‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺷﺒﻜﻪ ﺍﻱ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻗﺪﺭﺕ ﺩﺭ ﺑﺮﺍﺑﺮ ﻧﻮﺳﺎﻧﺎﺕ ﺯﺍﻭﻳﻪ ﺍﻱ ﺷﺒﻜﻪ ﭘﻴﺸﻨﻬﺎﺩ‬ ‫ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ‪.‬‬ ‫ﻣﻮﺭﺩ ﺍﻧﺘﻈﺎﺭ ﺑﻮﺩ‪ .‬ﺑﺎﺱ ﻣﺮﺟﻊ ﺩﺭ ﺍﻳﻦ ﺷﺒﻴﻪ ﺳﺎﺯﻳﻬﺎ ﺑﺮﺍﻱ ﻛﻞ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ‬ ‫ﺑﺎﺱ ‪ ۴۰۰‬ﻛﻴﻠﻮﻭﻟﺖ ﻋﻠﻲ ﺁﺑﺎﺩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺷﻜﻞ)‪ (۱۵‬ﺭﻓﺘﺎﺭ ‪ VCI‬ﻧﻮﺍﺣﻲ ‪ ۶‬ﮔﺎﻧﻪ ﺑﺎﺭ‪ ،‬ﻓﺮﻭﭘﺎﺷﻲ ﻭﻟﺘﺎﮊ ﺷﺒﻜﻪ ﺭﺍ ﺩﺭ‬ ‫ﺣﻮﺍﺩﺙ ‪ ۱‬ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ‪ .‬ﭘﺎﻳﺪﺍﺭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﭘﺲ ﺍﺯ ﺣﺎﺩﺛﻪ ﺷﻤﺎﺭﻩ ‪ ۲‬ﻭ‬ ‫ﭘﺸﺖ ﺳﺮ ﮔﺬﺍﺷﺘﻦ ﻧﻮﺳﺎﻧﺎﺕ ﺗﻮﺍﻥ‪ ،‬ﺩﺭ ﺭﻓﺘﺎﺭ ‪ VCI‬ﻧﻮﺍﺣﻲ ‪ ۶‬ﮔﺎﻧﻪ ﺩﺭ ﺷﻜﻞ‬ ‫)‪ (۱۶‬ﻗﺎﺑﻞ ﻣﺸﺎﻫﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺗﻨﻈﻴﻢ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﺣﻔﺎﻇﺘﻲ ﺑﺮ ﺍﺳﺎﺱ ‪VCI‬‬ ‫ﻧﻴﺰ ﺑﺎﻳﺪ ﺑﻪ ﻧﻮﺳﺎﻧﺎﺕ ﺗﻮﺍﻥ ﮔﺬﺭﺍﻱ ﺷﺒﻜﻪ ﺑﺮﺍﻱ ﺟﻠﻮﮔﻴﺮﻱ ﻋﻤﻠﻜﺮﺩ ﻧﺎ ﺑﻪ ﺟﺎﻱ‬ ‫ﺣﻔﺎﻇﺘﻲ‪ ،‬ﺗﻮﺟﻪ ﺩﺍﺷﺖ‪.‬‬ ‫ﻣﺰﻳﺖ ﺍﻳﻦ ﺭﻭﺵ‪ ،‬ﺩﻗﺖ ﺑﺎﻻﻱ ﺁﻥ ﺩﺭ ﻧﺸﺎﻥ ﺩﺍﺩﻥ ﺣﺎﺷﻴﻪ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ‬ ‫ﻧﻮﺍﺣﻲ ﺑﺎﺭ ﺷﺒﻜﻪ ﻫﻤﺰﻣﺎﻥ ﺑﺎ ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭﻱ ﻣﻲ ﺑﺎﺷﺪ ﻭ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻋﻤﻠﻜﺮﺩ‬ ‫ﻧﺎﺣﻴﻪ ﺍﻱ ﺁﻥ‪ ،‬ﺩﺭﻙ ﺩﺭﺳﺖ ﻭ ﺳﺎﺩﻩ ﺍﻱ ﺍﺯ ﻭﺿﻌﻴﺖ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﺩﺭ ﻧﻮﺍﺣﻲ‬ ‫ﺑﺎﺭ ﻣﺨﺘﻠﻒ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﺪ ﻛﻪ ﺑﻪ ﺑﻬﺮﻩ ﺑﺮﺩﺍﺭﻱ ﺍﺯ ﺷﺒﻜﻪ ﺩﺭ ﺣﺎﺷﻴﻪ ﻭﻟﺘﺎﮊ‬ ‫ﻣﻨﺎﺳﺐ ﻛﻤﻚ ﻣﻲ ﻛﻨﺪ‪.‬‬ ‫‪[1] P. Kundur, Power System Stability and Control. New York:‬‬ ‫‪McGraw-Hill, 1994.‬‬ ‫‪[2] C. W. Taylor, Power System Voltage StabilityNew‬‬ ‫‪York: McGraw-Hill, 1994‬‬ ‫‪[3] U.S.-Canada Power System Outage Task Force.‬‬ ‫‪(2004) Final Report on the August 14, 2003 Blackout in‬‬ ‫‪the United States and Canada: Cause Recommendations.‬‬ ‫‪[Online]. Available: http://www.nerc.com‬‬ ‫‪[4] S. Larsson and E. Ek, “TheBlackout in Southern‬‬ ‫‪Sweden and Eastern Denmark, September 23, 2003,” in‬‬ ‫‪Proc. IEEE PES General Meeting, Denver, CO, 2004.‬‬ ‫‪[5] G. Vrbic and Gubina,“ A New Concept of Voltage‬‬‫‪Collapse Protection Based on Local Phasors,” IEEE‬‬ ‫‪Transactions on Power Delivery, Vol. 19, No. 2, pp. 576‬‬‫‪581, April, 2004‬‬ ‫‪[6] B. Milǒsević, M. Begović , “ Voltage-Stability‬‬ ‫‪Protection and Control using a Wide-Area Network of‬‬ ‫‪Phasor Measurements” IEEE Transaction on Power‬‬ ‫‪Systems, Vol. 18, No.1, pp. 121-126, Feb. 2003.‬‬ ‫‪[7] K.Vu, M. Begović, D. Novosel, M. M. Saha, “Use of‬‬ ‫‪Local Measurements to Estimate Voltage-Stability‬‬ ‫‪Margin,” in IEEE Transaction on Power System, Vol. 14,‬‬ ‫‪No. 3, pp 1029-1034, August 1999.‬‬ ‫‪[8]User's Guide of DIgSILENT 13.1 software,‬‬ ‫‪DIgSILENT company, German‬‬ ‫‪[9] ”Modeling of Voltage CIGRE Task Force 38-02-10,‬‬ ‫‪Collapse Including Dynamic Phenomena,” 1993‬‬ ‫]‪ [۱۰‬ﻣﺤﻤﺪﺭﺿﺎ ﺩﺍﺩﺍﺵ ﺯﺍﺩﻩ ﻃﺎﻫﻮﻧﭽﻲ‪“ ،‬ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻗﺪﺭﺕ‬ ‫ﺑﺮﺍﻱ ﺍﺭﺯﻳﺎﺑﻲ ﺍﻟﻜﻮﺭﻳﺘﻤﻬﺎﻱ ﺣﺬﻑ ﺑﺎﺭ‪ “،‬ﭘﺎﻳﺎﻥ ﻧﺎﻣﻪ ﮐﺎﺭﺷﻨﺎﺳﻲ ﺍﺭﺷﺪ‪ ،‬ﺩﺍﻧﺸﮕﺎﻩ‬ ‫ﺗﻬﺮﺍﻥ‪ ،‬ﺍﺳﻔﻨﺪ ‪.۸۳‬‬ ‫‪[11]IEEE/PES, Power System Stability Subcommittee‬‬ ‫‪Special Publication, “Voltage Stability Assessment:‬‬ ‫‪Concepts, Practices and Tools,” August 2002.‬‬ ‫‪[12]M.S. Sachdev, “A Technique for Real Time‬‬ ‫‪Detection of Voltage Collapse in Power System” 2004,‬‬ ‫‪DPSP, Netherland.‬‬ ‫‪[13]I. Musirin, T.A. Rahman, “On-Line voltage stability‬‬ ‫‪based contingency ranking using fast voltage stability‬‬ ‫‪index (FVSI),” IEEE/PES Transmission and Distribution‬‬ ‫‪Conference, vol. 2, pp. 1118-1123, October 2002.‬‬ ‫‪[14] M. Larsson, C. Rehtanz and J. Bertsch, “Real Time‬‬ ‫‪Voltage Stability Assessment of Transmission Corridors,‬‬ ‫‪“,IFAC Power Plants and Power Systems, 2003.‬‬ ‫‪ -۸‬ﻧﺘﻴﺠﻪ ﮔﻴﺮﻱ‬ ‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺿﻤﻦ ﺑﺮﺭﺳﻲ ﺭﻓﺘﺎﺭ ﺑﺎﺭﻫﺎﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺩﺭ ﻭﻟﺘﺎﮊﻫﺎﻱ ﭘﺎﻳﻴﻦ ﻭ ﺩﺭ‬ ‫ﺗﻐﻴﻴﺮﺍﺕ ﭘﻠﻪ ﺍﻱ ﻭﻟﺘﺎﮊ‪ ،‬ﺑﻪ ﻣﺪﻟﺴﺎﺯﻱ ﺩﻳﻨﺎﻣﻴﻜﻲ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺑﺮﺍﻱ‬ ‫ﻣﻄﺎﻟﻌﺎﺕ ﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ ﻭ ﺑﻠﻨﺪ ﻣﺪﺕ‪ ،‬ﭘﺮﺩﺍﺧﺘﻪ ﺷﺪ‪ .‬ﺳﭙﺲ ﺩﻭ ﺣﺎﺩﺛﻪ‬ ‫ﺑﺰﺭﮒ ﻛﻪ ﺩﺭ ﻳﻜﻲ ﺷﺒﻜﻪ ﺩﭼﺎﺭ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﮔﺬﺭﺍﻱ ﻭﻟﺘﺎﮊ ﺷﺪ ﻭ ﺩﺭ ﺩﻳﮕﺮﻱ‬ ‫ﺷﺒﻜﻪ ﭘﺎﻳﺪﺍﺭ ﮔﺮﺩﻳﺪ‪ ،‬ﺑﺮﺭﺳﻲ ﻭ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺷﺪ‪.‬‬ ‫ﭘﺲ ﺍﺯ ﻣﺮﻭﺭ ﺑﺮﺧﻲ ﺭﻭﺷﻬﺎﻱ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﻭﻟﺘﺎﮊ ﻛﻪ ﺩﺭ‬ ‫ﺳﺎﻟﻬﺎﻱ ﺍﺧﻴﺮ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻳﻚ ﺭﻭﺵ ﺟﺪﻳﺪ ﺑﺎ ﻣﻌﻴﺎﺭ ‪ VCI‬ﻣﻌﺮﻓﻲ ﺷﺪ‬ ‫ﻭ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺁﻥ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺍﺭﺍﺋﻪ ﮔﺮﺩﻳﺪ‪ .‬ﺭﻭﺵ ‪ VCI‬ﺑﻪ ﺩﻟﻴﻞ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺤﻠﻴﻞ ﻣﺪﺍﻝ ﺩﺭ ﻫﺮ ﻧﺎﺣﻴﻪ ﻭ ﻣﻘﺎﻳﺴﻪ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﺑﺤﺮﺍﻧﻴﺘﺮﻳﻦ ﺑﺎﺱ‬ ‫ﻫﺮ ﻧﺎﺣﻴﻪ ﺑﺎ ﻓﺎﺯﻭﺭ ﻭﻟﺘﺎﮊ ﻳﻜﻲ ﺍﺯ ﻗﻮﻳﺘﺮﻳﻦ ﺑﺎﺳﻬﺎﻱ ﺷﺒﻜﻪ ﻛﻪ ﺑﻪ ﺁﻥ ﻧﺎﺣﻴﻪ‬ ‫ﻧﺰﺩﻳﻚ ﺍﺳﺖ‪ ،‬ﺩﺭ ﺷﻨﺎﺧﺖ ﻧﻮﺍﺣﻲ ﺑﺤﺮﺍﻧﻲ ﻫﻢ‪ ،‬ﺭﻭﺵ ﺗﻮﺍﻧﺎﻳﻲ ﺍﺳﺖ‪ .‬ﻧﻴﺎﺯ ﺍﻳﻦ‬ ‫ﺭﻭﺵ ﺑﻪ ﻣﺤﻴﻂ ﻣﺨﺎﺑﺮﺍﺗﻲ ﺳﺮﻳﻊ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﭘﻴﺸﺮﻓﺖ ﺭﻭﺯﺍﻓﺰﻭﻥ ﺍﻳﻦ ﺍﺩﻭﺍﺕ‬ ‫ﺩﺭ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻗﺪﺭﺕ ﻭ ﺍﻣﻜﺎﻥ ﭘﻴﺎﺩﻩ ﺳﺎﺯﻱ ﺁﻧﻬﺎ ﺩﺭ ﺳﻴﺴﺘﻤﻬﺎﻱ ﺍﻧﺘﻘﺎﻝ ﻭ‬ ‫ﻓﻮﻕ ﺗﻮﺯﻳﻊ ﺩﺭ ﺁﻳﻨﺪﻩ ﺍﻱ ﻧﻪ ﭼﻨﺪﺍﻥ ﺩﻭﺭ ﺑﺮﺁﻭﺭﺩﻩ ﺧﻮﺍﻫﺪ ﺷﺪ‪.‬‬ ‫ﺑﻪ ﻃﻮﺭ ﻛﻠﻲ ﻣﺸﻜﻞ ﻋﻤﺪﻩ ﻣﺸﺘﺮﻙ ﺭﻭﺷﻬﺎﻱ ﺗﺨﻤﻴﻦ ﺑﻪ ﻫﻨﮕﺎﻡ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ‬ ‫ﻭﻟﺘﺎﮊ ﻛﻪ ﺑﺮﺧﻲ ﺍﺯ ﻣﻬﻤﺘﺮﻳﻦ ﻧﻤﻮﻧﻪ ﻫﺎﻱ ﺁﻥ ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﻣﺮﻭﺭ ﺷﺪ‪ ،‬ﻋﻤﻠﻜﺮﺩ‬ ‫ﺁﻧﻬﺎ ﺩﺭ ﺷﺮﺍﻳﻂ ﻧﻮﺳﺎﻧﺎﺕ ﺗﻮﺍﻥ ﭘﺲ ﺍﺯ ﺣﻮﺍﺩﺙ ﺑﺰﺭﮒ ﺩﺭ ﺳﻴﺴﺘﻤﻬﺎﻱ ﻗﺪﺭﺕ‬ ‫ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺭﻭﺵ ‪ VCI‬ﻫﻤﻤﻲ ﺗﻮﺍﻧﺪ ﺩﺭ ﺑﺮﺧﻲ ﺣﺎﻻﺕ ﺑﺎ ﺍﻳﻦ ﻣﺸﻜﻞ ﻣﻮﺍﺟﻪ‬ ‫ﺷﻮﺩ‪ .‬ﺩﺭ ﺷﺒﻴﻪ ﺳﺎﺯﻳﻬﺎﻱ ﺍﻧﺠﺎﻡ ﮔﺮﻓﺘﻪ ﺑﺮ ﺭﻭﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺩﻳﺪﻩ ﺷﺪ ﻛﻪ‬ ‫ﺩﺭ ﺑﺮﺧﻲ ﺍﺭ ﺣﻮﺍﺩﺙ ﻛﻪ ﺷﺒﻜﻪ ﺷﺮﺍﻳﻂ ﭘﺎﻳﺪﺍﺭ ﺧﻮﺩ ﺭﺍ ﺑﻪ ﺩﺳﺖ ﻣﻲ ﺁﻭﺭﺩ‪،‬‬ ‫ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎﻱ ﺣﻔﺎﻇﺘﻲ ﺩﺭ ﺑﺎﺯﻩ ﺯﻣﺎﻧﻲ ﺯﻳﺮ ‪ ۱۰‬ﺛﺎﻧﻴﻪ ﭘﺲ ﺍﺯ ﺣﺎﺩﺛﻪ ﻣﻲ ﺗﻮﺍﻧﻨﺪ‬ ‫ﺑﺎ ﻋﻤﻠﻜﺮﺩ ﺧﻮﺩ ﻭﺿﻌﻴﺖ ﺷﺒﻜﻪ ﺭﺍ ﺗﺤﺖ ﺗﺄﺛﻴﺮ ﻗﺮﺍﺭ ﺩﻫﻨﺪ‪ .‬ﺑﻪ ﻧﻈﺮ ﻣﻲ ﺭﺳﺪ‬ ‫ﺑﺮﺍﻱ ﺟﻠﻮﮔﻴﺮﻱ ﺍﺯ ﻋﻤﻠﻜﺮﺩ ﻧﺎ ﺑﻪ ﺟﺎﻱ ﺍﻳﻦ ﺍﻟﮕﻮﺭﻳﺘﻤﻬﺎ ﺑﺎﻳﺪ ﺍﺯ ﭘﺎﺭﺍﻣﺘﺮﻫﺎﻱ‬ ‫ﺷﺒﻜﻪ ﻛﻤﻚ ﮔﺮﻓﺖ‪ .‬ﻣﺜﻼﹰ ﺭﻭﺷﻬﺎﻱ ﺗﺨﻤﻴﻦ ﺯﺍﻭﻳﻪ ﻛﻪ ﺍﻣﺮﻭﺯﻩ ﺩﺭ ﺣﻔﺎﻃﺖ‬ ‫‪۱۱‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫ﻣﺮﺍﺟﻊ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ 4 Area1 Area2 Area3 Area4 Area5 Area6 3.5 3 VCI 2.5 2 1.5 1 0.5 0 500 1000 1500 2000 Time(Sec.) 2500 VCI ‫ ﻧﺎﺣﻴﻪ ﺑﺎﺭ ﺩﺭ ﺭﻭﺵ‬۶ ‫ ﺗﻘﺴﻴﻢ ﺑﻨﺪﻱ ﺷﺒﻜﻪ ﺧﺮﺍﺳﺎﻥ ﺑﻪ‬-۱۲ ‫ﺷﻜﻞ‬ 3000 ‫ ﺩﺭ ﺣﺎﺩﺛﻪ ﻧﺎﭘﺎﻳﺪﺍﺭﻱ ﺑﻠﻨﺪ ﻣﺪﺕ ﻭﻟﺘﺎﮊ‬VCI ‫ ﺷﺒﻴﻪ ﺳﺎﺯﻱ‬-۱۴ ‫ﺷﻜﻞ‬ 2.5 Area1 Area2 Area3 Area4 Area5 Area6 2 VCI 1.5 0.5 0 0 0.2 0.4 0.6 0.8 1 Time(Sec.) 1.2 1.4 1.6 1.8 2 ۱ ‫ ﺩﺭ ﺣﺎﺩﺛﻪ ﺍﻏﺘﺸﺎﺵ ﺑﺰﺭﮒ ﺷﻤﺎﺭﻩ‬VCI ‫ ﺷﺒﻴﻪ ﺳﺎﺯﻱ‬-۱۵ ‫ﺷﻜﻞ‬ 2.5 2 VC I 1.5 Area1 1 Area2 Area3 Area4 0.5 Area5 Area6 0 0 1 2 3 4 Time(Sec.) 5 6 7 8 ‫ ﺩﺭ ﺣﺎﺩﺛﻪ ﺍﻏﺘﺸﺎﺵ ﺑﺰﺭﮒ‬VCI ‫ ﺷﺒﻴﻪ ﺳﺎﺯﻱ‬-۱۶‫ﺷﻜﻞ‬ ۲ ‫ﺷﻤﺎﺭﻩ‬ VCI ‫ ﻓﻠﻮﭼﺎﺭﺕ ﺍﻟﮕﻮﺭﻳﺘﻢ‬-۱۳ ‫ﺷﻜﻞ‬ ۱۲ 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 1 ‫ﺿﻤﻴﻤﻪ‬ Area 1 2 3 Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 4 Bus Name birjand nehbandan sarbishe sedeh asadabad sahlabad ghaen bushruye ferdos sarayan tabas hajiabad gonabad bjnurd dargaz dashtjvn davarzan ghazi istghazd jajarm jlgrkh mchnelec sabzvar simnbjn fariman khaf kheirabad solat taybad trbtjam sangan Active Load (MW) 42.33 9.26 6.61 8.07 10.76 7.94 20 9.26 13.23 6.61 18.52 13.23 37.04 46.29 18.52 37.04 13.23 21.16 9.26 37.04 23.81 17.2 64.81 10.58 46.29 22.49 30.42 18.28 29.1 64.81 3.97 Reactive Load (MW) 17.2 6.12 2.65 2.65 0 0 0 3.97 2.65 2.65 2.65 2.64 17.2 18.52 7.94 13.24 3.97 6.61 4.48 10.58 2.65 6.61 13.23 3.97 11.9 1.32 7.94 6.26 9.26 11.9 1.92 Area 5 6 Active Load (MW) 42.33 14.55 17.2 67 74.07 29.1 17.2 90 25 31.74 21.16 9.26 27.78 51.59 13.35 5.29 60.84 39.68 17.2 170 105 120 37.04 44.97 58.2 29.1 150 5.29 19.84 230 Bus Name feizabad kashmar abousaed attar bardskn beihagh dolatabad fldkhsn neishabour rashtkhr sahel salehabad sltnabad trbathydarieh sangbast gholaman ghuchan golbahar golshahr khajerabi6 kohsangi63 mashhad mehrgan nmyshgh pardis sarakhs shariati63 shirvan toosG tous63 Reactive Load (MW) 3.97 2.65 7.94 15 14.55 6.61 3.97 40 18 7.94 0 4.48 9.26 13.23 4.092 2.56 30.42 19.21 8.33 118 20 90 13.23 26.45 26.45 13.23 130 2.56 9.605 0 ‫ﺯﻳﺮﻧﻮﻳﺲﻫﺎ‬ 1 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ ۱۳ PDF created with pdfFactory Pro trial version www.pdffactory.com PMU: Phasor Measurement Unit ‫ﻣﺪﻟﺴﺎﺯﯼ ﭘﺪﻳﺪﺓ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺩﺭ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﺟﺪﻳﺪ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﻫﺴﺘﻪ‬ ‫ ﺷﺎﻫﺮﺥ ﻓﺮﻫﻨﮕﯽ‬،‫ ﺣﺴﻴﻦ ﻣﺤﺴﻨﯽ‬،‫ ﻣﺠﻴﺪ ﺻﻨﺎﻳﻊ ﭘﺴﻨﺪ‬،‫ﺍﻓﺸﻴﻦ ﺭﺿﺎﺋﯽ ﺯﺍﺭﻉ‬ ‫ ﺩﺍﻧﺸﮕﺎﻩ ﺗﻬﺮﺍﻥ‬- ‫ﺩﺍﻧﺸﮑﺪة ﻣﻬﻨﺪﺳﯽ ﺑﺮﻕ ﻭ ﮐﺎﻣﭙﻴﻮﺗﺮ‬ ‫ﺗﻬﺮﺍﻥ – ﺍﻳﺮﺍﻥ‬ Preisach ‫ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﺌﻮﺭﯼ‬.‫ ﭘﺪﻳﺪﺓ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺩﺭ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎ ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ ﻭ ﻣﺪﻟﺴﺎﺯﯼ ﻗﺮﺍﺭ ﻣﯽ ﮔﻴﺮﺩ‬،‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ‬ :‫ﭼﮑﻴﺪﻩ‬ ‫ ﺍﻳﻦ ﻣﺪﻝ ﺑﺮ ﺍﺳﺎﺱ ﺗﺌﻮﺭﯼ‬،‫ﻳﮏ ﻣﺪﻝ ﺟﺪﻳﺪ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮﺩ ﮐﻪ ﺑﺮﺧﻼﻑ ﺑﻴﺸﺘﺮ ﻣﺪﻟﻬﺎﯼ ﻣﻮﺟﻮﺩ ﮐﻪ ﻣﺪﻟﻬﺎﯼ ﺻﺮﻓﺎﹰ ﺭﻳﺎﺿﯽ ﺑﻮﺩﻩ‬ ‫ ﺩﺭ ﻧﺘﻴﺠﻪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺍﻳﻦ ﻣﺪﻝ ﺩﻗﻴﻘﺘﺮ ﻣﯽ ﺗﻮﺍﻥ ﺣﻠﻘﻪ ﻫﺎﯼ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻣﻮﺍﺩ ﻓﺮﻭﻣﻐﻨﺎﻃﻴﺲ ﺭﺍ‬.‫ﻓﻴﺰﻳﮑﯽ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﻴﺎﻥ ﻣﯽ ﺷﻮﺩ‬ ‫ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ‬.‫( ﺗﺸﺮﻳﺢ ﺷﺪﻩ ﻭ ﻧﺘﺎﻳﺞ ﺁﻥ ﺍﺭﺍﺋﻪ ﻣﯽ ﮔﺮﺩﺩ‬VT) ‫ ﺗﺴﺖ ﺁﺯﻣﺎﻳﺸﮕﺎﻫﯽ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﺮ ﺭﻭﯼ ﻳﮏ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ‬.‫ﻣﺪﻟﺴﺎﺯﯼ ﮐﺮﺩ‬ ‫ ﻣﻮﺭﺩ ﺷﺒﻴﻪ ﺳﺎﺯﯼ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻪ ﻭ ﺭﻓﺘﺎﺭ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺑﺎ ﻧﺘﺎﻳﺞ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪﻩ ﻣﻘﺎﻳﺴﻪ ﻣﯽ‬VT ‫ ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬،‫ﺍﺯ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫ ﮐﻪ ﺑﻪ ﻋﻨﻮﺍﻥ ﻳﮑﯽ ﺍﺯ ﺑﻬﺘﺮﻳﻦ ﻣﺪﻟﻬﺎﯼ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻣﻮﺟﻮﺩ ﺷﻨﺎﺧﺘﻪ ﻣﯽ‬EMTP ‫ ﻫﻤﭽﻨﻴﻦ ﺭﻓﺘﺎﺭ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﺮﻧﺎﻣﺔ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ‬.‫ﮔﺮﺩﺩ‬ ‫ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ﺍﺛﺮ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻫﺴﺘﻪ‬،‫ ﻧﺘﺎﻳﺞ ﺍﻳﻦ ﺑﺮﺭﺳﯽ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﻨﺪ ﮐﻪ ﺩﺭ ﻣﻄﺎﻟﻌﺎﺕ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬.‫ ﺟﻬﺖ ﻣﻘﺎﻳﺴﻪ ﺍﺭﺍﺋﻪ ﻣﯽ ﮔﺮﺩﺩ‬،‫ﺷﻮﺩ‬ ‫ ﻗﺎﺩﺭ ﺑﻪ ﻣﺪﻟﺴﺎﺯﯼ‬EMTP ‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺍﻟﺰﺍﻣﯽ ﺑﻮﺩﻩ ﻭ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﻗﻴﻘﺘﺮ ﺍﺯ ﺳﺎﻳﺮ ﻣﺪﻟﻬﺎﯼ ﻣﻮﺟﻮﺩ ﻣﺎﻧﻨﺪ ﻣﺪﻝ ﺑﺮﻧﺎﻣﺔ‬ .Preisach ‫ ﺗﺌﻮﺭﯼ‬,‫ ﻫﻴﺴﺘﺮﺯﻳﺲ‬,‫ ﻫﺴﺘﻪ‬,‫ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬,‫ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ‬:‫ﻭﺍﮊﻩ ﻫﺎﻱ ﻛﻠﻴﺪﻱ‬ Ferroresonance Modeling in Transformers Based on a Novel Hysteretic Core Model Afshin Rezaei-Zare, Majid Sanaye-Pasand, Hossein Mohseni, Shahrokh Farhangi School of Electrical and Computer Engineering University of Tehran, Tehran, Iran Abstract : Based on the Preisach theory in hysteresis, this paper presents a novel transformer core model. Unlike existing mathematical-based hysteresis models, the proposed model is based on a physically correct hysteresis model and can precisely represent the actual behaviors of magnetic materials. In addition, the experimental results of a ferroresonance test of a Voltage Transformer (VT) are presented. The accuracies of the proposed model and the EMTP hysteretic model in duplicating the experimental results are investigated. This paper concludes that in studying ferroresonance phenomenon, the hysteresis of the transformer core must be accurately represented. Furthermore, the proposed model presents more accurate results, compared with the EMTP hysteresis model. Keywords: Transformer, Ferroresonance, Iron Core, Hysteresis, Preisach Theory. ١٤ 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 .‫ﭘﺪﻳﺪﺓ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺍﺳﺖ‬ ‫‪ -۱‬ﻣﻘﺪﻣﻪ‬ ‫ﻳﻜﻲ ﺍﺯ ﭘﺪﻳﺪﻩ ﻫﺎﻱ ﺟﺎﻟﺐ ﻭ ﭘﻴﭽﻴﺪﻩ ﻣﺮﺗﺒﻂ ﺑﺎ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎ‪ ،‬ﭘﺪﻳﺪﺓ‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺍﺳﺖ‪ .‬ﺳﺎﻟﻬﺎﻱ ﻣﺘﻤﺎﺩﻱ ﺍﺳﺖ ﻛﻪ ﺍﻳﻦ ﭘﺪﻳﺪﻩ ﺩﺭ ﺳﻄﻮﺡ ﻣﺨﺘﻠﻒ‬ ‫ﻭﻟﺘﺎﮊﻱ ﺷﺒﻜﻪ ﻫﺎﻱ ﻛﺸﻮﺭﻫﺎﻱ ﻣﺨﺘﻠﻒ ﺭﺥ ﻣﻲﺩﻫﺪ ]‪ [1]-[3‬ﻛﻪ ﻋﻤﺪﺗﺎﹰ ﺑﻪ ﺍﺯ‬ ‫ﺑﻴﻦ ﺭﻓﺘﻦ ﺗﺠﻬﻴﺰﺍﺕ ﺷﺒﻜﻪ ﻣﻨﺠﺮ ﺷﺪﻩ ﺍﺳﺖ ﻭﻟﻲ ﻫﻨﻮﺯ ﻧﻤﻲ ﺗﻮﺍﻥ ﭘﻴﺶ ﺑﻴﻨﻲ‬ ‫ﻛﺮﺩ ﻛﻪ ﻣﻮﺭﺩ ﺑﻌﺪﻱ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻛﻲ ﻭ ﺩﺭ ﭼﻪ ﻣﺤﻠﻲ ﻣﻤﻜﻦ ﺍﺳﺖ ﺭﺥ ﺩﻫﺪ‪.‬‬ ‫ﺍﺯ ﻋﻠﻞ ﺍﺻﻠﻲ ﺁﻥ ﻣﻲﺗﻮﺍﻥ ﺑﻪ ﻧﺎﻛﺎﻓﻲ ﺑﻮﺩﻥ ﺩﺍﻧﺶ ﺍﻣﺮﻭﺯﻱ ﺩﺭ ﺯﻣﻴﻨﻪ ﺭﻓﺘﺎﺭ‬ ‫ﻣﻮﺍﺩ ﻣﻐﻨﺎﻃﻴﺴﻲ ﺩﺭ ﺷﺮﺍﻳﻂ ﮔﺬﺭﺍﻱ ﺍﻟﻜﺘﺮﻭﻣﻐﻨﺎﻃﻴﺴﻲ‪ ،‬ﻋﺪﻡ ﺍﻣﻜﺎﻥ ﺗﺤﻠﻴﻞ‬ ‫ﻗﻮﻱ ﻭ ﺟﺎﻣﻊ ﺳﻴﺴﺘﻢﻫﺎﻱ ﻏﻴﺮ ﺧﻄﻲ ﻭ ﺩﺭ ﺩﺳﺖ ﻧﺒﻮﺩﻥ ﻣﺪﻝ ﻣﻨﺎﺳﺐ‬ ‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺟﻬﺖ ﺗﺤﻠﻴﻞ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺍﺷﺎﺭﻩ ﻛﺮﺩ‪ .‬ﻋﻼﻭﻩ ﺑﺮ ﺍﻳﻦ ﻣﺸﻜﻼﺕ‪،‬‬ ‫ﻋﺪﻡ ﺍﻣﮑﺎﻥ ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﻫﻤﺔ ﺗﺮﻛﻴﺒﺎﺕ ﻣﺨﺘﻠﻒ ﺷﺮﺍﻳﻂ ﺍﻭﻟﻴﻪ ﻭ ﺣﺎﻟﺖ ﻫﺎﻱ‬ ‫ﮔﺬﺭﺍ ﺑﺎﻋﺚ ﻣﻲ ﺷﻮﺩ ﻛﻪ ﺗﺠﺰﻳﻪ ﻭ ﺗﺤﻠﻴﻞ ﻭ ﭘﻴﺶ ﺑﻴﻨﻲ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﭼﻨﺪﺍﻥ‬ ‫ﺑﺎ ﺍﻃﻤﻴﻨﺎﻥ ﺍﻧﺠﺎﻡ ﻧﺸﻮﺩ‪.‬‬ ‫ﺗﺤﻘﻴﻘﺎﺕ ﺍﻧﺠﺎﻡ ﺷﺪﻩ ﺩﺭ ﺯﻣﻴﻨﺔ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﻨﺪ ﮐﻪ ﻧﺘﺎﻳﺞ‬ ‫ﺷﺒﻴﻪ ﺳﺎﺯﻱ ﺣﺴﺎﺳﻴﺖ ﺯﻳﺎﺩﻱ ﺑﻪ ﺭﻭﺵ ﺗﻌﺮﻳﻒ ﻣﺸﺨﺼﺔ ﺍﺷﺒﺎﻉ ﻣﻐﻨﺎﻃﻴﺴﻲ ﻭ‬ ‫ﺗﻠﻔﺎﺕ ﻫﺴﺘﻪ ﺩﺍﺷﺘﻪ ﻭ ﻣﺪﻟﻬﺎﻱ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻣﻮﺟﻮﺩ ﺩﺍﺭﺍﻱ ﺧﻄﺎﻱ ﺯﻳﺎﺩﻱ‬ ‫ﺩﺭ ﻣﺪﻟﺴﺎﺯﯼ ﻭ ﺷﺒﻴﻪ ﺳﺎﺯﯼ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻫﺴﺘﻨﺪ ]‪ .[1‬ﺗﻠﻔﺎﺕ ﻫﺴﺘﻪ ﺍﺯ ﺗﻠﻔﺎﺕ‬ ‫ﺟﺮﻳﺎﻥ ﮔﺮﺩﺷﯽ ﻭ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺗﺸﮑﻴﻞ ﻣﯽ ﺷﻮﺩ‪ .‬ﺗﻠﻔﺎﺕ ﺟﺮﻳﺎﻥ ﮔﺮﺩﺷﯽ ﺑﺎ‬ ‫ﺗﻮﺍﻥ ﺩﻭ ﺷﺎﺭ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻭ ﻓﺮﮐﺎﻧﺲ ﻣﺘﻨﺎﺳﺐ ﺍﺳﺖ‪ .‬ﺩﺭ ﻧﺘﻴﺠﻪ ﻳﮏ ﻣﻘﺎﻭﻣﺖ‬ ‫ﺛﺎﺑﺖ ﺑﺎ ﺩﻗﺖ ﺧﻮﺑﯽ ﻣﯽ ﺗﻮﺍﻧﺪ ﺍﻳﻦ ﺗﻠﻔﺎﺕ ﺭﺍ ﻣﺪﻝ ﮐﻨﺪ ]‪ .[4‬ﻭﻟﯽ ﺗﻠﻔﺎﺕ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﻪ ﻓﺮﮐﺎﻧﺲ ﻭ ﺳﻄﺢ ﻣﺤﺼﻮﺭ ﺩﺭ ﻣﻨﺤﻨﯽ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻭ ﺩﺭ‬ ‫ﻧﺘﻴﺠﻪ ﺑﻪ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻭﺍﺑﺴﺘﻪ ﺍﺳﺖ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﺑﺮﺍﯼ ﻣﺪﻟﺴﺎﺯﯼ ﺩﻗﻴﻖ‬ ‫ﺷﮑﻞ ‪ -۱‬ﻣﺸﺨﺼﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺩﻭﻗﻄﺒﯽ ﭘﺎﻳﺔ ﻣﺪﻝ ‪Preisach‬‬ ‫ﺍﻋﻤﺎﻝ ﺷﺪﻩ ﺑﻪ ﺍﻳﻦ ﺩﻭ ﻗﻄﺒﯽ ﺑﻪ ﻣﻘﺪﺍﺭ ‪ H=α‬ﻣیﺮﺳﺪ‪ ،‬ﺍﻳﻦ ﺍﻟﻤﺎﻥ ﺑﻄﻮﺭ‬ ‫ﻧﺎﮔﻬﺎﻧﯽ ﺍﺯ ﺣﺎﻟﺖ ﻣﻨﻔﯽ ﺑﻪ ﺣﺎﻟﺖ ﻣﺜﺒﺖ ﺩﺭ ﻣﯽ ﺁﻳﺪ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ ﺑﺮﺍﯼ ﻳﮏ‬ ‫ﻣﻴﺪﺍﻥ ﮐﻢ ﺷﻮﻧﺪﻩ ﺗﻐﻴﻴﺮ ﻭﺿﻌﻴﺖ ﺩﻭ ﻗﻄﺒﯽ ﺩﺭ ‪ H=β‬ﺭﺥ ﻣﻴﺪﻫﺪ‪ .‬ﺩﺭ ﻣﻮﺍﺩ‬ ‫ﻣﻐﻨﺎﻃﻴﺴﯽ ﻫﻤﻴﺸﻪ ‪ α‬ﺍﺯ ‪ β‬ﺑﺰﺭﮔﺘﺮ ﺍﺳﺖ ﻭ ﺣﺎﻟﺖ ‪ α=β‬ﺣﺎﻟﺖ ﺑﺮﮔﺸﺖ‬ ‫ﭘﺬﻳﺮﯼ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺎﺩﻩ ﺭﺍ ﻣﺪﻟﺴﺎﺯﯼ ﻣﯽ ﮐﻨﺪ‪.‬‬ ‫ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ ﺩﺭ ﺷﮑﻞ )‪ (۱‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻣﯽ ﺗﻮﺍﻥ ﺑﺮﺍﯼ ﺍﻳﻦ ﺩﻭ‬ ‫ﻗﻄﺒﯽ‪ ،‬ﺩﻭ ﻣﻴﺪﺍﻥ ‪ hm‬ﮐﻪ ﻣﻴﺪﺍﻥ ﺟﺎﺑﺠﺎﻳﯽ ﻭ ‪ hc‬ﮐﻪ ﻣﻴﺪﺍﻥ ‪Coercive‬‬ ‫ﻧﺎﻣﻴﺪﻩ ﻣﯽ ﺷﻮﻧﺪ‪ ،‬ﺗﻌﺮﻳﻒ ﮐﺮﺩ‪ .‬ﺗﻌﺪﺍﺩ ﺩﻭﻗﻄﺒﯽ ﻫﺎﻳﯽ ﮐﻪ ﺩﺭ ﻣﺤﺪﻭﺩة ‪(hc,‬‬ ‫)‪(۱‬‬ ‫‪dn = γ ( h c , h m ) dh c dh m‬‬ ‫ﺗﺎﺑﻊ ‪ γ‬ﺗﺎﺑﻊ ﭼﮕﺎﻟﯽ ﺗﻮﺯﻳﻊ ﺩﻭ ﻗﻄﺒﯽ ﻫﺎ ﺩﺭ ﻣﺎﺩﻩ ﺍﺳﺖ ﻭ ﺩﺍﺭﺍﯼ ﻣﺸﺨﺼﺎﺕ ﺯﻳﺮ‬ ‫ﺍﺳﺖ‪:‬‬ ‫ﻣﺸﺨﺼﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻭ ﺗﻠﻔﺎﺕ ﻫﺴﺘﻪ ﮐﻪ ﺩﻭ ﭘﺎﺭﺍﻣﺘﺮ ﺍﺻﻠﯽ ﺩﺭ ﻣﻄﺎﻟﻌﺔ ﭘﺪﻳﺪة‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻫﺴﺘﻨﺪ ﻭ ﻫﻤﭽﻨﻴﻦ ﺑﺮﺍﯼ ﺗﮑﻤﻴﻞ ﻣﺪﻟﻬﺎﯼ ﻣﻮﺟﻮﺩ‬ ‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ‪ ،‬ﺑﺎﻳﺪ ﻣﺪﻝ ﺩﻗﻴﻘﯽ ﺍﺯ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﻪ ﺍﻳﻦ ﻣﺪﻟﻬﺎ ﺍﺿﺎﻓﻪ ﺷﻮﺩ‪.‬‬ ‫ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﺑﺮ ﺍﺳﺎﺱ ﻳﮑﯽ ﺍﺯ ﺩﻗﻴﻖ ﺗﺮﻳﻦ ﺗﺌﻮﺭﯼ ﻫﺎﯼ ﻓﻴﺰﻳﮑﯽ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﮐﻪ ﺑﻪ ﺗﺌﻮﺭﯼ ‪ Preisach‬ﻣﻮﺳﻮﻡ ﺍﺳﺖ ]‪ [5‬ﻳﮏ ﻣﺪﻝ ﺟﺪﻳﺪ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﺎ ﻓﺮﻣﻮﻝ ﺑﻨﺪﯼ ﺟﺪﻳﺪ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﻭ ﺩﺭ ﺑﺮﻧﺎﻣﺔ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ‬ ‫‪ PSCAD/EMTDC‬ﭘﻴﺎﺩﻩ ﺳﺎﺯﯼ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺫﻳﻞ ﻣﻮﺭﺩ ﺑﺤﺚ ﻭ‬ ‫ﺑﺮﺭﺳﯽ ﻗﺮﺍﺭ ﻣﯽ ﮔﻴﺮﺩ‪.‬‬ ‫)‪(۲‬‬ ‫ﺑﺮﺍﯼ ‪: hc<0‬‬ ‫ﺑﺮﺍﯼ ﺳﺎﻳﺮ ﻣﻘﺎﺩﻳﺮ ‪: hc‬‬ ‫‪γ ( hc , h m ) = 0‬‬ ‫) ‪γ ( hc , hm ) = γ ( hc , − hm‬‬ ‫ﺍﻳﻦ ﺗﺎﺑﻊ ﭼﮕﺎﻟﯽ ﺑﺮﺍﯼ ﻣﻮﺍﺩ ﻣﺨﺘﻠﻒ ﻣﺘﻔﺎﻭﺕ ﺑﻮﺩﻩ ﻭ ﺑﺮﺍﯼ ﺑﻴﺸﺘﺮ ﻣﻮﺍﺩ ﺑﻪ‬ ‫ﺻﻮﺭﺕ ﺗﺎﺑﻊ ﺗﻮﺯﻳﻊ ﻧﺮﻣﺎﻝ ﺯﻳﺮ ﺍﺳﺖ ]‪:[6‬‬ ‫)‪(۳‬‬ ‫‪ (h − h ) 2 ‬‬ ‫‪ h2 ‬‬ ‫‪1‬‬ ‫‪exp − c 2c  exp − m2 ‬‬ ‫‪2πσ cσ m‬‬ ‫‪2σ c ‬‬ ‫‪ 2σ m ‬‬ ‫‪‬‬ ‫‪ -۲‬ﻣﺪﻝ ﺟﺪﻳﺪ ﻫﻴﺴﺘﺮﺯﻳ ﺲ ﺑﺮ ﺍﺳﺎﺱ ﺗﺌﻮﺭﯼ‬ ‫= ) ‪γ (hc , hm‬‬ ‫‪Preisach‬‬ ‫ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺭﺍﺑﻄﻪ ‪ hc‬ﻣﻴﺪﺍﻥ ‪ coercive‬ﻣﺘﻮﺳﻂ ﻭ ‪ σc‬ﻭ ‪ σm‬ﺑﻪ ﺗﺮﺗﻴﺐ‬ ‫ﺍﻧﺤﺮﺍﻑ ﻣﻌﻴﺎﺭ ﻣﻴﺪﺍﻥ ‪ coercive‬ﻭ ﻣﻴﺪﺍﻥ ﺗﺤﺮﻳﮏ ﺩﺭ ﺗﺎﺑﻊ ﺗﻮﺯﻳﻊ ﻧﺮﻣﺎﻝ‬ ‫ﻫﺴﺘﻨﺪ‪.‬‬ ‫ﺩﺭ ﺗﺌﻮﺭﯼ ‪ Preisach‬ﻳﮏ ﺍﻟﻤﺎﻥ ﺩﻭﻗﻄﺒﯽ ﭘﺎﻳﻪ ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮﺩ ﮐﻪ ﻣﺸﺨﺼﺔ‬ ‫ﺁﻥ ﺩﺭ ﺷﮑﻞ )‪ (۱‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﺎﺩﻩ ﻣﺠﻤﻮﻋﻪ ﺍﯼ ﺍﺯ ﺍﻳﻦ ﺍﻟﻤﺎﻥ ﻫﺎ‬ ‫ﺍﺳﺖ ﮐﻪ ﺩﺍﺭﺍﯼ ﺭﻓﺘﺎﺭ ﻣﺴﺘﻘﻠﯽ ﻫﺴﺘﻨﺪ ﻭ ﺩﺭ ﺳﺮﺍﺳﺮ ﻣﺎﺩﻩ ﺑﺼﻮﺭﺕ ﺗﺼﺎﺩﻓﯽ‬ ‫ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﻧﺪ‪ .‬ﺍﻳﻦ ﺩﻭ ﻗﻄﺒﯽ ﺩﻭ ﻭﺿﻌﻴﺖ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻧﺴﺒﯽ ‪ +۱‬ﻭ ‪ -۱‬ﻣﯽ‬ ‫ﺗﻮﺍﻧﺪ ﺩﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﺑﺮﺍﯼ ﻳﮏ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺍﻓﺰﺍﻳﺸﯽ‪ ،‬ﻭﻗﺘﯽ ﻣﻴﺪﺍﻥ‬ ‫‪١٥‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫)‪ hm‬ﺗﺎ )‪ (hc+dhc, hm+dhm‬ﻫﺴﺘﻨﺪ ﺍﺯ ﺭﺍﺑﻄﺔ ﺯﻳﺮ ﺑﺪﺳﺖ ﻣﯽ ﺁﻳﺪ‪:‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺑﺎ ﻣﻌﻠﻮﻡ ﺑﻮﺩﻥ ﺗﺎﺑﻊ ﺗﻮﺯﻳﻊ ﭼﮕﺎﻟﯽ ﺩﻭﻗﻄﺒﯽ ﻫﺎﯼ ‪ ،γ‬ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﻥ‬ ‫ﻣﺎﺩﻩ ﺩﺭ ﻣﺪﻝ ‪ Preisach‬ﺑﻮﺳﻴﻠﺔ ﺩﻳﺎﮔﺮﺍﻡ ‪ Preisach‬ﺗﻌﻴﻴﻦ ﻣﯽ ﺷﻮﺩ‪ .‬ﺑﺎ‬ ‫ﺗﻮﺟﻪ ﺑﻪ‬ ‫)‪(۴‬‬ ‫‪f (t ) = ∫∫ + γ (α , β )dαdβ‬‬ ‫) ‪(t‬‬ ‫‪S‬‬ ‫‪− ∫∫ − γ (α , β )dαdβ‬‬ ‫) ‪S (t‬‬ ‫ﺷﮑﻞ‪ -۲‬ﺩﻳﺎﮔﺮﺍﻡ ‪ Preisach‬ﻭ ﻣﺜﻠﺚ ﺣﺪﯼ ‪T‬‬ ‫ﺷﮑﻞ‪ -۳‬ﺩﻳﺎﮔﺮﺍﻡ ‪ Preisach‬ﺑﻪ ﺍﺯﺍﺀ ﻳﮏ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺑﺎ ﻣﺎﮐﺰﻳﻤﻢ ﻫﺎ ﻭ‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫ﺍﻳﻦ ﻧﮑﺘﻪ ﮐﻪ ‪ β‬ﻧﻤﯽ ﺗﻮﺍﻧﺪ ﺍﺯ ‪ α‬ﺑﺰﺭﮔﺘﺮ ﺑﺎﺷﺪ‪ ،‬ﺩﺭ ﺻﻔﺤﺔ ‪ α-β‬ﮐﻪ ﺩﺭ ﺷﮑﻞ‬ ‫)‪ (۲‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ ﻭ ﺑﻪ ﺩﺓﺍﮔﺮﺍﻡ ‪ Preisach‬ﻣﻮﺳﻮﻡ ﺍﺳﺖ ﻧﺎﺣﻴﺔ‬ ‫ﻣﻌﺘﺒﺮ ﻗﺮﺍﺭ ﮔﺮﻓﺘﻦ ﺩﻭ ﻗﻄﺒﯽ ﻫﺎﯼ ﻣﻐﻨﺎﻃﺔﺳﯽ‪ ،‬ﻗﺴﻤﺖ ﺳﻤﺖ ﭼﭗ ﻭ ﺑﺎﻻﯼ‬ ‫ﺧﻂ ‪ α=β‬ﺍﺳﺖ‪ .‬ﻫﻤﭽﻨﺔﻥ ﺑﻪ ﻋﻠﺖ ﻣﺘﻨﺎﻫﯽ ﺑﻮﺩﻥ ﺗﻌﺪﺍﺩ ﺩﻭﻗﻄﺒﯽ ﻫﺎ‪ ،‬ﻧﺎﺣﻴﺔ‬ ‫ﺑﺎﻻﯼ ﺍﻳﻦ ﺧﻂ ﺑﻮﺳﻴﻠﺔ ﻣﺜﻠﺚ ‪ T‬ﮐﻪ ﺑﻪ ﻣﺜﻠﺚ ﺣﺪﯼ ﻣﻮﺳﻮﻡ ﺍﺳﺖ‪ ،‬ﻣﺤﺪﻭﺩ‬ ‫ﻣﯽ ﺷﻮﺩ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﮐﻞ ﺩﻭ ﻗﻄﺒﯽ ﻫﺎﯼ ﻣﺎﺩﻩ ﺩﺭ ﻧﺎﺣﻴﺔ ﺩﺍﺧﻞ ﻣﺜﻠﺚ ‪ T‬ﻗﺮﺍﺭ‬ ‫ﺩﺍﺭﻧﺪ‪ .‬ﻣﺨﺘﺼﺎﺕ ﺭﺍﺱ ﻣﺜﻠﺚ ‪ T‬ﮐﻪ ﺑﺎ )‪ (α0,β0‬ﻣﺸﺨﺺ ﻣﯽ ﺷﻮﺩ ﻣﻌﺮﻑ‬ ‫ﺩﺍﻣﻨﺔ ﺑﺰﺭﮒ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺍﺳﺖ ﮐﻪ ﺑﻪ ﺍﺯﺍﺀ ﺁﻥ ﻣﺎﺩﻩ ﺑﻄﻮﺭ ﮐﺎﻣﻞ ﺍﺷﺒﺎﻉ‬ ‫ﻣﯽ ﺷﻮﺩ‪.‬‬ ‫ﺑﻄﻮﺭ ﮐﻠﯽ ﺑﺎ ﻳﮏ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺘﻐﻴﺮ ﮐﻪ ﺩﺍﻣﻨﺔ ﻧﻘﺎﻁ ﻣﺎﮐﺰﻳﻤﻢ‬ ‫ﻣﺤﻠﯽ ﺁﻥ ‪ ،‬ﺑﻪ ﺻﻮﺭﺕ ﻳﮑﻨﻮﺍ ﺩﺭ ﺣﺎﻝ ﮐﺎﻫﺶ ﻭ ﻧﻘﺎﻁ ﻣﻴﻨﻴﻤﻢ ﻣﺤﻠﯽ ﺁﻥ‪ ،‬ﺑﻪ‬ ‫ﺻﻮﺭﺕ ﻳﮑﻨﻮﺍ ﺩﺭ ﺣﺎﻝ ﺍﻓﺰﺍﻳﺶ ﺍﺳﺖ ﺩﻳﺎﮔﺮﺍﻡ ‪ Preisach‬ﺑﻪ ﺻﻮﺭﺕ ﺷﮑﻞ )‪(۳‬‬ ‫ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪ .‬ﺩﺭ ﺍﻳﻦ ﻧﻤﻮﺩﺍﺭ ﻧﻘﺎﻁ }‪ {u1, u3‬ﻧﻘﺎﻁ ﻣﺎﮐﺰﻳﻤﻢ ﻭ ﻧﻘﺎﻁ }‪{u2, u4‬‬ ‫ﻧﻘﺎﻁ ﻣﻴﻨﻴﻤﻢ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺍﻋﻤﺎﻝ ﺷﺪﻩ ﺑﻪ ﻣﺎﺩﻩ ﻫﺴﺘﻨﺪ‪ .‬ﻣﻘﺪﺍﺭ‬ ‫ﻣﻴﻨﻴﻤﻢ ﻫﺎﯼ ﻧﺰﻭﻟﯽ‬ ‫‪ -۳‬ﭘﻴﺎﺩﻩ ﺳﺎﺯﯼ ﻣﺪﻝ ‪ Preisach‬ﺩﺭ ﺑﺮﻧﺎﻣﺔ ﺣﺎﻟﺖ ﮔﺬﺭﺍ‬ ‫ﻣﺪﻝ ‪ Preisach‬ﻣﯽ ﺗﻮﺍﻧﺪ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺍﺑﻂ )‪ (۳‬ﻭ )‪ (۴‬ﺑﻪ ﺻﻮﺭﺕ ﻋﺪﺩﯼ‬ ‫ﭘﻴﺎﺩﻩ ﺳﺎﺯﯼ ﺷﻮﺩ ﻭﻟﯽ ﺍﺳﺘﻔﺎﺩﻩ ﻣﺴﺘﻘﻴﻢ ﺍﺯ ﺍﻳﻦ ﺭﻭﺍﺑﻂ ﺩﺭ ﻳﮏ ﺑﺮﻧﺎﻣﺔ ﺣﺎﻟﺖ‬ ‫ﮔﺬﺭﺍ ﺩﺍﺭﺍﯼ ﺩﻭ ﻣﺸﮑﻞ ﺍﺳﺎﺳﯽ ﺍﺳﺖ‪ .‬ﺍﻭﻟﻴﻦ ﻣﺸﮑﻞ‪ ،‬ﻣﺤﺎﺳﺒﺔ ﻳﮏ ﺍﻧﺘﮕﺮﺍﻝ‬ ‫ﺩﻭﮔﺎﻧﻪ ﺑﻪ ﺭﻭﺵ ﻋﺪﺩﯼ ﺍﺳﺖ ﮐﻪ ﺑﺴﻴﺎﺭ ﻭﻗﺖ ﮔﻴﺮ ﺍﺳﺖ‪ .‬ﻣﺸﮑﻞ ﺑﻌﺪﯼ ﻣﺮﺑﻮﻁ‬ ‫ﺑﻪ ﻣﺤﺎﺳﺒﺔ ﺗﺎﺑﻊ ﭼﮕﺎﻟﯽ ﺗﻮﺯﻳﻊ ﺩﻭﻗﻄﺒﯽ ﻫﺎﯼ ‪ γ‬ﺍﺳﺖ‪ .‬ﺟﻬﺖ ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ‬ ‫ﺍﻳﻦ ﺗﺎﺑﻊ ﺍﺯ ﺩﺍﺩﻩ ﻫﺎﻳﯽ ﮐﻪ ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺳﺖ ﺑﺎﻳﺪ ﻣﺸﺘﻖ‬ ‫ﮔﻴﺮﯼ ﻧﻤﻮﺩ‪ .‬ﺍﻳﻦ ﮐﺎﺭ ﺑﺎﻋﺚ ﺍﻳﺠﺎﺩ ﻧﻮﻳﺰ ﺩﺭ ﻣﺤﺎﺳﺒﺎﺕ ﺷﺪﻩ ﻭ ﺩﻗﺖ ﻣﺤﺎﺳﺒﺎﺕ‬ ‫ﺭﺍ ﮐﺎﻫﺶ ﻣﯽ ﺩﻫﺪ‪ .‬ﻟﺬﺍ ﺑﻬﺘﺮ ﺍﺳﺖ ﻧﺘﻴﺠﻪ ﺍﻧﺘﮕﺮﺍﻝ )‪ (۴‬ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﺗﺎﺑﻊ‬ ‫ﺗﺤﻠﻴﻠﯽ ‪ F‬ﺑﺪﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻣﺤﺎﺳﺒﺎﺕ ﺑﺴﻴﺎﺭ ﺳﺎﺩﻩ ﺗﺮ ﻭ ﺳﺮﻳﻌﺘﺮ‬ ‫ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬ ‫‬‫‪+‬‬ ‫ﻣﺮﺯ ﺑﻴﻦ ﺩﻭ ﻧﺎﺣﻴﺔ ‪ S‬ﻭ ‪ S‬ﺗﻮﺳﻂ ﻳﮏ ﻣﺮﺯ ﭘﻠﻪ ﺍﯼ ﺷﮑﻞ ﺗﻌﻴﻴﻦ ﻣﯽ‬ ‫ﺷﻮﺩ ﮐﻪ ﻣﺨﺘﺼﺎﺕ ﻧﻘﺎﻁ ﺁﻥ ﻳﮏ ﺳﺮﯼ ﺍﺯ ﻣﺎﮐﺰﻳﻤﻢ ﻫﺎ ﻭ ﻣﻴﻨﻴﻤﻢ ﻫﺎﯼ ﻣﺤﻠﯽ‬ ‫ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺷﮑﻞ )‪ (۴‬ﺁﻧﻬﺎ ﺭﺍ ﺑﻪ ﺗﺮﺗﻴﺐ ﺑﺎ ‪ Mk‬ﻭ ‪mk‬‬ ‫ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﻴ ﻢ‪ .‬ﺑﺎ ﻣﻌﻠﻮﻡ ﺑﻮﺩﻥ ﺗﺎﺑﻊ ‪ F‬ﻣﻘﺪﺍﺭ ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﮔﯽ ﻣﺎﺩﻩ ﺑﻪ ﺍﺯﺍﺀ‬ ‫ﻳﮏ ﻣﻴﺪﺍﻥ ﺍﻓﺰﺍﻳﺸﯽ ﺑﺮﺍﺑﺮ ﺍﺳﺖ ﺑﺎ ]‪:[۷‬‬ ‫ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﮔﯽ ﻣﺎﺩﻩ ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ ﺑﻪ ﺩﻭ ﻧﺎﺣﻴﺔ ﺗﻘﺴﻴﻢ ﺷﺪة ﻣﺜﻠﺚ ﺣﺪﯼ‬ ‫‪ T‬ﺩﺭ ﺁﻥ ﻟﺤﻈﻪ ﻭﺍﺑﺴﺘﻪ ﺑﻮﺩﻩ ﻭ ﺑﺮ ﺍﺳﺎﺱ ﻧﻮﺍﺣﯽ )‪ S+(t‬ﻭ )‪ S-(t‬ﺗﻌﻴﻴﻦ ﻣﯽ‬ ‫ﺷﻮﺩ‪ .‬ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺗﻌﺮﻳﻒ ﻣﺮﺯ ﺑﻴﻦ ﺩﻭ ﻧﺎﺣﻴﻪ ﺑﺮ ﺍﺳﺎﺱ ﻣﺎﮐﺰﻳﻤﻢ ﻭ ﻣﻴﻨﻴﻤﻢ‬ ‫ﻫﺎﯼ ﻣﺤﻠﯽ ﻭ ﻗﺒﻠﯽ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ‪ ،‬ﻣﻘﺪﺍﺭ ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﮔﯽ ﻣﺎﺩﻩ ﺩﺭ ﻫﺮ‬ ‫ﻟﺤﻈﻪ ﺑﻪ ﺳﺎﺑﻘﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺎﺩﻩ ﻭﺍﺑﺴﺘﻪ ﺍﺳﺖ‪ .‬ﺩﺭ ﻋﻤﻞ ﻧﻴﺰ ﻫﻴﺴﺘﺮﺯﻳﺲ‬ ‫ﻣﻮﺍﺩ‪ ،‬ﻭﻳﮋﮔﯽ ﺍﺛﺮ ﭘﺬﻳﺮ ﺑﻮﺩﻥ ﺍﺯ ﺷﺮﺍﻳﻂ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻗﺒﻠﯽ ﺭﺍ ﺍﺯ ﺧﻮﺩ ﻧﺸﺎﻥ ﻣﯽ‬ ‫ﺩﻫﻨﺪ‪ .‬ﺑﻨﺎﺑﺮﺍﻳﻦ ﻣﺪﻝ ‪ Preisach‬ﺑﻪ ﺧﻮﺑﯽ ﻗﺎﺩﺭ ﺑﻪ ﻣﺪﻟﺴﺎﺯﯼ ﺳﺎﺑﻘﺔ‬ ‫ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﻮﺍﺩ ﺍﺳﺖ ﺩﺭ ﺣﺎﻟﯽ ﮐﻪ ﻣﺪﻟﻬﺎﯼ ﺻﺮﻓﺎﹰ ﺭﻳﺎﺿﯽ ﻓﺎﻗﺪ ﺍﻳﻦ ﻭﻳﮋﮔﯽ‬ ‫)‪(۵‬‬ ‫) ‪f (t ) = − F (α 0 , β 0‬‬ ‫‪n ( t ) −1‬‬ ‫]) ‪+ 2 ∑ [F (M k , mk −1 ) − F (M k , mk‬‬ ‫ﻣﯽ ﺑﺎﺷﻨﺪ‪ .‬ﻣﻘﺪﺍﺭ ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﮔﯽ ﻣﺎﺩﻩ ﺩﺭ ﻫﺮ ﻟﺤﻈﻪ ﺍﺯ ﺭﺍﺑﻂة ﺯﻳﺮ ﺑﺪﺳﺖ‬ ‫‪k =1‬‬ ‫ﻣﯽ ﺁﻳﺪ‪:‬‬ ‫]) ) ‪+ 2[F (M n , mn−1 ) − F (M n , u (t‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪١٦‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫)‪(٨‬‬ ‫ﻫﻤﭽﻨﻴﻦ ﻣﯽ ﺗﻮﺍﻥ ﻧﺸﺎﻥ ﺩﺍﺩ ﮐﻪ ﺑﺮﺍﯼ ﻳﮏ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺩﺭ ﺣﺎﻝ‬ ‫ﮐﺎﻫﺶ‪ ،‬ﻣﻘﺪﺍﺭ ﻣﻐﻨﺎﻃﻴﺲ ﺷﺪﮔﯽ ﻣﺎﺩﻩ ﺑﺮﺍﺑﺮ ﺍﺳﺖ ﺑﺎ‪:‬‬ ‫ﮐﻪ ﺩﺭ ﺁﻥ ‪ kB‬ﺿﺮﻳﺐ ﺷﺎﺭ ﭘﻴﻮﻧﺪﯼ ‪ λ‬ﻭ ﺛﺎﺑﺖ ﺍﺛﺮ ﻣﺘﻘﺎﺑﻞ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺍﺳﺖ‪ .‬ﺑﺎ‬ ‫ﺗﻮﺟﻪ ﺑﻪ ﺭﻭﺍﺑﻂ ﺑﺎﻻ‪ ،‬ﻣﯽ ﺗﻮﺍﻥ ﺍﻧﺪﻭﮐﺘﺎﻧﺲ ﻣﺘﻐﻴﺮ ﻫﺴﺘﻪ ﺭﺍ ﺑﺎ ﻣﺤﺎﺳﺒﺔ‬ ‫ﭘﺮﻣﺎﺑﻠﻴﺘﻪ ﻣﺘﻐﻴﺮ ﻣﺎﺩﻩ ﺗﻌﻴﻴﻦ ﮐﺮﺩ‪ .‬ﭘﺮﻣﺎﺑﻠﻴﺘﻪ ﻣﺎﺩﻩ ﺑﺮﺍﯼ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﺩﺭ‬ ‫ﺣﺎﻝ ﺍﻓﺰﺍﻳﺶ ﻭ ﮐﺎﻫﺶ ﺑﻪ ﺗﺮﺗﻴﺐ ﺍﺯ ﺭﻭﺍﺑﻂ )‪ (۹‬ﻭ )‪ (۱۰‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ‬ ‫ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﺷﻮﺩ‪:‬‬ ‫) ‪u (t‬‬ ‫‪M1‬‬ ‫‪M2‬‬ ‫‪Mk‬‬ ‫‪−‬‬ ‫)‪(٩‬‬ ‫‪−‬‬ ‫‪tk‬‬ ‫‪+‬‬ ‫‪t‬‬ ‫‪−‬‬ ‫‪t2‬‬ ‫‪+‬‬ ‫‪tk‬‬ ‫‪t0‬‬ ‫‪t1‬‬ ‫) ‪H e = H + kB .λ ( H e‬‬ ‫‪∂F (α , β ) ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪dλ ‬‬ ‫‪∂α‬‬ ‫‪‬‬ ‫‪=‬‬ ‫‪dH  1 − k . ∂F (α , β ) ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪B‬‬ ‫‪∂α‬‬ ‫‪‬‬ ‫‪α = H e ( t ), β = mn−1‬‬ ‫‪+‬‬ ‫‪t1‬‬ ‫‪t2‬‬ ‫‪mk‬‬ ‫)‪(۱۰‬‬ ‫‪m2‬‬ ‫‪m1‬‬ ‫ﺷﮑﻞ‪ -۴‬ﻳﮏ ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻧﻤﻮﻧﻪ ﺑﺎ ﻧﻘﺎﻁ ﺍﮐﺴﺘﺮﻣﻢ ﻣﺤﻠﯽ ﺑﻪ ﻋﻨﻮﺍﻥ‬ ‫‪∂F (α , β ) ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪dλ ‬‬ ‫‪∂β‬‬ ‫‪‬‬ ‫=‬ ‫‪dH  1 − k . ∂F (α , β ) ‬‬ ‫‪B‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪∂β‬‬ ‫‪‬‬ ‫‪ β = H e (t ),α = M n‬‬ ‫ﺣﺎﻓﻈﺔ ﻣﺪﻝ ‪Preisach‬‬ ‫) ‪f (t ) = − F (α 0 , β 0‬‬ ‫)‪(۶‬‬ ‫ﺟﻬﺖ ﻣﻄﺎﻟﻌﺔ ﭘﺪﻳﺪة ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﺎ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ‪ ،‬ﻳﮏ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ‬ ‫‪n ( t ) −1‬‬ ‫]) ‪+ 2 ∑ [F (M k , mk −1 ) − F (M k , mk‬‬ ‫ﻧﺎﻣﯽ‬ ‫ﻭﻟﺘﺎﮊﻫﺎﯼ‬ ‫ﺑﺎ‬ ‫ﭘﻴﭽﻪ‬ ‫ﺳﻴ ﻢ‬ ‫ﺳﻪ‬ ‫ﻭﻟﺘﺎﮊ‬ ‫)‪ (۳۳kV/√۳)/(۱۱۰V/√۳)/(۱۰۰V/۳‬ﻭ ﺗﻮﺍﻥ ﻧﺎﻣﯽ ‪ ۹۰VA‬ﻣﻮﺭﺩ ﺁﺯﻣﺎﻳﺶ‬ ‫ﻗﺮﺍﺭ ﮔﺮﻓﺖ‪ .‬ﻣﺪﺍﺭ ﺗﺴﺖ ﺩﺭ ﺷﮑﻞ )‪ (۵‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﻣﺪﺍﺭ‬ ‫ﻣﻨﺒﻊ ﻭﻟﺘﺎﮊ ﻓﺸﺎﺭ ﻗﻮﯼ ﻳﮏ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺗﮑﻔﺎﺯ ﻓﺸﺎﺭﻗﻮﯼ ﺑﺎ ﻭﻟﺘﺎﮊ ﻧﺎﻣﯽ‬ ‫‪ ۲۲۰V/۱۰۰kV‬ﺍﺳﺖ ﮐﻪ ﻭﻟﺘﺎﮊ ﻭﺭﻭﺩﯼ ﺁﻥ ﺗﻮﺳﻂ ﻳﮏ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻣﺘﻐﻴﺮ‬ ‫ﺍﺯ ﺻﻔﺮ ﺗﺎ ﻭﻟﺘﺎﮊ ‪ ۲۲۰V‬ﻗﺎﺑﻞ ﺗﻐﻴﻴﺮ ﻣﯽ ﺑﺎﺷﺪ‪ .‬ﻣﻘﺎﻭﻣﺖ ﺳﺮﯼ ‪ RS‬ﺟﻬﺖ‬ ‫ﻣﺤﺪﻭﺩ ﮐﺮﺩﻥ ﺟﺮﻳﺎﻥ ﻋﺒﻮﺭﯼ ﺩﺭ ﻫﻨﮕﺎﻡ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻣﻮﺭﺩ ﺍﺳﺘﻔﺎﺩﻩ ﻗﺮﺍﺭ ﻣﯽ‬ ‫ﮔﻴﺮﺩ‪ .‬ﺧﺎﺯﻥ ‪ CS‬ﻧﻴﺰ ﺩﺭ ﻭﺍﻗﻊ ﺧﺎﺯﻧﯽ ﺍﺳﺖ ﮐﻪ ﺑﺎ ﺍﻧﺪﻭﮐﺘﺎﻧﺲ ﻏﻴﺮ ﺧﻄﯽ‬ ‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ‪ ،‬ﻣﺪﺍﺭ ﺍﺻﻠﯽ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺭﺍ ﺗﺸﮑﻴﻞ ﻣﯽ ﺩﻫﻨﺪ‪.‬‬ ‫ﺟﻬﺖ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺟﺮﻳﺎﻥ ﻭ ﻭﻟﺘﺎﮊﻫﺎﯼ ﻧﻘﺎﻁ ﻣﺨﺘﻠﻒ ﺍﺯ ﺩﻭ ﻣﻘﺴﻢ ﺧﺎﺯﻧﯽ‬ ‫ﻭ ﻳﮏ ﻣﻘﺴﻢ ﻣﻘﺎﻭﻣﺘﯽ ﻭ ﻳﮏ ﺷﻨﺖ ﺟﺮﻳﺎﻥ ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻭﻟﺘﺎﮊ‬ ‫ﺗﺮﻣﻴﻨﺎﻝ ﻓﺸﺎﺭ ﻗﻮﯼ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ ﻭ ﻭﻟﺘﺎﮊ ﺳﻤﺖ ﻣﻨﺒﻊ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺩﻭ‬ ‫ﻣﻘﺴﻢ ﺧﺎﺯﻧﯽ ﺑﺎ ﻣﻘﺪﺍﺭ ﻇﺮﻓﻴﺖ ﻣﻮﺛﺮ ‪ Cm1‬ﻭ ‪ Cm2‬ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫ﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﺩﺭ ﻣﻘﺎﺑﻞ ﺍﻧﺪﺍﺯﻩ ﻇﺮﻓﻴﺖ ‪ CS‬ﮐﻮﭼﮏ ﻣﯽ ﺑﺎﺷﻨﺪ‪ .‬ﻭﻟﺘﺎﮊ ﺳﻤﺖ‬ ‫ﺛﺎﻧﻮﻳﺔ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ ﺑﻪ ﻋﻠﺖ ﻓﺸﺎﺭ ﺿﻌﻴﻒ ﺑﻮﺩﻥ ﻭﻟﺘﺎﮊ ﺑﻪ ﺭﺍﺣﺘﯽ ﺑﺎ ﻳﮏ‬ ‫ﻣﻘﺴﻢ ﻣﻘﺎﻭﻣﺘﯽ ‪ Rsh2‬ﻭ ‪ Rsh3‬ﺑﺎ ﺍﻧﺪﺍﺯﻩ ﻫﺎﯼ ﻣﻘﺎﻭﻣﺘﯽ ﭼﻨﺪ ﺻﺪ ﮐﻴﻠﻮ ﺍﻫﻢ‬ ‫ﻗﺎﺑﻞ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﻣﻘﺎﻭﻣﺖ ﻫﺎ ﺑﺎﻳﺪ ﺩﺭ ﺣﺪ ﺍﻣﮑﺎﻥ ﺑﺰﺭﮒ ﺍﻧﺘﺨﺎﺏ‬ ‫ﺷﻮﻧﺪ ﺗﺎ ﺑﺼﻮﺭﺕ ﺑﺎﺭ ﺑﺮﺍﯼ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻇﺎﻫﺮ ﻧﺸﻮﻧﺪ‪ .‬ﺟﺮﻳﺎﻥ ﻋﺒﻮﺭﯼ ﺍﺯ ﺍﻭﻟﻴﻪ‬ ‫‪ VT‬ﻧﻴﺰ ﺑﺎ ﻗﺮﺍﺭ ﺩﺍﺩﻥ ﻳﮏ ﻣﻘﺎﻭﻣﺖ ﮐﻮﭼﮏ ﺩﺭ ﺳﻤﺖ ﺗﺮﻣﻴﻨﺎﻝ ﺯﻣﻴﻦ ﺳﻴﻢ‬ ‫‪k =1‬‬ ‫) ‪+ 2 F (u (t ), mn −1‬‬ ‫ﺩﺭ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ‪ ،‬ﺗﺎﺑﻊ ‪ F‬ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪﻩ ﻭ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ ﻭ‬ ‫ﺗﻌﺪﺍﺩ ﺟﻤﻠﻪ ﻫﺎﯼ ﺁﻥ ﺑﺎ ﺑﺮﺍﺯﺵ ﻣﻨﺤﻨﯽ ﺑﻪ ﺩﺍﺩﻩ ﻫﺎﯼ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪة ﺣﻠﻘﺔ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﺪﺳﺖ ﻣﯽ ﺁﻳﺪ‪:‬‬ ‫)‪(۷‬‬ ‫[‬ ‫]‬ ‫‪1 q‬‬ ‫)‪λi tanh(Pi x) + c sec h 2 ( Pi x‬‬ ‫∑‬ ‫‪2 i =1‬‬ ‫ﮐﻪ ﺩﺭ ﺭﺍﺑﻄﺔ ﺍﺧﻴﺮ‪:‬‬ ‫ﺑﺮﺍﯼ ﻗﺴﻤﺖ ﺑﺎﻻﻳﯽ ﺣﻠﻘﺔ ﺍﺻﻠﯽ‬ ‫‪x = β , 0 ≤ c ≤ 0.5‬‬ ‫ﺑﺮﺍﯼ ﻗﺴﻤﺖ ﭘﺎﻳﻴﻨﯽ ﺣﻠﻘﺔ ﺍﺻﻠﯽ‬ ‫‪x = α , − 0.5 ≤ c ≤ 0‬‬ ‫‪Pi > 0‬‬ ‫‪λi > 0‬‬ ‫= )) ‪F ( x(α , β‬‬ ‫‪= λs‬‬ ‫‪∑λ‬‬ ‫‪i‬‬ ‫ﺑﺮﺍﯼ ﺍﻳﻨﮑﻪ ﺍﺛﺮ ﻣﺘﻘﺎﺑﻞ ﺣﻮﺯﻩ ﻫﺎﯼ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺎﺩﻩ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﻮﺩ‪ ،‬ﻳﮏ‬ ‫ﻣﻴﺪﺍﻥ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﻮﺛﺮ ﺑﻪ ﺻﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻭ ﺩﺭ ﻣﺪﻝ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﻲ‬ ‫ﺷﻮﺩ‪:‬‬ ‫‪١٧‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫‪ -۴‬ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫‪CS‬‬ ‫‪Voltage Transformer‬‬ ‫‪RS‬‬ ‫) ‪(33kV/ 3 ) / (110V/ 3‬‬ ‫) ‪/ (100V/ 3‬‬ ‫‪C m2‬‬ ‫‪Variable‬‬ ‫‪Transformer‬‬ ‫‪0 - 220 V, 50 Hz‬‬ ‫‪C m1‬‬ ‫‪Rsh2‬‬ ‫‪Rsh3‬‬ ‫‪Rsh1‬‬ ‫‪High Voltage‬‬ ‫‪Transformer‬‬ ‫‪220 V/100 kV‬‬ ‫‪Measurements‬‬ ‫‪Interface‬‬ ‫&‬ ‫‪Data‬‬ ‫‪Acquisition‬‬ ‫‪Computer‬‬ ‫ﺷﮑﻞ ‪ -۵‬ﻣﺪار ﺗﺴﺖ ﻓﺮورزوﻧﺎﻧﺲ ﺗﺮاﻧﺴﻔﻮرﻣﺎﺗﻮر وﻟﺘﺎژ‬ ‫‪ (۱/۱۴ pu) ۲۱/۷۱‬ﻭ ﭘﻴﮏ ﻭﻟﺘﺎﮊ‪ VT‬ﺑﻪ ‪ (۱/۱۳۶pu) ۳۰/۶ kV‬ﻣﯽ ﺭﺳﺪ‪،‬‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺍﺗﻔﺎﻕ ﻣﯽ ﺍﻓﺘﺪ ﻭ ﻭﻟﺘﺎﮊ ‪ VT‬ﺩﺭ ﻣﺪﺕ ﮐﻮﺗﺎﻫﯽ ﺑﻪ ﺣﺪﻭﺩ ‪۱/۷‬‬ ‫ﺑﺮﺍﺑﺮ ﺟﻬﺶ ﭘﻴﺪﺍ ﻣﯽ ﮐﻨﺪ‪ .‬ﭘﺲ ﺍﺯ ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﺎ ﻣﮑﺚ‬ ‫ﮐﻮﺗﺎﻫﯽ ﺩﺭ ﻭﻟﺘﺎﮊ ‪ ، ۲۱/۷۱ kV‬ﺑﻪ ﺁﺭﺍﻣﯽ ﭘﺎﻳﻴﻦ ﺁﻭﺭﺩﻩ ﻣﯽ ﺷﻮﺩ‪ .‬ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ‬ ‫ﺩﺭ ﺷﮑﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﻼﻓﺎﺻﻠﻪ ﻗﻄﻊ ﻧﻤﯽ ﺷﻮﺩ ﻭ ﺗﺎ‬ ‫ﻭﻗﺘﯽ ﮐﻪ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﻪ ‪ (۰/۵۱ pu) ۹/۶۵ kV‬ﺑﺮﺳﺪ‪ ،‬ﺍﺩﺍﻣﻪ ﻣﯽ ﻳﺎﺑﺪ‪ .‬ﺩﺭ‬ ‫ﻟﺤﻈﺔ ﻗﻄﻊ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻭﻟﺘﺎﮊ ‪ VT‬ﺍﺯ ﻣﻘﺪﺍﺭ ﭘﻴﮏ ‪(۱/۴۳ pu) ۳۸/۴ kV‬‬ ‫ﺑﻪ‪ ۱۱/۸ kV‬ﺟﻬﺶ ﭘﻴﺪﺍ ﻣﯽ ﮐﻨﺪ‪.‬‬ ‫ﭘﻴﭻ ﺍﻭﻟﻴﻪ ﻗﺎﺑﻞ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺍﺳﺖ‪ .‬ﻣﻘﺪﺍﺭ ﺍﻳﻦ ﻣﻘﺎﻭﻣﺖ ﺑﺴﺘﻪ ﺑﻪ‬ ‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ ﺩﺭ ﻣﺤﺪﻭﺩﺓ ﭼﻨﺪ ﺍﻫﻢ ﺗﺎ ﭼﻨﺪ ﺩﻩ ﺍﻫﻢ ﻣﻨﺎﺳﺐ ﻣﯽ ﺑﺎﺷﺪ‪.‬‬ ‫ﻭﺭﻳﺴﺘﻮﺭﻫﺎﯼ ﻣﺤﺪﻭﺩ ﮐﻨﻨﺪة ﻭﻟﺘﺎﮊ ﻣﺠﻬﺰ ﻣﯽ ﺑﺎﺷﺪ ﺗﺎ ﻗﺴﻤﺖ ﺩﻭﻡ ﻭ ﮐﺎﻣﭙﻴﻮﺗﺮ‬ ‫ﺭﺍ ﺩﺭ ﻣﻘﺎﺑﻞ ﺍﺿﺎﻓﻪ ﻭﻟﺘﺎﮊﻫﺎﯼ ﮔﺬﺭﺍﯼ ﺍﺣﺘﻤﺎﻟﯽ ﻣﺤﺎﻓﻈﺖ ﮐﻨﺪ‪ .‬ﺑﺨﺶ ﺩﻭﻡ‬ ‫ﻣﺪﺍﺭ ﻭﺍﺳﻂ ﻳﮏ ﮐﺎﺭﺕ ‪ Data Acquisition‬ﺷﺎﻣﻞ ﻳﮏ ﻣﺒﺪﻝ ﺁﻧﺎﻟﻮﮒ ﺑﻪ‬ ‫ﺩﻳﺠﻴﺘﺎﻝ )‪ (A/D‬ﺑﺎ ﺳﺮﻋﺖ ﻧﻤﻮﻧﻪ ﺑﺮﺩﺍﺭﯼ ‪ ۱۰۰ kHz‬ﻭ ﻳﮏ ﺣﺎﻓﻈﻪ ﺑﺮﺍﯼ‬ ‫ﺫﺧﻴﺮﻩ ﮐﺮﺩﻥ ﻣﻮﻗﺖ ﺩﺍﺩﻩ ﻫﺎﯼ ﺗﺒﺪﻳﻞ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﻓﺮﮐﺎﻧﺲ ﺟﻬﺖ ﺛﺒﺖ‬ ‫ﺗﻐﻴﻴﺮﺍﺕ ﻭﻟﺘﺎﮊ ﻭﺟﺮﻳﺎﻥ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﮐﺎﻓﯽ ﺍﺳﺖ ﺯﻳﺮﺍ ﻣﻮﻟﻔﻪ ﻫﺎﯼ ﻓﺮﮐﺎﻧﺴﯽ‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﮐﻪ ﺩﺭ ﺗﺴﺖ ﻫﺎﯼ ﻋﻤﻠﯽ ﺩﻳﺪﻩ ﺷﺪﻩ ﺍﺳﺖ ﺯﻳﺮ ‪ ۲ kHz‬ﻭ ﻋﻤﺪﺗﺎﹰ‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪20‬‬ ‫‪0‬‬ ‫ﺯﻳﺮ ‪ ۱ kHz‬ﺍﺳﺖ ]‪ .[8‬ﺍﻧﺪﺍﺯة ﭘﺎﺭﺍﻣﺘﺮﻫﺎﯼ ﻣﺪﺍﺭ ﺗﺴﺖ‪ ،‬ﺩﺭ ﭘﻴﻮﺳﺖ )ﺍﻟﻒ( ﺩﺍﺩﻩ‬ ‫‪-20‬‬ ‫ﺷﺪﻩ ﺍﺳﺖ‪.‬‬ ‫]‪Voltage [kV‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﺟﻬﺖ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﻭ ﺛﺒﺖ ﺳﻴﮕﻨﺎﻝ ﻫﺎﯼ ﺟﺮﻳﺎﻥ ﻭ ﻭﻟﺘﺎﮊ ﺍﺯ‬ ‫ﻳﮏ ﻣﺠﻤﻮﻋﺔ ﺳﻴﺴﺘﻢ ﺩﻳﺠﻴﺘﺎﻝ ﻣﺘﺸﮑﻞ ﺍﺯ ﻳﮏ ﻣﺪﺍﺭ ﻭﺍﺳﻂ ﻭ ﻳﮏ ﮐﺎﻣﭙﻴﻮﺗﺮ‬ ‫ﺍﺳﺘﻔﺎﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﻣﺪﺍﺭ ﻭﺍﺳﻂ ﮐﻪ ﺩﺭ ﺁﺯﻣﺎﻳﺸﮕﺎﻩ ﻓﺸﺎﺭﻗﻮﯼ ﺩﺍﻧﺸﮕﺎﻩ ﺗﻬﺮﺍﻥ‬ ‫ﻃﺮﺍﺣﯽ ﻭ ﺳﺎﺧﺘﻪ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺍﺯ ﺩﻭ ﺑﺨﺶ ﺗﺸﮑﻴﻞ ﻣﯽ ﺷﻮﺩ‪ .‬ﺑﺨﺶ ﺍﻭﻝ‬ ‫ﺩﺍﺭﺍﯼ ﺗﺮﻣﻴﻨﺎﻟﻬﺎﻳﯽ ﺟﻬﺖ ﺍﺗﺼﺎﻝ ﮐﺎﺑﻞ ﻫﺎﯼ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﻣﺪﺍﺭ‬ ‫ﺳﻴﮕﻨﺎﻟﻬﺎﯼ ﺩﺭﻳﺎﻓﺘﯽ ﭘﺲ ﺍﺯ ﺩﺭﻳﺎﻓﺖ ﺑﻪ ﺧﺮﻭﺟﯽ ﮐﻪ ﺑﻪ ﺑﺨﺶ ﺩﻭﻡ ﻣﺪﺍﺭ‬ ‫ﻭﺍﺳﻂ ﻣﺘﺼﻞ ﺍﺳﺖ ﻓﺮﺳﺘﺎﺩﻩ ﻣﯽ ﺷﻮﺩ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺍﻳﻦ ﻗﺴﻤﺖ ﺑﻪ‬ ‫‪-40‬‬ ‫ﺩﺭ ﺍﻳﻦ ﺁﺯﻣﺎﻳﺶ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺍﺯ ﺻﻔﺮ ﺑﻪ ﺁﺭﺍﻣﯽ ﺑﺎﻻ ﺑﺮﺩﻩ ﺷﺪ ﺗﺎ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫ﺭﺥ ﺩﻫﺪ‪ .