THREE PHASE SYNCHRONOUS GENERATORS Introduction: An electrical machine, which converts mechanical energy into electrical energy of alternating current in nature, is called an ALTERNATOR or AC GENERATOR. It is also called as SYNCHRONOUS GENERATOR as its operation is in synchronous with other generators or other AC sources when it is operated along with them. Principle of operation: Synchronous Generator (Alternator) operates on the fundamental principle of Faraday’s Laws of electromagnetic induction, i.e. whenever the magnetic flux linking the armature conductor changes, an Electro Motive Force (EMF) is induced in the conductor. The direction of induced E.M.F. is given by Fleming’s Right-hand rule. When there is a relative motion between the conductor and magnetic field, the induced EMF is called as dynamically induced EMF. In alternators, there are two types of construction i) Stationary field winding and rotating armature winding-like DC generators (only for small capacity alternators of few KW rating) ii) Stationary armature winding and rotating field winding (Suitable for MW size Synchronous Generators) The field windings of alternators require direct current for excitation. Excitation is supplied by a DC generator called an exciter which is mechanically coupled with the rotor shaft. The DC exciter supplies required power for the rotating field winding to produce magnetic field. As the prime mover rotates, the rotor of an alternator also rotates and the stator conductors being stationary are cut by magnetic flux of rotor poles, hence an E.M.F. is induced in the stator conductors. As the rotor magnetic poles are alternatively North and South, they induce an alternating E.M.F in the stator conductors. The frequency of alternating E.M.F. depends on the number of North and South poles moving past the conductors in one second. Constructional features and types of 3 phase Synchronous generators: Compared to the DC generators, the major differences in construction of Synchronous Generators of MW size are: a) In a DC generator the armature winding rotates and the field system is stationary whereas in an Alternator of MW size, the armature winding is mounted on a stationary frame and the field winding on a rotating frame. b) The Stationary armature of an alternator is connected directly to load which receives AC supply and the rotating field winding is connected to DC supply using two low capacity slip rings. This makes the construction of alternator simpler. Advantages of having the stationary armature and rotating field: a) Insulation of stationary armature conductors working at high voltage is easier. b) Tapping of electrical energy from a stationary armature is simpler. 1 c) The use of slip rings and brushes are eliminated as the load is directly connected to the alternator terminals d) The machine can operate at higher speeds enabling a larger output from the alternator. Construction of Alternator (Synchronous generator) : Basically an alternator consist of two parts: a) Stator b) Rotor as shown in Fig1a. Fig 1a. Construction of Alternator Fig 1b Stator slots a) Stator: It consists of stator frame, stator core and windings. i) Stator Frame: It is a cast iron or welded steel protective frame and gives support to the entire machine assembly. In small machines it is made of a single piece of cast iron. In large sized machines, the frame is fabricated by sections of cast iron sheet steel welded together to form a cylindrical drum. ii) Stator Core: It is made of special magnetic iron or steel alloy laminations. They are laminated to minimize the core losses. These laminations are insulated from one another and pressed together to form the core. Slots are provided on its inner periphery to