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Transformer Design Examples: Core & Winding Calculations
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Anand Jain, Govt. Polytechnic Hanumangarh TRANSFORMER DES IGN EXAMPLES-3 TRANSFORMER DES IGN EXAMPLES-3 Anand Jain, Govt. Polytechnic Hanumangarh Design magnetic frame and winding for a 50 KVA, 11000/400 V, 50Hz, three phase delta/star core type distribution transformer. Assume flux density 1.2 T, current density (aluminum conductor) 1.5 A/mm2, window space factor=0.2, having window area 10 times net iron area. Use three stepped cores. Given Data : kVA=50, f = 50 Hz, VHV=11000 V delta VLV=400 V star Bm=1.2 T d=1.5 A/mm2 Kw=0.2 Aw/Ai =10 Output equation of transformer is given as πΈ = π. ππ π π©π π¨π° π²πΎ π¨πΎ πΉ × ππ−π here So π¨π × π¨πΎ = πππ¨π π = π¨πΎ = ππ π¨π° πΈ×πππ π.ππ π π©π π²πΎ πΉ = πππππ π.ππ ×ππ×π.π×π.π×π.π×πππ Check πππ figure in current density value π¨π π = ππ. πππ × ππ−π or π¨π =. πππππππ ππ = ππ. ππ πππ Hence emf per turn πΈπ‘ = 4.44 ππ©π π¨π = 4.44 × 50 × 1.2 ×. πππππππ = π. πππ volt/turn With such medium size 50KVA transformers three stepped or more stepped cores are used. When we use higher number of steps in core, we utilize the iron space better. By increasing the number of steps, the area of circumscribing circle is more effectively utilized for iron part. The relation between circumscribe circle diameter “d” and core cross section “Ai” can be expressed as follows π¨π = π π π The value of constant k depends upon the number of steps of core of the transformer, given as Core type Square Cruciform 3 stepped 4 stepped 5 stepped 6 stepped Constant k 0.45 0.56 0.6 0.62 0.64 0.65 for three stepped core circumscribing circle diameter π = The most economical dimensions of various steps for a three-stepped core can be calculated. The results are π = π. ππ π = π. ππ × ππ. ππ = ππ. ππ ≈ ππ. π ππ π = π. ππππ = π. πππ × ππ. ππ = π. πππ ≈ π. π ππ πππ π = π. ππ π = π. ππ × ππ. ππ = π. πππ ≈ π. π ππ π¨π π = ππ.ππ π.π = ππ. ππ ππ It is given that window area is 10 times of net iron area so π¨π = ππ π¨π = ππ × π. πππππππ = π. ππππππ ππ = πππ. ππ πππ Window area is determined as product of width and height of the window. The height of the window, is usually taken 2 to 4 times of width of window. π»π ππ = 2 π‘π 4 When height of window is taken high the mean turn length will decrease but leakage flux will increase. Similarly, less height and more width of window will increase the mean turn length but decrease leakage flux by some amount. Let us take height of window 2.5 times of width of window. π¨πΎ = πππ. ππ πππ = π»π × ππ = 2.5 ππ × ππ or ππ = π¨πΎ 2.5 = so height of window 912.85 2.5 = 19.11 ≈ 19.1 ππ π»π = 2.5 ππ = 2.5 × 19.11 = 47.8 ππ or ππ = 19.1 ππ so height of window π»π = 2.5 ππ = 2.5 × 19.11 = 47.8 ππ One significant dimension in core is center to center limb distance π· = ππ€ + π = 19.1 + 12.3 = 31.4 ππ Overall width of core π = 2π· + π = 2 × 31.4 + 11.2 = 74 ππ Overall height of core π» = π»π + 2 π = 47.8 + 2 × 11.2 = 70.2 ππ Winding design ππβ = ππΏ 3 = 400 3 Low voltage winding 400 V star connection πΈ = π. ππ π π©π π¨π° π²πΎ π¨πΎ πΉ × ππ−π here = 231.2 π No of turns ππΏπ = Current in LV πΌπΏπ = π πΈπ‘ = π 3ππβ 231.2 2.432 = = 95.06 ≈ 95 π‘π’πππ 50000 3×231.2 Cross section area of conductor ππΏπ = π¨πΎ = ππ π¨π° πΈπ‘ = 4.44 ππ©π π¨π = π. πππ volt/turn = 72.088 π΄ πΌπΏπ πΏ = 72.088 1.5 = 48.05867 ππ2 We will select rectangle conductor of next higher standard size from conductor table, one can also use foil winding. High voltage winding 11KV Delta ππβ = ππΏ = 11000 π π No of turns ππ»π = ππΏπ ππ»π = 95 × Current in HV πΌπ»π = πΏπ π 3ππβ = 50000 3×11000 Cross section area of conductor ππ»π = 11000 231.2 = 4519.89 ≈ 4520 π‘π’πππ = 1.5151 