‬ﺳﭙﺲ ﺑﻪ ﺁﺭﺍﻣﯽ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺗﺎ ﺻﻔﺮ ﮐﺎﻫﺶ ﺩﺍﺩﻩ ﺷﺪ ﻭ ﺳﻴﮕﻨﺎﻟﻬﺎﯼ‬ ‫ﻭﻟﺘﺎﮊ ﻭ ﺟﺮﻳﺎﻥ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪ‪ .‬ﺗﻐﻴﻴﺮﺍﺕ ﻭﻟﺘﺎﮊ ‪ VT‬ﺩﺭ ﻃﻮﻝ ﺍﻳﻦ ﺗﺴﺖ ﺩﺭ‬ ‫ﺷﮑﻞ )‪ (۶‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ .‬ﺩﺭ ﺣﺎﻟﺘﯽ ﮐﻪ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺣﺪﻭﺩ ‪kV‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪-60‬‬ ‫‪80‬‬ ‫‪70‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪50‬‬ ‫]‪Time [sec‬‬ ‫‪30‬‬ ‫‪20‬‬ ‫‪10‬‬ ‫‪0‬‬ ‫ﺷﮑﻞ ‪ -۶‬ﺗﻐﻴﻴﺮﺍﺕ ﻭﻟﺘﺎﮊ ‪ VT‬ﺩﺭ ﻃﻮﻝ ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫‪١٨‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺁﻧﻬﺎ ﺑﺴﻴﺎﺭ ﻣﺘﻔﺎﻭﺕ ﺍﺳﺖ‪ .‬ﺍﺑﺘﺪﺍ ﻣﺪﻝ ‪ EMTP‬ﻭ ﺳﭙﺲ ﻣﺪﻝ‬ ‫ﭘﻴﺸﻨﻬﺎﺩﯼ ﺑﻪ ﺗﺮﺗﻴﺐ ﺑﺎ ﺍﻓﺰﺍﻳﺶ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﻪ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻣﯽ ﺭﻭﻧﺪ‪.‬‬ ‫ﺩﺍﻣﻨﺔ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺩﺭ ﻫﻨﮕﺎﻡ ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﺮﺍﯼ ﺍﻳﻦ ﻣﺪﻝ ﻫﺎ ﺑﻪ‬ ‫ﺗﺮﺗﻴﺐ ﺑﺮﺍﺑﺮ ‪ ۲۵/۸۵ kV‬ﻭ ‪ ۳۰/۵ kV‬ﻣﯽ ﺑﺎﺷﺪ‪ .‬ﻧﺘﺎﻳﺞ ﺗﺴﺖ ﻧﺸﺎﻥ ﻣﯽ‬ ‫ﺩﻫﺪ ﮐﻪ ‪ VT‬ﺩﺭ ﻭﻟﺘﺎﮊ ﺑﺎﻻﺗﺮ ‪ ۳۰/۷ kV‬ﺑﻪ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻣﯽ ﺭﻭﺩ‪.‬‬ ‫ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ ﺩﺭ ﺷﮑﻞ )‪ (۸‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﻧﺰﺩﻳﮏ ﺗﺮﻳﻦ ﻧﺘﺎﻳﺞ ﺷﺒﻴﻪ‬ ‫ﺳﺎﺯﯼ ﺑﻪ ﻧﺘﺎﻳﺞ ﺗﺴﺖ ﺍﺯ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺑﺪﺳﺖ ﻣﯽ ﺁﻳﺪ‪ .‬ﻣﻄﺎﺑﻖ ﺍﻳﻦ ﺷﮑﻞ‬ ‫ﭘﻴﮏ ﻭﻟﺘﺎﮊ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﺣﺎﻟﺖ ﻗﺒﻞ ﺍﺯ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‪،‬‬ ‫ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ﻭ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﺴﻴﺎﺭ ﺑﻪ ﻧﺘﺎﻳﺞ ﺁﺯﻣﺎﻳﺶ‬ ‫ﻧﺰﺩﻳﮏ ﺍﺳﺖ‪.‬‬ ‫‪ -۵‬ﻣﻘﺎﻳﺴﺔ ﻧﺘﺎﻳﺞ ﺷﺒﻴﻪ ﺳﺎﺯﯼ ﺑﺎ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫ﺑﻪ ﻣﻨﻈﻮﺭ ﺑﺮﺭﺳﯽ ﺍﺛﺮ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﺮ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻭ ﺗﻔﺎﻭﺕ ﺭﻭﺷﻬﺎﯼ ﻣﺨﺘﻠﻒ‬ ‫ﻣﺪﻟﺴﺎﺯﯼ ﻣﺸﺨﺼﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻫﺴﺘﻪ‪ ،‬ﺭﻓﺘﺎﺭ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﻭ ﻣﺪﻝ ﺑﺮﻧﺎﻣﺔ‬ ‫‪ EMTP‬ﺑﺎ ﻧﺘﺎﻳﺞ ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ‪ VT‬ﻣﻘﺎﻳﺴﻪ ﻣﯽ ﮔﺮﺩﺩ‪ .‬ﺣﻠﻘﺔ ﺍﺻﻠﯽ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﻣﺪﻝ ‪ EMTP‬ﺑﺮ ﺍﺳﺎﺱ ﻧﺘﺎﻳﺞ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺗﻌﺮﻳﻒ ﻣﯽ ﺷﻮﺩ‪.‬‬ ‫ﻫﻤﭽﻨﻴﻦ ﺑﺎ ﺑﺮﺍﺯﺵ ﻣﻨﺤﻨﯽ ﺑﻪ ﺩﺍﺩﻩ ﻫﺎﯼ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪﻩ ﻫﻴﺴﺘﺮﺯﻳﺲ‪،‬‬ ‫ﭘﺎﺭﺍﻣﺘﺮﻫﺎﯼ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺭﻭﺍﺑﻂ )‪ (۷‬ﻭ )‪ (۸‬ﺑﻪ ﺻﻮﺭﺕ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺩﺭ‬ ‫ﭘﻴﻮﺳﺖ )ﺏ( ﺑﺪﺳﺖ ﻣﯽ ﺁﻳﻨﺪ‪.‬‬ ‫ﺷﮑﻞ )‪ (۷‬ﻣﺸﺨﺼﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺭﺍ ﺩﺭ‬ ‫ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪة ‪ VT‬ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ‬ ‫ﺷﮑﻞ ﻫﺎﯼ )‪ (۹‬ﺗﺎ )‪ (۱۱‬ﻧﺘﺎﻳﺞ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺯ ﻣﺪﻝ ‪ EMTP‬ﺭﺍ ﺩﺭ‬ ‫ﺩﺭ ﺍﻳﻦ ﺷﮑﻞ ﻣﺸﻬﻮﺩ ﺍﺳﺖ‪ ،‬ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺑﺎ ﺩﻗﺖ ﺧﻮﺑﯽ ﻣﯽ ﺗﻮﺍﻧﺪ‬ ‫ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻧﺘﺎﻳﺞ ﺗﺴﺖ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﺷﮑﻞ )‪ (۹‬ﺗﻐﻴﻴﺮﺍﺕ ﺗﻠﻒ ﺗﻮﺍﻥ ‪ VT‬ﺭﺍ‬ ‫ﺩﺭ ﻫﻨﮕﺎﻡ ﺗﻐﻴﻴﺮ ﻣﺪ ﺍﺯ ﺣﺎﻟﺖ ﻋﺎﺩﯼ ﺑﻪ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪.‬‬ ‫‪180‬‬ ‫‪160‬‬ ‫‪70‬‬ ‫‪140‬‬ ‫‪Proposed‬‬ ‫‪Model‬‬ ‫‪120‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫]‪Core Flux [V.s‬‬ ‫‪80‬‬ ‫‪55‬‬ ‫‪50‬‬ ‫‪45‬‬ ‫‪40‬‬ ‫‪20‬‬ ‫‪60‬‬ ‫‪50‬‬ ‫‪10‬‬ ‫‪20‬‬ ‫‪30‬‬ ‫‪40‬‬ ‫]‪Magnetizing Current [mA‬‬ ‫‪0‬‬ ‫‪60‬‬ ‫‪0‬‬ ‫‪35‬‬ ‫‪-20‬‬ ‫‪30‬‬ ‫‪-40‬‬ ‫‪25‬‬ ‫‪-10‬‬ ‫‪32‬‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫‪31‬‬ ‫‪27‬‬ ‫‪28‬‬ ‫‪29‬‬ ‫‪30‬‬ ‫]‪Source Peak Voltage [kV‬‬ ‫‪26‬‬ ‫‪25‬‬ ‫]‪VT Peak Voltage [kV‬‬ ‫‪100‬‬ ‫‪65‬‬ ‫‪20‬‬ ‫‪24‬‬ ‫ﺷﮑﻞ ‪ -٨‬ﺗﻐﻴﻴﺮﺍﺕ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ‪ VT‬ﺑﺮ ﺣﺴﺐ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﺪﺳﺖ ﺁﻣﺪﻩ‬ ‫ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﻭ ﻣﻘﺎﻳﺴﻪ ﺁﻥ ﺑﺎ ﻣﺪﻟﻬﺎ‬ ‫ﺷﮑﻞ ‪ -٧‬ﻣﺸﺨﺼﺔ ﻣﻐﻨﺎﻃﻴﺴﯽ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻫﻴﺴﺘﺮﺯﻳﺲ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴ ﺮﯼ ﺷﺪﻩ‬ ‫‪220‬‬ ‫ﺣﻠﻘﺔ ﺍﺻﻠﯽ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺭﺍ ﻣﺪﻝ ﮐﻨﺪ‪ .‬ﻫﻴﺴﺘﺮﺯﻳﺲ ﻫﺴﺘﻪ ﺩﺭ ﻗﺴﻤﺖ ﺯﺍﻧﻮ‬ ‫ﺩﺍﺭﺍﯼ ﻋﺮﺽ ﺑﻴﺸﺘﺮﯼ ﻧﺴﺒﺖ ﺑﻪ ﻗﺴﻤﺖ ﻫﺎﯼ ﺩﻳﮕﺮ ﺍﺳﺖ‪ .‬ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫ﻧﻴﺰ ﺑﻪ ﺧﻮﺑﯽ ﺍﻳﻦ ﻭﺿﻌﻴﺖ ﺭﺍ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺷﻴﺐ ﻧﻬﺎﻳﯽ‬ ‫ﻣﺸﺨﺼﺔ ﻫﻴﺴﺘﺮﺯﻳﺲ ﻧﻴﺰ ﺑﻪ ﺧﻮﺑﯽ ﺗﻮﺳﻂ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﻣﺪﻝ ﻣﯽ ﺷﻮﺩ‪.‬‬ ‫ﻣﺪﺍﺭ ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺷﮑﻞ )‪ (۵‬ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﻭ ﻣﺪﻝ‬ ‫‪ EMTP‬ﻣﻮﺭﺩ ﺷﺒﻴﻪ ﺳﺎﺯﯼ ﻗﺮﺍﺭ ﮔﺮﻓﺖ‪ .‬ﺍﻳﻦ ﺷﺒﻴﻪ ﺳﺎﺯﯼ ﻫﺎ ﺑﺎ ﺷﺮﺍﻳﻂ ﺍﻭﻟﻴﻪ‬ ‫ﻳﮑﺴﺎﻥ ﺷﺎﺭ ﭘﺴﻤﺎﻧﺪ ﺻﻔﺮ ﻭ ﺩﺍﻣﻨﺔ ﺍﻭﻟﻴﻪ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﺮﺍﺑﺮ ﺻﻔﺮ ﺍﻧﺠﺎﻡ ﺷﺪ‪.‬‬ ‫ﺷﮑﻞ )‪ (۸‬ﺗﻐﻴﻴﺮﺍﺕ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ‪ VT‬ﺭﺍ ﮐﻪ ﺍﺯ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﻭ ﺩﻭ ﻣﺪﻝ ﺗﺤﺖ‬ ‫ﻣﻄﺎﻟﻌﻪ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺳﺖ ﺭﺍ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﺍﻳﻦ ﺗﻐﻴﻴﺮﺍﺕ ﺩﺭ ﻃﻮﻝ‬ ‫ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻭ ﺑﺮ ﺣﺴﺐ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﺍﺳﺖ‪ .‬ﺍﻳﻦ‬ ‫ﺷﮑﻞ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ ﮐﻪ ﺍﮔﺮﭼﻪ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﻭ ﻣﺪﻝ ‪ EMTP‬ﺑﺮ ﺍﺳﺎﺱ‬ ‫ﻳﮏ ﻣﺠﻤﻮﻋﻪ ﺩﺍﺩﻩ ﻫﺎﯼ ﺗﺴﺖ ﺗﻌﺮﻳﻒ ﺷﺪﻩ ﺍﻧﺪ‪ ،‬ﻭﻟﯽ ﻭﻟﺘﺎﮊ ﺷﺮﻭﻉ‬ ‫‪200‬‬ ‫‪180‬‬ ‫‪140‬‬ ‫‪120‬‬ ‫‪100‬‬ ‫]‪Power Loss [W‬‬ ‫‪160‬‬ ‫‪80‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪200‬‬ ‫‪150‬‬ ‫‪100‬‬ ‫]‪Time [ms‬‬ ‫‪50‬‬ ‫‪20‬‬ ‫‪0‬‬ ‫ﺷﮑﻞ‪ -٩‬ﺗﻐﻴﻴﺮﺍﺕ ﺗﻠﻔﺎﺕ ‪ VT‬ﻣﺪﻝ ‪ EMTP‬ﺩﺭ ﻫﻨﮕﺎﻡ ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫ﻣﺪﻝ ‪EMTP‬‬ ‫‪١٩‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫‪Measurement‬‬ ‫‪EMTP‬‬ ‫‪Type-96‬‬ ‫‪Hysteretic‬‬ ‫‪Model‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺷﮑﻞ )‪ (۱۳‬ﻧﺘﺎﻳﺞ ﺑﺴﻴﺎﺭ ﻧﺰﺩﻳﮏ ﻭﻟﺘﺎﮊ ﺣﺎﻟـﺖ ﻣﺎﻧـﺪﮔﺎﺭ ﻓﺮﻭﺭﺯﻭﻧـﺎﻧﺲ ﻣـﺪﻝ ﻭ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺭﺍ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺷﮑﻞ )‪ (۱۴‬ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ ﮐﻪ ﺩﺭ‬ ‫ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ‪ VT‬ﺍﺯ ﺣﺎﻟﺖ ﻋﺎﺩﯼ ﺑﻪ ﻓﺮﻭﺭﺯﻭﻧـﺎﻧﺲ‪ ،‬ﻭﻟﺘـﺎﮊ ﮔـﺬﺭﺍﯼ‬ ‫ﻣﺮﺑﻮﻃﻪ ﻭ ﻣﻘﺪﺍﺭ ﭘﻴﮏ ﺁﻥ ﺑﺎ ﺩﻗـﺖ ﺑـﺴﻴﺎﺭ ﺧـﻮﺑﯽ ﺗﻮﺳـﻂ ﻣـﺪﻝ ﭘﻴـﺸﻨﻬﺎﺩﯼ‬ ‫ﺗﻌﻴﻴﻦ ﻣﯽ ﺷﻮﺩ‪ .‬ﻧﺘﺎﻳﺞ ﺑﺮﺭﺳﯽ ﻫﺎﯼ ﺩﻳﮕﺮ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺩﺭ ﺗﺮﺍﻧـﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎﯼ‬ ‫ﻗﺪﺭﺕ ]‪ [9] ،[۷‬ﻭ ﻫﻤﭽﻨﻴﻦ ﻣﻄﺎﻟﻌـﺔ ﺣﺎﻟﺘﻬـﺎﯼ ﮔـﺬﺭﺍﯼ ﺗﺮﺍﻧـﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎﯼ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺟﺮﻳﺎﻥ ]‪ [10] ،[۷‬ﻧﻴـﺰ ﻣﻮﻳـﺪ ﺩﻗـﺖ ﺑـﺎﻻﯼ ﺍﻟﮕـﻮﺭﻳﺘﻢ ﻭ ﻣـﺪﻝ‬ ‫ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﻣﺪﻟﺴﺎﺯﯼ ﺭﻓﺘﺎﺭ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﻫﺴﺘﺔ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭﻫﺎ ﺍﺳﺖ‪.‬‬ ‫ﺗﻠﻒ ﺗﻮﺍﻥ ‪ VT‬ﻗﺒﻞ ﺍﺯ ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ‪ ۲۹ W‬ﺍﺳﺖ ﮐـﻪ ﭘـﺲ ﺍﺯ ﻃـﯽ‬ ‫ﻳﮏ ﺣﺎﻟﺖ ﮔﺬﺭﺍ ﺑﻪ ﻣﻘﺪﺍﺭ ﻣﺎﻧﺪﮔﺎﺭ ‪ ۱۰۳ W‬ﻣﯽ ﺭﺳﺪ‪ .‬ﺑﺎ ﻭﺟـﻮﺩ ﺍﻳﻨﮑـﻪ ﻣـﺪﻝ‬ ‫‪ EMTP‬ﺑﺎ ﻭﻟﺘﺎﮊ ﮐﻤﺘﺮ ﺑﻪ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻣﯽ ﺭﻭﺩ ﻭﻟـﯽ ﺗﻠـﻒ ﺗـﻮﺍﻥ ‪VT‬‬ ‫ﺍﻳﻦ ﻣﺪﻝ ﺍﺯ ﻣﻘﺪﺍﺭ ﺗﺴﺖ ﺑﻴﺸﺘﺮ ﺍﺳﺖ‪ .‬ﻗﺒﻞ ﺍﺯ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺗﻠﻔـﺎﺕ ﺍﻳـﻦ ﻣـﺪﻝ‬ ‫ﺑﺮﺍﺑﺮ ‪ ۳۵ W‬ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺣﺎﻟﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺑﻪ ﻣﻘـﺪﺍﺭ ﺍﻧـﺪﺍﺯﻩ ﮔﻴـﺮﯼ ﺷـﺪة‬ ‫‪ ۱۰۳W‬ﻣﯽ ﺭﺳﺪ‪ .‬ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ ﺩﺭ ﺷﮑﻞ )‪ (۹‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳـﺖ‪ ،‬ﻣـﺪﻝ‬ ‫‪ EMTP‬ﻗﺎﺩﺭ ﺑﻪ ﻣﺪﻟﺴﺎﺯﯼ ﺩﻗﻴﻖ ﺗﻠﻔﺎﺕ ﮔﺬﺭﺍﯼ ‪ VT‬ﺩﺭ ﻫﻨﮕـﺎﻡ ﺗﻐﻴﻴـﺮ ﻣـﺪ‬ ‫ﻧﻴﺴﺖ‪.‬‬ ‫ﺷﮑﻞ )‪ (۱۰‬ﺷﮑﻞ ﻣﻮﺝ ﻭﻟﺘﺎﮊ ﻣﺪﻝ ‪ EMTP‬ﺭﺍ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫ﺩﺭ ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎﺭ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺷﮑﻞ‪ ،‬ﺷﮑﻞ ﻣﻮﺟﻬﺎ‬ ‫‪60‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪40‬‬ ‫‪20‬‬ ‫]‪Voltage [kV‬‬ ‫‪0‬‬ ‫‪0‬‬ ‫‪-20‬‬ ‫] ‪V o lta g e [k V‬‬ ‫‪20‬‬ ‫‪-20‬‬ ‫‪-40‬‬ ‫‪-40‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007‬‬ ‫‪-60‬‬ ‫‪45‬‬ ‫‪40‬‬ ‫‪35‬‬ ‫‪30‬‬ ‫‪20‬‬ ‫‪25‬‬ ‫]‪Time [ms‬‬ ‫‪15‬‬ ‫‪10‬‬ ‫‪5‬‬ ‫‪-60‬‬ ‫‪0‬‬ ‫‪110‬‬ ‫ﺷﮑﻞ‪ -١٠‬ﻭﻟﺘﺎﮊ ‪ VT‬ﻣﺪﻝ ‪ EMTP‬ﺩﺭ ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎﺭ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫‪50‬‬ ‫‪70‬‬ ‫]‪Time [ms‬‬ ‫‪90‬‬ ‫‪30‬‬ ‫‪10‬‬ ‫ﺷﮑﻞ‪ -١١‬ﺗﻐﻴﻴﺮﺍﺕ ﻭﻟﺘﺎﮊ ‪ VT‬ﺩﺭ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ﺍﺯ ﺣﺎﻟﺖ ﻋﺎﺩﯼ ﺑﻪ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴ ﺮﯼ‬ ‫ﻣﺪ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ )ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ(‬ ‫ﻣﺪﻝ ‪EMTP‬‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴ ﺮﯼ‬ ‫ﻣﺪﻝ ‪EMTP‬‬ ‫ﺑﻪ ﻫﻢ ﺷﺒﻴﻪ ﺑﻮﺩﻩ ﻭﻟﯽ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ﻣﺪﻝ ‪ EMTP‬ﺑﻪ‪ ۴۸ kV‬ﻣـﯽ ﺭﺳـﺪ ﮐـﻪ‬ ‫ﮐﻤﺘﺮ ﺍﺯ ﻣﻘﺪﺍﺭ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷـﺪة ‪ ۵۲/۴ kV‬ﺍﺳـﺖ‪ .‬ﺷـﮑﻞ )‪ (۱۱‬ﺗﻐﻴﻴـﺮﺍﺕ‬ ‫‪ -۶‬ﻧﺘﻴﺠﻪ ﮔﻴﺮﯼ‬ ‫ﻭﻟﺘﺎﮊ ‪ VT‬ﺭﺍ ﺩﺭ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﭘﻴﮏ ﻭﻟﺘـﺎﮊ ‪ VT‬ﺩﺭ‬ ‫ﺍﻳﻦ ﺣﺎﻟﺖ ﮐﻪ ﺑﻴﺸﺘﺮﻳﻦ ﺩﺍﻣﻨﺔ ﻭﻟﺘﺎﮊ ﺑﻮﺩﻩ ﻭ ﺍﺯ ﻧﻈﺮ ﻋﺎﻳﻘﯽ ﺑﺴﻴﺎﺭ ﺣﺎﺋﺰ ﺍﻫﻤﻴﺖ‬ ‫ﺍﺳﺖ ﺑﻪ ‪ ۶۳/۵ kV‬ﻣیﺮﺳﺪ‪ ،‬ﺩﺭ ﺣﺎﻟﯽ ﮐﻪ ﭘﻴﮏ ﻭﻟﺘﺎﮊ ﺑﺪﺳﺖ ﺁﻣـﺪﻩ ﺍﺯ ﻣـﺪﻝ‬ ‫‪ EMTP‬ﺑﺮﺍﺑﺮ ‪ ۵۲/۱ kV‬ﺍﺳﺖ ﮐﻪ ﺑﻄﻮﺭ ﻗﺎﺑﻞ ﻣﻼﺣﻈـﻪ ﺍﯼ ﮐﻤﺘـﺮ ﺍﺯ ﻣﻘـﺪﺍﺭ‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺍﺳﺖ‪ .‬ﺩﺭ ﻣﺠﻤﻮﻉ ﻣـﺪﻝ ‪ EMTP‬ﭼﻨـﺪﺍﻥ ﻗـﺎﺩﺭ ﺑـﻪ ﻣﺪﻟـﺴﺎﺯﯼ‬ ‫ﺩﻗﻴﻖ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ﺍﺯ ﺣﺎﻟﺖ ﻋﺎﺩﯼ ﺑﻪ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻧﻴﺴﺖ‪.‬‬ ‫در اﯾﻦ ﻣﻘﺎﻟﻪ ﻣﺪل ﺟﺪﯾﺪي از ﻫﯿﺴﺘﺮزﯾﺲ ﻫﺴﺘﻪ آﻫﻨﯽ ﺑﺮ اﺳـﺎس ﺗﺌـﻮري‬ ‫‪ Preisach‬و ﺑﺎ ﻓﺮﻣﻮل ﺑﻨﺪي ﺟﺪﯾﺪ ﻣﻌﺮﻓـﯽ ﮔﺮدﯾـﺪ‪ .‬ﻫﻤﭽﻨـﯿﻦ ﻣـﺪار و روال‬ ‫اﻧﺠﺎم آزﻣـﺎﯾﺶ ﻓﺮورزوﻧـﺎﻧﺲ ﯾـﮏ ﺗﺮاﻧـﺴﻔﻮرﻣﺎﺗﻮر وﻟﺘـﺎژ ‪ 33 kV‬ﺗـﺸﺮﯾﺢ و‬ ‫ﻧﺘﺎﯾﺞ آن اراﺋﻪ ﮔﺮدﯾﺪ‪ .‬ﺳﭙﺲ آزﻣﺎﯾﺶ ﻓﺮورزوﻧﺎﻧﺲ ﺑﺎ اﺳﺘﻔﺎده از ﻣﺪل ﻫـﺴﺘﮥ‬ ‫ﭘﯿﺸﻨﻬﺎدي و ﻣﺪل ﺑﺮﻧﺎﻣﮥ ‪ EMTP‬ﮐﻪ از دﻗﯿﻘﺘﺮﯾﻦ ﺑﺮﻧﺎﻣﻪ ﻫﺎي ﺣﺎﻟﺖ ﮔـﺬرا‬ ‫ﻣﺤﺴﻮب ﻣﯽ ﺷﻮد‪ ،‬ﻣﻮرد ﺷﺒﯿﻪ ﺳﺎزي ﻗﺮار ﮔﺮﻓﺖ‪.‬‬ ‫ﺷﮑﻞ )‪ (۱۲‬ﺗﻠﻔﺎﺕ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺭﺍ ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﺍﻧـﺪﺍﺯﻩ‬ ‫ﮔﻴﺮﯼ ﻧﺸﺎﻥ ﻣﯽ ﺩﻫﺪ‪ .‬ﻫﻤﺎﻧﻄﻮﺭ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺷﮑﻞ ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﺷﺪﻩ ﺍﺳﺖ‪ ،‬ﺍﻳﻦ‬ ‫ﻣﺪﻝ ﻗﺎﺩﺭ ﺍﺳﺖ ﺗﻠﻔﺎﺕ ‪ VT‬ﺭﺍ ﺩﺭ ﻫﺮ ﺳﻪ ﺣﺎﻟﺖ ﻗﺒﻞ ﺍﺯ ﻓﺮﻭﺭﺯﻭﻧـﺎﻧﺲ‪ ،‬ﺣﺎﻟـﺖ‬ ‫ﮔﺬﺭﺍﯼ ﺗﻐﻴﻴﺮ ﻣﺪ ﻭ ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎﺭ ﻓﺮﻭﺭﺯﻭﻧـﺎﻧﺲ ﺑـﺼﻮﺭﺕ ﺩﻗﻴـﻖ ﻣـﺪﻝ ﮐﻨـﺪ‪.‬‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫ﻧﺘﺎﻳ ﺞ ﺗﺴﺖ ﺁﺯﻣﺎﻳﺸﮕﺎﻫﯽ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭﻟﺘﺎﮊ ﻧﺸﺎﻥ ﻣﯽ‬ ‫ﺩﻫﻨﺪ ﮐﻪ ﺩﺭ ﻫﻨﮕﺎﻡ ﺍﻓﺰﺍﻳﺶ ﺗﺪﺭﻳﺠﯽ ﻭﻟﺘﺎﮊ ﻣﻨﺒﻊ‪ ،‬ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺩﺭ ﻭﻟﺘﺎﮊﯼ‬ ‫‪٢٠‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ ‫ﺑﺎﻻﺗﺮ ﺍﺯ ﺁﻧﭽﻪ ﻣﺪﻟﻬﺎ ﺗﻌﻴﻴﻦ ﻣﯽ ﮐﻨﻨﺪ ﺭﺥ ﻣﯽ ﺩﻫﺪ ﻭ ﻧﺰﺩﻳﮏ ﺗﺮﻳﻦ ﻭﻟﺘﺎﮊ‬ ‫ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻧﺴﺒﺖ ﺑﻪ ﻧﺘﺎﻳﺞ ﺗﺴﺖ‪ ،‬ﻣﺮﺑﻮﻁ ﺑﻪ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺍﺳﺖ‪.‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪.‬‬ ‫‪220‬‬ ‫‪0‬‬ ‫‪200‬‬ ‫‪-20‬‬ ‫‪180‬‬ ‫‪140‬‬ ‫‪120‬‬ ‫‪100‬‬ ‫]‪Power Loss [W‬‬ ‫‪160‬‬ ‫‪80‬‬ ‫‪150‬‬ ‫‪200‬‬ ‫‪100‬‬ ‫]‪Time [ms‬‬ ‫‪-40‬‬ ‫‪-60‬‬ ‫‪110‬‬ ‫‪90‬‬ ‫‪70‬‬ ‫‪50‬‬ ‫]‪Time [ms‬‬ ‫‪30‬‬ ‫‪10‬‬ ‫ﺷﮑﻞ‪ -١٤‬ﺗﻐﻴﻴﺮﺍﺕ ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ ﺷﺪة ﻭﻟﺘﺎﮊ ‪ VT‬ﺩﺭ ﻣﻘﺎﻳﺴﻪ ﺑﺎ ﻣﺪﻝ‬ ‫‪60‬‬ ‫‪50‬‬ ‫]‪Voltage [kV‬‬ ‫‪20‬‬ ‫‪40‬‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﺣﺎﻟﺖ ﮔﺬﺭﺍﯼ ﺗﻐﻴﺮ ﻣﺪ ﺍﺯ ﺣﺎﻟﺖ ﻋﺎﺩﯼ ﺑﻪ ﻣﺪ‬ ‫‪20‬‬ ‫‪0‬‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ )ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ(‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫ﺷﮑﻞ‪ -١٢‬ﺗﻐﻴﻴﺮﺍﺕ ﺗﻠﻔﺎﺕ ‪ VT‬ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﻫﻨﮕﺎﻡ‬ ‫ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫ﺷﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫ﻫﻤﭽﻨﻴﻦ ﺍﻳﻦ ﻣﺪﻝ ﺑﻬﺘﺮ ﻭ ﺩﻗﻴﻖ ﺗﺮ ﺍﺯ ﻣﺪﻝ ‪ EMTP‬ﻗﺎﺩﺭ ﺑﻪ ﺗﻌﻴـﻴﻦ ﺍﺿـﺎﻓﻪ‬ ‫ﻭﻟﺘﺎﮊﻫﺎ‪ ،‬ﺷﮑﻞ ﻣﻮﺝ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﻭ ﺗﻠﻔﺎﺕ ﻫﺴﺘﻪ ﺩﺭ ﺷـﺮﺍﻳﻂ ﮔـﺬﺭﺍ ﻭ ﻣﺎﻧـﺪﮔﺎﺭ‬ ‫ﺍﺳﺖ‪ .‬ﺍﺿﺎﻓﻪ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍﯼ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﮐﻪ ﺩﺍﺭﺍﯼ ﺑﺰﺭﮔﺘـﺮﻳﻦ ﺩﺍﻣﻨـﻪ ﺍﺳـﺖ ﺍﺯ‬ ‫ﻧﻈﺮ ﻣﻼﺣﻈﺎﺕ ﻋﺎﻳﻘﯽ ﻭ ﻫﻤﭽﻨﻴﻦ ﻫﻤﺎﻫﻨﮕﯽ ﻋـﺎﻳﻘﯽ ﺳﻴـﺴﺘﻢ ﻗـﺪﺭﺕ ﺩﺍﺭﺍﯼ‬ ‫ﺍﻫﻤﻴﺖ ﻓﻮﻕ ﺍﻟﻌﺎﺩﻩ ﺍﺳﺖ ﻭ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﻣﯽ ﺗﻮﺍﻧـﺪ ﺍﻳـﻦ ﺍﺿـﺎﻓﻪ ﻭﻟﺘـﺎﮊ ﺭﺍ‬ ‫ﺑﻄﻮﺭ ﺩﻗﻴﻖ ﺗﻌﻴﻴﻦ ﻧﻤﺎﻳﺪ‪.‬‬ ‫‪60‬‬ ‫‪40‬‬ ‫‪20‬‬ ‫]‪Voltage [kV‬‬ ‫‪0‬‬ ‫‪-20‬‬ ‫‪-40‬‬ ‫‪45‬‬ ‫‪40‬‬ ‫‪35‬‬ ‫‪30‬‬ ‫‪20‬‬ ‫‪25‬‬ ‫]‪Time [ms‬‬ ‫‪15‬‬ ‫‪10‬‬ ‫‪5‬‬ ‫‪0‬‬ ‫‪-60‬‬ ‫ﻧﮑﺘﺔ ﺟﺎﻟﺐ ﺗﻮﺟﻪ ﺩﻳﮕﺮ ﺁﻥ ﺍﺳـﺖ ﮐـﻪ ﺑـﺎ ﻭﺟـﻮﺩ ﺍﻳﻨﮑـﻪ ﺩﺭ ﻧﻈـﺮ ﮔـﺮﻓﺘﻦ‬ ‫ﻫﻴﺴﺘﺮﺯﻳﺲ ﺩﺭ ﻳﮏ ﻣﺪﻝ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺑﺎﻋﺚ ﻣﯽ ﺷﻮﺩ ﮐﻪ ﺁﻥ ﻣﺪﻝ ﺍﺯ ﻧﻈـﺮ‬ ‫ﻓﻴﺰﻳﮑﯽ ﺻﺤﻴﺢ ﺗﺮ ﺑﺎﺷﺪ‪ ،‬ﻭﻟﯽ ﻧﺘﺎﻳﺞ ﺑﺮﺭﺳﯽ ﺍﻳﻦ ﻣﻘﺎﻟﻪ ﻧﺸﺎﻥ ﻣـﯽ ﺩﻫـﺪ ﮐـﻪ‬ ‫ﭼﻨﺎﻧﭽﻪ ﻫﻴﺴﺘﺮﺯﻳﺲ ﺑﻪ ﺻﻮﺭﺕ ﺩﻗﻴﻖ ﻣﺪﻝ ﻧﺸﻮﺩ ﻣـﯽ ﺗﻮﺍﻧـﺪ ﺑﺎﻋـﺚ ﺧﻄـﺎﯼ‬ ‫ﺯﻳﺎﺩ ﺷﻮﺩ‪ .‬ﺩﺭ ﻧﻤﻮﻧﺔ ﺑﺮﺭﺳﯽ ﺷﺪﻩ ﺩﺭ ﺍﻳﻦ ﻣﻘﺎﻟـﻪ‪ ،‬ﺧﻄـﺎﯼ ﻣـﺪﻝ ‪ EMTP‬ﺩﺭ‬ ‫ﺗﻌﻴﻴﻦ ﻭﻟﺘﺎﮊ ﺷـﺮﻭﻉ ﻓﺮﻭﺭﺯﻭﻧـﺎﻧﺲ ﺑﺮﺍﺑـﺮ ‪ %۱۳/۸‬ﺍﺳـﺖ ﺩﺭ ﺣـﺎﻟﯽ ﮐـﻪ ﻣـﺪﻝ‬ ‫ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺍﺭﺍﯼ ﺧﻄﺎﯼ ‪ %۰/۶۵‬ﺍﺳﺖ‪ .‬ﻫﻤﭽﻨﻴﻦ ﺧﻄﺎﯼ ﻣـﺪﻝ ‪ EMTP‬ﺩﺭ‬ ‫ﺗﻌﻴﻴﻦ ﭘﻴﮏ ﺍﺿﺎﻓﻪ ﻭﻟﺘﺎﮊ ﮔﺬﺭﺍ ﻭ ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎﺭ ﺑـﻪ ﺗﺮﺗﻴـﺐ ﺑﺮﺍﺑـﺮ ‪ %۱۷/۹۵‬ﻭ‬ ‫‪ %۸/۶‬ﺑﻮﺩﻩ ﻭ ﺍﻳﻦ ﺧﻄﺎﻫﺎ ﺩﺭ ﻣﻮﺭﺩ ﻣﺪﻝ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺑﺮﺍﺑـﺮ ‪ %-۰/۶۳‬ﻭ ‪%۰/۲۹‬‬ ‫ﺍﺳﺖ ﮐﻪ ﻧﺸﺎﻥ ﺩﻫﻨﺪة ﺩﻗﺖ ﺑﺎﻻﯼ ﻣﺪﻝ ﻣـﺬﮐﻮﺭ ﺩﺭ ﻣﺪﻟـﺴﺎﺯﯼ ﺭﻓﺘـﺎﺭ ﺣﺎﻟـﺖ‬ ‫ﺷﮑﻞ‪ -١٣‬ﻭﻟﺘﺎﮊ ‪ VT‬ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ ﺩﺭ ﺣﺎﻟﺖ ﻣﺎﻧﺪﮔﺎﺭ‬ ‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫ﮔﺬﺭﺍﯼ ﻫﺴﺘﺔ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﻭ ﭘﺪﻳﺪة ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ ﺍﺳﺖ‪.‬‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴﺮﯼ‬ ‫ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ ﭘﻴﺸﻨﻬﺎﺩﯼ‬ ‫‪ -۷‬ﺿﻤﻴﻤﻪ‬ ‫ﺍﻟﻒ( ﭘﺎﺭﺍﻣﺘﺮﻫﺎﯼ ﻣﺪﺍﺭ ﺗﺴﺖ ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ ‫‪٢١‬‬ ‫‪Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007‬‬ ‫ﺍﻧﺪﺍﺯﻩ ﮔﻴ ﺮﯼ‬ ‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‪ -‬ﺳﺎل ﭼﻬﺎرم‪ -‬ﺷﻤﺎره دوم ‪ -‬ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‪1386‬‬ ‫‪PDF created with pdfFactory Pro trial version www.pdffactory.com‬‬ :‫ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺁﺯﻣﺎﻳﺸﮕﺎﻫﯽ ﻓﺸﺎﺭ ﻗﻮﯼ‬ 220 V/ 100 kV, 50 Hz, 5 kVA, ZSC = 2.6% :‫ﺳﺎﻳﺮ ﭘﺎﺭﺍﻣﺘﺮﻫﺎ‬ RS=50 kΩ, CS=1200 pF, Cm1=100 pF, Cm2=300 pF, RSh1=20 Ω, RSh2=630 kΩ, RSh3=33 kΩ :Preisach ‫ﺏ( ﭘﺎﺭﺍﻣﺘﺮﻫﺎﯼ ﻣﺪﻝ ﻫﻴﺴﺘﺮﺯﻳﺲ‬ n =3, λ1=78.997, λ2=24.3, λ3=62.453, P1=186.2, P2=56.18, P3=18.98, c1=0.21355, c2=0.0956, c3=0.26015, kB =0.0001 [1] Iravani M. R., Chaudhary A. K. S., Giesbrecht W. J., et. Al. “Modeling and Analysis Guidelines for Slow Transients—Part III: The Study of Ferroresonance”, Slow Transients Task Force of the IEEE Working Group on Modeling and Analysis of Systems Transients Using Digital Programs, IEEE Trans. On Power Delivery, Vol. 15, No. 1, Jan. 2000. [2] Jacobson D., “Examples of Ferroresonance in a High Voltage Power System”, IEEE PES annual meeting, Toronto, Canada, July 2003 [3] Dugan, R.C.; “Examples of Ferroresonance in Distribution Systems”, IEEE Power Engineering Society General Meeting, Vol. 2, 13-17 July 2003. [4] Dommel H.W., EMTP Theory Book, Bonneville Power Administration, Portland, August 1986. [5] Preisach F., “Uber die magnetische nachwerikung”, Zeitschrift fur Physik, Vol. B 94, pp. 227-302, 1935. [6] Liorzou F., Phelps B. and Atherton D. L., “Macroscopic Models of Magnetization”, IEEE Trans. Magn., Vol. 36, No. 2, March 2000. ‫ "ﻣﺪﻟﺴﺎﺯﯼ ﺗﺮﺍﻧﺴﻔﻮﺭﻣﺎﺗﻮﺭ ﺟﻬﺖ ﺗﺤﻠﻴﻞ‬،‫ ﺍﻓﺸﻴﻦ‬،‫[ ﺭﺿﺎﺋﯽ ﺯﺍﺭﻉ‬۷] ۱۳۸۵ ‫ ﺩﯼ ﻣﺎﻩ‬،‫ ﺻﻔﺤﻪ‬۱۹۰ ،‫ ﺩﺍﻧﺸﮕﺎﻩ ﺗﻬﺮﺍﻥ‬،‫ ﺭﺳﺎﻟﺔ ﺩﮐﺘﺮﺍ‬،"‫ﻓﺮﻭﺭﺯﻭﻧﺎﻧﺲ‬ [8] Mork B.A. and Stuehm D.L., “Application of Nonlinear Dynamics and Chaos to Ferroresonance in Distribution Systems”, IEEE Trans. on Power Systems, Vol.9, No.2, pp. 1009-1017, Apr. 1994. [9] Rezaei-Zare A., Sanaye-Pasand M., Mohseni H., Farhangi Sh., Iravani R., Analysis of Ferroresonance Modes in Power Transformers Using Preisach-Type Hystertic Magnetizing Inductance , IEEE Trans. On Power Delivery, Vol. 22, No. 2, pp. 919-929, April 2007. [10] Rezaei-Zare A., Iravani R., Sanaye-Pasand M., Mohseni H., Farhangi Sh., An Accurate Current Transformer Model Based on Preisach Theory for the Analysis of Electromagnetic Transients , IEEE Trans. On Power Delivery, Vol. 23, No. 1, pp. 233-242, January 2008. ٢٢ 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 ‫ ﻣﺮﺍﺟﻊ‬-۸ ٢٣ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers Vol.4, No.2, Fall and Winter 2007 Proprietor: H. Ghafoori Fard Director: M. Hojjat Editor–in–Chief: G. B. Gharehpetian Executive Director: A. H. Ranjbar Secretary: Z . Haghsheno The Journal of Iranian Association of Electrical and Electronics Engineers is a bilingual (English and Persian) periodical which publishes full length, refereed contributions, describing significant developments in all branches of electrical engineering. The board of editors will be pleased to receive contributions from all over the world. Authors are invited to submit their original manuscript electronically sending e-mail to editor-in-chief (grptian@aut.ac.ir). After peer review, the authors are informed about the reviewers’ comments. The format of the journal can be found on the website. PDF created with pdfFactory Pro trial version www.pdffactory.com A Publication of IAEEE ISSN 1735-7152 Pagination: Amirkabir University Press Price: 50000 Rials Address: Journal of Iranian Association of Electrical and Electronics Engineers North Felestin Ave, No. 39, Bld. 55, 2nd Floor, 14158 Tehran, Iran Tel:( +9821) 64543504 Fax: (+9821) 66406469 E-mail:grptian@aut.ac.ir http://www.iaeee-iran.org PDF created with pdfFactory Pro trial version www.pdffactory.com Editorial Board Electronics Group Control Group H. Ghafoori Fard Amirkabir Univ. of Tech., Tehran, Iran P. Jabedar Maralani Tehran Univ., Tehran, Iran K. Faez Amirkabir Univ. of Tech., Tehran, Iran A. Khaki Sedigh K.N. Toosi Univ. of Tech., Tehran, Iran K. Mafinezhad Ferdowsi Univ., Mashad, Iran S. Khanmohammadi Tabriz Univ., Tabriz, Iran S. Mohajerzadeh Tehran Univ., Tehran, Iran C. Lucas Tehran Univ., Tehran, Iran M.K. Moravvej Tarbiat Modares Univ., Tehran, Iran M. B. Menhaj Amirkabir Univ. of Tech., Tehran, Iran A. Rostami Tabriz Univ., Tabriz, Iran S.K.Y. Nikravesh Amirkabir Univ. of Tech., Tehran, Iran N. Sadati Sharif Univ. of Tech, Tehran, Iran M. Shafiee Amirkabir Univ. of Tech., Tehran, Iran Power Group M. Abedi Amirkabir Univ. of Tech., Tehran, Iran M. Ahmadian Water& Power Univ., Tehran, Iran H. Askarian Abiane Amirkabir Univ. of Tech., Tehran, Iran J. Feiz Tehran Univ., Tehran, Iran A. Agha-Golzadeh Tabriz Univ., Tabriz, Iran G.B. Gharehpetian F. Hojat Kashani Iran Univ. of Science & Tech., Tehran, Iran M. Hakkak Tarbiat Modares Univ., Tehran, Iran M. Hojat Amirkabir Univ. of Tech., Tehran, Iran Energy Ministry Research Center, Tehran, Iran Energy Ministry, Iran M. Kamarei Tehran Univ., Tehran, Iran H. Hosseini Tabriz Univ., Tabriz, Iran H. Oraizi Iran Univ. of Science & Tech., Tehran, Iran M. Moalem Isfahan Univ. of Tech, Isfahan, Iran J. Salehi Sharif Univ. of Tech, Tehran, Iran H. Mohseni Tehran Univ., Tehran, Iran G. Heidari H. Oraee Sharif Univ. of Tech, Tehran, Iran H.A. Shayanfar Iran Univ. of Science & Tech., Tehran, Iran Communications Group Advisory Board M. Abtahi Telecom Research Center, Tehran, Iran F. Rahbar Niroo Consulting Co. Tehran, Iran M. Ahmadipoor Moshanir Co., Iran H. Soltanianzadeh Tehran Univ., Tehran, Iran H. Bakhtiarizadeh Ghods Niroo Co., Iran A.R. Shirani Monenco Co., Tehran, Iran H. Borssi Univ. of Hannover, Germany S. H. H. Sadeghi Amirkabir Univ. of Tech., Tehran, Iran M. Parsa Pars Tableau Co., Iran R. Safabakhsh Amirkabir Univ. of Tech., Tehran, Iran M. Pourrafi Arbani Moshanir Co., Iran M. Fardis Telecom & IT Ministry, Iran G. Hasani Sadr Telecom Education Center, Iran A. Farschtschi Chemnitz Univ. of Tech., Chemnitz, Germany A. Khademzadeh Telecom Resrarch Center, Iran M. Farzaneh Quebec Univ., Quebec, Canada A. Khoei Oremieh Univ., Oremieh, Iran Swiss Federal Inst. of Tech.,Lausanne, Switzerland Mishigan Univ., USA M. Ghazizadeh Power & Water Univ., Tehran, Iran A. Ghanbari Essex Univ., U.K. H. Abachi Monash Univ., Australia F. Rashidi G.H. Roeintan 1 PDF created with pdfFactory Pro trial version www.pdffactory.com Vol. 4 Reviewers Board Dr. Aghagolzadeh Dr. Analoei Dr. Afsharnia Dr. Ehsan Dr. Akbari Dr. Bathaee Dr. Pariz Dr. Parsa Moghaddam Dr. Tamaddon Dr. Javidi Dr. Hossieni Dr. Hossien Zadeh Dr. Dr. Haeri Dr. Khanmohammadi Dr. Rashed Mohsel Dr. Rahim Pour Dr. Radan Dr. Shafiee Dr. Shayesteh Dr. Sameti Dr. Sanaye Pasand Dr. Tarafdar Hagh Dr. Abachi Dr. Askarian Dr. Abedi Dr. Fatehi Eng. Ghasem Zadeh Dr. Gharehpetian Eng. Kazemi Dr. Oloomi Dr. Lesani Dr. Moein Dr. Nabavi Dr. Homayoon Pour 2 PDF created with pdfFactory Pro trial version www.pdffactory.com Comprehensive Electromechanical Analysis of MEMS Variable Gap Capacitors Hooman Nabovati1, Khalil Mafinezhad1,2, Aydin Nabovati3, Hosseyn Keshmiri2 1- Department of Electrical Engineering, Sadjad University, Mashhad, Iran 2- Department of Electrical Engineering, Ferdowsi University, Mashhad, Iran 3- Department of Mechanical Engineering, University of New Brunswick, Fredericton, Canada nabovati@sadjad.ac.ir This paper presents a comprehensive case study on electro-mechanical analysis of MEMS1 variable capacitors. Using the fundamental mechanical and electrical equations, static and dynamic behaviors of the device are studied. The analysis is done for three different modes, namely: dc (static mode), small signal ac and large signal regime. A complete set of equations defining dynamic behavior of the MEMS, and an ac small signal equivalent circuit are presented. The mathematical models are defined and examined by the Matlab Simulink and a complete set of simulation results is reported for various cases separately. The results of this study would be useful in design and analysis of the MEMS based circuits which have some kind of mechanical dynamic action. Some examples of such devices may include VCO2s, frequency modulators, tunable filters and parametric effect circuits. The recent applications of the MEMS technologies in the voltage tunable capacitors are using two kinds of methods, namely: the electro-thermal method and the electrostatic method. In electrostatic method, capacitance is tuned by varying the distance between two parallel flat plates using an electrostatic force caused by a bias voltage. The desired capacitance accomplished by the fast tuning and small space, but the theoretical tuning range is limited to only 150% of the reference value [5]. Among all the MEMS tunable capacitors developed so far, the parallel plate configuration with electrostatic actuation is the most commonly used [4, 5]. Keywords: MEMS, Variable capacitors, Electromechanical modeling 1. Introduction The increasing demand for light weight and miniaturized cell phones, laptops, global positioning system receivers and remote sensors, has spawned an explosive growth in the wireless technology in the recent decade. As the demand for smaller devices and more efficient use of allocated spectral frequency range increases, much more capable implantation technologies are required. In recent years, MEMS technology has begun to be used in wireless communication systems to improve performance of the existing devices based on the structural and operational principles. At present the ultimate miniaturization of super heterodyne transceivers is mainly restricted by the need for numerous off-chip frequency selective passive components such as variable capacitors and inductors. 1 2 In the present work, Electro-mechanical behavior of a MIM3 MEMS variable capacitor has been analytically studied. Dynamic analysis of the structure is useful for studying the transient response of the MEMS. Moreover some applications of the MEMS varactor devices, such as modulators, frequency multipliers and parametric-effect amplifiers are based on the dynamic behavior of the MEMS device. The analysis has been done using the classical electro-mechanical equations and verified and examined by the Matlab modeling capabilities. Beside, a general dynamic model for the MEMS variable capacitors has been presented in dc, small signal and large signal regime separately. All the models have been examined by the Matlab Simulink, and the simulation results are in very good agreement with the analytical calculations. - Micro Electro Mechanical System - Voltage Controlled Oscillator 3 3 - Metal Insulator Metal 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Variable capacitor is a basic component of a voltage controlled oscillator (VCO) used in frequency synthesizer, which generates the local oscillator signals. They can be also used in tunable filters, frequency modulators and parametric effect circuits as well. Recent demonstration of the voltage tunable capacitors comprised of micro-machined, movable metal plates offer substantial improvements over varactor diodes. Compared with the solid state varactors, micro-machined variable capacitors have the advantage of lower loss, lower noise, higher quality factor and potentially greater tuning range [1-4]. Abstract: C= 2. MEMS Varactor Specification Figure (1) shows the studied structure schematically, [6]. The top plate is moving and suspended by four oblique cantilever beams, bottom plate is fixed. Oblique beams act as a spring with higher elastic constant in compare with the normal arms which results in a higher resonance frequency and a broader tenability range. Figure (2) shows the six layers of the structures which are used in the MUMPS4 technology. The capacitor characterization was captured using the electromagnetic simulation of the structure. The full wave electromagnetic simulation of the capacitor was done using the MEM Research EM3DS 6.1 software [7, 8]. After a full wave analysis, the y parameters of the structure were extracted in a wide frequency range for different distances between the capacitor plates. RS = Im ( y12 ) (1) 2π f Rp (2) 1 + Qc2 where, Qc = Rp Cω is the capacitor quality factor, and Rp indicates the MEMS equivalent parallel Resistor, which was calculated using the following equation; 1 Re ( y12 ) Rp = (3) Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 The values of the equivalent circuit elements were calculated for various device dimensions. According to these calculations, a behavioral intrinsic model was extracted which defined the C and RS as a function of the gap distance. At this stage, it was assumed that like a classical parallel plate capacitor, the capacitance is a linear function of the inverse of the plate distance (1/d). Because of parasitic effects, e.g. fringing, the intrinsic capacitor has a 29.5fF offset when 1/d tends to zero. Equation (4) presents the capacitance variation as a function of the gap distance for the structure under study. The parameter extraction algorithm is realized by the MATLAB 7.0 software from the Mathworks. The variation of RS with the gap distance is almost negligible. . C ( fF ) = 29.5 + Fig. 1: Schematics of the MEMS variable capacitor 462.8 d ( µ m) (4) The results verified the structure capacitance can be calculated as a classic parallel plate capacitor. 3. Principles of the Operation As it is shown in figure (3), dynamic analysis of the MEMS variable capacitor is based on the suspended resonator model. The system is described by the following differential equation [9-12], Fig. 2: Profile of The MEMS Layers m A simple equivalent circuit for the structure consists of a MEMS intrinsic capacitor in series with a resistance, which models the structure dissipation. Using the results of full wave electromagnetic analysis, the equivalent circuit parameters were extracted and scaled according to the gap distance; the calculated y parameters in the last step were used for this purpose. The procedure is straightforward and is presented in equations (1) and (2). 