house the stator conductors. Slots provided on the stator are of three types: Wide Open, Semi-Closed and closed are shown in Fig1b. The wide open type slots are more commonly used because the defective coils can be easily removed and replaced. The laminations also have openings which make axial and radial ventilations for the purpose of cooling. iii) Stator Windings (armature windings): These are insulated copper conductors housed in stator slots in some specific manner of inter connections. b) Rotor: It is the rotating part, with North and South poles attached to it. Poles carry field windings which are supplied with direct current through two slip rings and brushes. Rotors are of two types: i) Salient Pole Type ii) Smooth Cylindrical or Non-salient Pole Type 2 i) Salient Pole Type: this type of rotor is like a magnetic fly wheel made of cast iron or steel and a number of alternate North and South poles are bolted to it as shown in Fig 2a. The Salient or projecting poles are made of thick steel laminations, riveted together and fixed to the rotor poles. The ends of the field windings are connected to the DC supply through slip rings carrying brushes. Such rotors have large diameter and small axial length. Fig.2a. Salient-pole rotor Advantages: a) Less expensive b) It provides sufficient space for field coils Disadvantages: a) If the salient poles are driven at high speed, it will cause excessive windage losses and would tend to produce noise. b) As the rotor is not robust in construction, it cannot withstand mechanical stress if driven at high speed. Application: Used for low and medium speed alternators Examples: Hydro Electric Power Plants, Diesel Power Plants and Gas Turbine Power Plants. ii) Smooth Cylindrical or Non-salient Pole Type: These rotors are cylindrical in construction and are made from solid forged steel alloy having a number of slots on its outer periphery at regular intervals for accommodating field coils. Field coils are connected to a DC supply by means of slip rings and brushes for excitation purpose. The regions forming the central polar areas are left unslotted. The field coils are so arranged around these polar areas that flux density is maximum on the central polar areas. These types of rotors are characterized by small diameter and very long axial length. 3 Fig. 2b Phase-wound (Non-salient) Rotor Advantages: a) Gives better balance b) Noiseless operation c) Less windage loss d) Better E.M.F. waveform Application: Used in very high speed turbo alternators. Example: Steam turbines Frequency of the induced E.M.F. or Relationship between Speed and Frequency: Consider an alternator whose rotor is being driven at a constant speed of N r.p.m. Let P = Number of poles f = frequency of induced E.M.F. In one complete revolution of the rotor, each of the North and South poles move past all the stator conductors. When one pair of North and South poles moves past the armature conductor, the induced E.M.F. undergoes one full cycle. Therefore in a Ppole machine, in one complete revolution of the field system, the induced E.M.F. in the armature conductors will complete P 2 cycles of waveform. Number of cycles of EMF induced/second= no. of cycles of emf per revolution x No. of revolutuions per sec i.e. Frequency in cycles/second = i.e. f P N 2 60 PN Hz 120 or N 120 f r.p.m P Note: In order to keep the frequency constant, the speed N must remain unchanged. Synchronous generator connected to grid runs at a constant speed known as synchronous speed in steady state. 