π΄ πΌπ»π πΏ = 1.5151 1.5 = 1.01 ππ2 We will select round conductor of next higher standard size from conductor table. Design magnetic frame and winding for a 10 KVA 11000/230 V, 50Hz, single phase core type transformer. Assume flux density 1.1 T, current density 2.2 A/mm2, window space factor=0.25, constant K=0.8 for single phase core type transformer. Use cruciform two stepped core. Given Data : Hence emf per turn kVA=10, VHV=11000 V f = 50 Hz, VLV=230 V Bm=1.1 T d=2.2 A/mm2 Kw=0.25 K=0.8 πΈπ‘ = πΎ π = 0.8 10= 2.53 volt/turn π¬ The net core cross section area Ai is given as π¨π = π.ππ ππ π© π Bm – maximum flux density in the core of the transformer in Wb/ m2 f – Frequency of the power supply in Hz With very small size transformers, rectangular core can be used with either circular or rectangular coils. With small size transformers less than 5KVA, square core can be used, with circular coils. With medium and large transformers, cruciform (two stepped) or more stepped cores are used. Stepped core utilizes the iron space better. π¨π = π¬π π. ππ = = π. ππππππππ ππ = πππ. π πππ π. ππ π π©π π. ππ × ππ × π. π The relation between circumscribe circle diameter “d” and core cross section “Ai” can be expressed as follows π¨π = π π π The value of constant k depends upon the number of steps in core of the transformer, it is given as Core type Square Cruciform 3 stepped 4 stepped 5 stepped 6 stepped Constant k 0.45 0.56 0.6 0.62 0.64 0.65 for cruciform core circumscribing circle diameter π = π¨π π = πππ.π π.ππ = ππ. π ππ By increasing the number of steps, the area of circumscribing circle is more effectively utilized. The most economical dimensions of various steps for a multi-stepped core can be calculated. for two step size of core : π = π. ππ π = π. ππ × ππ. π = ππ. ππ ≈ ππ. π ππ πππ π = π. πππ = π. ππ × ππ. π = π. π ππ We can find out window area from output equation given as πΈ = π. ππ π π©π π¨π° π²πΎ π¨πΎ πΉ × ππ−π So πΈ×πππ π π¨π° π²πΎ πΉ π¨πΎ = π.ππ π π© πππππ = π.ππ×ππ×π.π×π.πππππ×π.ππ×π.π×πππ = π. πππππ ππ = πππ πππ Check πππ figure in current density value Window area is determined as product of width and height of the window. The height of the window, is usually taken 2.5 to 4 times of width of window. π―πΎ πΎπΎ = π. π ππ π When height of window is taken high the mean turn length will decrease but leakage flux will increase. Similarly, less height and more width of window will increase the mean turn length but decrease leakage flux by some amount. Let us take height of window three times of width of window. Thus, from the above equations, the height of the window & the width of the window can be calculated. π¨πΎ = πππ πππ = π»π × ππ = 3 ππ × ππ or ππ = π¨πΎ 3 = 144 3 = 6.93 ≈ 6.9 ππ so height of window π»π = 3 ππ = 3 × 6.93 = 20.8 ππ One significant dimension in core is center to center limb distance π· = ππ€ + π = 6.9 + 13.6 = 20.5 ππ Overall width of core π = π· + π = 20.5 + 11.6 = 32.1 ππ Overall height of core π» = π»π + 2 π = 20.8 + 2 × 11.6 = 44 ππ The transformer core frame with dimensions is as Winding design Low voltage winding No of turns ππΏπ = Current in LV πΌπΏπ = π πΈπ‘ π π = = 230 2.53 = 90.9 ≈ 91 π‘π’πππ 10000 230 = 43.48 π΄ πΌπΏπ πΏ Cross section area of conductor ππΏπ = = 43.48 2.2 = 19.763 ππ2 We will select rectangle conductor of next higher standard size from conductor table, one can also use foil winding. High voltage winding No of turns ππ»π = ππΏπ 4352 π‘π’πππ Current in LV πΌπ»π = π π = ππ»π ππΏπ = 91 × 10000 11000 11000 230 = 4352.17 ≈ = 0.909 π΄ Cross section area of conductor ππ»π = πΌπ»π πΏ = 0.909 2.2 = 0.4132 ππ2 We will select round conductor of next higher standard size from conductor table. Design magnetic frame and winding for a 250 KVA, 11000/230 V, 50Hz, three phase delta/star core type distribution transformer. Assume flux density 1.2 T, current density 2.5 A/mm2, window space factor=0.28, constant K=0.45 for three phase core type distribution transformers. Use three or four stepped cores. Given Data : kVA=250, Bm=1.2 T d=2.5 A/mm2 f = 50 Hz, VHV=11000 V delta VLV=230 V star Hence emf per turn π¬π = π² πΈ = π. ππ The net core cross section area Ai is given as π¨π = πππ π Kw=0.28 K=0.45 = π. π volt/turn π¬π π.