4 d 2x dt 2 +β dx + kx = fe ( x, t ) dt where m , β , k , and fe are mass of the movable top plate, damping coefficient, spring constant and electrical force, respectively. These parameters are related to the physical specifications of the structure and for a rectangular plate with 4 oblique cantilever arms, we have, m = ρabt - Multi User MEMS Process 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ (5) 4 PDF created with pdfFactory Pro trial version www.pdffactory.com (6) and, k= 12 EI l3 1 εAV 2 E = CV 2 = 2 2(x 0 − x) (7) where ρ, a, b, t, E, l and I are density of the plate material, length, width and thickness of capacitor plate, Young’s module of the cantilever beam’s material, the cantilever beam length and moment of inertia of the cantilever beam. The values of these parameters are summarized in table (1) for the proposed structure. (9) Electrostatic force between two plates is then calculated as follows: Fe = − ∂E 1 εAV 2 = ∂ (x 0 − x) 2 (x 0 − x) 2 (10) The static mechanical force exerted to the top plate due to the deflection of the four oblique beams, can be calculated using the equation (1); in static analysis it is simplified as: Fm = kx = 1 ε AV 2 12 EI = 3 x 2 2 ( x0 − x) l Using equation (12), the plate displacment can be calculated as a function of the bias voltage and the structure physical parameters. It is important to note that the corresponding value of V at x = x0/3 is the critical point and is called pull-in voltage. If V is increased beyond this limit, no equilibrium can be achieved and the top plate will move toward the bottom one until they snap into contact; this phenomenon is called the pull-in effect. Therefore according to equation (8), theoretically the maximum capacitance of the variable capacitor is 150% of its initial value at V=0. Figure (4) shows the distance of two plates versus the applied bias voltage. The initial distance was assumed to be equal to 1.2μm and the pull-in effect occurred in 2.88V; at this point the distance between two plates reached the critical value of 0.8μm. Table 1: Physical parameters for the capacitor 2.32 200 Physical Specification b t l E (µm) (µm) (µm) (GPa) 200 0.5 42 170 I (µm3) 2.9×107 4. DC Analysis In static mode, when a DC bias voltage is applied to the plates, an electrostatic force will be generated between the two plates which forces the top plate to move toward the fixed one, until equilibrium between the electrostatic and mechanical forces -exerted by the oblique arms which act as four springs- is achieved. According to the previous chapter, neglecting the fringe effect, the capacitance of the structure, which is formed between two plates, can be written as: C=ε A x0 − x (12) (8) where x, x0, A, ε are the top plate displacement, initial gap size, plate surface area and permittivity of air gap. x0x is the minimum gap size between two plates. When a DC bias voltage, V, is applied, the stored electrical energy in the capacitor is calculated as follows: Fig. 4: displacement of the plates verses bias voltage 5 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 The damping coefficient, β , expresses the energy dissipation in the system by airflow force, squeeze force and internal friction. It has been related to the mechanical quality factor, Q, and will be discussed in next chapters. a (µm) (11) Regarding static equilibrium between the electrostatic and mechanical forces, one can write: Fig. 3: dynamic mechanical model for MEMS variable capacitor ρ (g/cm3) 12 EI x l3 i ≈ Cv&ac +Vc& = jC ωvâc + j ωvâc kx 20 C 2V 2 + j ω bx 20 C 2V 2 − ω 2 mx 20 C 2V 2 5. Small Signal Analysis In the linear analysis or small signal regime, it was assume the displacement, x, was small compared to the initial gap distance. The structure was driven by a small ac voltage vac, superimposed on the dc bias V, which induced the small displacement variations. The dynamics of the resonator was approximately determined by the equation (5), where fe, the small signal electrostatic force expressed by the following equation [13-16], εAVvac  ∂f  v  f e =  e  vac = = 2Fe  ac  2 x0  ∂V   V  (20) An equivalent circuit model can be defined for the structure [12]. The equivalent circuit model is presented in figure (5), and its admittance can be determined as follows: Y = jωC0 + (13) 1 jω L1 + R1 + 1 jωC1 (21) In this equation, Fe is the static electric force and vac was assumed to be a small signal sine voltage so the equation (5) can be solved to find the displacement in the phasor form, as follows: x̂ = 2Fe vˆ ac V k + jωb − mω2 (14) Fig. 5: Equivalent circuit model for small signal analysis The structure current could be considered as a nonlinear capacitor, in the form of: Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 d dc dv i = ( cv ) = ⋅ v + c ⋅ dt dt dt Circuit parameters can then be calculated by the analogy to the equivalent circuit equations. Effect of the mechanical properties of the structure is shown in the following equations. (15) where c indicates the time dependant nonlinear capacitor. Equation (8) can be rewritten in differential form as; dc dc dx εA = × ≈ jω 2 xˆ dt dx dt x0 (16) bx0 2 C 2V 2 mx 2 L1 = 2 0 2 CV C0 = C R1 = where x^ is the phasor of the displacement. Considering small variation in v and c, we can replace c and v by the following equations, v = V + vac ≈ V (17) (18) where c(t) indicates the variations in structure capacitance and C is the static MEMS capacitance as, C= εA x0 ω0 = (19) Therefore the MEMS current can be calculated as follows: 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ (22) (23) (24) (25) In the present study the mechanical quality factor and the dc bias voltage were assumed to be 20 and 1V. Using these values, the equivalent circuit parameters were calculated as 10.5fF, 3.09GΩ, 767H and 295fF for C1, R1, L1 and C0, respectively. The resonance frequency and the electro-mechanical quality factor of the MEMS are defined as, and; c = C + c(t) ≈ C C 2V 2 kx0 2 C1 = Q= 1 k = m L1C1 1 ωL ωm = 0 1= 0 ω0 R1C1 R1 b 6 PDF created with pdfFactory Pro trial version www.pdffactory.com (26) (27) When the mechanical parameters of the structure are fully determined, there is a straightforward procedure to find out the equivalent circuit model. An alternative routine method is to use the electromagnetic simulation. In this method the structure geometry and its electromagnetic factors are defined in a full wave electromagnetic simulator, e.g. the Ansoft HFSS or the MEM Research EM3DS. The simulation results would be small signal parameters of the network, such as S or Y parameters. These parameters can be examined through a wide frequency range and their resonance frequency and quality factor could be compared with the electro-mechanical analysis. The equivalent circuit parameters can then be determined directly as summarized in following equations, 1 Re( y12 ) ω =ω 1 C1 ≈ ωo QR1 1 L1 ≈ C1ωo2 y Co ≈ 12 ω ω >>ω current (nA) 15 analytical results 5 0 10 20 30 40 50 60 70 frequency (KHz) 80 90 100 Figure (7) depicts a comparison between the current calculated from the electrical equivalent circuit and the current obtained from the analytical solution using equation (15) over a wide frequency range of 10-100 kHz. The Electrical simulation results are in very good agreement with the analytical results. Since the structure current is small, the effect of the MEMS series resistance was neglected. (28) o (29) (30) 6. Large Signal Analysis When a large signal is applied to the MEMS, the structure acts completely as a nonlinear time variant capacitor. It is useful to investigate this behavior because of its applications in the parametric effect circuits, [17]. With increasing the applied voltage, the structure current can be high enough to make a considerable voltage drop on any serial resistor including the source impedance and the MEMS series resistor. If va indicates the applied voltage and Rs stands for the total serial resistance, by using the equation (15) voltage of the MEMS can be calculated by the following equation, (31) o v = va − Rs d (cv) dt (32) As it was mentioned before, in this regime the MEMS behaves like a nonlinear time variant capacitor; therefore the electrical stored energy is calculated as, 400 200mV 100mV E (t ) = ∫ vidt = ∫ v 350 capacitance (fF) circuit analysis Fig. 7: Capacitor current with 100mV sinusoidal excitation versus frequency (results of analytical calculations and circuit analysis) The small signal electro-mechanical model of the structure was simulated in the Matlab Simulink environment. In this simulation, sinusoidal signals of the amplitude of 100mV and 200 mV were applied to the MEMS structure. It could be seen that if the exerted signal amplitude was less than 140mV, it was restricting the displacement of the plates to less than 10% of xo. Figure (6) represents the MEMS capacitance. It can be seen that in small signal analysis, capacitance variation is almost a sinusoidal function. Using the fast Fourier transform to determine the capacitor variation spectrum resulted that the capacitance distortion was almost insignificant. The frequency of input signal was selected as 59 KHz which was equal to the resonance frequency of the structure. 295 d (cv) 3 dt = cv2 dt 2 (33) and the electrical force can be determined as, 250 200 0 10 fe = 100 200 300 400 dE (t ) dx (34) using equation (8), the electrical force is presented in the following form: 500 time (us) Fig. 6: Capacitance variation versus time with 100200mV small signal excitation 7 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 R1 ≈ 20 3 εA v2 2 ( x0 − x )2 50 (35) 40 capacitance (fF) fe = The large signal model can be defined using equations (32), (35) and the MEMS dynamic mechanical equation, equation (5). The model has been implemented in the Matlab Simulink environment. For the time domain transient analysis, the input voltage was supposed to be a sinusoidal voltage of 1V amplitude and frequency of 59 kHz. 0 0 100 150 200 frequency (KHz) 250 300 7. Conclusion A complete case study on the electro-mechanical behavior of MEMS variable gap capacitors was presented. The device modeling was captured in three different modes; namely: dc, small signal ac and large signal stimulation. For each mode, a comprehensive set of electro-mechanical equations were presented which were implemented in the Matlab Simulink environment. An ac equivalent circuit model, was also elaborated which described the device electro-mechanical dynamic behavior according to its geometry and the physical characteristics of the proposed structure. The results of this study are useful in design and analysis of the MEMS based circuits which include mechanical dynamic behavior; e.g. VCOs, frequency modulators, tunable filters and parametric effect circuits n (36) n Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Determining c(t) from the electromechanical simulations, the coefficients an and bn or γn and φn were evaluated by numerical methods. The capacitor variation spectrum is presented in figure (9). Using these calculations, γ1 and γ2 were evaluated to be equal to 33fF and 43fF for this level of excitation. Acknowledgement The authors would like to thank Ms. Gelareh-Veysi for her assistance and Professor Marco Farina from the MEM Research for his guidance and providing EM3DS tool to carry out this work. The supports of the Iran Telecommunication Research Center and the Sadjad Research Center are also acknowledged. 440 420 400 capacitance (fF) 50 Fig. 9: capacitance variation spectrum c (t ) = a0 + ∑ an cos(nωt ) + bn sin(nωt ) = 380 References 360 [1] C.T.Nguyen, “Communication Application of Miroelectromechanical Systems”, Proceedings, 1998 Sensors Expo, San Jose, CA, pp. 447-455, May 1998. [2] L.P.B. Katehi, J.F. Harvey, E. Brown, “MEMS and Si Micromachined Circuits for High-Frequency Applications”, IEEE Transaction on Microwave Theory and Techniques, pp. 858-866, Vol. 50, No. 3, March 2002. [3] H.J. De Los Santos, RF MEMS Circuit Design, Artech House, Boston, 2002. [4] N. Bushyager, M.M. Tentzeris, M.M. Gatewood, L. DeNatale, “A novel adaptive approach to modeling MEMS tunable capacitors using MRTD and FDTD techniques”, Microwave Symposium Digest, 2001 IEEE MTT-S International, pp. 2003 –2006, Vol. 3 , 20-25 May 2001. [5] J. Zou, C. Liu, J. Schutt-Aine, J. Chen, S. Kang, “Development of a wide tuning range MEMS tunable capacitor for wireless communication systems”, Electron 340 320 300 280 0 20 10 Figure (8) shows the structure capacitance as a function of time using the large signal analysis. It can be seen that the MEMS capacitance is a nonlinear function of the input signal and does not vary sinusoidal. To describe the nonlinear behavior of the device, the Fourier expansion in the form of equation (15) was used to describe the capacitance as follows: a 0 + ∑ γ n cos (ωt + ϕn ) 30 100 200 300 400 500 time (us) Fig. 8: capacitance variation when a 2V sinusoidal large excitation is applied 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 8 PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Devices Meeting, IEDM Technical Digest International, pp. 403-406, Dec. 2000. [6] H. Nabovati, K. Mafinezhad, H. Keshmiri, A. Nabovati, “Design and Simulation of an Oblique Suspender MEMS Variable Capacitor”, Scientia Iranica Journal, Vol. 12, No 1, 2005. [7] M. Farina, T. Rozzi, “A 3-D integral equation-based approach to the analysis of real-life MICs application to microelectro-mechanical systems”, IEEE transaction on microwave theory and techniques, Vol. 49, No. 12, , pp. 2235-2240, December 2001. [8] EM3DS user manual, Release 1.5, MEM Research, May 2003. [9] Y. Kim, S.G. Lee, S. Park, “Design of the Two-Movable Plate Type MEMS Voltage Tunable Capacitor” Technical proceeding of 2002 of the 2002 international conference on modeling and simulation of Microsystems, Nanotech, 2002. [10] F.P. Beer and E.R. Johnston, Mechanics of Materials, McGraw Hill, 1992. [11] R.N. Simons, Coplanar waveguide circuits, components and systems, New York, NY, John Wiley & Sons, 2001. [12] H. Eskelinen, P. Eskelinen, Microwave component mechanics, Norwood MA, Artech House, 2003. [13] J.P. Raskin, A.R. Brown, T. Khuri-Yakub, G.M. Rebeiz, “A novel parametric effect MEMS amplifier”, Journal of microelectromechanical systems, Vol. 9, No. 4, pp. 528-536, Dec 2000. [14] E.M. Abdel-Rahman, A.H. Nayfeh, M.I. Younis, “Dynamics of an electrically actuated resonant microsensor”, International Conference on MEMS, NANO and Smart Systems Proceedings, pp. 188-196, July 2003. [15] C. Mandelbaum, S. Cases, D. Bensaude, L. Basteres, P. Nachtergaele, “Behavioral Modeling and Simulation of Micromechanical Resonator for Communications Applications”, IEEE Conference on Design, Test, Integration and Packaging of MEMS and MOEM, pp. 2126, May 2003. [16] A. Cruaul, P. Nicole, G. Lissorgues, C. Tassed, “Influence of RF signal power on tunable MEMS capacitors”, IEEE 33rd European Microwave Conference, pp. 663-666, 2003. [17] H. Nabovati, K. Mafinezhad, H. Keshmiri, “Design and Simulation of Low Noise Upconverter Using MEMS Variable Capacitor”, ICEE2007 Proceeding, 2007. 9 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Combined MEG and fMRI Model Abbas Babajani-Feremi,1Hamid Soltanian-Zadeh,1,2 1- Image Analysis Lab., Radiology Department, Henry Ford Hospital, Detroit, MI 48202, USA 2- Control and Intelligent Processing Center of Excellence, Electrical and Computer Engineering Department, University of Tehran, Tehran 14395-515, Iran In recent years, numerous efforts have been directed at multimodal data fusion. Electroencephalography (EEG), magnetoencephalography (MEG), and functional Magnetic Resonance Imaging (fMRI) are innovative functional brain imaging techniques. The spatiotemporal resolution of these techniques is different. EEG and MEG have good temporal resolutions in the order of millisecond, but their spatial resolutions are poor due to ill-posedness of the inverse solution. On the other hand, fMRI has good spatial resolution in the order of millimeter but poor temporal resolution due to the limited rates of the image acquisition methods and change in the hemodynamic response. Since M/EEG and fMRI are different views of a common source (neural activity), their integrated analysis should improve the overall spatiotemporal resolution. Several sophisticated methods have been introduced for M/EEG and fMRI combined analysis [9,1,25,30] in order to extract as much information as possible using a data-driven strategy (the authors refer to them as top-down methods). Although integrated M/EEG and fMRI model (bottom-up modeling) is an active area of research, there is limited work about it in the literature [5,37,38,40]. We introduce an integrated model [5] based on the physiological principles of the cortical minicolumns and their connections. In the integrated model, we use our proposed extended neural mass (ENM) model to generate MEG/fMRI signals. In this model, MEG signals are generated by synaptic activations of the pyramidal cells and sub-sequential currents in minicolumns that have been collectively modeled as an equivalent current dipole (ECD). We extract the fMRI signal from the proposed extended neural mass model by introducing a relationship between the stimulus and the overall neural activity and using it as the input of the EBM. By comparing the simulation results with the experimental results, we validate the proposed model. Abstract: Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 An integrated modelmagnetoencephalography (MEG) and functional Magnetic Resonance Imaging (fMRI) is proposed. In the proposed model, MEG and fMRI outputs are related to the corresponding aspects of neural activities in a voxel. Post synaptic potentials (PSPs) and action potentials (APs) are two main signals generated by neural activities. In the model, both of MEG and fMRI are related to the PSPs without any correlation to the APs. Each PSP is modeled by the direction and strength of its current flow, which are treated as random variables. The overall neural activity in each voxel is used for equivalent current dipole in MEG and as input of the extended Balloon model for producing Blood Oxygen Level Dependent (BOLD) signal in fMRI. The proposed model shows possibility of detecting activation by fMRI in a voxel while the voxel is silent for MEG and vice versa. This is according to the fact that fMRI signal reflects the sum of PSPs’ strengths (independent of their directions) but MEG signal reflects the vector sum of the PSPs (which depends on their directions). The model also shows that the crosstalk from neural activities of adjacent voxels in fMRI and properties of the inverse problem in MEG generate different spatial responses in the two modalities. We use real auditory MEG and Fmri datasets from 2 normal subjects to estimate the parameters of the model. Goodness of the real data our model shows the possibility of using the proposed model to simulate realistic datasets. Keywords:Blood Oxygen Level Dependent (BOLD); Equivalent Current Dipole (ECD); Post Synaptic Potential (PSP); Action Potential (AP); extended Balloon model. 1- Introduction In another work, David et al. in [10 ] propose an extended neural mass model based on the 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ Janssens model [21] to generate EEG/MEG data. They consider multiple cortical areas with Bottomup, Top-down and Lateral connections between 10 PDF created with pdfFactory Pro trial version www.pdffactory.com use PSP instead of PSC and also the direction of PSC is not important for fMRI, we use PSP throughout this paper. The organization of the rest of the paper is as follows. The background material and details of the proposed model are described in Section II. Analysis of proposed model is presented and discussed in Section III. Estimation of the parameters of the model using real auditory datasets is presented in Section IV. Conclusions are given in Section V. using real auditory and visual data [11]. It is noticeable that although the model proposed in [10] is based on and neural mass, but their model is not an integrated EEG/MEG and fMRI model. Sotero and Trujillo-Barreto propose an integrated EEG/fMRI model based on neural mass [40]. They use Jansen’s model as the base of their neural mass model and derive the relationship between inhibitory and excitatory activities with the resultant BOLD and EEG signals. The effects of the inhibitory and excitatory activities on the resultant BOLD signal are different in their model. They consider the neural mass model in each voxel which describes the neuronal dynamics within the voxel. By defining short-range interactions (connection within an area) and long-range interactions (inter area connection), they generate EEG and fMRI signals of the whole brain. In the integrated model proposed by Riera, et al. [36,38], a two-dimensional autoregressive model with exogenous variables (ARx) is proposed to describe the relationships between synaptic activity and hemodynamics. They use a static nonlinear function to describe the electro-vascular coupling through a flow-inducing signal. In this work, a linear relationship between cerebral blood flow (CBF) and Blood Oxygen Level Dependent (BOLD) is assumed which is not generally valid [7]. In this paper, we propose an integrated model totally different from the integrated model in [38]and does not have its limitation. As mentioned in the previous paragraph, the main limitation of the Riera’s model is related to this fact that considering linear relationship between CBF and the BOLD signal does not generally correct. The nonlinear relationships among CBF, cerebral blood volume (CBV), and the resultant BOLD signal are formulated in Balloon model in [7]. Friston and his colleagues proposed the extended Balloon model [13] and added a model of CBF changes to the Balloon model, based on synaptic activation and CBF autoregulation. We use the extended Balloon model in our proposed model to remove the limitation of the Riera’s model. The proposed model is consistent with the fact that fMRI signal reflects the sum of PSPs’ strengths (independent of their directions) but MEG signal reflects the vector sum of the PSPs (which depends on their directions). The model also shows that the crosstalk from neural activities of adjacent voxels in fMRI and properties of the inverse problem in MEG generate different spatial responses in the two modalities. These are illustrated by the simulation studies in this paper. For validation of the proposed model in real conditions, we use real auditory MEG and fMRI datasets from 2 normal subjects to estimate the parameters of the model. Goodness of fit of the real data with our model suggests that the proposed model can be used in real conditions. It should be noted that whenever we refer to the direction of the PSP, it is scientifically better to use PSC (postsynaptic current) instead of PSP (postsynaptic potential). However, since many of the MEG literature 2. Proposed Model Combined MEG/fMRI Neuron is the principal building block of the brain. The overall activities of adjacent neurons in a region can be detected by MEG or fMRI. In the proposed model, the activities of neurons in a voxel are used for constructing MEG and fMRI signals. A voxel in the order of 1 mm³ contains approximately 105 pyramidal cells and thousands of synapses per neuron [15]. Activity of each neuron starts with activities of its synapses that produce PSPs. The overall activities of synapses may produce action potentials (APs). PSPs and APs are two main indices for showing neural activities. MEG and fMRI are related to neural activities and thus to the PSPs and/or the APs. The proposed integrated model is constructed based on the principle that PSPs are the main link between the two techniques. We construct a stochastic model for PSPs so that each parameter (like direction and strength of PSPs) has a probability density function (pdf). The input of the model is the waveform of the external stimulation (Fig. 1). The number of PSPs at each time is constructed with a stochastic model according to the waveform of the input stimulus. The MEG signal is produced according to the pdfs of the direction and strength of the PSPs. The BOLD signal only depends on the overall strengths of PSPs, which is the input of the extended Balloon model for producing the BOLD signal. The overview of the relevant previous work and physiological principles underlying the proposed integrated model is presented in the following subsection before introducing the model. 2.1. Physiological Bases of MEG and FMRI Compartments of a neuron are the soma, the dendrites, and the axon. The soma (the cell body) contains the nucleus and much of metabolic machinery. The stimuli from other cells are received by synapses on the dendrites. The axon is a single long fiber that carries the nerve impulse away from the soma to other cells (see Fig. 2). There are typically thousands of synapses (connections) from other neurons in the dendrites and soma. The intracellular potential increases by input through the excitatory synapses called excitatory post synaptic potential (EPSP), but decreases by inhibitory input called inhibitory post synaptic potential (IPSP). When the potential at the axon hillock reaches a certain 11 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 them. Then, they estimate parameters of their model Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 implies that it is impossible to conclude whether the spike activity (or AP) in a given brain region is increased or decreased on the basis of increases in CBF (and consequently the BOLD signal). They report that the CBF or BOLD increases when the LFP is increased and the relation between LFP and CBF is an increasing function that may be nonlinear. This also indicates that PSPs affect the BOLD signal. In addition to the above, we can verify the relation between the BOLD and the AP or the PSP with a structural neurovascular coupling view. The average activity in a given region largely correlates with the density of the vascular network in the region. Most investigators report high spatial correlations between vascular density and the number of synapses rather than the number of neurons [28]. The human cortical vascular network can be subdivided into four layers parallel to the surface. The vascularization of Lamina IVc (layer 4, part c) is the highest and that of Lamina I (layer 1) is the lowest. The average IVc/I ratio across animals is approximately 3. On the other hand, in the striate cortex of macaque the IVc/I ratio of synaptic and neurons densities are 2.43 and 78.8, respectively [28]. This implies that the vascular density is correlated with the density of perisynaptic elements (sources of PSPs) rather than that of neuronal somata (sources of APs). Relation between BOLD and PSP can be verified from brain energy metabolism. Attwell and Iadecola [3] reported the allotment of energy consumption in primate for post synaptic potential, pre synaptic terminals, action potential, glia and resting potential as 75%, 7%, 10%, 6% and 2%, respectively. Thus, the main part of energy is consumed by PSP. Since the blood flow increases in proportion to the energy consumption [17], PSP has the highest correlation with BOLD signal compared to the others. EPSP and IPSP have different polarizations and therefore canceling effects for MEG. Do they have same effect on the BOLD signal in fMRI? Experimental study of Caesar and colleagues is one of the newest studies that answer this question [8]. They performed experiments in 10 male Wistar rats and recorded the single-unit spiking activities (APs) and local extracellular synaptic field potentials (LFPs) of Purkinje cells in the cerebellar cortex with a single electrode at a depth of 300–600 μm of vermis segments 5 and 6. They stimulated the cerebellar climbing fibers (CF; excitatory) and parallel fibers (PF; inhibitory) alone and in combination and simultaneously recorded the rCBF in the Purkinje cells. They reported that stimulation of the excitatory climbing fiber (EPSP) or inhibitory parallel fibers (IPSP) increases the CBF amplitude and there is no any difference between EPSP and IPSP in this regard. Thus, they concluded that the EPSP and IPSP have similar effects on the BOLD signal. In summary, considering the above facts and experimental studies, we conclude that both of equivalent current dipole (ECD) in MEG and BOLD signal in fMRI are mainly correlated to the PSPs and it is reasonable to ignore the effect of APs. The BOLD is an increasing but threshold level, the neuron fires an action potential (AP). The peak value of each PSP is in the order of 10 mV and has a duration of approximately 2-10 ms. For the AP, the peak value is in the order of 100 mV and its duration is approximately 1 ms [15]. The relationship between PSPs and APs with MEG and BOLD signals is inferred in this section. First, we deal with the MEG signal. Both action and synaptic currents generate magnetic fields. Approximately, the action potential can be considered as two opposite oriented current dipoles, which form a current quadrupole. The magnetic field produced by a quadrupole of AP decreases as 1/r³ where r is the distance between dipole and detection sensor. However, the magnetic field produced by a PSP is dipolar and decreases as 1/r². Moreover, longer duration of a PSP (tens of ms) allows more effective temporal summation of neighboring currents than with the 1 ms lasting APs. Thus, the MEG signals are likely produced by the synaptic current flow [15]. It is also reported in other papers [4,35] that PSP is the main source of the MEG signal. Thus, we only consider the effect of PSP on the MEG signal and ignore the effect of AP. Now, the relationship between the BOLD signal and the neural activities (PSPs and/or APs) is discussed. This relationship has been addressed experimentally in a number of studies [16,27,28,29,36,41]. Logothetis and colleagues have done many experimental studies for illustrating the relationship between BOLD signal and PSPs (synaptic activities) or APs (spike activities) [27,28,29]. They use especial instruments for high spatiotemporal resolution fMRI. They achieve the resolution of 75×150×300 μm³ which reflects the activity of as few as 600-1200 cortical neurons. They simultaneously gather BOLD signal and neural electrical activities with microelectrode and then separate two types of neural signals (MUA and LFP) based on their different frequency characteristics. The Multiple Unit spiking Activities (MUAs) are a weighted sum of the extracellular APs and the Local Field Potentials (LFPs) are the weighted average of synchronized dendro– somatic components of the synaptic signals. Thus, MUAs and LFPs are similar to the APs and PSPs, respectively. In an experimental study, Logothetis and colleagues did the experiment on 10 monkeys with elicited visual cortical responses to a checkerboard pattern using a block design [29]. They saw that although MUA rises after activation, but it returns to baseline after 2-4 sec. Conversely, LFP was always elevated for the duration of the stimulus, similar to the BOLD signal. Both BOLD and LFP increased when the contrast of checkerboard stimuli increased, but the relation between BOLD and LFP remained nonlinear. They concluded that the LFPs were the only neural signals associated with the BOLD response. Lauritzen and Gold have summarized results form several experimental studies [24]. They used the rat cerebellar cortex for detailed studies of the relationship among AP, synaptic activity, and changes in CBF. Their final result 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 12 PDF created with pdfFactory Pro trial version www.pdffactory.com nonlinear function of PSPs. Although EPSP and IPSP have opposite effects in MEG, both of them have the same increasing effect on BOLD signal. We have used these facts for constructing the proposed model (see below). The proposed model relates the MEG and fMRI signals in an active voxel of the brain. There are a huge number of neurons and synapses in a voxel. If during external stimulation a voxel belongs to the active region of the brain, there are many PSPs and APs in this voxel whose numbers and strengths show the rate of neural activities. According to our discussion in the previous section, we consider the PSPs as the single link between MEG and fMRI in the proposed model and ignore the effects of APs. The number and strengths of PSPs show the overall neural activities that produce MEG signal and change the blood flow for producing BOLD signal as shown in Fig. 1. The proposed model contains multiple blocks, which we will discuss in the following subsections. 