4 E.M.F. Equation: Consider a 3-Phase alternator with P-Poles driven at a constant speed of N r.p.m. Let Z = Number of conductors or coil sides in series per phase = 2T ----where T is the number of turns per phase. = useful flux/pole in Webers f = frequency in Hz Kd = distribution factor or winding factor or breadth factor Kp = pitch factor Consider an armature conductor on the stator of an alternator. Let the alternator rotor move through one revolution in t=60/N seconds. In one revolution of the rotor, all the P poles on the rotor move past each of the stator conductors. Flux cut by the conductor in one rev olution P Wb According to Faraday’s second law of electromagnetic induction, Av erageE.M.F.induced in the conductor E av d dt where d = flux cut/stator conductor in one revolution of rotor = P dt = time taken for one revolution of rotor = So the average emf induced per conductor Eav= Wb 60 seconds N = The emf induced in Z number of conductors, Eav= But N= 120f/P , Eav= RMS value of emf/phase =1.11 x = == = = volt The above equation of induced E.M.F./phase is true only if the winding is concentrated in one slot. But practically the winding for each phase under each pole is distributed and for such cases Kp and Kd are considered. Thus, E.M.F./phase will be, E r.m.s./phase = 4.44fTKpKd Volts. If the alternator is star connected, then the line voltage is El = x 4.44fTKpKd Volts. Winding factors:(Kw=KpKd) For the following advantages windings always short pitched by 1 or 2 slots • The primary advantage of short-pitch coils is we achieve saving of copper. 5 • Short pitched winding reduces the MMF harmonics produced by the armature winding . • Short pitched winding reduces the EMF harmonics induced in the windings, without reducing the magnitude of the fundamental EMF wave to a great extent. Pitch factor Kp= emf induced in a short pitched coil/ emf induced in a full pitched coil Kp = cos α/2 where α is called short pitched angle. Note: For full pitched windings Kp = 1 Fig. 3a Resultant emf for full pitched coil Fig. 3b Resultant emf for short pitched coil Concentrated windings in which all conductors of a given phase per pole are concentrated in a single slot, are not commercially used because they have the following disadvantages, 1. They fail to use the entire inner periphery of the stator iron efficiently. 6 2. They make it necessary to use extremely deep slots where the windings are concentrated. This causes an increase in the mmf required to setup the desired airgap flux. 3. Deep slots also increase the armature leakage flux and the armature reactance. 4. They result in low copper-to-iron ratios by not using the armature iron completely. 5. They fail to reduce harmonics as effectively as distributed windings. Distribution factor Kd = (emf induced in a distributed winding)/ (emf induced in a concentrated winding) = vector sum of the emf/ arithmetic sum of the emf Distribution factor Kd = ( sin mβ/2) / (m sin β/2) where m = number of slots per pole per phase, β = slot angle Example Problems: 1. A 3Φ, 50 Hz, star connected salient pole alternator has 216 slots with 5 conductors per slot. The winding is distributed with Kd= 0.959 and full pitched. The flux per pole is 30 mwb and the alternator runs at 250 rpm. Determine the phase and line voltages of emf induced. Solution: Ns = 250 rpm, f = 50 Hz, P = 120 x f/Ns = 120 x 50/250 = 24 poles Kd= 0.9597 , Kp = 1 for full pitched winding. Total no of conductor Z = conductor/ slot x number of slots = 216 x 5 = 1080 Conductor per phase Zph= 1080/3=360 Turns per phase Tph= Zph/2 = 360/2=180 Therefore Eph = 4.44 KpKd f Ф Tph = 4.44 x 1 x 0.9597 x 50 x 30 m x 180 = 1150.488 volts Hence the line Voltage EL = √3 Eph = √3 x1150.488 = 1992.65 volts 2. A three phase 16-pole alternator has a star connected winding with 144slots and 10 conductors/slot. The flux/pole is 0.03Wb and the speed is 375 r.p.m. Find the frequency, the phase E.M.F. and line E.M.F. Assume full