ππ π π©π Bm – maximum flux density in the core of the transformer in Wb/ m2 f – Frequency of the power supply in Hz With very small size transformers, rectangular core can be used with either circular or rectangular coils. With small size transformers less than 5KVA, square core can be used, with circular coils. With medium and large transformers, cruciform (two stepped) or more stepped cores are used. Stepped core utilizes the iron space better. π¨π = π¬π π. π = = π. ππππ ππ = πππ πππ π. ππ π π©π π. ππ × ππ × π. π The relation between circumscribe circle diameter “d” and core cross section “Ai” can be expressed as follows π¨π = π π π The value of constant k depends upon the number of steps of core of the transformer, given as Square 0.45 Core type Constant k Cruciform 0.56 3 stepped 0.6 4 stepped 0.62 for four stepped core circumscribing circle diameter π = π¨π π = πππ π.ππ = ππ. ππ ππ By increasing the number of steps, the area of circumscribing circle is more effectively utilized. The most economical dimensions of various steps for a four-stepped core can be calculated. The results are a = π. ππ π = π. ππ × ππ. ππ = ππ. ππ ≈ ππ. π ππ π = π. π π = π. π × ππ. ππ = ππ. π ππ π = π. π π = π. π × ππ. ππ = π. π ππ πππ π = π. ππ π = π. ππ × ππ. ππ = π. π ππ 5 stepped 0.64 6 stepped 0.65 We can find out window area from output equation given as πΈ = π. ππ π π©π π¨π° π²πΎ π¨πΎ πΉ × ππ−π So πΈ×πππ π π¨π° π²πΎ πΉ π¨πΎ = π.ππ π π© ππππππ = π.ππ ×ππ×π.π×π.ππππ×π.ππ×π.π×πππ = π. ππππ ππ = ππππ πππ Check πππ figure in current density value Window area is determined as product of width and height of the window. The height of the window, is usually taken 2 to 4 times of width of window. π»π ππ = 2 π‘π 4 When height of window is taken high the mean turn length will decrease but leakage flux will increase. Similarly, less height and more width of window will increase the mean turn length but decrease leakage flux by some amount. Let us take height of window 2.5 times of width of window. Thus, from the above equations, the height of the window & the width of the window can be calculated. π¨πΎ = ππππ πππ = π»π × ππ = 2.5 ππ × ππ or ππ = π¨πΎ 2.5 so height of window = 1161 2.5 = 21.55 ≈ 21.6 ππ π»π = 2.5 ππ = 2.5 × 21.55 = 53.9 ππ One significant dimension in core is center to center limb distance π· = ππ€ + π = 21.6 + 15.8 = 37.4 ππ Overall width of core π = 2π· + π = 2 × 37.4 + 14.7 = 89.5 ππ Overall height of core π» = π»π + 2 π = 53.9 + 2 × 14.7 = 83.3 ππ The transformer core frame with dimensions is as Winding design: Low voltage winding 400 V star connection π½π·π = π½π³ π = No of turns ππΏπ = Current in LV πΌπΏπ = πππ π π πΈπ‘ = πππ. π π½ = π 3ππβ 231.2 4.1 = = 56.39 ≈ 56 π‘π’πππ 250000 = 360.44 π΄ 3×231.2 Cross section area of conductor ππΏπ = πΌπΏπ πΏ = 360.44 2.5 = 144.176 ππ2 We will select rectangle conductor of next higher standard size from conductor table, one can also use foil winding. High voltage winding 11KV Delta ππβ = ππΏ = 11000 π No of turns π΅π―π½ = π΅π³π½ Current in LV π½π―π½ π½π³π½ πΌπ»π = = ππ × π 3ππβ = πππππ πππ.π 250000 3×11000 Cross section area of conductor ππ»π = = ππππ. ππ ≈ ππππ πππππ = 7.5757 π΄ πΌπ»π πΏ = 7.5757 2.5 = 3.03 ππ2 We will select round conductor of next higher standard size from conductor table.
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