2.3. PSP Production Mechanism In each voxel, there is a network of neurons that have many interconnections (by synapses) and may have inputs from peripheral nerves or neurons in the neighboring voxels. After external stimulation, the activation in a voxel will start from activation of neurons that have peripheral nerve inputs or input connections with active neurons of another voxel. Gradually the number of active PSPs (also active neurons) in a voxel increases to its maximum number when most of the interconnection synapses are activated. After this time, it is logical to say that the number of active PSPs does not almost change during the stimulation and this maximum number depends on the strength of the external stimulation. Block 1 of Fig. 1 implements the relationship between the external stimulus and the number of active PSPs. The number of active PSPs at each time point is assumed as the output of a linear system whose input is the external stimulus, similar to the linear model relating the external stimulus to the evoked transient in [37]. r ∑α k k =0 d k N (t ) = N ss Stm(t − t af ) dt k (1) where taf is the delay due to different relay processes in the long afferent pathways. The first order linear model with α0 = 1 and α1 = 50 ms is used as the simplest linear model. For block design, Stm(.) is the unit function and Nss is the steady state value of the N(t). For event related design, Stm(.) is the Dirac delta function and Nss / α1 is the peak value of N(t). Physiological noise is modeled by ε(t) in Fig. 1 and represents the number of active PSPs, which is not related to the external stimulus and is related 2.4. Extracting Relationship Between fMRI and PSPs The second block of the model (Fig. 1) shows the relationship between different aspects of PSPs and MEG or fMRI. Each PSP is like a small current dipole, a vector with direction and magnitude. Both direction and magnitude of this vector are important for MEG, but only magnitude is important for fMRI. The magnitude or strength of each PSP depends on the kind of neuron, synapse, and dendrite parameters. In addition, direction of the current dipole for each PSP depends on the shape and structure of dendrite trees. Since there are no deterministic models for these parameters, we consider them as random variables in the proposed model. The kind of PSP (IPSP or EPSP) is important for MEG because of their opposite polarities, but is not important for fMRI according to our previous discussions. The total number and ratio of excitatory and inhibitory synapses are different in different regions of the brain, but the number of excitatory synapses generally is more than inhibitory synapses [14]. The single pyramidal cell has about 12 mm dendrites and receives around 30,000 excitatory and 1,700 inhibitory inputs in rat hippocampal CA1 area [32]. We consider the ratio of IPSP number to all PSP as a parameter in our model and change it for verifying its effect on MEG. The relationships between produced PSPs and MEG or fMRI signals are illustrated in block 3 of Fig. 1. We start discussing the fMRI part of the model followed by the MEG part. The first block in the fMRI part of the model is “Crosstalk from Neural Activities of Adjacent Voxels.” Neural activities in a voxel change the blood flow of this voxel and also can affect the blood flow of the adjacent voxels. In an experimental study on rats, it is reported that the diameter of local arterioles (at the stimulation site) increases 26% and local blood flow increases 55% while in an up stream region with a distance of about 2 mm from the stimulation site, the diameter of arterioles increases 8.7% and blood flow increases 15% [20]. In another experimental study on rats with electrical stimulation of the cerebellar parallel fiber, the local CBF at the stimulation site changes 55% while at sites with 4.5 mm horizontal and 1 mm vertical distance from the stimulation site, CBF changes 13% and 11%, respectively [19]. Thus, the synaptic activities in a voxel can affect the CBF and resultant BOLD signal in adjacent voxels. The Gaussian spatial smoothing function is used for modeling the spatial crosstalk of BOLD signal in our proposed model. We consider the effective synaptic activities as below: (2) r = ( x, y, z )  u e (r ; t ) = G (r ) ∗ u (r ; t );  1 x2 y2 y2 G (r ) = exp( − 2 − 2 − 2 ) 3  2σ x 2σ y 2σ y σ x σ y σ z ( 2π) 2  13 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 2.2. Details of Proposed Model to the spontaneous activity. It can be modeled as a Poisson process. Balloon model) proportional to the total consumed energy by the PSPs. We need to solve the Hodgkin-Huxley (HH) equation for computing the voltage, current and energy of PSP. The PSP’s voltage is modeled by multiplying a constant peak value ∆V and a normalized waveform ϕ (t ) [Almeida and Stetter, 2002; Larkum et al., 1998]: where u(r ; t) is synaptic activities in the voxel located at r(x,y,z), G(r ) is a 3D Gaussian kern and “*” shows 3D convolution. σ in (2) is the only fMRI parameter in the model that can show the difference between fMRI and MEG spatial responses as discussed in the next section. We use the reported data from [19,20] and estimate σ with curve fitting of the reported data into a 3D Gaussian function. The estimated σ is 2.6 mm in the horizontal direction (axial slice) and 0.7 mm in the vertical direction (normal to axial slice) of the brain. The “extended Balloon model” is used as the main mechanism for relating PSPs as the neural activity input and BOLD signal as the output. The Balloon model was originally proposed by Buxton and colleagues [Buxton et al., 1998]. In this model, a model of oxygen exchange is linked to the venous dilation processes due to CBF variations, and the BOLD signal is derived from the total deoxyhemoglobin content within a voxel. Friston and colleagues [13] added a model of CBF changes to this Balloon model, based on synaptic activation and CBF autoregulation. We use this extended Balloon model in our proposed model. In the extended Balloon model, the neural activity u(t) is related to the BOLD signal y(t) by the following equations:  s& = εu ( t ) − s / τs − (fin − 1) / τ f (3) & fin = s Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007   E ( fin , E0 ) = 1 − (1 − E 0 )1 / fin  1/ α τ 0 v& = fin − fout (v) , fout = v  E ( fin , E0 ) − fout (v)q / v τ 0 q& = fin E0  7 E 0 (1 − q ) + 2(1 − q / v) +  y( t ) = V0   ( 2E 0 − 0.2)(1 − v)  − ϕ (t ) = te ( t −τ PSP ) τ PSP (6) τ PSP V (t ) = ∆Vϕ (t ) (7) where τ PSP is time constant of ϕ (t ) and is considered as a random variable with truncated Gaussian distribution τ PSP ~ TN (2,1 ; 0, ∞) ms according to the data reported in [12]. The truncated Gaussian variable denoted by x ~ TN(μ,σ;a,b) is a variable whose probability for x<a or x >b is zero and its pdf is like the Gaussian distribution (except for a scalar normalization) in the interval x ∈ [ a , b] with mean μ and standard deviation σ. The consumed energy by PSP is found by: ∞ E = ∫ V (t ).I (t )dt (8) 0 where I( t) is postsynaptic current. For simplicity, we use a constant value for I(t) and according to (6)(8) get: (4) E = Iτ PSP ∆V (9) (5) If N(t) PSPs fire at time t, the consumed energy for each of them is represented by (9). The neural activity should be proportional to the sum of the consumed energies. Therefore, the following equation relates the synaptic activity (or neural activity) u(t) to the parameters of the PSPs: where V0 is resting blood volume fraction, E 0 is resting net oxygen extraction fraction by the capillary bed, v is normalized venous volume, q is normalized total deoxyhemoglobin voxel content, f in and f out are inflow and outflow from the venous compartment, s is some flow inducing signal, and there are four fixed parameters that must be estimated. The mean values of these parameters are ε = 0.5, τ s = 0.8, τ f = 0.4, τ 0 = 1, α = N (t ) N (t ) N (t )  k k E = E = I τ ∆ V ∝ τ PSP ∆Vk  ∑ k ∑ PSP k ∑ k =1 k =1 k =1 (10)  N (t ) k  u (t ) ∝ ∑τ PSP ∆Vk  k =1 0.2. We consider V0 = 0.02 and E 0 = 0.8 in our simulations according to [13]. Input of the extended Balloon model is the overall synaptic activities which are linearly related to the regional cerebral blood flow. To find a relationship between synaptic activity and PSPs, we note the following. Each PSP consumes a little energy and causes a small change in the blood flow. Thus, it is logical to consider synaptic activity (as input of the extended 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ The temporal resolution of MEG is in the order of ms and so we choose the sampling time of 1 ms for synaptic activities in our model. Thus, the sampling time of BOLD output in the Balloon model is 1 ms. With conventional imaging systems, the temporal resolution of the BOLD signal is in the order of seconds. The output of the Balloon model is down sampled and shown by “Down 14 PDF created with pdfFactory Pro trial version www.pdffactory.com Sampling” box in Fig. 1. We choose the rate of 1 ms/2 s down sampling in the simulations. thus, q n acts as a noise for MEG sensors having no correlation with the stimulation. On the other hand, the E[ q p ] is nonzero and can be sensed by the MEG sensors 2.5. Extracting Relationship between MEG and PSPs as a signal. When σ → ∞ in (13), distribution of θ tends to uniform distribution and then E[ q p ] → 0 . This From a distance, the PSP looks like a current dipole oriented along the dendrite. Approximately, the current dipole according to PSP is [15]: (11) generates a strong signal highly correlated with the stimulation and detectable by the MEG sensors. If N PSPs of the pyramidal cells fire at time t, then the ECD from the sum of their activities according to (12) is: (12) where d is the diameter of the dendrite, σ in is the N r r q (t ) = ∑ wk β k ∆Vkϕ k (t ) ⋅ nk intracellular conductivity, ∆V is change of voltage r during PSP and n is the unit vector showing current dipole orientation along the dendrite. Using the typical −1 where wk is +1 for EPSP and -1 for IPSP, ∆Vk shows −1 values d = 1 μm, σ in = 1 Ω m and ∆V = 25 mV from [Hämäläinen et al., 1993], we calculate q ≈ 20 fAm for a single PSP. There are many types of neurons with different shapes and sizes of dendritic tree (Fig. 3). The pyramidal cells (Figs. 1 and 3-d) are relatively large. Their apical dendrites are parallel to each other and tend to be perpendicular to the cortical surface [15]. Since the apical dendrites of pyramidal cells are parallel, their current dipoles of PSPs can be summed effectively. The dendrites of Purkinje cells (Fig. 3-e) are not unidirectional and so the current dipoles at different branches of their dendrites may cancel each other. We consider a random variable for the direction of current dipoles (of PSP) for modeling different kinds of neurons and dendrite tree structures. We define “reference vector” as a vector that is perpendicular to the cortical surface in each voxel. The angle between the reference vector and each current dipole (θ) is considered as a truncated Gaussian random variable with the following pdf: 2 2σ2 the peak value of PSP, β k is a coefficient according to (12) that models parameters of the kth synapse and its neighboring dendrite and ϕ k (t ) is unitary peak waveform for the kth PSP at time t according to (6). For modeling different kinds of synapses, we consider σ erf ( e k π βk and ∆Vk as random variables using truncated Gaussian and uniform distributions. The pdf of the uniformly distributed random variable denoted by x ~ uniform(a,b) is constant in the interval of [a,b] and zero elsewhere. We assume ∆Vk as a truncated Gaussian distribution ( ∆Vk ~ TN (10,5 ; 0, ∞) mV ) [12] and β k according to (12) as a function of two random variables (d ~ uniform(0.1,2) −1 μm and σ in ~ uniform(0.1,2) Ω m −1 ), based on the −1 −1 typical values of d =1 μm and σ in =1 Ω m [15]. The number of pyramidal PSPs in a voxel that start to fire at time t is considered as N(t). We sample N(t) every millisecond in the simulations. The ECD in this voxel is derived from (14): −θ f Θ (θ) = (14) k =1 D N (t −d ) r r Q (t ) = ∑ ∑ wk β k ∆Vkϕ k (t + d ) ⋅ n k ; k = 2π d =0 (15) k =1 ) ,-π < θ ≤ π (13) 2σ where erf(.) is the error function. The pdf of θ is shown in Fig. 4 for some values of σ. The current dipole q in (12) is projected onto two vectors, first vector ( q p ) is parallel to where ϕ k (t + d ) is the waveform of the kth PSP whose activation started at the previous d sample time and D is the maximum duration of PSP which we set at D = 30 ms according to the maximum value of τ PSP in (6). The the reference vector with the value of qcos(θ) and the second vector ( q n ) is orthogonal to the reference vector projections of Q(t ) onto two normal vectors can be found as: r with the value of qsin(θ). The E[ q n ] is zero (due to odd property of sin(.) and even property of fΘ (θ ) in (13)), 15 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 r π r q = d 2σ in ∆V ⋅ n 4 r r π q = β ∆V ⋅ n , β = d 2σ in 4 condition models neurons like Purkinje cells with random direction of its dendrites. If σ → 0 , θ has a distribution concentrated around the reference vector. The pyramidal cells can be modeled with this condition where E[ q p ] D N( t −d ) r r Q ( t ) [ w V ( t d ) cos( )] n = β ∆ ϕ + θ ⋅ ∑ ∑ k k k k k p  d =0 k =1  + [ D N( t −d ) w β ∆V ϕ ( t + d) sin(θ )] ⋅ nr ∑ k k k k k n  d∑ =0 k =1 r r r  (16)  Q( t ) = Q p ( t ) n p + Q n ( t ) n n is the unit vector parallel to the reference n p where from (3)-(5) is derived from the following equations: finss = 1+ ε u τ f v ss = ( finss ) α , q ss = (1 − (1 − E0 )1 / fin )v ss / E0 (19) ss y( t ) = V0 {k 1 (1 − q ss ) + k 2 (1 − q ss / v ss ) + k 3 (1 − v ss )} (20) where superscript “ss” shows the final value of each parameter after its steady state. u in (18) stands for synaptic activities. Although, the relation between CBF is the unit vector orthogonal to it. nn vector and The “Lead Field from Forward Problem” is the final part of the MEG modeling in Fig. 1. Electrical potential and magnetic field produced by activation in some voxels can be computed by quasi-static approximation of Maxwell equations [14]. After choosing a head model (spherical approximation or realistic head model), the following matrix equation relates the measured magnetic field and ECDs of voxels in the brain: ss ( f in ) and synaptic activities (u) is linear in the proposed model as described by (18), the nonlinearity from synaptic activities to CBF can be modeled by considering a nonlinear function of u in (18). Two candidates for this nonlinear function are “sigmoid function” [34] and “inverse sigmoid function” [22]. The nonlinearity r r B(t ) = L(rQ ) Q (t ) (17) r where Q(t ) is ECDs in region of interest in the brain, L ss between CBF ( f in in (19)) and BOLD (y(t) in (20)) makes our model nonlinear. The relation between synaptic activities and BOLD is depicted in Fig. 5 for both impulse and step responses and shows that BOLD is an increasing saturated function of synaptic activities. The nonlinear relationship between CBF and BOLD signal in this figure are related to the nonlinearity of the extended balloon model (due to Eqs. 18-20) which is in consistence with the experimental results [34,24]. is lead field matrix and B(t) is measured field by sensors. 3. Results Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 The proposed model contains several parameters whose values can be adjusted to reflect practical conditions. The effects of these parameters on the MEG and fMRI signals are analyzed and illustrated in this section. First, the nonlinear relation between synaptic activity and BOLD signal, reported in several papers, is shown. Then, a mathematical analysis of the model is presented to find the conditions under which there is a detectable BOLD signal in a voxel but the voxel is silent for MEG and vice versa. These conditions are verified and illustrated using simulation studies. Next, the difference between spatial responses of MEG and fMRI is shown. 3.2. Exploring Relationship Between MEG and fMRI Using the simulation results of the proposed model, we show that it is possible to detect the BOLD signal in a voxel while the voxel is silent for MEG and vice versa. Our model is based on Equations (1) to (17) as shown in Fig. 1. There are several parameters in the model, some of which are considered stochastic and others deterministic. In all simulations, the values for deterministic and pdfs for stochastic parameters are as described in the previous sections; any deviations from these values will be explained. 3.1. Nonlinearity Between Synaptic Activities and BOLD It is generally accepted that the relation between stimulus and BOLD signal is nonlinear. This nonlinearity stems from stimulus to synaptic activities, from synaptic activity to CBF, and from CBF to BOLD. The relation between stimulus and synaptic activities has been reported to be nonlinear [31] but since the synaptic activities are input for both MEG and BOLD in our model, we do not focus on this relation. The relation between synaptic activities and CBF has been reported linear in some studies [13,31] and nonlinear in others [22,34]The nonlinearity between CBF and BOLD is explained by the Balloon model and included in our model. For evaluation of the nonlinearity in the proposed model, we consider impulse and step responses of synaptic activities according to block and event related stimuli in fMRI. The steady state (ss) response to the step function 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ (18) 3 5 There are approximately 10 neurons per mm of cortex and thousands of synapses per neuron [15]. If the external stimulus causes activation in one percent of the 6 synapses, then there are on the order of 10 active 3 synapses in a voxel with the volume of 1 mm . As mentioned in the previous section, the number of excitatory synapses generally is more than inhibitory synapses and we consider 10% for the ratio of IPSPs to all PSPs (we call this ratio as “IPSP ratio” hereafter). Fig. 3 6 shows simulation results in a voxel of 1 mm with N ss = 10 6 active PSPs (according to (1)) and IPSP ratio of 10%. The stimulus duration is 1 second. The number of active PSPs (sum of EPSPs and IPSPs) during stimulation is depicted in Fig. 6-a. The current dipole produced by each PSP has an angle (θ) with the reference 16 PDF created with pdfFactory Pro trial version www.pdffactory.com vector, in the [-π , π ] range. Fig 6-b shows its pdf which is close to a uniform pdf. The projected ECD to the reference vector ( Q p (t ) ) and detectable MEG signal is produced. The normalized synaptic activity is shown in Fig. 6-e and used as input to the extended Balloon model. Finally, Fig. 6-f shows the BOLD signal output of the model without considering additive noise. The maximum contrast of the BOLD signal is 1.58%. The simulation results in Fig. 7 show special cases where the BOLD signal is detectable but the MEG signal is not. There are two parameters in our model for this condition: the pdf of θ and the IPSP ratio. When the pdf of θ tends to uniform, then the directions of current dipoles are uniformly distributed and can cancel each other. Also, if although the pdf of θ tends to a uniform pdf and it is expected that PSPs cancel each other. This is because the small difference between the pdf of θ and uniform pdf is amplified by the huge number of active PSPs and thus External Stimulation Linea r Filter Block 3 Block 2 Block 1 ε(t) Kind of PSP: EPSP or IPSP + Direction of PSP PSP Production Mechanism Block 4 Instrumenta l Noise Σ ECD: Vector Sum of PSPs in the Voxel + Strength of PSP Balloon model Lead Field from Forward Problem + Down Sampling + Crosstalk from Neural Activities of Adjacent Voxels MEG Signal fMRI BOLD Signal Instrumenta l Noise Fig. 1: Schematic Diagram for the proposed integrated MEG and Fmri model. 17 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 normal to this vector ( Qn (t ) ) are depicted in Figs. 6-c and 6-d, respectively. According to (13) and the odd property of the sine function, the average value of ECD is zero as shown in Fig. 6-d. Assuming the ECD peak value in the order of 10 nAm can be detected by the MEG sensors [15], the Q p (t ) in Fig. 6-c can be detected, (b) Fig. 2: Typical pyramidal neuron. (a) Schematic illustration of three magnified synapses. (b) Pyramidal neuron [15]. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 (a) (b) (d) (e) (c) (f) Fig. 3: Depending on the brain region, neurons with dendritic trees exist in all sorts of shapes and sizes. The dendritic trees for some kinds of neuron: (a) a vagal motorneuron; (b) an olivary neuron; (c) a layer 2/3 pyramidal cell; (d) a layer 5 pyramidal cell; (e) a Purkinje cell; and (f) an α-motorneuron. Scale bars, 100 μm [Segev, 1998]. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 18 PDF created with pdfFactory Pro trial version www.pdffactory.com θ (radian) Fig. 5: Illustration of the nonlinear relationship between the BOLD signal and the normalized average synaptic activities. Solid line shows the step response of BOLD output from (18) – (20). ‘o’ plot shows the steady state solution values of the BOLD response with step input using “Simulink” toolbox in MATLAB for solving equations (3) – (5). The dotted plot is the same as ‘o’ for peak value of the impulse response. α = 0.33, E0 = 0.34 and V0 = 0.02 is considered in the Balloon model. 19 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Fig. 4: pdf of θ (angle between current dipole and reference vector) according to (13). The values of σ are 1, 2, 3 and 5 from maximum to minimum peak value of the 4 plotted functions. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Fig. 6: Illustration of the capability of the proposed model to generate both MEG and fMRI signals. The small black rectangle shows the duration of stimulation. (a) Number of active synapses according to (1) with τ d = 50 ms. (b) pdf of θ where θ is the angle between PSP dipole and direction perpendicular to the cortical surface. (c) Projected ECD in the direction perpendicular to the cortical surface, Q p (t ) in (19). (d) Projected ECD in the direction tangent to the cortical surface, Qn (t ) in (19). (e) Average synaptic activity according to (9). (f) BOLD output according to (3)-(5). 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 20 PDF created with pdfFactory Pro trial version www.pdffactory.com Q = ϕ V β N (1 − 2r ) g (σ θ ) The numbers of IPSP and EPSP are equal (the IPSP ratio tends to 50%), they cancel each other because of opposite polarities. Since Q p (t ) is the only component correlated (23) where E[.] is “expected value”, r is the mean value of IPSP ratio, V is mean amplitude of PSP, β is mean of to the stimulation, it is the only component shown in Fig. 7. All conditions (except for the pdf of θ and IPSP ratio) in Fig. 7 are the same as Fig. 6. Therefore, the BOLD output for all subplots of Fig. 7 will be the same as Fig. 6-f (not shown avoid repetitions) and so there will be detectable BOLD signal in all subplots. The Q p (t ) for a conventional condition is shown in Fig. β according to (12), ϕ = D ∑ E[ϕ d =0 k (d )] according to ϕ (t ) in (6) with τ PSP ~ TN (2,1 ; 0, ∞) ms and g (σ θ ) shows average effects of projected ECD onto the reference vector. The second term of (21) vanishes in averaging because of odd property of the sine function and even property of the pdf of θ. The g (σ θ ) is defined by: 7-a, where the pdf of θ is the same as that in Fig. 6-b and the IPSP ratio is 10%. The best condition for detecting MEG is shown in Fig. 7-b, where all current dipoles are θ2 − 2 considered parallel ( f Θ (θ ) = δ (θ ) in (13)) and also all π 2σ 24) e π dθ ; k = 2π σ erf ( ) PSPs are considered EPSPs without any IPSP (IPSP ratio cos(θ ) k 2σ is zero). The amplitude of ECD in this condition is about π 2 2 −π 30 times larger than that of Fig. 7-a. The pdf of θ is 2πσ 2σ 2 2 e ) considered to be uniform and the IPSP ratio is set to 10% σ (1 − k in Fig. 7-c. In Fig. 7-d, the IPSP ratio is set to zero and the pdf of θ is the same as that of Fig. 6-b. The ECD in where σ θ is the standard deviation of θ. It is plotted both Figs. 7-c and 7-d is like random noise with zero versus σ and σ θ in Fig. 8. When σ → 0 , then mean and so there is no detectable MEG signal correlated with the stimulus, although there are detectable BOLD σ θ → 0 and the pdf of θ is like the Dirac delta function signals for both figures. 