pitched coils. f=PN/120=(16*375)/120=50 Hz n=slots/pole =144/16=9 slot angle= β β=180/n=180/9=20 degree electrical m=(slots/pole)/phase =144/(16x3)=3 Kd = ( sin mβ/2) / (m sin β/2) = sin(3*20/2)/(3*sin(20/2))=0.9598 7 Total no of conductor Z = number of slots x conductor/ slot = 144 x 10 = 1440 Conductor per phase Zph= 1440/3=480 Turns per phase Tph= Zph/2 = 480/2=240 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 1 x 0.9598 x 50 x 0.030 x 240 = 1534.144 volts The line Voltage EL = √3 Eph = √3 x1534.144 = 2657.215 volts 3. A 8 pole, 750 rpm three phase star connected alternator has 72 slots, each of which having 10 conductors. Calculate the RMS value of the emf per phase if the flux per pole is 0.1 wb and the winding factor is 0.96. Solution: Winding factor Kw=Kp*Kd= 0.96(given) P=8, Speed N=750 rpm f=PN/120=(8*750/120)=50 Hz Total no of conductor Z = number of slots x conductor/ slot = 72 x 10 = 720 Conductor per phase Zph= 720/3=240 Turns per phase Tph= Zph/2 = 240/2=120 Eph = 4.44 Kw f Ф Tph = 4.44 x 0.96 x 50 x 0.10 x 120 = 2557.44 volts The line Voltage EL = √3 Eph = √3 x2557.44 = 4429.616 volts 4. A 8 pole, three phase, 50 Hz, star connected a.c. generator has 24 stator slots. Find the number of conductors per slot if the flux per pole is 60mWb and the terminal voltage is 1100 V. Assume full pitch coils Solution: Given P=8, f=50, S=24 N=120f/P=(120*50)/8=750 rpm n=slots/pole =24/8=3 slot angle= β β=180/3=60 degree electrical 8 m=(slots/pole)/phase =24/(8x3)=1 Kd = ( sin(mβ/2)) / (m sin (β/2)) = sin(1*60/2)/(1*sin(60/2))=1 Kp=1; full pitched coils Flux = Ф=0.06 wb Terminal voltage=1100 V(line voltage given) Eph=E1/sqrt(3) = 1100/sqrt(3)=635.085 V Total no of conductors Z = to be determined Eph = 4.44 Kp Kd f Ф Tph Therefore 635.085 = 4.44 Kp Kd f Ф Tph = 4.44 x 1 x 1 x 50 x 0.06 x Tph Tph=47.68 ≈48 Conductors per phase= Zph=48*2 =96 Z=Zph*number of phases=96*3=288 Conductors/slot=288/24=12 5. A 4 pole, three phase, 50 Hz, star connected a.c. generator has 24 stator slots. Find the number of conductors per slot if the flux per pole is 61.7mWb and the terminal voltage is 1100 V. Assume full pitch coils. Given P=4, f=50, S=24 N=120f/P=(120*50)/4=1500 rpm n=slots/pole =24/4=6 slot angle= β β=180/6=30 degree electrical m=(slots/pole)/phase =24/(4x3)=2 Kd = ( sin(mβ/2)) / (m sin (β/2)) = sin(2*30/2))/(2*sin(30/2))=0.9659 Kp=1; full pitched coils Flux = Ф=0.06 wb Terminal voltage=1100 V(line voltage given) 9 Eph=E1/sqrt(3) = 1100/sqrt(3)=635.085 V Total no of conductors Z = to be determined Eph = 4.44 Kp Kd f Ф Tph Therefore 635.085 = 4.44 Kp Kd f Ф Tph = 4.44 x 1 x 0.9659 x 50 x 0.0617 x Tph Tph=48.002 ≈48 Conductors per phase= Zph=48*2 =96 Z=Zph*number of phases=96*3=288 Conductors/slot=288/24=12 6. A 8 pole, 750 rpm three phase star connected alternator has 72 slots, each of which is having 10 conductors. Calculate the RMS value of the emf per phase and line voltage. The flux per pole is 0.1 wb. The coils are short pitched by one slot and the windings are distributed P=8, Speed N=750 rpm f=PN/120=(8*750/120)=50 Hz Total no of conductor Z = number of slots x conductor/ slot = 72 x 10 = 720 Conductor per phase Zph= 720/3=240 Turns per phase Tph= Zph/2 = 240/2=120 n=slots/pole =72/8=9 slot angle= β =180/9=20 degree electrical m=(slots/pole)/phase =72/(8x3)=3 Coils are short pitched by one slot hence short pitch angle α= β =20 degree Kp= cos (α/2)= cos(20/2)=0.9848 Kd = ( sin(mβ/2)) / (m sin (β/2)) = sin(3*20/2))/(3*sin(20/2))=0.9598 Kw=Kp*kd =0.9848*0.9598 =0.9452 10 Therefore Eph = 4.44 Kw f Ф Tph = 4.44 x 0.9452 x 50 x 0.10 x 120 = 2518.0128 volts The line Voltage EL = √3 Eph = √3 x2518.0128 =4361.326 volts 7. A three phase 16-pole alternator has a star connected winding with 