2 and g (σ θ ) → 1 . When σ → ∞ , then σ θ → π / 3 Since 2/3 of neurons in gray matter are pyramidal cells [35], we expect the pdf of θ be similar to Fig. 6-b or even and the pdf of θ is uniform and g (σ θ ) → 0 . more concentrated around zero. Also, in most neurons, The synaptic activities in fMRI are derived from the IPSP ratio is less than 20% [14,31], thus Fig. 6-a (10): shows a real condition for many regions of the brain. N However, in some regions like cerebellum (that contains  u E [ ∝ τ kPSP ∆Vk ] ∑ Purkinje cells) the pdf of θ tends to uniform and we  k =1 expect conditions like Fig. 7-c for MEG signal from this (25)  N region. Although the number of excitatory synapses is u ∝ N τ PSP V ⇒ u = u m  more than inhibitory synapses in most neurons, there are max( N ) some neurons with considerable number of inhibitory where um is the synaptic activity that produces the synapses compared to excitatory synapses [14] and so saturated maximum output in the extended Balloon conditions like Fig. 7-d is also possible. model and max(N) shows the maximum number of PSPs Now, we intend to quantitatively evaluate effects of pdf in a voxel that can be activated by an external stimulus. of θ and IPSP ratio on MEG and fMRI signals. After the Inserting (25) in (23), we have: number of active synapses reaches its final steady state u  value according to (1), the number of active synapses Q = ϕ V β max( N) (1 − 2r) g (σ θ )  becomes almost fixed. Referring to (16), we have:  u r D N r Q = [ ∑ ∑ w k β k ∆ V k ϕ k ( d ) cos( θ k )] ⋅ n p + d = 0 k =1 N D r [ ∑ ∑ w k β k ∆ V k ϕ k ( d ) sin( θ k )] ⋅ n n d = 0 k =1 ( 21 ) where N is the average number of active synapses after steady state. If all random variables in (21) are considered independent, the mean value of ECD is:  u Q = Q m (1 − 2r) g (σ θ )  um (26) Considering (3)-(5) in the extended Balloon model and (26), the relation between BOLD signal and ECD is: u  Q = Q m (1 − 2r ) g(σ θ )  um  r D N Q = { ∑ ∑ E[w k ]E[β k ]E[∆Vk ]E[ϕ k (d)]E[cos(θ k )]} BOLD Output = Balloon Model (u ) d = 0k =1 r ⋅ n p = Q.n p (22) 21 m (27) 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 ∫ may be no detectable MEG signal. In Figs. 10-c and 10-d, the value of ECD is set to a detectable level (10% of its maximum) and the resultant BOLD contrast is plotted as functions of σ and r. Note that with even very low value of ECD, increasing σ and r may increase the BOLD contrast to its maximum saturation value. The relations between ECD ( Q ) in MEG, average synaptic activities ( u ), and BOLD output in fMRI are summarized in (27). This equation shows that the relation between ECD and BOLD is nonlinear and segregates to two parts: linear relation between ECD and u and nonlinear relation between BOLD and u according to the nonlinearity of the Balloon model. 3.3. Spatial Response of MEG and fMRI The neural activities in each voxel are independent of other voxels in the proposed model and therefore there is no crosstalk between ECDs. However, the nonuniqueness property of the “Inverse Problem” in MEG may cause some voxels without neural activity to show activity in the solution of linear equation (17) [26], which we call “crosstalk.” On the other hand, neural activities in a voxel can change CBF and BOLD signal in the neighboring voxels and cause false detection of activity in these voxels, as discussed in Section II-B-2 and considered in our proposed model (Fig. 1). Accordingly, in the spatial response of each method, it is possible that some voxels are detected as active without containing any neural activity, and so the spatial response of the two modalities may be different. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Fig. 9 illustrates the relation between ECD and BOLD. Fig. 9-a shows this relation according to (27) with r = 0 and σ θ = 0 ( g (σ θ ) = 1 ) where BOLD increases as ECD moment increases with an increasing saturated function. This function can be separated to three regions. For increasing ECD from zero to 1%, the BOLD contrast is less that 15% of its maximum. The ECD and BOLD signals are very small and cannot be detected in this region of the curve. The second part contains the steepest part of the curve for the BOLD signal, where increasing ECD from 1% to 27% increases BOLD from 15% to 90%. The BOLD signal is saturated in the third part where 73% increase in ECD increases BOLD signal by only 10%. As illustrated in Fig. 5, the nonlinear relationship between the neural activity and the BOLD signal (which is reported in experimental results [Nielsen and Lauritzen, 2001; Lauritzen and Gold, 2003]) can be generated in the proposed model. We expect nonlinear relationship between the ECD and the BOLD signal according to the linear relationship between the neural activity and the ECD (as we assumed in the model) and nonlinear relationship between the neural activity and the BOLD signal. The figs. 5 and 9 are actually similar if the plot in fig. 5 is considered as logarithmic plot. Fig. 11 illustrates the effect of spatial crosstalk in fMRI. All parameters for producing simulated data are the same as the first simulation in Section III-B and Fig. 6. One of the middle axial slices of MRI is used as the base image. The region of interest is limited to a window with the size of 64 × 64 voxels (pixels) where a pixel in the center of the window is the single active pixel (Fig. 11-a). The 2 pixel size is 0.75 × 0.75 mm and is selected smaller than its conventional value to manifest the effect of spatial blurring. The average synaptic activities and the BOLD output in this pixel are shown in Fig. 6-e and Fig. 6-f, respectively. Fig. 11-b shows BOLD signal after down sampling with TR = 2 sec. For modeling the crosstalk effect, we use (2) with 2D Gaussian distribution for G and σ x = σ y = σ = 1.5 mm, i.e., Effects of pdf of θ on ECD and BOLD signals are shown in Fig. 9-b. Three curves are plotted for σ = 0, 10 and 25 with r = 0 for all curves. Fig 9-b shows that for a high value of σ = 25 (pdf of θ tends to uniform) even though the BOLD signal is saturated at its maximum value, the ECD is less than 0.2% of its maximum and is not detectable. Effects of IPSP ratio (r) on ECD and BOLD are shown in Fig. 9-c for three values of IPSP ratio, r = 0, 20% and 40% and σ = 0 for all curves. When r tends to 50% (canceling EPSPs with IPSPs), the ECD tends to zero although the BOLD signal is detectable at its maximum value. For a 1.5 T scanner and TE = 40 ms, parameters k1, k2, and k3 in equation (20) have been evaluated to be k1= 7E0, k2 = 2, and k3 = 2E0-0.2 in [7]. The maximum BOLD contrast in this condition is about 6% which is shown in Fig. 9. G ( x , y) = 1 e ( x − x 0 ) 2 + ( y − y0 ) 2 2πσ x 0 = 32, y 0 = 32 (28) 2 2 σ2 ; (28) where ( x0 , y0 ) = (32,32) shows a central pixel of the image that is the single active pixel. The induced average synaptic activity in each pixel (according to (2) and (32)) is used as the input of the Balloon model, whose output is the BOLD signal of each pixel. Duration of stimulus is 1 sec and each period of BOLD signal contains 12 samples (12*2 = 24 sec) We assume a detectable signal in each case of ECD or BOLD and show effects of σ (pdf of θ) and r (IPSP ratio) on the detection of the other one in Fig. 10. The BOLD contrast is fixed at 2% in Figs. 10-a and 10-b and the resulting ECD is plotted as functions of σ and r. Note that increasing σ and r decreases ECD to zero and thus even though the BOLD signal is detectable, there 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ − 22 PDF created with pdfFactory Pro trial version www.pdffactory.com The data is repeated for 20 periods and so the total number of samples in each pixel is 12*20=240. Additive Gaussian white noise is added to all pixels so that the contrast to noise is 1. We use the “cross-correlation method” for activation detection. For the reference waveform in this method, we first calculate the impulse response of the Balloon model for an average neural activity, then construct the reference waveform by convolving stimulus pulse and the calculated impulse response. The false alarm rate is set to 1%. The detected active pixels are shown in Fig. 11-c. Except 4 falsely detected pixels on the periphery of the image, the other detected pixels concentrate around the center of the image where we put the single active pixel. The number of active pixels is 25 and maximum distance between the detected pixels and the center is 3 pixels (2.25 mm). As the number of periods and the contrast to noise increase, the number of active pixels and activation radius will also increase. This simulation shows the possibility of detecting false activations adjacent to the active pixels in fMRI BOLD analysis. Now, we deal with the effect of inverse problem on spatial response of MEG. The Minimum Norm (MN) method is used for solving the inverse problem according to the forward problem in (17) as [42]: plane is parallel and z axis is perpendicular to the axial slice. The false alarm rate and contrast to noise ratio are set to 0.1% and 0.2, respectively. The other parameters of neural activities related to this single active voxel are the same as the previous simulation in Fig. 11. The spatial blurring in fMRI response and spread of the MN solution of MEG are shown in Fig. 13. In summary, neural activity in a voxel can produce BOLD signal in the neighboring voxels and cause blurring in the spatial response of the fMRI. Also, the non-uniqueness property of the MEG inverse problem spreads the solution to a wide region. Therefore, if there are neural activity in a voxel that produce detectable ECD and BOLD signal, the spatial response of fMRI and MEG are not necessarily the same. 4. Estimation of the Parameters Using Real Data For validation of the proposed model in real conditions, we use real auditory MEG and fMRI datasets from 2 normal subjects to estimate the parameters of the model. Details of our work can be found in [5]. However, we try to summarize the methods and results in this section. (29) where Q is the current dipole moment in each voxel in the region of interest, L is lead field matrix, B is detected 4.1. Auditory Task Data Parameters of the proposed model are estimated using real datasets of auditory block stimulus from two healthy male and female subjects. Each block consists of 12 seconds of tones on followed by 12 seconds of tones off. During the tones on period, 3 tone bursts presented with a 15 ms rise/fall time at a rate of one per second for each of 4 tone frequencies 500Hz, 750 Hz, 1000 Hz, and 1200 Hz as illustrated in Fig. 14. The MEG datasets gather using 148 channel whole head Neuromagnetometer (4D Neuroimaging). 50 blocks (epochs) of MEG data are acquired with sample rate of 508.63 Hz. The heart artifact is removed and the datasets are filtered using a band-pass filter (0.5 Hz to 50 Hz) before analysis. The MEG signal of the male subject (subject # 1) is illustrated in Fig. 15. For this subject, the 78th sensor (near to the primary auditory cortex) has most significant signal compared to other sensors. The average signal of this sensor over all 50 epochs is illustrated in Fig. 15-a. We used independent component analysis (ICA) on the raw data (before averaging over 50 epochs) as the next preprocessing stage after discarding the nuisance channels. Then, the averaged ICA component over all epochs is calculated. The stimulus correlated component of ICA is illustrated in Fig. 15-b. The contour map of this component in all sensors is shown in Fig. 16. # signal in the MEG sensors, L is pseudo-inverse of L, and Q̂ is MN solution for estimated current dipole. We used the coordinate of BTi Magnes 2500WHS neuromagnetometer system with 147 active magnetometer detectors in our simulation. A volumetric structural MRI data of head with 314 × 256 × 256 voxels and volume of each voxel approximately 0.75 × 0.75 × 3 0.75 mm is used for co-registration. The solution is considered at representative axial slice of the MRI (Fig. 12-c) and the region of interest is restricted to only gray matter with 17,970 pixels as shown in Fig. 12-a. Active region contains only one pixel whose current dipole is perpendicular to the cortical surface (Fig. 12-a). Fig. 12-b shows the MN solution for the moment of the current dipole. The direction of maximum moment in the solution space is shown in Fig. 12-c. The simulation results of 3D whole head model are shown in Fig. 13. Thirty-three axial slices of MRI are considered which contain cortical voxels. The volume 3 contains 64 × 79 × 33 voxels of size 3 × 3 × 3 mm (Fig 13-a). Only 1 voxel is considered as active voxel whose location is shown in Fig. 13-a. The region of interest in MEG is limited to 24,271 voxels of gray mater. The direction of ECD in the active voxel and the MN solution are shown in Fig. 13-a. The voxel size in the fMRI 3 simulation is considered as 0.75 × 0.75 × 0.75 mm for 23 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007  B( t ) = L Q( t )  # Q̂( t ) = L B( t ) enhanced observation of spatial blurring. The 3D Gaussian distribution for G is considered in (2) with σ x = σ y = 2.6 mm and σ z = 0.7 mm where the x-y (a) (b) (c) (d) Fig. 7: Illustration of cases that MEG signal is significant or small, using the effects of pdf of θ and ratio of IPSPs number to all PSPs on ECD ( Q p (t ) ) in MEG signals. (a) pdf of θ is same as Fig. 6-b and IPSP ratio is set to 10%. (b) fΘ (θ ) = δ (θ ) and IPSP ratio is set to zero. (c) pdf θ is set to uniform distribution around [-π, π] and IPSP ratio is set to 10%. (d) pdf θ is same as Fig. 6-b and IPSP ratio is set to 50% Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 (b) (a) g (σ θ ) g (σ θ ) σ σθ Fig. 8: Illustration of the nonlinear function that relates the standard deviation of θ to ECD according to (24). (a) g (σ θ ) versus σ . (b) g (σ θ ) versus σ θ . 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 24 PDF created with pdfFactory Pro trial version www.pdffactory.com (a) σ = 10 σ = 25 (b) σ =0 (c) r = 0, 20 % and 40 % fMRI signals. Relation between ECD and BOLD according to (31) for: (a) r = 0 and σ = 0 ( g (σ θ ) = 1 ). The horizontal lines show 15%, 90% and 100% of maximum BOLD signal. (b) r = 0 and σ = 0, 10 and 25. (c) σ = 0 and r = 0, 20% and 40%. (a) (b) σ IPSP ratio (r) (d) (c) σ IPSP ratio (r) Fig. 10: Illustration of the conditions where detectable fMRI signal is considered but MEG signal changes as a function of σ (pdf of θ) and r (IPSP ratio) and vice versa. (a) Contrast of BOLD is fixed at 2% and r = 0. (b) Contrast of BOLD is fixed at 2% and σ= 0. (c) Value of ECD is fixed at 10% of its maximum value and r = 0. (d) Value of ECD is fixed at 10% of its maximum value and σ = 0. 25 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Fig. 9: Illustration of the effects of two parameters (standard deviation of theta and ratio of IPSP to all PSP) on the MEG and Fig. 11: Illustration of the effect of spatial crosstalk on the fMRI response. All parameters are the same as Fig. 6. (a) The region of interest is limited to a window with 64 × 64 pixels and the location of active pixel is shown by circle. (b) One period of BOLD output from the Balloon model with neural activities of Fig. 6-e. The small black rectangle shows the duration of stimulation. (c) The black pixels are detected active pixels. The white pixel at the center of the image shows the location of neural activities. The pixel size is 0.75 × 0.75 mm 2 and σ x = σ y = σ = 1.5 mm according to (32). Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 (a) (b) (c) Fig. 12: Solution of Minimum Norm (MN) for MEG inverse problem. (a) The middle axial slice of MRI used for region of interest (ROI). The ROI is limited to general regions of gray matter shown with higher brightness. The source is current dipole in a single pixel. Its direction is perpendicular to the cortical surface. (b) Solution of MN where brightness reflects strength of dipoles. Location of source is shown by circle. (c) The location and direction of maximum moment dipole in the solution space. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 26 PDF created with pdfFactory Pro trial version www.pdffactory.com The resolution of the 3-D anatomical MRI data is 256x256x66 voxels where the voxel size is 0.9375x0.9375x2.5 mm3. We use MEG-Tools (http://www.megimaging.com/) for coregistration of the MEG data with the 3-D anatomical MRI data. The MEG localizations are computed in reference to the Cartesian coordinate system defined by a set of three anatomical landmarks (fiducial points): the right and left external meatus or pre aurical and nasion. Prior to the MEG scan, the head surface is digitized using laser fast track scanning. The head digitization points (about 3,000 points) are used to ensure a precise registration, when the points laid on the scalp surface of the MRI scan. For the fMRI studies, we use the GE product echo planner imaging (EPI) sequence with 64 by 64 data acquisition matrix, TE of 30 ms, TR of 2 s, field of view of 240 mm, and slice thickness of 5 mm. Each volume contains 16 slices. After discarding first few volumes, 16 block sequences of the fMRI data are acquired using the same MEG stimulus. Auditory stimulus is presented through air conductance tubes to headphones to reduce external noise. Motion is corrected using the statistical parametric mapping (SPM) and then the linear drift is removed from the data. We use the t-test [2] for activation detection and assume a simple linear model for the hemodynamic response function. SPM is used for the registration of the detected activation in the fMRI slices to the 3D anatomical MRI data. the mean of all random variables in (23). According to (30), the spatial and temporal parts of ECD in each voxel can be separated into two parts: KM and N(t). N(t) can be assumed proportional to the waveform of the main ICA component. Moreover, KM in each voxel is the magnitude of the dipole calculated by the inverse solution of the scalar map shown in Fig. 16. After assuming the main ICA component as N(t), parameters of the linear filter in (1) can be estimated. For both subjects, we found that a first order linear filter according to (1) generates reasonable estimation results. Thus, we use the following first order linear filter. Tp dN ( t ) + N( t ) = K Stm( t − Td ) dt (31) 4.2. MEG Parameters Estimation After registering the MEG coordinates to the 3D anatomical MRI data, the cortical model is constructed using 2,734 cortical locations in the subjects’ gray matters. The concentric spherical head model is used to construct the forward model in (17). We use the stimulus correlated component of ICA for activation detection in MEG and we call this component as “main ICA component” hereafter. If main ICA component is considered as the MEG signal in all sensors, the time course of each sensor will be equal to the time course of this component multiplied by a scalar. The spatial pattern of the ICA component is the values of this scalar in all sensors. The temporal and spatial patterns of the main ICA component for subject # 1 are shown in Figs. 15-b and 16, respectively. The Multi-Resolution FOCUSS (MR-FOCUSS) [23] is used to solve the MEG inverse problem and activation detection. The relationship between the dipoles and the measured field by the sensors is linear according to (29). Thus, the time courses of the activation in all cortical voxels are similar to the time course of the main ICA component and the differences between them are the magnitude and direction of the current dipole in each voxel. Assuming known pdfs for all random variables, we have the following equation according to Eq. (23): 4.3. fMRI Parameters Estimation The parameters of the proposed model which are related to the fMRI part of the model can be partitioned into two sets: parameters related to the spatial crosstalk in (2); and parameters of the EBM according to Eqs. (18)-(20). At First, we estimate the parameters related to the spatial crosstalk. The detected activation from the fMRI data of subject # 2 co-registered to 3-D anatomical MRI is illustrated in Fig. 17. For estimating the spatial crosstalk represented by σ = (σ x , σ y , σ z ) in Eq. (2), two Gaussian kernels are fitted to the main clusters of the detected activation areas in left and right primary auditory cortices. The hotspot of the cluster is assumed as the center of the Gaussian kernel. All neighboring voxels to the central voxel in a sphere with a diameter of 25 mm are considered for curve fitting. The estimated σ is given in Table 1. For estimating the parameters of the EBM, we use average BOLD responses over 16 blocks of all active voxels for both subjects. We try to fit an EBM to average BOLD response of each voxel by estimating the parameters of the EBM. The parameters of the linear filter in Eq. (31) are estimated using the MEG Q ( t ) = K M .N ( t ) (30) where KM is a spatial parameter that represents 27 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 where Tp , Td , and K are parameters to be estimated and N(t) is the main ICA component. We estimate the parameters of this linear filter using the stimulus profile shown in Fig. 14 and assuming N(t) as the calculated main ICA component. For estimating these parameters, we used “fminsearch” function of the MATLAB which is an iterative method for finding the minimum of the mean square error between N(t) and its estimation according to (31). N(t) and its estimation for subject # 1 are shown in Fig. 15-d. The estimated values of Tp, Td, and K for both subjects are given in Table 1. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 (a) (b) Fig. 13: Simulation in 3D whole head model for observing the difference in spatial responses of fMRI and MEG. (a) MN solution of inverse problem in MEG where brightness reflects strength of dipoles. The volume contains 33 axial slices and the 3 voxel size is 3 × 3 × 3 mm . The region of interest is limited to 24,271 voxels of gray matter in the MN solution. The source is only 1 active voxel as single ECD whose location and direction is shown. (b) fMRI detected activation. The active voxel is the 3 central voxel in the middle slice of the 5 axial slices. Voxel size is 0.75 × 0.75 × 0.75 mm . Note that the fMRI response is limited to a focused area of an ellipsoid with radii of 11mm and 1.5 mm but the MEG response is spread in all slices on the brain with wide regions in each slice. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 28 PDF created with pdfFactory Pro trial version www.pdffactory.com tone off: 12 Sec ≈ 500Hz 750Hz 1000Hz 1200Hz 500 ms 500 ms 500 ms 500 ms 500 ms 500 ms 500 ms 500 ms Fig. 14: Illustration of one epoch (block) of the stimulus profile for an auditory excitation. Each epoch contains 12 seconds of tones on and 12 second of tones off period. During the tones on period, 3 tone bursts were presented with a 15 ms rise/fall time at a rate of one per second for each of 4 tone frequencies 500Hz, 750 Hz, 1000 Hz, and 1200 Hz. MEG data of both subjects Fig. 15: Averaged MEG data and estimated model of the number of the active PSPs, N(t) for subject # 1. (a) Average MEG 29 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 containe 50 epochs. data over 50 blocks in the 78th sensor, which has strongest signal among all sensors. (b) The main ICA component averaged over 50 blocks. (c) Stimulus profile. (d) N(t) (blue plot) and its estimated model (red plot). Fig. 16: Contour map of the amplitudes of the main ICA component (MEG data of subject # 1). The time course of the main ICA component is illustrated in Fig. 15-b. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Fig. 17: Illustration of the detected activation from the fMRI data of subject # 2 co-registered to 3-D anatomical MRI data after removing single active voxels. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 30 PDF created with pdfFactory Pro trial version www.pdffactory.com Table 1: stimated values of the parameters of the proposed integrated model using real auditory data. The parameter Tp, Td, and K are related to the linear filter in Eq. (31). Parameters of the model which are related to the fMRI part of the model are according to Eqs. (2) and (18)-(20). MEC Parameters fMRI Parameters Unit Subject #1 Subject #2 Td (Afferent Delay) ms 59 72 Tp (Time Constant of Linear Filter) ms 44 31 K - 0.019 0.020 σ = [σx , σy , σz] (Spatial Crosstalk of fMRI) mm [ 7.5 , 7.5 , 5.5 ] [ 10.0 , 10.0 , 7.0] ε (Neural Efficiency) - 0.13 0.15 τ s (Signal Decay) s 20.05 25.36 τ f (Autoregulation) s 3.45 3.75 τ 0 (Transit Time) s 4.94 3.74 α (Stiffness) - 0.21 0.21 E0 (Oxygen Extraction) - 0.67 0.57 31 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Fig.18: Number of active PSPs (N(t)) and real and estimated BOLD responses (subject # 2). (a) Estimated N(t) as input of the EBM. (b) Real (-o- plot) and estimated BOLD signals of the 6th slice of fMRI volume where the average BOLD responses of all active voxels in the slice are used. (c) Same as (b) for the 7th slice. (d) Same as (b) for the 8th slice. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Brain. Doctorial dissertation, Electrical and Computer Engineering Faculty, University of Tehran, Iran. [6] Babajani A and Soltanian-Zadeh H, (2006): Integrated MEG/EEG and fMRI model based on neural masses. IEEE Trans. Biomed. Eng. 53(9):1794-1801. [7] Buxton RB, Wong EC, Frank LR (1998): Dynamics of blood flow and oxygenation changes during brain activation: the balloon mode. Magn Reson Med 39:855-864. [8] Caesar K, Gold L, Lauritzen M (2003): Context sensitivity of activity dependent increases in cerebral blood flow. Proc Nal Acad Sci USA 100:4239-4244. [9] Dale AM, Liu AK, Fisch BR (2000): Dynamic Statistical Parametric Mapping: Combining fMRI and MEG for HighResolution Imaging of Cortical Activity. Neuron 26:55-67. 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[26] Liu AK, Dale AM, Belliveau JW (2002): Monte Carlo simulation studies of EEG and MEG localization accuracy. data and the estimated N(t) is considered as the overall synaptic activity ( u (t ) in Eq. (25)). Effect of the scalar coefficient between N(t) and u (t ) in (25) is considered in the neural efficiency (ε) in (18). The estimation process for the parameters of the EBM is started by choosing proper initial values. The “fminsearch” function, which uses the simplex search method, minimizes the sum square error between the real and estimated BOLD signals by iteratively changing the parameters of the EBM. “Simulink” is used to solve the nonlinear statespace equation (6) by the iterations of the “fminsearch” minimization. The estimated parameters of the EBM for both subjects are given in Table 1. Fig. 18 illustrates the real and estimated BOLD signals related to subject # 2.V. Summary and Conclusion The purpose of this paper is to present an integrated MEG and fMRI model (Fig. 1). The MEG and fMRI BOLD signals are related to neural activities. The number of PSPs and APs show the overall neural activities. Based on the existing experimental studies and physiological facts, both MEG and fMRI signals are mainly related to PSPs and have almost no correlation with APs. The proposed stochastic model is based on the parameters of PSPs that are considered as random variables. In our model, the overall effect of PSPs is related to ECD in MEG and average neural activities as the input of the extended Balloon model in fMRI. Neural activities in a voxel can change CBF and produce BOLD signal in the neighboring voxels. We model this spatial blurring property of BOLD signal as “Crosstalk from Neural Activities of Adjacent Voxels.” The effects of model’s parameters are explored and illustrated using multiple simulation studies. These simulations show that the parameters of the model can explain conditions for which there is a detectable fMRI signal in a voxel but this voxel is silent for MEG and vice versa. Possible differences in the spatial responses of MEG and fMRI are also shown using our model (Figs. 11, 12 and 13). The crosstalk in fMRI and non-uniqueness property of the inverse problem in MEG are attributing sources for some of the differences in the spatial responses of the two modalities. We use real auditory MEG and fMRI datasets from 2 normal subjects to estimate the parameters of the model. Goodness of fit of the real data with our model suggests that the proposed model can be used in real conditions. References [1] Almeida R, Stetter M (2002): Modeling the link between functional imaging and neuronal activity: synaptic metabolic demand and spike rates. Neuroimage 17:1065-1079. [2] Ardekani B A and Kanno (1998): Statistical methods for detecting activated regions in functional MRI of the brain. 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Neuroimage. 39(1):290-309. [41] Tsubokawa T, Katayama Y, T Kondo, Ueno Y, Hayashi N, Moriyasu N (1980): Changes in local cerebral blood flow and neuronal activity during sensory stimulation in normal and sympathectomized cats. Brain Res 190:51–64. [42] Wang JZ, Williamson SJ, Kaufman L (1992): Magnetic Source Images Determined by a lead-Field Analysis: The Unique Minimum-Norm Least-Square Estimation. IEEE Trans Biomed Eng 39:665-675. 