144slots and 10 conductors/slot. The flux/pole is 0.03Wb and the speed is 375 r.p.m. Find the frequency, the phase E.M.F. and line E.M.F. The coils are short chorded by two slots. f=PN/120=(16*375)/120=50 Hz n=slots/pole =144/16=9 slot angle=β=180/n=180/9=20 degree electrical m=(slots/pole)/phase =144/(16x3)=3 Short pitch angle α= 2*β =2*20=40 degree Kp= cos (40/2)= cos(40/2)=0.9397 Kd = ( sin mβ/2) / (m sin β/2) = sin(3*20/2)/(3*sin(20/2))=0.9598 Total no of conductor Z = number of slots x conductor/ slot = 144 x 10 = 1440 Conductor per phase Zph= 1440/3=480 Turns per phase Tph= Zph/2 = 480/2=240 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 0.9397 x 0.9598 x 50 x 0.030 x 240 = 1441.635 volts The line Voltage EL = √3 Eph = √3 x 1441.635 = 2496.985 volts 8. A three phase star connected alternator with 12 poles generates 1100V on open circuit at a speed of 500 rpm. Assume 180 turns per phase, a distribution factor of 0.9598 and coils are short pitched by one slot. Find useful flux per pole, frequency, winding factor and estimate the number of stator slots and conductors/slot if slots per pole per phase is 3. f=PN/120=(12*500)/120=50 Hz 11 Kd = ( sin(mβ/2)) / (m sin (β/2))=0.9598(given) Slots/pole/phase=m=3 Kd= sin(3*β/2))/(3*sin(β/2))=0.9598 Solving, we get, slot angle =β=20 degree ele • n=slots/pole = 180/β =180/20=9 Total number of slots= S=(slots/pole)*poles =9*12=108 Short pitch angle α= 1*β =1*20=20 deg Kp = cos (20/2)= 0.9848 Kw=Kp*kd =0.9848*0.9598 =0.9452 Eph=1100/√3=635.085 • Therefore Eph = 4.44 Kw f Ф Tph 635.085= 4.44 x 0.9452 x 50 x Ф x 180 Ф = 0.0168144 wb Total conductors Z=180*3*2=1080 Conductors/slot=1080/108=10 9. A three phase 60 Hz, 16-pole alternator has a star connected winding with 144 slots and 5 conductors/layer. The winding is double layer. The flux/pole is 24.8 mwb is sinusoidally distributed. Find the speed, the phase E.M.F. and line E.M.F. The coils are short chorded by one slot. N=120f/P=(120*60)/16=450 rpm n=slots/pole =144/16=9 slot angle=β=180/n=180/9=20 degree electrical m=(slots/pole)/phase =144/(16x3)=3 Short pitch angle α= 1*β =1*20=20 degree Kp= cos (20/2)= cos(20/2)=0.9848 Kd = ( sin mβ/2) / (m sin β/2) = sin(3*20/2)/(3*sin(20/2))=0.9598 Total no of conductors Z 12 Z= number of slots *(conductors/ layer) *number of layers = 144 x 5x2 = 1440 Conductor per phase Zph= 1440/3=480 Turns per phase Tph= Zph/2 = 480/2=240 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 0.9848 x 0.9598 x 60 x 0.0248 x 240 = 1498.739 volts The line Voltage EL = √3 Eph = √3 x 1498.739 = 2595.892 volts 10. A 4 pole, three phase, 50 Hz, star connected alternator has 60 stator slots with 4 conductors/slot. Coils are short pitched by 3 slots. If the Phase spread is 60 degree, find the line voltage induced for a flux of 0.943 wb sinusoidally distributed in space All the turns per phase are in series. Calculate the speed of the alternator N=120f/P=(120*50)/4=1500 rpm n=slots/pole =60/4=15 Phase spread=m β=60 deg m=(slots/pole)/phase =60/(4x3)=5 slot angle=β=60/5=12 degree electrical Also, β=180/n=180/15=12 deg Short pitch angle α= 3*β =3*12=36 degree Kp= cos (α /2)= cos(36/2)=0.9511 Kd = ( sin mβ/2) / (m sin β/2) = sin(5*12/2)/(5*sin(12/2))=0.9567 Total no of conductors Z Z= number of slots *(conductors/ slot) = 60 x 4 = 240 Conductor per phase Zph= 240/3=80 Turns per phase Tph= Zph/2 = 80/2=40 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 0.9511 x 0.9567 x 50 x 0.943 x 40 = 7619.5025 volts The line Voltage EL = √3 Eph = √3 x 7619.5025 = 13197.366 volts 13 11. A 4 pole, three phase, 50 Hz, star connected alternator slots/pole/phase=4 with 4 conductors/slot arranged in two layer winding. Coil span=150 deg electrical. Find the no load line voltage induced emf