33 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com TAC: A Topology-Aware Chord-based Peer-to-Peer Network Javad Taheri, Mohammad Kazem Akbari Advanced Information Technologies Lab. Department of Computer Engineering and IT Amirkabir University of Technology, Tehran, Iran {j.taheri, akbarif}@aut.ac.ir between overlay and physical network which would lead to inefficient routing of messages. Up to now, many structured DHT-based P2P systems have been proposed. Chord 0, CAN 0, Pastry 0 and Tapestry 0 are the most well known. Among these systems, Chord has achieved wide popularity for its noticeable features like simplicity, high scalability, and flexibility in frequent node arrivals and departures. However, it is known that this protocol has low efficiency in data lookup. This problem comes from the fact that Chord does not consider underlying physical topology to build the overlay network and results in mismatch between nodes’ adjacency in the physical and overlay networks. Abstract: Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Among structured Peer-to-Peer systems, Chord has a general popularity due to its salient features like simplicity, high scalability, small path length with respect to network size, and flexibility on node join and departure. However, Chord doesn’t take into account the topology of underlying physical network when a new node is being added to the system, thus resulting in high routing latency and low efficiency in data lookup. In this paper, we introduce the TAC, a novel topology-aware protocol which is based on Chord. TAC introduces the local ring concept by dividing the geographical space into smaller areas. Through binding each new node to a proper local ring concerning its physical location, TAC considers the physical network topology of the overlay network to demonstrate more efficient key lookup. Simulation results show that TAC performs better in terms of more efficient routing and less bandwidth usage. The main contribution of this paper is introduction of TAC (Topology Aware Chord) algorithm. TAC is a modified version of Chord which considers physical network topology through dividing the geographical space in which the nodes are distributed, into smaller zones and then binding the nodes within each zone to a local ring. The local ring of a zone lets the nodes inside that zone to become aware of each other’s existence. At the cost of keeping more information, TAC allows every node to be familiar with other proximate nodes and do a better routing by selecting the next hop more appropriately. As a result, the average distance that must be traversed by each message is significantly reduced. Moreover, less bandwidth is required in average to route a query from its source to the destination. In other words, TAC exploits underlying network topology information to perform better message routing. Keywords: Peer-to-Peer Systems, Routing Efficiency, Topology Awareness, Chord 1. Introduction EER-TO-PEER (P2P) networks are types of distributed systems with neither centralized control nor hierarchical organization. These systems are overlay networks which are built on top of physical layer network. Every node in this systems is a self-organizing peer which is logically connected to the network through its neighbors. An important feature of P2P systems is that each node can operate either as a client or a server. Due to this feature, P2P systems are considered to be a good substrate for developing many applications in a variety of fields like data sharing, content distribution, distributed programming and so forth 00. However, the Initial P2P systems like Napster 0 and Gnutella 0 have the problem of weak scalability when the number of nodes grows. To solve this problem, a new type of P2P systems called structured P2P systems which is based on using Distributed Hash Tables (DHTs) was introduced. Notwithstanding acceptable scalability, many of DHT-based P2P systems suffer from topology mismatch P 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ The rest of this paper is organized as follows: Section 2 briefly discusses Chord protocol and previous works related to topology awareness issue. In section 3, the proposed protocol is presented in detail and the experimental evaluation is given in section 4. Finally, concluding remarks are presented in section 5. 2. Background A structured P2P network is constructed of some computer nodes and a set of data in form of {key, value} pairs. Each node is responsible for maintaining some of the pairs in a way that the following requirements are satisfied: 34 PDF created with pdfFactory Pro trial version www.pdffactory.com address of an overlay node. The jth finger of node i is the first node that succeeds i by at least 2j in the identifier space, where 0 < j < m and m is number of identifier bits. As a result, the finger table contains more nearby nodes rather than faraway nodes at a doubling distance. 1) every node should keep almost the same number of pairs 2) Every node should be able to lookup the value of a given key by searching a relatively small and bounded number of other nodes Therefore, there should be some mechanisms to solve following problems: • Distribution of data evenly among the overlay nodes • Finding the node which is responsible for a given key by traversing a bounded and small number of other nodes Using the finger table, Chord uses finger routing to forward lookup messages. The node i looks up the key k, by forwarding a lookup message to the node whose identifier most immediately precedes the successor node of k in the finger table. Each node repeats this process and the message gets closer and closer to the destination and finally reaches the destination. 2.1. The Chord Protocol Chord 0 assigns the responsibility of each {key, value} pair to the proper node using the consistent hashing method. In this protocol, an m-bit identifier is assigned to each node and key by hashing its name or IP_address. The resulted set of identifiers forms a modulo 2m one-dimensional circular space (Fig. 1). A P2P system is a logical network which is built on top of the underlying physical network. Each node in this system communicates with other nodes through its neighbors. Therefore, every node needs to be bound to its neighbors at its arrival time. The selection process of neighbor nodes is an important task. If the neighbors of a node are selected on the basis of its physical topology, the quality of message routing between overlay nodes can be improved. In other words, if overlay neighbors of a node are fairly its neighbors in physical layer, the distance between two communicating overlay nodes is less. Furthermore, as a result of coincidence of overlay and physical neighbors, the messages transmission is faster and consequently the network traffic will be reduced. Consider a sample physical network with four nodes (A, B, C and D) which is shown in Fig. 2. The numbers shown next to each edge, indicate the physical distance between two nodes. Fig. 3 shows two overlay networks which are built using these four nodes. The difference between two overlays is that each is built using different neighbors. In the overlay of Fig. 3(a), if A send the message m to B, the logical path Fig. 1: Assigning keys to appropriate nodes in Chord0 According to global ring, every key is assigned to the first peer whose identifier is equal to or follows the key. This scheme tends to balance the load on the system, since each peer receives approximately the same number of keys 0. The other important property is that with high probability, when a new node joins or leaves the network, only a small number of the keys has to be moved. A→C→B must be traversed (suppose a clockwise unidirectional communication). Mapping this path to the physical topology would result in: A→R1→R2→C→R2→R1→B In Chord, to lookup a key and retrieve it’s value, every node keeps a finger table which is comprised of at most O(Log N) records(fingers), where N is the total number of overlay nodes. Every finger keeps the identifier and IP physical 35 path. Therefore, the message 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com m Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 2.2. Topology Awareness in P2P Overlays Fig. 2: A physical network which connects 4 computer nodes A, B, C and D through routers R1, R2 and R3. The edge between every two nodes depicts a physical link with its distance label. (a) (b) Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Fig. 3: Two different overlay networks from nodes of Fig. 2. has to walk through a physical path with following length: data lookup. To solve these problems, many techniques have been proposed recently to take account of physical network topology in Chord routing. In this regard, PChord 0 presents a better awareness of physical topology than the original Chord by using proximity lists. The proximity list of a node is a list of geographically close nodes which the node discovers in its lifetime. The next hop is decided by the entries in both finger_table and the proximity list. Although this approach achieves better routing efficiency than Chord while keeping lightweight maintenance costs, it suffers from slow convergence and inefficiency in the case of churn, where the lifetime of a node in the overlay is relatively short [9]. Chord6 [10] is another protocol that deals with physical network topology in Chord. By utilizing hierarchical structure of IPv6 addresses, Chord6 assigns an identifier to each node in a way that the nodes in the same domain have close identifiers. However, the nodes in two close domains may have very different identifiers. Although this approach is simple and can reduce the average path length, however, because of large number of Internet domains and small number of overlay nodes in same domain, Chord6 seems to Dist A =1x + 4 x + 1x + 1x + 4 x + 1x = 12 x Similarly, the logical and physical path of the overlay network shown in Fig. 3(b), would be A→B and A→R1 →B respectively and results in the following physical distance: DistB =1x + 1x = 2x which is significantly shorter. The comparison of these two distances shows that the overlay network of Fig. 3(b) is more congruent with the underlying physical network than the overlay of Fig. 3(a)0. Of this, it can be concluded that in an overlay network, awareness of underlying physical network topology will decrease the length of traversed path and leads to more efficiency in routing and bandwidth usage. 2.3. Related Works In general, the Chord protocol provides support for just one operation: given a key, it maps the key onto a node 0. Having this in mind, the topology of underlying physical network is not considered in Chord. As a result, this protocol suffers from inefficient routing and high latency in 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 36 PDF created with pdfFactory Pro trial version www.pdffactory.com With this in mind, the detailed information of TAC, i.e. the process of geographical partitioning, local ring, zone finger table and routing algorithm, will come next. be inefficient. Furthermore, the current IPv4 based physical networks limit the implementation of this protocol. AChord 0 is a modified version of Chord which takes account of physical network topology in the overlay network using anycast mechanism. Anycast is one of the communication methods in IPv6 in which an address is given to a group of nodes. When a node from outside the group sends a message to this address, the message would be delivered to the nearest node in that anycast group. AChord considers all nodes in the overlay network as an anycast group. If a new node decides to join the overlay network, it sends a request to the anycast address of this group and then is connected to the nearest node in the overlay. However, besides the good routing efficiency, AChord assumes that the underlying network supports an ideal anycast i.e., the outside messages are always routed to the nearest node which in the current Internet, this is not always feasible. Moreover, similar to the Chord6 mechanism, AChord is designed on the basis of IPv6 protocol which is not widely operational yet. 3.2. Geographical Areas In Chord, the locality of the overlay nodes does not influence the key location routing. As we mentioned before, this lack of topology information results in poor efficiency in routing. To solve this problem, TAC partitions the nodes’ geographical space into smaller areas called zones and assigns every zone, the nodes which are enclosed in its boundaries. The size of each zone could be variable and we don’t set any precise rule here to determine each zone’s boundaries, because some non-engineering factors like politics or natural conditions may affect the size of each zone in the real world. However, we observed that there is a trade-off between the number of overlay nodes in a zone(which depends on zone’s size) and the worst-case latency among them. It is desirable to have more nodes within a zone with minimum worse-case latency. 3. Proposed Protocol In this section, the proposed protocol will be discussed. First we give a brief overview of TAC. The key idea behind TAC is to divide the geographical space in which the overlay nodes are located into smaller areas and then introduce the nodes inside each area to each other. TAC assumes that if geographically proximate nodes are aware of each other’s existence, the lookup messages will traverse smaller paths and the efficiency of routing will be significantly increased. Speaking in more detail, TAC improves the topology awareness of Chord by dividing the geographical space into smaller areas called zones. When a node joins the overlay, TAC introduces other nodes within same zone to this node by binding it to the zone’s local ring. Moreover, each node is responsible for maintaining another finger table which is related to the local ring nodes. This table, which is called zone finger table, is identical to original finger table in terms of formatting and the completion procedure, except that this table deals only with local ring nodes. The aim of this table is to maintain the information of proximate nodes (the nodes within same zone) and therefore let the lookup process to be done more efficiently. When a key lookup request is received in node n, it first looks for the entries in the zone finger table. If an appropriate node is found, it will be selected as the next hop. Otherwise, the next hop will be selected using the information of finger table using Chord’s original lookup algorithm. Fig. 4: Geographical space which is divided into 4 zones A fine granularity in space partitioning, i.e. creating small zones, will reduce the worst-case latency but will reduce the number of nodes. In the other hand, increasing the size of each area guarantees having more overlay nodes inside each zone, but will increase the worst-case latency. In this paper, we divide the space into Nz same-size zones where Nz is a variable. Fig. 4 shows a hypothetical global geographical space which is divided into 4 zones (Zone 14). Every node is depicted as a circle and the pattern of all nodes inside a zone is the same. 3.3. Local Rings In Chord, an m-bit identifier is assigned to every overlay node by hashing its IP address. The resulted set of identifiers, forms a modulo 2 m one-dimensional circular space. In this paper, we call this circular space the global ring, because all overlay nodes inside all zones are participated. In addition to the global ring, TAC forces the 37 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 3.1. Overview global ring, the IP address of successor and predecessor nodes of nnew in the local ring will also be sent to nnew. This information will be used to build complete the zone finger table gradually. overlay nodes of each zone to form another circular space called local ring. The main difference between the global and the local rings is that the former contains all of nodes but the latter is comprised of only the nodes of the related zone. Fig. 5 shows the global ring of the overlay nodes shown in Fig. 4. Moreover, the local ring of zone 4 is also depicted in dotted line. 3.4. Zone Finger Table Each node in Chord keeps a hash table in order to determine the next hop during key location. This table is called finger table and maintains information of about O(logN) other nodes where N is the number of overlay nodes in the global ring. To construct this table, every node first gets the IP address of its successor node in the global ring from the directory server and gradually finds other fingers and inserts their information in the table over the time. In addition to the finger table, in our proposed protocol every node keeps another hash table called zone finger table. This table is dedicated to keep the information of some proximate nodes which are registered in local ring. Speaking more specifically, It maintains the information of about O(LogM) overlay nodes, where M is the number of overlay nodes in the same zone. This table gets initialized by the IP address of successor node in the local ring. The other procedures are the same as those are used to build the finger table in original Chord. Fig. 5: Global and local rings Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Like the finger table, this table is used to find the proper next hop when there is a key location request. The detailed information is presented in the next subsection. Chord keeps the information of global ring in a directory server. When a new node n new decides to join the network, it sends a join request to the directory sever. Upon receiving the request, the server assigns an identifier to n new by hashing its IP address and then registers it in the proper position in the global ring regarding its identifier. Using the global ring information, directory server also sends the IP addresses of successor and predecessor to nnew. Having these addresses, n new will be able to gradually get familiar with other overlay nodes and build its finger table. 3.5. Key Location Procedure When a key location request arrives at a node, the node first checks to see if the value of requested key is stored in its own storage space. If not, the request will be forwarded to the next hop. In Chord, the next hop is selected using the available information in finger table and is the finger that has the closest identifier preceding the data key. In TAC protocol, the procedure for selecting next hop is slightly different. To find the proper next hop, every node first checks the identifier of requested key to see if it is smaller than the identifier of zone_successor (the node which is successor of current node in the finger table). If yes, the next hop is selected using the original procedure in Chord by selecting the closest preceding node from finger table. Otherwise, if the key’s identifier is greater than or equal to the identifier of zone_successor, the next hop is selected by finding closest preceding node from zone finger table. The pseudocode for this procedure is shown in Fig. 6. The size of finger table and zone finger table are assumed to be l and m respectively. In TAC, the directory server has slightly more responsibility. Besides keeping the information of global ring, it also keeps the information of geographical space partitioning and connectivity information of all local rings. In other words, the directory server is aware of all zones and their scopes. When nnew decides to join the overlay network, it sends its geographical coordinates to the server along with the join request. The directory server then registers n new with the global ring using same process in Chord. Moreover, by using the n new ‘s location coordinates, the server determines the zone in which n new is located and registers n new with the local ring of that zone. Like the 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 38 PDF created with pdfFactory Pro trial version www.pdffactory.com We implemented TAC protocol in Java, using SimJava 0 simulation library. To produce the network topology for our simulation, we used Brite 0 which is a well known representative internet topology generator. Brite gets some parameters about the topology from user and then gives the physical location of nodes in a square-shaped plane, under different placement models. These input parameters are the number of nodes n, the size of square side A, and the distribution model M under which the topology will be generated. In our experiments, we used two distribution models: random and heavy-tailed. In the random distribution model, every node is placed in a random location in the plane. However, in the heavy-tailed model, placement of nodes is done by focusing on some particular points. This model of distribution is more compatible with real world topologies since heavy-tailed distributions have been observed in the context of topological properties of Internet 0. Fig. 7 shows two sample network topologies generated by Brite using random and heavy-tailed distribution models. We simulated TAC protocol using both random and heavytailed topologies with n=1000 and A=1000. Furthermore, we divided the geographical space into different number of zones. The distance metric is based on topological distance between every two nodes on the plane. We distributed 2000 key among nodes using consistent hashing and set every node to submit a lookup query in every 100 milliseconds for 100 times. Furthermore, we divided the geographical space (plane in the Brite) into different number of zones (form 1 to // search the finger_table for the highest predecessor of id n.closest_zone_preceding_node(id) for i = m downto 1 if (zone_finger[i] (n; id)) return zone_finger[i]; return n; // search the zone_finger_table for the highest predecessor of id n.closest_preceding_node(id) for i = l downto 1 if (zone_finger[i] (n; id)) return zone_finger[i]; return n; Fig. 6: Pseudocode for selecting next hop in TAC Let’s clarify the procedure by an example. Referring to the global and local rings shown in Fig. 5, assume that a key location request which the identifier of its key is 24 arrives in node N3. The node N3 first compares the key with its zone_successor (here is N15) and finds that the key is larger. Therefore, it uses the closest_zone_preceding_node() procedure and finds that N15 is the proper next hop (closest preceding node in the zone’s finger table) and forwards the request to this node. In the other hand, when node N15 receives this request, finds that the requested key is smaller than its zone_successor (N26) and uses closest_preceding_node() to find the proper next hop. This operation will be repeated as long as the responsible node for this key is not found. a) random distribution b) heavy-tailed distribution 4. Experimental Results In this section, we evaluate the routing efficiency of TAC by means of experimental results which we have obtained by simulation. First, we describe the simulation environment in which the experiments are done. Second, to evaluate the proposed protocol, we used three metrics and compared the experimental results with Chord. These metrics are Distance Ratio (DR), Bandwidth Usage, and Hop Number which are discussed respectively. Fig. 7: Distribution of nodes by using two different models in Brite topology generator 1600) and evaluated TAC in all of them. In our experiments, the size of all zones is the same. 4.2. Distance Ratio The first metric we used to evaluate TAC, is Distance Ratio (DR): the ratio of the distance which a lookup query traverses to reach its destination node to the distance between its source and destination 0. It is clear that the 39 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 4.1. Simulation Environment // ask node n to find the successor of id n.find_sucessor(id) if ( id (n, zone_ successor)) n next = closest_preceding_node(id); else n next = closest_zone_preceding_node(id); return n next.find_successor(id); 4.3. Bandwidth Usage more efficient a routing protocol is, the less DR its packets have. In an ideal case, the traversed path will be equal to the distance between source and destination and thus DR will be 1. Bandwidth usage is the second metric which is used to evaluate the proposed protocol. Since TAC is more efficient in key location, it is expected to occupy less bandwidth during key lookups. To prove this claim, we considered the Average number of lookup Queries which are in Transit in the network (AQT) during key location. Fig. 9 shows the experimental results about AQTs which were obtained by partitioning the geographical space into different number of zones and using both random (Fig. 9(a)) and heavy-tailed (Fig. 9(b)) topology models. Similar to DR metric, the diagrams indicate that there is an optimum number of zones in which the bandwidth usage has its minimum value. Referring to Table 1 we can find that in comparison to Chord, TAC saves the bandwidth by %23 at least. Fig. 8 shows the average DR of lookup queries in Chord and TAC when the geographical space is divided into different number of zones. The experimental results which are shown in Fig. 8(a) and (b) are obtained by using the topologies which are created with random and heavy-tailed distribution models respectively. The DR of Chord is the same in all zones and shown in the diagram. As it can be seen, DR of both Chord and TAC are equal when the number of zones is 1. This is predictable since TAC with just 1 zone presents Chord. Furthermore, as the number of zones increases, the DR of TAC decreases. By dividing the geographical space into an optimum number of zones (10 in random model and 16 in heavy-tailed model), the DR reaches its minimum value. After this optimum point, the number of zones has a reverse effect on DR. The reason is that when the number of nodes of a zone decreases; the knowledge of nodes about their proximate nodes becomes lesser and the DR begins to increase. The numerical values shown in Table 1 indicate that by dividing the geographical space into an optimum number of zones, TAC reduces the average DR of Chord by %29.1 and %31 in random and heavy-tailed topologies respectively. 4.4. Hop Number The third metric we are going to talk about is the average number of hops which every lookup query traverses to reach its destination. Despite two previous metrics in which TAC surpasses the Chord, Fig. 10 shows that using TAC slightly increases average number of hops a query has to traverse. However this increase is negligible and according to Table 1 is less than %1.5. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 TABLE 1: Comparing experimental results of Chord and TAC when the number of zones is optimum Optimu Chord m Topology Distance model number Ratio of zones Random Heavy- 10 16 3.40 3.48 TAC Distance Ratio 2.41 2.4 Chord Chord TAC Averag Distance Bandwidth Bandwidt Bandwidth e Hop Ratio Usage h Usage Usage Numbe Change (query/seco (query/sec Change r nd) ond) - %29.2 - %31 20976 21417 5. Conclusions - %21.3 - %23.8 6.85 6.85 In our future work, we will focus on methods of calculating the optimum number of zones which would result in least average DR of queries. Furthermore, we are going to propose a mechanism to use TAC as an efficient local caching structure in P2P applications. Due to its lack of physical network topology information, Chord suffers from low routing efficiency, and ineffective use of bandwidth in data lookup. To alleviate this problem, we proposed TAC, a topology-aware Peer-to-Peer system which is based on Chord. In TAC, the geographical space is divided into smaller zones and the nodes within each zone are logically connected to each other. At the expense of storing the information of additional nodes, TAC improves routing efficiency of lookup queries. Our simulation results were promising and showed more efficient routing and less bandwidth usage. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 16506 16307 Hop TAC Avera Number Change ge Hop Numb er 6.96 %1.5 6.95 %1.4 40 PDF created with pdfFactory Pro trial version www.pdffactory.com (a) (b) Fig. 8: Average Distance Ratio of lookup queries in different number of zones; (a) (b) Fig. 9: Average number of lookup Queries in Transit in the network(AQT) in different number of zones; a)using random topology b)using heavy-tailed topology (a) (b) Fig. 10: Average number of hops traversed by lookup queries in different number of zones; (a) using random topology (b)using heavy-tailed topology 41 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 a)using random topology b) using heavy-tailed topology References Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 [1] Stoica, R. Morris, D. Karger, M. F. Kaashoek, and H. Balakrishnan, "Chord: A scalable peer-to-peer lookup protocol for internet applications", IEEE/ACM Transactions on Networking, vol. 11, no. 1, pp. 17–32, 2003. [2] Lua E. K., Crowcroft J., Pias M., Sharma R. and Lim S.,"A Survey and Comparison of Peer-to-Peer Overlay Network Schemes", IEEE Communication survey and tutorial, March 2004. [3] Napster. [Online]. Available: http://www.napster.com/ [4] Gnutella development forum, the gnutella v0.6 protocol. [Online]. Available: http://groups.yahoo.com/group/the gdf/files/ [5] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and S. Shenker, "A scalable content addressable network", in Processings of the ACM SIGCOMM, 2001, pp. 161–172. [6] Rowstron and P. Druschel, "Pastry: Scalable, distributed object location and routing for large-scale peer-to-peer systems", in Proceedings of the Middleware, 2001. [7] Y. Zhao, L. Huang, J. Stribling, S. C. Rhea, A. D. Joseph, and J. D. Kubiatowicz, "Tapestry: A resilient global-scale overlay for service deployment", IEEE Journal on Selected Areas in Communications, vol. 22, no. 1, pp. 41–53, January 2004. [8] Rostami H., Habibi J."Topology awareness of overlay P2P networks" Journal of Concurrency and Computation: Practice and Experience, InterScience, 2006 [9] F. Hong, M. Li, J. Yu, and Y. Wang, "PChord: Improvement on chord to achieve better routing efficiency by exploiting proximity," in Proceedings of the 25th IEEE International Conference on Distributed Computing Systems Workshops (ICDCSW’05), June 2005. [10] J. Xiong, Y. Zhang, P. Hong, and J. Li, "Chord6: IPv6 based topology-aware Chord," in Proceedings of the Joint International Conference on Autonomic and Autonomous Systems and International Conference on Networking and Services (ICAS/ICNS 2005), Aug 2005 [11] Dao L. H., Kim J.,"AChord: Topology-Aware Chord in Anycast-Enabled Networks", IEEE International Conference on Hybrid Information Technology (ICHIT'06), 2006. [12] F. Howell and R. McNab, "SimJava: A Discrete Event Simulation Package For Java With Applications In Computer Systems Modelling", First International Conference on Web-based Modelling and Simulation, San Diego, CA, Society for Computer Simulation, January 1998. [13] Brite, 2003. http://www.cs.bu.edu/brite/ December 2005 [14] Mirrezaei S. I., Shahparian J., Ghodsi M. "RAQNet: A topology-Aware Overlay Network", A.K. Bandara and M. Burgess (Eds.): AIMS 2007. Springer 2007. 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 42 PDF created with pdfFactory Pro trial version www.pdffactory.com An Intelligent Control Strategy in a Parallel Hybrid Vehicle Arezoo D. Abdollahi , S.K.Nikravesh , M.B.Menhaj management problem arises from the complex and coupling nature of sub-system efficiencies, together with the diverse driving scenarios. In particular, management of energy and distribution of torque (power) are two of the key issues in the development of hybrid electric vehicles [1]-[5]. These issues can be summarized as follows: 1- How to meet the driver's torque demand while achieving both satisfactory fuel consumption and emissions. 2- How to maintain the battery state of charge (SOC) at a satisfactory level to enable effective delivery of torque to the vehicle over a wide range of driving situations. In order to address these issues, an extensive set of studies has been conducted over the past two decades [1][16]. In particular, some logic based control strategies for distributing power demand have been suggested in Refs. [1]-[6]. These approaches are adopted mainly due to their effectiveness in dealing with problems appearing in the complexity of hybrid drive train via both heuristics (and human expertise) and mathematical models. However, these approaches generally do not address the driving situation that may affect the operation of the vehicle. As noted in Refs. [7]-[9], the application of optimal control theory to power distribution for hybrid vehicles appears promising. In addition, a number of studies, dating back to 1980s, have focused on the application of dynamic programming to HEVs [10]-[11]. These and the aforementioned optimal control strategies are, however, generally based on a fixed drive cycle, and as such do not deal with the variability in the driving situation. In view of this issue a number of alternative approaches have been proposed in the literature [12]-[13]. In particular, [14] formulated a drive cycle dependent optimization approach that selects the optimal power split ratio between the motor and the engine according to the characteristic features of the drive cycle. With noting to their selective drive cycles that may not track any chosen pattern, the risk of misclassification may be high. Furthermore, they didn't mention anything about Abstract: This paper presents a design procedure for an adaptive power management control strategy based on a driving cycle recognition algorithm. The design goal of the control strategy is to minimize fuel consumption and engine-out NOx, HC and CO emissions on a set of diversified driving schedules. Seven facility-specific drive cycles are considered to represent different driving scenarios. For each facility-specific drive cycle, the fuel economy and emission are optimized and obtained proper split between the two energy sources (engine and electric motor). A driving pattern recognition algorithm is subsequently developed and used to classify the current driving cycle into one of the facility-specific drive cycles; thus, the most appropriate control algorithm is adaptively selected. This control scheme was tested on a typical driving cycle and was found to operate satisfactorily. Keywords : Hybrid vehicle, torque distribution, fuzzy rule base, neural network, drive cycle. 1. Introduction A hybrid vehicle, using a combination of an internal combustion engine and electric motor, is an important concept to improve fuel economy and to reduce emission of vehicles as well. Therefore, Hybrid electric vehicles (HEVs) have great potential as new alternative means of transportation. Design and implementation of HEVs present a number of challenging problems. The objective of the power management control strategy is to develop a near optimal power management strategy that determines the proper power split to minimize the fuel consumption and emissions of the hybrid vehicle. In addition, the control strategy also needs to ensure that the power demand from the driver is satisfied and the state of charge (SOC) in the battery is maintained within a pre-determined range under all driving conditions. The main challenge of the power 43 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Electrical Engineering, Department Amirkabir University of Technology, Tehran, Iran initial condition at the start times of vehicle's driving, their results may be far from optimal results. Another issue explained in [15],[16] is Intelligent Energy Management Agent (IEMA) that includes a driving situation identifier whose role is to identify the roadway type, the driving style of the driver as well as the current driving mode and trend. This information is subsequently integrated in a fuzzy logic based torque. Because of using the experimental results to generate fuzzy rules, there isn't any indicator to show how much it works optimally. Hence, the concept of fuel consumption and emission in hybrid vehicles is very sensitive to a drive cycle. So, if the driving control strategy of HEV is not suitable for a current drive cycle, vehicle performance can be worse than that of a conventional vehicle. Table 1: The calculated correlation between facility specific drive cycles Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 In this paper, there are three main topics. First, we develop an algorithm to cluster a current drive cycle as one of nine facility- specific drive cycles by using a neural network. Second, we introduce a control algorithm that adapts the driving control strategy to a current drive cycle using the driving cycle identifier. Third, if during the first 150s of driving, driving data is not sufficient to extract a rich set of driving information, we develop an algorithm to identify initial conditions. In order to show the effectiveness of the proposed control strategy, we run some simulations. The results are promising. Finally, conclusions are drawn in the last part of the paper. Regard to Table 1 , we can choose the drive cycles having correlation value more than "0.5" to be the same cycle. This threshold is selected in order to have enough drive cycles while they are quasi-independent. For example , cycle 2 can be considered as representative of cycles 1, 2, 3 and cycle 5 is representative of cycles 5 , 6 and cycle 11 is representative of 10 , 11. Furthermore we will use only seven facility specific cycles instead of eleven cycles (see Fig. 1.). 2. Selection of Seven Facility-Specific Drive Cycles 2.1. Facility-Specific Drive Cycles we adopted a set of eleven drive cycles developed in Sierra Research Inc.[15],[17], each of which has its own facility-specific characteristics (for operation over a range of facilities on congestion levels, LOS1). In [17], authors claimed the original area-wide cycle concept was to develop a family of composite driving cycles to represent overall travel within urban areas with different levels of congestion and average speed (facilityspecific drive cycles). We used these cycles to identify current drive cycle but some misclassification were occurred. So, we calculate their correlation to choose quasi-independent facility specific cycles. In order to do that, we should build characteristic parameters vector by using Table 2 (in section 2.2) for each facility-specific drive cycles and calculate their correlation (see Table 1). 1 Fig. 1: Facility-specific driving cycles 2.2. Characteristic Parameters of a Drive Cycle The mission of this part is to extract the key statistical features, or characteristic parameters of the driving pattern. While according to Ericsson [18] up 40 characteristic parameters may be extracted from a given drive cycle such as average speed, average acceleration and etc.(see Table 2). Level Of Service 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 44 PDF created with pdfFactory Pro trial version www.pdffactory.com selected due to its effectiveness in the classification on complex and nonlinearly separable target classes [20]. Table 2: Driving pattern parameters that were calculated for each driving cycle, v = speed , a = acceleration , r = deceleration ,Ericsson [18] 2.3.1. LVQ Network Driving cycle parameter Average speed % of time 2.5>a>1.5, m/s2 Standard deviation of % of time 1.5>a>1, m/s2 speed Average acceleration % of time 1>a>0.5, m/s2 Acceleration Standard % of time 0.5>a>0, m/s2 deviation Average deceleration % of time 0>r>-0.5, m/s2 Deceleration Standard % of time –0.5>r>-1, deviation m/s2 Number of adjacent max % of time -1>r>-1.5, and min values of the m/s2 speed curve>2km/h per 100s Number of adjacent max % of time –1.5>r>-2.5, and min values of the m/s2 speed curve>2km/h per 100m Number of adjacent max % of time r<-2.5, m/s2 and min values of the speed curve>10km/h per 100s Number of adjacent max % of time speed <2km/h and min values of the speed curve>10km/h per 100m Relative positive Average stop duration acceleration The integral of Number of stops per acceleration kilometer % of time 0<v<15 , km/h % of time when (v.a)<0 % of time 15<v<30 , km/h % of time when (v.a) is 0-3 % of time 30<v<50 , km/h % of time when (v.a) is 3-6 % of time 50<v<70, km/h % of time when (v.a) is 6-10 % of time 70<v<90, km/h % of time when (v.a) is 10-15 % of time 90<v<110 , % of time when (v.a) is km/h >15 % of time v>110 , km/h Average (v.a) % of time a>2.5, m/s2 Positive kinetic energy A LVQ network classifies its input vector into one of the number of target classes through a two stage process. In the first stage, a competitive layer is used to identify the subclasses of input vectors. In the second stage, a linear layer is used to combine these subclasses into the appropriate target classes. The structure of the LVQ network is shown in Fig. 2. 2.3.2. Training of LVQ Network and Validation In order to train the LVQ network for roadway type classification, the statistics of nine facility-specific drive cycles (Fig. 1.) were calculated in terms of the characteristic parameters defined in Table 1. The initial training data set of the LVQ network is consisted of a [40 × 7] matrix. When we validated this network, we figured out that five of 40 parameter in Table 2 have larger values in comparing with the others. They are: • Average speed • Max speed • Trip time • Relative positive acceleration 1 va + dt , ∫ x RPA = x = total distance, dv + a = >0 dt , v=speed 2.3. A Neuro-based Drive Cycle Recognition For real-time drive cycle recognition, we employ the Learning vector Quantization (LVQ) algorithm and its modifications [19]. For the purpose of classification, in this study a supervised competitive LVQ Network is • PKE : Positive Kinetic Energy, X =distance, 45 ∑ (v 2 f − vs2 ) x , v f = final speed, v s = start speed 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Fig. 2: The LVQ network architecture Each neuron in the competitive layer of the network computes the Euclidean distance between the given input vector, p and a prototypical subclass vector w. With this in mind, for instance, the ith neuron in the competitive layer computes: d = wi − P Subsequently, the competitive layer (designated as "C") assigns a 1 to the closest subclass to the given input vector and 0 to all other subclasses represented in the network. The linear layer combines the given identified subclasses into a (target) class. 1 − ω di 1 + ω < < 1+ω d j 1−ω Then, these parameters avoid other parameters to contribute in training. Thus following [15], each parameter value (input vector) was transformed into an array with entries of 1 and -1 as to four levels. For example, in case of first characteristic parameter (average speed), the value at each facility-specific drive cycles is 60.8, 29.84, 18.71, 34.29, 24.6, 19.12, 12.16 (mph) , so, their average m is 28.5(mph) and their standard deviation std is 16.04(mph). The level of each parameter is decided by three standards, which are m+a × std, m, m-a × std for example, if the value of any parameter is larger than m+ a × std, its level is 1,etc. (see Table 3). where d i and d j are the Euclidean distance of p from wi and wj , respectively. A relative window width ω in the interval [0.2,0.3] is recommended by Kohonen, while its legitimate range is 0< ω <1.) In the case of fulfilling the afore-mentioned conditions, the update rule is: wi (t + 1) = wi (t ) + α (t )[ p − wi (t)] wj (t + 1) = wj (t ) − α (t )[ p − wj (t )] Table 3: Each parameter transforms into an array P > m+ a × std m+ a × std >P > m m-a × std <P < m P < m-a × std Leve1 1:{1, 1, 1} Leve1 2:{1, 1, -1} Let p be an input vector (from training set): where wi is network weighting supposed to be in the same class as p , and wj is network weighting in a different class. Leve1 3:{1, -1, -1} Leve1 4:{-1,- 1, -1} Our competitive network give perfect match because we selected quasi-independent drive cycles in section 2.1 Then the results were verified with some test data which were obtained from ADVISOR's2 default (for example, Fig. 4. and Fig. 14.) and actual drive cycles library with same Characteristic parameters. This LVQ network using the facility-specific driving cycle data given in [17], will be proper roadway type identifier (Fig. 3.). a is a tuning parameter and is chosen as 0.5. Because of this transformation, number of neurons in competitive layer is increased to avoid over training phenomenon. Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 We validated this network again and because of using single set of characteristic parameters for relatively long drive cycles [15], we still found indispensable error. Thus each drive cycle was divided into an appropriate number of 150 seconds that constitute subclasses of the whole drive cycle (its seven subclasses convert to approximately 33 subclasses). In order to enhance the training performance of the network, we used LVQ 2.1 after LVQ for fine tuning of decision borders. (Kohenen [19] recommended that the learning process be started with LVQ, and if necessary continued by LVQ2.1, with a low initial learning rate value). Learning here is similar to that in LVQ except two vectors of layer 1 that are closest to the input vector may be updated providing that one belongs to the correct class and one belongs to a wrong class and further providing that the input falls into a "window" near the mid plane of the two vectors. The window is defined by [19]: Fig. 3: The result of network for classifying 7 drivecycles with considering 33 subclasses 1. One of them should belong to the correct class (as the label of p) and the other one to a wrong class. 2. p should fall in the window that is defined around the mid-plane of wi and wj . (p is defined to fall in the window If 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 2 ADvanced VehIcle SimulatOR 46 PDF created with pdfFactory Pro trial version www.pdffactory.com shaft and λ f is the gear ratio of final differential. Equation (1) above is a two degrees of freedom of three control variables Tice , Tem and ng , because the value of Tw is defined at each time. The optimization process is performed under the mechanical constraints imposed by the driveline design [13 ] . 0 < Tice (t ) < Tice _ max Tem _ min < Tem (t ) < Tem _ max 0 ≤ ωem (t ) ≤ ωmax (a) ωice _ min ≤ ωice (t ) ≤ ωice _ max Where ωice is speed of engine and ωem is speed of electric motor. Another constraint is that the battery state of charge (SOC) is maintained within a prescribed range: SOClow < SOC (t ) < SOChigh Ideally the power distribution has to be chosen to minimize the overall engine fuel consumption over a given driving cycle within the constraints listed above, such as: (2) Min ∑ m& f (t ) (b) Fig. 4: (a) HWFET, One of the highway drive cycles of advisor's library. (b)Identified roadway type as will be explained in Table 4. 3. Control Strategy Implementation & f (t ) = Engine fuel flow rate. With m 3.1. Optimization of Control Parameters at Each Facility-Specific Drivecycle In this study, regardless of dynamic model of vehicle, we consider a parallel HEV with static and quasi-static models in ADVISOR whose required power in driving is supplied by 41kw engine and 75kw electric motor. Thus, we have some efficiency map and lookup table for our optimization. Then, we used the approach which is based on static optimization methods. & feq defined We used equivalent fuel consumption m The control strategies’ objective was minimum possible fuel consumption and emission for a given drive cycle. The behavior and the limitations of the powertrain’s components were adapted by optimization process [13]. The method is an offline tool that is based on optimal control theory. According to the mechanical arrangement, of the vehicle, (Fig.5.), the relationship between torques is [13 ]: Tw = ((λt (ng ).Tice + λb .Tem ).λ f (1) & f (t ) (see (2)). Where the equivalent below instead of m fuel flow rate cost function is simply defined as the sum of the actual fuel consumption of the engine and the equivalent fuel rate used due to the electric motor (positive or negative): & feq = m &f +m & fem m Commonly, electric power is translated into an equivalent amount of (steady-state) fuel rate in order to calculate the overall fuel cost [22]. Fig. 5: Mechanical arrangement Where Tw is the total torque required at wheel, Tice is the torque provided by the ICE engine (positive only), Tem is the torque provided by the electric motor (positive or negative ), λt ( ng ) is the gear ratio of the transmission Step 1: Define the range of candidate operating points, represented by the range of acceptable motor torques for the current torque request [22]: This relationship between engine, motor, and requested torque is described by (3). [22]. and a function of the gear selected ng , λb is the belt Tengine = Trequest − ratio × Tmotor ratio of coupling between the electric motor and the drive 47 (3) 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 {Tem (t ), n g ( t )} Where: ratio = motor-to-engine gear ratio expected increase in SOC from regenerative braking is deemed “free energy” because no fuel energy must be consumed to obtain it. Then, in order to apply a strategy at nine given drive cycles, we can run electric vehicle (the vehicle just have an electric motor) in ADVISOR and obtain ∆SOCregen , in Step 2: For each candidate operating point, calculate the constituent factors for optimization [22 ]: • Fuel energy consumed by engine: For a given torque request and motor torque, Equation (3) sets the engine torque. At this torque and given speed, the engine map provides the fuel consumed by the engine (see Fig.6.). battery when vehicle is in braking mode. Braking act in ADVISOR is distributed between driveline braking (regeneration) and friction braking (normal). So, we first ran vehicle simulator (ADVISOR) at nine given drive cycles in electric mode (only there exists an electric motor in powertrain) when both of two kinds of braking (regeneration and friction) are considered. The second run included just friction braking. Difference between two obtained SOC results, would be ∆SOCregen . To explain this procedure, we give an example. Consider a simple drive cycle with one braking part (as shown in Fig. 9. ). We obtain ∆SOCregen as mentioned above and it is shown in Fig.9 . Fig. 6: Engine energy efficiency map Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 • Calculate the effective fuel energy that would be consumed by electromechanical energy conversion(equivalent): Fig.9: a Drive cycle with its Finally, combine the two curves given in figures 7,9 and into fuel energy as shown in Fig. 10. Find fuel energy with respect to motor torque: Fig. 7: Fuel energy with respect to motor torque Fig. 10.: Fuel energy with respect to motor torque • Emissions produced by engine: Ereference in Fig. 7 indicates the case where Tmotor is zero, or where engine supplies all of the requested torque. Find ∆SOC with respect to motor torque,(see Fig. 8.). In general, the relationship between ∆SOC and motor torque is nonlinear for two reasons: 1) the motor efficiency map is nonlinear, and 2) charge and discharge resistances of batteries typically differ. The calculation of emissions produced over the range of torque is very similar to the engine energy consumption calculation (using emission maps). Step 3: we first normalize each of them (energy and emission), then apply our weighting to their curves and finally compute the impact function (objective). Step 4: Finally, we find minimum of the objective function and its corresponding torque. This optimization scheme results in a proper split between the two energy sources using steady-state efficiency maps [13] , [21] . We carry out this optimization scheme at each facility-specific drive cycles and store engine torque (Tengine), demand torque (Trequest) and state of charge (SOC) in each step. Fig. 8: ∆SOC with respect to motor torque During operation, a hybrid vehicle recaptures a certain amount of energy through regenerative braking. The 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ ∆SOCregen 3.2. Extracting Fuzzy Rule Base 48 PDF created with pdfFactory Pro trial version www.pdffactory.com After storing all data (Tengine , Trequest , SOC) calculated in the last part, we apply them to ANFIS toolbox in MATLAB (Trequest & SOC as inputs and Tengine as an output) to extract a proper fuzzy rule base to implement the control strategy.(see Fig. 11. ). information, so, we developed an algorithm to identify first 150s. We used a standard competitive network to identify initial conditions after starting the vehicle as we did in section 2. Although because of insufficient data we cannot extract all characteristic parameters that used in section 2, we only used 8 of them that were found to have large effects on either or all of emission factors of CO2 , HC, and NOx (g/km) and fuel consumption (per 10 kilometers). Those were [18]: • Factor for acceleration with strong power demand • Stop factor • Factor for acceleration with moderate power demand • Extreme acceleration factors • Factor for speed 50-70mph • Factor for speed 70-90mph • Deceleration factor • Speed oscillation factor We trained our network with these parameters and classified first seconds driving information as one of seven facility-specific drive cycles and switch to the corresponding control strategy. Then we updated driving data each 5 seconds. So this competitive network give fairly good match and its result is better than that of random roadway type selection. Fig. 11: Buzzy rule base controller Then, we can find electric motor torque using (3). 3.3. Selection of Control Strategy in Current Driving Cycle Fig.12. shows the concept of this control strategy, where “1 s ” is the sampling time step for measuring vehicle input signals and generating control commands. First, characteristic parameters in the historical window ‘150 s ’ are extracted, based on which the driving cycle over this historical window will be determined. Next, the control algorithm will be switched to the relative control algorithm corresponding to the newly identified facilityspecific drive cycles. Finally, the control actions will continue for the next 5 seconds. In this section, we present the simulation study to evaluate the proposed energy management system.For the simulation study, a typical parallel drivetrain with manual 5-speed transmission is used. The models of the power train components are taken from [22]. The vehicle has a total mass of 1350 kg. An internal combustion engine with a displacement of 1.0 L, peak power of 41 kW and peak efficiency of 34% is chosen. In order to satisfy the requirement for acceleration, a motor with a power of 75 kW and peak efficiency of 92% is selected. The battery capacity of 26Ah (with 12v) with a weight of 275 kg is chosen. The battery’s type is VRLA. Typical parallel drivetrain is shown in Fig. 13. Fig. 12: Control strategy configuration We run the program of characteristic parameter extraction and drive cycle recognition less than ‘0.71s’; we should notice that the sampling time step is 1 sec. Therefore, we may consider it as a real time procedure. 