for a flux of 0.12 wb sinusoidally distributed in space. Also calculate the winding factor m=(slots/pole)/phase = 4(given) Total number of slots=4*3*4=48 n=slots/pole=4*3=12 slot angle=β=180/n=180/12=15 degree ele Coil span=150 deg electrical Short pitch angle=180-coil span(in degree ele) Short pitch angle α= 180-150 =30 degree Kp= cos (α /2)= cos(30/2)=0.9659 Kd = ( sin mβ/2) / (m sin β/2) = sin(4*15/2)/(4*sin(15/2))=0.9577 Winding factor=Kp*Kd=0.9659*0.9577=0.9250 Total no of conductors Z Z= number of slots *(conductors/ slot) = 48 x 4 = 192 Conductor per phase Zph= 192/3=64 Turns per phase Tph= Zph/2 = 64/2=32 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 0.9659 x 0.9577 x 50 x 0.12 x 32 = 788.5802 volts The line Voltage EL = √3 Eph = √3 x 788.5802 = 1365.861 volts 12. Calculate the no-load terminal voltage of a three-phase, 8 pole, star connected alternator running at 750 rpm having following data: flux/pole= 50mwb , Stator slots=72 , Number of conductors/slot=10. Calculate the percentage rise in open circuit terminal voltage if the windings were concentrated and accommodated in 24 slots with depth increased to house 30 conductors per slot 14 Solution: case-1 : with72 slots m=(slots/pole)/phase = (72/8)/3 =3 n=slots/pole=72*8=9 slot angle=β=180/n=180/9=20 degree ele Coil span=180 deg electrical (Assuming full pitched coils) Short pitch angle α= 180-180 =0 degree Kp= cos (α /2)= cos(0/2)=1 Kd = ( sin mβ/2) / (m sin β/2) = sin(3*20/2)/(3*sin(20/2))=0.9598 Winding factor=Kp*Kd=1*0.9598=0.9598 Total no of conductors Z Z= number of slots *(conductors/ slot) = 72 x 10 = 720 Conductor per phase Zph= 720/3=240 Turns per phase Tph= Zph/2 = 240/2=120 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 1 x 0.9598 x 50 x 0.05 x 120 = 1278.4536 volts The line Voltage EL = √3 Eph = √3 x 1278.4536 = 2214.3466 volts Solution: case-2 : with 24 slots m=(slots/pole)/phase = (24/8)/3 =1 n=slots/pole=24*8=3 slot angle=β=180/3=180/3=60 degree ele Coil span=180 deg electrical (Assuming full pitched coils) Short pitch angle α= 180-180 =0 degree Kp= cos (α /2)= cos(0/2)=1 Kd = ( sin mβ/2) / (m sin β/2) = sin(1*60/2)/(1*sin(60/2))=1 Winding factor=Kp*Kd=1*1=1 Total no of conductors Z Z= number of slots *(conductors/ slot) = 24 x 30 = 720 15 Conductor per phase Zph= 720/3=240 Turns per phase Tph= Zph/2 = 240/2=120 Therefore Eph = 4.44 Kp Kd f Ф Tph = 4.44 x 1 x 1 x 50 x 0.05 x 120 = 1332 volts The line Voltage EL = √3 Eph = √3 x 1332 = 2307.0917 volts Percentage increase in terminal voltage =((2307.0917- 2214.3466)/ 2214.3466)*100 =4.19% Tutorial Problems: 1. A three phase 16-pole alternator has a star connected winding with 144slots and 10conductors/slot. The flux/pole is 0.03Wb and the speed is 375r.p.m. Find the frequency, the phase E.M.F. and line E.M.F. assume pitch factor Kp = 1 and distribution factor Kd = 0.96 [50Hz, 1534.464, 2657.77V] 2. A 6 pole, 3 phase, 50Hz alternator has an armature with 90 slots and 8 conductors per slot and revolves at 1000rpm. The flux per pole being 0.05Wb. Calculate the emf generated if the winding factor is 0.97 and all the conductors in each phase are in series.(1292.04V/phase) 3. A 3 phase 16 pole alternator has a star connected winding with 144 slots and 10 conductors per slot. The flux per pole is 0.03Wb and the speed is 375 rpm. Find the frequency and the phase and line emf if the distribution factor Kd=0.96 and the pitch factor =1.[50Hz,2657.76V] 4. A 3 phase , 50Hz star connected alternator has 200 conductors per phase and flux per pole of 0.06Wb. Find i) emf generated per phase ii) emf between terminals. Assume the winding to be full pitched and distribution factor to be 0.966. [1286.7,2228.65V] ************************* **************************** 16