4. Identification of First 150s of Driving Noting that during the first 150s of driving, driving data is not sufficient to extract a rich set of driving Fig. 13: Parallel hybrid vehicle configuration[22] 49 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 5. Simulation Results In this section, the performance of the vehicle under the supervision of our control strategy on the US06 is investigated. This drive cycle (US06) was developed to represent vehicle operation under urban driving conditions characterized as ones over a relatively long route that traverses numerous roadway links. The preliminary simulation study on the US06 indicates that the US06 (see Fig. 14.a ,14.b.) is a composite cycle that can be decomposed into different types of roadway. For instance, especially in this simulation, the US06 is decomposed into the facility-specific drive cycles considered (see Table 4) in this study as shown in Fig. 14.b . low and there exists sufficient amount of regenerative SOC that compensates the lack of battery's SOC. We carried out the simulation in ADVISOR and compared our control strategy results with those of fuzzy logic control (baseline and emission mode [22]) in ADVISOR. The results show that our applied control strategy performance such as fuel-consumption and emission are superior, see Table 5. Table 5: Performance result on the US06 US06 Table 4: Facility specific drive cycle (mile/ga l) Fuel econom y 64.4 (grams/mile) HC CO NOx 0.317 2.659 0.21 60 0.346 2.157 0.266 35.4 0.536 7.977 0.508 Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Type Facility specific drive cycle 1 Freeway under LOS A-C 2 Freeway under LOS E 3 Freeway under LOS F 4 Freeway ramp 5 Arterial under LOS A-B 6. Conclusions 6 Arterial under LOS C-D 7 Local roadway A proposed control strategy based on the driving pattern recognition scheme was developed for a hybrid electric vehicle to minimize fuel consumption and engine-out emissions over various driving scenarios. So, we used seven facility-specific drive cycles developed in Sierra Research. And we developed a real-time driving cycle recognition algorithm using LVQ network. final algorithm was the control strategy which switches a current driving control strategy to the algorithm optimized in a recognized facility-specific drive cycle. then we verified the performance of this control strategy in fuel consumption and emission reduction by using an initial interval of driving identifier. The simulation results were very promising . Proposed control strategy Emission mode Baseline (a) Acknowledgment (b) The authors wish to thank professor Langari and Dr. Ericsson for their help. References [1] C. Liang, W. Qingnian, L. Youde, M. Zhimin, Z. Ziliang, and L. Di, "Study of the electric control strategy for the power train of hybrid electric vehicle", in Proc. of the IEEE International Vehicle Electronics Conf. (IVEC '99), vol. 1, Changchun, China, September 1999, pp. 383-386. [2] N. Jalil, N. A. Kheir, and M. Salman, "A rule-based energy management strategy for a series hybrid vehicle", in Proc. of the American Control Conf., vol. 1, Albuquerque, NM, June 1997, pp. 689 -693. [3] B. M. Brahma,"Inteligent control strategies for hybrid vehicles using neural network and fuzzy logic",Elect. Eng; ohio state univ. ,coluombos, 1997 [4] N. J. Schouten, M. Salman, and N. Kheir, "Fuzzy logic control for parallel hybrid vehicles" ,IEEE Trans. on Cont. © Fig. 14: (a) US06 drive cycle, (b) identified current drive cycle, (c) SOC varies in range 0.4 -0.7 As shown in Fig. 14. a. and Fig. 14.c. two parts that marked A and B explain us some useful information. The drive cycle types identified in part A, belong to roadway types 1-4. So, in these road way types torque request will be high and we have too little regenerative SOC then SOC decrease fast. But in part B, current drive cycle belongs to roadway type 4-7. So, the torque request is 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ 50 PDF created with pdfFactory Pro trial version www.pdffactory.com /advisor Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 Syst. Technology, vol. 10, no. 3, pp. 460-468, May 2002. [5] J.-S. Won and R. Langari, "Fuzzy torque distribution control for a parallel hybrid vehicle", Expert Systems: The International Journal of Knowledge Engineering and Neural Networks, vol. 19, no. 1, pp. 4-10,February 2002. [6] M. Salman, N. J. Schouten, and N. A. Kheir, "Control strategies for parallel hybrid vehicles", in Proc. of the American Control Conf.,Chicago, IL, June 2000, pp. 524-528. [7] A. Kleimaier and D. Schr®oder, "Optimization strategy for design and control of a hybrid vehicle", in Proc., 6th International Workshop on Advanced Motion Control, Nagoya, Japan, March 30 - April 1 2000,pp. 459-464. [8] S. Delprat, T. M. Guerra, and J. Rimaux, "Control strategies for hybrid vehicles: Optimal control", in Proc., Vehicular Technology Conf. (VTC 2002-Fall), vol. 3, Vancouver, Canada, September 2002, pp. 1681-1685. [9] S. E. Lyshevski and C. Yokomoto, "Control of hybridelectric vehicles",in Proc. of the American Control Conf., Philadelphia, PA, June 1998,pp. 2148-2149. [10] A. Brahma, Y. Guezennec, and G. Rizzoni, "Optimal energy management in series hybrid electric vehicles", in Proc. of the American Control Conf., Chicago, IL, June 2000, pp. 60-64. [11] M. Oprean, V. Ionescu, N. Mocanu, S. Beloiu, and C. Stanciu, "Dynamic programming applied to hybrid vehicle control", in Proc. of the International Conf. on Electric Drives (ICED 88), vol. 4, Poiana BRA W SOV, Romania, September 1988, pp. D2/10/1-20 [12] J.-S. Won, R. Langari, and M. Ehsani, "Energy management strategy for a parallel hybrid vehicle", in Proc. of International Mechanical Engineering Congress and Exposition (IMECE '02), New Orleans, LA,November 2002, pp. IMECE2002-33460. [13] G. Paganelli, M. Tateno, A. Brahma, G. Rizzoni, and Y. Guezennec,"Control development for a hybrid-electric sportutility vehicle: Strategy,implementation and test results", in Proc. of the American Control Conf.,vol. 6, Arlington, VA, June 2001, pp. 5064-5069. [14] C. C. Lin, S. Joen, H. Peng, J. M. Lee,"Driving pattern recognition for control of hybrid electric trucks" [15] J-S. Won and R. Langari, "Intelligent Energy Management Agent for a Parallel Hybrid Vehicle, Part I: System Architecture and Design of the Driving Situation Identification Process," IEEE Transactions on Vehicular Technologies, (accepted for publication 05/04.) [16] J-S. Won and R. Langari, "Intelligent Energy Management Agent for a Parallel Hybrid Vehicle, Part II: Torque Distribution and Charge Sustenance Strategies and Performance Results", IEEE Transactions on Vehicular Technologies. (accepted for publication 06/04.) [17] T. R. Carlson and R. C. Austin, "Development of speed correction cycles", Sierra Research, Inc., Sacramento, CA, Report SR97-04-01,April 30 1997. [18] E. Ericsson, "Independent driving pattern factors and their influence on fuel-use and exhaust emission factors", Transportation Research Part D,vol. 6, pp. 325-341.2001. [19] T. Kohonen, Self-Organizing Map, Springer, Berlin, 1995. [20] M. B. Menhaj, "Computational Intelligence (vol.1), Fundomentals of neural networks",2002 [21] C. Kim, E. NamGoong, and S. Lee, "Fuel Economy Optimization for Parallel Hybrid Vehicles with CVT", SAE Paper No. 1999-01-1148. [22] ADVISOR 2002, NREL, www.ctts.nrel.gov/analysis 51 1386‫ ﭘﺎﺋﯿﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﯿﻦ ﺑﺮق و اﻟﮑﺘﺮوﻧﯿﮏ اﯾﺮان‬ PDF created with pdfFactory Pro trial version www.pdffactory.com Development of Average Model for Control of a Full Bridge PWM DC-DC Converter Ali Asghar Ghadimi 1, Hassan Rastegar 1, Ali Keyhani 2 1- Department of Electrical Engineering Amirkabir University of Technology, Tehran, Iran 2- Department of Electrical and Computer Engineering The Ohio State University, Columbus, Ohio, USA demand of electric power and environmental regulations due to green house gas emission [1-3]. Advances in power electronics and energy storage devices for transient backup have accelerate penetration of the distributed generation into electric power generation plants. Most of this generation’s unit has DC output and in order to produce higher AC voltage than the DC output voltage, they must have a DC/DC boost converter and a DC/AC inverter as shown in figure 1. Abstract: Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 This paper presents a detailed small-signal and transient analysis of a full bridge PWM DC-DC converter designed for high voltage, high power applications using an average model. The derived model is implemented in a typical system and used to produce the small-signal and transient characteristics of the converter. Results obtained in the analysis of the high voltage and high power design example is validated by comparison for actual system and derived model. The derived small signal model is used to design a controller to regulate output voltage of the converter under several disturbances. A PD controller with combination of a feedforward input voltage is designed so that the output voltage is equal to desired voltage and the time response is very short under load and input voltage disturbances. Fig. 1: Basic block diagram of a power conversion system Keywords: Full Bridge DC-DC Converter, Modeling, Steady-State and Dynamic analysis, Voltage Regulation, Control DC-DC converters can be used to boost and regulate low output voltage of any DC source like some new distributed generation units to high voltage and compensate for its slow response during the transient. The main task of these converters is to maintain the output voltage at constant and predefined level. To boost low voltage DC to high voltage DC a forward boost converter, a push-pull boost converter or an isolated full-bridge DC to DC power converter can be selected. Among these power converters, Full-Bridge converters are the most attractive topology for high power generation [4-6]. 1. Introduction Today, new advances in power generation technologies and new environmental regulations encourage a significant increase of distributed generation resources around the world. Distributed generation systems have mainly been used as a standby power source for critical businesses. For example, most hospitals and office buildings have stand-by diesel generators as an emergency power source for use only during outages. However, the diesel generators is not inherently costeffective, and produce noise and exhaust that would be objectionable on anything except for an emergency basis. On the other hand, environmental-friendly distributed generation systems such as fuel cells, micro turbines, biomass, wind turbines, hydro turbines or photovoltaic arrays can be a solution to meet both the increasing 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ For control purpose and analyzing the behavior of converter, dynamic analysis of converter must be done. The choice of the average modeling method to study both large and small-signal characteristics of modern power converters has become widely accepted due to its adaptability to computer simulation. When an average 52 model is simulated, it requires with less computation time than the switched circuit model [5]. Dynamic performance of PWM dc-dc converter has been analyzed using state space averaging method in continues and discrete time domain [5-8]. In this paper, a large signal and small signal model of full-bridge dc-dc converter are studied. In this study, the parasitic resistances of switches are considered. This paper is presented in seven sections. In Section 2, a discussion of Full-Bridge converter’s operation is presented and in Section 3 the average model is described. The validity of derived model is verified by mean of simulation in section 4. Steady state analysis and dynamic model are presented in section 5, and in section 6 the proposed average model is validated by comparison to the switched circuit model. In section 7 design of controller for regulating output voltage and simulation result presented and finally in section 8, the conclusion of paper is presented. Fig. 2: Operation of full bridge converter Figure 2 shows the circuit schematics of a full bridge converter that consist of a full bridge power converter (Q1 to Q4), a high frequency transformer (with ratio 1:n), a bridge diode, and an output filter (L,C). The diagonally opposite switches (Q1 and Q2, or Q3 and Q4) are turned on and off simultaneously in a portion of each half cycle of switching frequency as shown in Figure 2 (for time interval D.TS). When all four switches are turned off, the load current freewheels through the rectifier diodes (for time interval TS/2-D.TS). The PWM pulse generator has input of Duty Cycle (D) and will produces appropriate pulses and sends them to switches. Figure 3 shows signal waveform for producing appropriate pulses according to desired duty cycle (D). Fig. 3: PWM generation for full bridge converter In order to reduce the size and the weight of magnetic components, it is desirable to increase the switching frequency for DC-DC converters. However, when the switching frequency is increased, switching losses would increase, and snubbers and protection are required, which introduce significant losses and lower the efficiency. As shown in figure 3, a constant signal (Reference) is compared with a rectangular high frequency signal (Carrier). When carrier signal go over reference signal a pulse will produce and similarly negative value of reference signal will compare with carrier for producing other half cycle pulse. As shown in this figure, by changing reference signal from 0 to 1 we can have pulse with duty cycle of 0.5*TS to zero. These two pulses give to pair of switch and the switches will conduct in each half period with duration of D.TS. 3. Deriving Average Model for FullBridge Converter For modeling the full bridge converter and driving averaged model, it is assumed: • Transistor and diodes are identical • Transistors and diodes have on resistance rT, rD respectively. • The output filter so designed that inductor current is continues in each switching period. 53 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 2. Full-Bridge Converter Operation In this circuit, there are two state variables including capacitor voltage and inductor current. As illustrated in previous section, full bridge converter has two modes of operations in each half cycle [9]: 3.1. Mode 1 In this mode, switches Q1 and Q2 are in on mode and delivering energy to load via transformer and two diodes. For this mode, the circuit model is as shown in figure 4. Using KVL and KCL, the state equation of the circuit can be derived as presented below. In this model the state variables are inductance current (X1) and capacitor voltage (X2): Fig. 5: Mode 2 of operation Again KVL and KCL yield this equation: KVL : 0 = rD X 1 + LX& 1 + X 2 X KCL : X 1 = CX& 2 + 2 R 2 where Rth = 2n rT + 2rD (3) X KCL : X 1 = CX& 2 + 2 R KVL : nVd = Rth X 1 + LX& 1 + X 2 And therefore state matrices in this mode are: (1) 1 ⎤ ⎡ rD − ⎢− L ⎥ L A2 = ⎢ ⎥ 1 1 ⎢ ⎥ − ⎢⎣ C RC ⎥⎦ C 2 = [0 1] ⎡0 ⎤ B2 = ⎢ ⎥ ⎣0 ⎦ (4) Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Finally, based on averaged model concept [5,9], and because the last half cycle is identical to first half, averaged model of this converter in TS/2 can be obtained as: X& = AX + BVd ⎡ Rth 2d + rD (1 − 2d ) ⎢− L ⎢ ⎢1 ⎢⎣ C Therefore the state space model and matrices in the interval d.Ts are: 1 ⎤ ⎡ R th − ⎥ ⎢− L L A1 = ⎢ ⎥ 1 ⎥ ⎢1 − ⎢⎣ C RC ⎥⎦ C1 = [0 1] , V0 = C1X ⎡n ⎤ B1 = ⎢ L ⎥ ⎢ ⎥ ⎣0 ⎦ V0 = CX A = A1 2d + A2 (1 − 2d ) = Fig. 4: Mode 1 of operation & = A X+BV X 1 1 d , ⎡ 2dn ⎤ B = B1 2d + B2 (1 − 2d ) = ⎢ L ⎥ ⎢ ⎥ ⎣0 ⎦ C = C1 2d + C 2 (1 − 2d ) = [0 (2) (5) 1] This averaged model state equation can be used for simulation of converter instead of the model with multiple switches that may have long simulation time and also this state equation can used for analysis of original one performance and development of controller and stability studies. Based on above average model, the following electrical circuit model can be derived and used for simulation, design of controller, and stability studies. 3.2. Mode 2 In this mode, all switches are off and load current flow through bridge diodes and circuit can be modeled as figure 5. 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ 1 ⎤ L ⎥ ⎥ 1 ⎥ − RC ⎥⎦ − 54 Fig. 6: Large signal average model of full bridge converter Fig. 7: Step change in duty cycle from 0.2 to 0.3 and voltage in modeled system and actual one 4. Model Validation To validate the proposed method, a 5 kW system with the parameter shown in table 1 is considered for the study. The PSCAD/EMTDC that is an industry standard simulation tool for studying the transient behavior of electrical networks [10] is used for simulation. In this study, the Output filter of the converter is so designed that there is 2% ripple in inductor current and 1% ripple in output voltage [11]. 7 Advanced Graph Frame 310 330 Vout_Actual (V) Vout_Model (V) 300 290 12.5 280 5e-3 270 260 250 240 230 For verifying the proposed model, actual system and averaged model in large signal are simulated in 3 cases: 220 210 Time 0.990 1.000 1.010 1.020 1.030 1.040 1.050 1.060 1.070 . . . Fig. 8: Simulation results for step change in load resistance 4.1. Step Change in Duty Cycle (D) In this case the actual system and averaged model simulated with d=0.2 and then in time 1 second the duty cycle change from 0.2 to 0.3. Figure 7 shows the simulation results in this case and the actual system and derived model results represented together for compare. Results show near perfect agreement, with the average model closely tracking those of the actual circuit and the model is valid in this large signal change in duty cycle (D). 4.3. Change in Input Voltage In final case study, a change in input voltage is simulated during changing input voltage from 50 volts to 40 volts in 0.5 sec and the results also show that two waveforms are identical (Figure 9). 55 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 In this case a load transient from 100% to 50% full load is simulated at 1 second by turning off the load switch. Results from the transient simulation from both methods are shown superimposed in figure 8. As the figure shows, two waveforms are exactly identical and it is impossible to separate them. The figure also shows that output voltage drop when load is increased in this open loop system. Output Voltage (V) Table 1: System Parameter Input Voltage-Vd Filter Inductance 50 (Volts) L (milli Henry) Transformer Filter Capacitance5 Power (kVA) C (micro Farad) Transformer Load Resistance-R 50:500 Voltages (ohms) Switching Switches on 2000 Frequency (Hz) Resistor (ohms) 4.2. Chang in Load Advanced Graph Frame 320 Vout_Actual (V) Figure 10 shows the dc output to input gain (m) versus duty cycle (D) in several load resistance. As the figure shows there is approximately linear relationship between dc gain and duty cycle and as D increase from 0 to its maximum value (0.5), output voltage to input voltage gain will increase approximately in a linear manner. From the curves, it is clear that an increase in load (by decreasing load resistance) result in a decreased gain for a constant duty cycle. Therefore, the steady state voltage must be regulated by changing duty cycle (D). Vout_Model (V) 300 280 Output Voltage (V) 260 240 220 200 180 160 140 Time 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 . . . 10 Fig. 9: Simulation waveform for step change in input voltage Steady State Gain of Converter Vo/Vi 9 5. Steady-State Analysis With the model of state space equation and matrices A,B,C a small ac perturbation (represented by ~) and dc steady state (In upper case letters) quantities for model parameter considered as: 8 7 6 R Increase 5 4 3 2 1 x= X +~ x , vo = Vo + v~o ~ d = D + d , vd = Vd + v~d 0 (6) 0 0.05 0.1 0.15 0.2 0.25 0.3 Duty cycle 0.35 0.4 0.45 0.5 Fig. 10: Steady state gain of converter in various load resistance versus duty cycle (D) Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 Substitution of this parameter into state equation (Eq. 5) yield: ~ ~ x& = AX + BVd + ( A~ x + Bv~d ) + [( A1 − A2 ) X + ( B1 − B2 )Vd ]2d ~ + terms with product of ~ x , d , v~d (negligible) ~ Vo + v~o = CX + C~ x + [(C1 − C2 ) X ]2d + ~ terms with product of d , v~ (negligible) 6. Small Signal Analysis (7) From Eq. 9 that consists of ac perturbations and using laplace transform: d ~ ~ x (s) = (SI − A) −1[(A1 − A2 ) X + (B1 − B2 )Vd ]2d (s) + (SI − A) −1 Bv~d (s) ~ v~o (s) = C~ x (s) + [(C1 − C2 ) X ]2d (s) The steady state equation can be obtained from Eq. 7 by setting all ac components to zero. Therefore the steady state equation is: AX + BV d = 0 and for output : Vo = CX (8) From Eq. 11 output voltage laplace transform in term of input voltage and duty cycle is as below: And therefore in Eq. 7 the small signal components have this relation: ~ ~ x& = A~ x + Bv~d + [( A1 − A2 ) X + ( B1 − B2 )Vd ]2d ~ v~ = C~ x + [(C − C ) X ]2d o 1 v~o ( s) = {C ( SI − A) −1[( A1 − A2 ) X + ( B1 − B2 )Vd ] + ~ (C1 − C2 ) X }2 d ( s ) + C ( SI − A) −1 B v~d ( s) Vo R = −CA−1 B = 2 Dn Vd R + Rth 2 D + rD (1 − 2 D) (12) (9) For obtaining transfer function of output voltage to duty cycle, the perturbation of input voltage is assumed to be zero and therefore: 2 Using Eq. 8 and value of matrices in Eq. 5 the steady state dc voltage transfer function is: m= (11) v~o ( s ) = 2C ( SI − A) −1[( A1 − A2 ) X + ( B1 − B2 )Vd ] ~ d (s) + 2(C1 − C2 ) X (10) (13) Substituting matrices from Eq. 5 and simplification, the 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ 56 transfer function can be derived as Eq. 14: (14) Vd, X1, and D are steady state value for input voltage, inductance current and duty cycle respectively. Based on the small signal model derived in previous section, it can be seen that the full bridge converter acts like a second order system. But as transfer function equation shows, dynamic of converter depend on operating point since inductor current and duty cycle steady state value of operating exist in proposed model. To validate the average model a step change in duty cycle (d from 0.3 to 0.28) has been introduced and the results are shown in figure 11. Fig. 12: Small signal model and actual model simulation for large change (0.1) in d 7. Controller Design For regulating output voltage of full bridge dc-dc converter, a compensation technique for output voltage control is implemented in this section. A negative feedback control circuit is widely used to regulate the output voltage against both line and load variations. Feedforward control can also be used to reduce the disturbances and thereby improve the output voltage characteristics of PWM dc-dc converters [13–15]. The feedforward control technique uses disturbance signal to prevent a change in the output voltage. The disturbance signal is monitored and a control signal is derived to adjust the duty ratio such that the output voltage is not affected by the disturbance. In contrast, the negative feedback technique detects a change in the output voltage and then tries to reduce this change. A combination of both negative feedback and feedforward techniques is able to achieve superior performance. Based on the small signal model derived in previous section, it can be seen that the full bridge converter act like a second order system and a simple PD controller can be designed for regulating the output voltage under step load change or input voltage change. Figure 13 presents the block diagram of combined control system for regulate the output voltage of the converter. The control system detects output voltage and compares it with the desired reference voltage and compensates it by changing in duty ratio of switches. The feedforward controller multiplies a gain to final duty ratio. Since system is linear and second order a PD Controller designed for the system according to minimizing the integral of time multiplied by the absolute value of error (ITAE) criterion [16]. The optimal parameter for proportional and derivation factor derived according to that method as 1.05 and 2.34 respectively. Fig. 11: Small signal model and actual model simulation for small change (0.02) in d As shown in figure 11 the derived small signal response is very close to the switched circuit model; hence the transfer function can be used for dynamic analysis of the converter and designing controller. Another case is studied for a large change in duty cycle from 0.3 to 0.2, and result of voltage for this case is shown in figure 12. As the figure shows, in this case the small signal model has difference with actual one but this difference is very small. According to small-signal and steady state characteristics of this converter, compensation techniques for output voltage control are needed. 57 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 2 nVd + (rD − Rth ) X 1 v~o ( s) = ~ den( s ) d ( s ) LC Where : 1 R′ R′ 1 den(s) = s 2 + ( ) + )s + ( + RC L RLC LC and R′ = Rth 2 D + rD (1 − 2 D) figure 15. It can be seen that the controller can regulate voltage in the desired voltage in proper time with changing the duty cycle of converter. Output Voltage (V) Advanced Graph Frame 251.20 251.00 250.80 250.60 250.40 250.20 250.00 249.80 249.60 249.40 Vout(V) Duty Cycle 0.320 0.310 y 0.300 0.290 0.280 0.270 0.260 0.250 Fig. 13: Closed loop system block diagram Time 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 . . . Fig. 15: Closed loop system response to change in input voltage The closed loop system with designed controller is simulated for two cases. 8. Conclusions 7.1. Step Change in Load Advanced Graph Frame 280 Vout(V) Output Voltage (V) 270 260 250 240 230 220 0.320 Duty Cycle 0.300 0.280 References 0.260 0.240 y Journal of Iranian Association of Electrical and Electronics Engineers – Vo1.4- No.2- Fall and Winter 2007 This paper presents an average model for full bridge dcdc converter. The model used for steady state, dynamic analysis, and large signal analysis of this converter. The developed model is used to study the characteristics and dynamics of full bridge converter and also is applicable to simulation and controller design. Simulation results for the full bridge converter show the feasibility of the proposed model for steady-state analysis and small signal analysis and verify the derived model. Validation of the derived model is based on a comparison of dc, smallsignal, and large-signal simulation results to those obtained from the simulation of the actual circuit. In last section, a PD controller with combination of input voltage feedforward control have been presented and it is shown that the controller is effective in regulating the output voltage of converter in changing load and input voltage disturbances. In this case, a step change in load is performed at t=0.1 sec and the load is changed to its initial value at t=0.3 sec. Simulation results are shown in figure 14. The controller can regulate voltage in the desired voltage. The output voltage has reached to desired value in approximately 0.03 seconds and it has very fast. Figure 14 also shows controller output e.g. Duty Cycle (d) of converter, and regulated output voltage. [1] M. N. Marwali and A. Keyhani, “Control of Distributed Generation Systems, Part I: Voltages and Currents Control,” IEEE Transaction on Power Electronics, Vol. 19, No. 6, pp. 1541-1550, 2004. [2] M. N. Marwali, J. W. Jung, and A. Keyhani, “Control of Distributed Generation Systems, Part II: Load Sharing Control,” IEEE Transaction on Power Electronics, Vol. 19, No. 6, pp. 1551-1561, 2004 [3] A. A. Chowdhury, S. K. Agarwal, D. O. Koval, “Reliability modeling of distributed generation in conventional distribution systems planning and analysis,” IEEE Transactions on Industry Applications, vol. 39, pp. 1493-1498, Sept.-Oct. 2003 0.220 0.200 0.180 0.160 Time 0.050 0.100 0.150 0.200 0.250 0.300 0.350 . . . Fig. 14: Closed loop system response to change in load 7.2. Step Change in Input Voltage In this case, a step change in input voltage happened at 0.5 sec from 50 volts to 40 volts, and again changed back to initial value at t=1 sec. Simulation results are shown in 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬ 58 Journal of Iranian Association of Electrical and Electronics Engineers - Vol.4- No.2- Fall and Winter 2007 [4] J. W. Jung, and A. Keyhani, “Modeling and Control of Fuel Cell Based Distributed Generation Systems in a standalone Ac Power System,” Journal of Iranian Association of Electrical and Electronics Engineers, Vol. 2, No. 1, pp: 10-23, 2005 [5] Chris Iannello, Shiguo Luo, and Issa Batarseh, “SmallSignal and Transient Analysis of a Full-Bridge, ZeroCurrent-Switched PWM Converter Using an Average Model”, IEEE Transaction on Power Electronics, Vol. 18, No. 3, 2003 [6] Guinjoan, F.; Poveda, A.; Martinez, L.; Vicuna, L.G.; Majo, J., “An accurate small-signal modelling approach for switching DC-DC converters,” IEEE International Symposium on Circuits and Systems, 1993 [7] Piero G. Maranesi, Marco Riva, “Automatic Modeling of PWM DC–DC Converters,” IEEE Power Electronics Letters, Vol. 1, No. 4, 2003 [8] Czarkowski, D.; Kazimierczuk, M.K. , “SPICE compatible averaged models of PWM full-bridge DC-DC converter,” Proceedings of the 1992 International Conference on Industrial Electronics, Control, Instrumentation, and Automation, 1992 [9] Mohan, Undeland, Robbins, Power Electronics Converter. Application, and Design, third edition, wiley, 2003 [10] Manitoba HVDC research center Inc., “PSCAD/EMTDC V4.1.0”, 2006 [11] A. Pressman, Switching power Supply Design, Second edition, McGraw-Hill, 1998 [12] R. C. Dorf, R.H. Bishop, Modern Control Systems, 9th Edition, 2000 [13] Marian K. Kazimierczuk and LaVern A. Starman, “Dynamic Performance of PWM DC-DC Boost Converter with Input Voltage Feedforward Control,” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, VOL. 46, NO. 12, DECEMBER 1999 [14] M. K. Kazimierczuk and A. Massarini, “Feedforward control of dc-dc PWM boost converter,” IEEE Transactoon on Circuits and System, vol. 44, pp. 143–148, Feb. 1997. [15] B. Arbetter and D. Maksimović, “Feedforward pulse width modulators for switching power converters,” IEEE Trans. Power Electron., vol. 12, Mar. 1997 [16] Dorf, Richard C., Modern Control System, 9th Edition, Prentice Hall, 2000 59 1386‫ ﭘﺎﺋﻴﺰ و زﻣﺴﺘﺎن‬- ‫ ﺷﻤﺎره دوم‬-‫ ﺳﺎل ﭼﻬﺎرم‬-‫ﻣﺠﻠﻪ اﻧﺠﻤﻦ ﻣﻬﻨﺪﺳﻴﻦ ﺑﺮق و اﻟﻜﺘﺮوﻧﻴﻚ اﻳﺮان‬

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