Electrical Machine - IES Academy
Electrical Machine - IES Academy Electrical Machine - IES Academy
India’s No. 1 IES Academy Transformer Chapter-1 The voltage regulation of a transformer can be obtained from its approximate equivalent circuit referred to primary or secondary. Approximate equivalent circuit of a 2-winding transformer, referred to secondary and the phasor diagram of the circuit for a lagging power factor load. E 2 = OC = OA + AB + BC( or B ' C ') = OA + AB 'cos θ 2 + DB 'sinθ2 = V + I r cos θ + I x sin θ 2 2 e2 2 2 e2 2 Thus the voltage drop in the secondary terminal voltage E − V = I r cos θ + I x sin θ = 2 2 2 e2 2 2 e2 2 Per unit voltage regulation for any load current I 2 is E − V Ir Ix = cos θ + sin θ 2 2 2 e2 2 e2 2 2 E2 E2 E2 Ir E voltage drop across r at rated current = = p.u. equivalent resistance or p.u. Rated(=base) voltage E 2 e2 e2 2 2 resistance drop = ε r 2 ε = Ir 2 e2 I2r re2 r E = E I = 2 2 2r I2xe2 Similarly, for rated current I2, let E = ε 2 x Ohmic lossat rated current Rated VA The per unit voltage regulation at rated current is given by ε r cosθ2 + εxsinθ2 At lagging p.f., voltage regulation would be always positive. At leading p.f., E2 = OC = V2 + I2re2 cosθ2 −I2xe2sinθ 2 E2 − V2 = I2re2 cos θ2 −I2xe2sinθ 2 ∴ p.u. voltage regulation at any load current I 2 is given by www.iesacademy.com E-mail: iesacademy@yahoo.com Page-12 25, 1 st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290
India’s No. 1 IES Academy Transformer Chapter-1 Ir Ix cos θ − sinθ 2 e2 2 e2 2 2 E2 E2 In case I2 is the rated (or full-load) current, then p.u. voltage regulation is given by ε cosθ − ε sinθ r 2 x 2 Hence, at leading p.f. voltage regulation may become negative. Phasor diagrams for 1-phase transformer for (a) negative voltage regulation (V.R.) (b) zero V.R. and (c) maximum V.R. Condition for Zero Voltage Regulation Voltage regulation varies with load power factor. If load power factor is varied with constant values of load current and secondary emf, then zero voltage regulation will occur when εr cos θ 2 +εx sinθ 2 = 0 εr Ir r tan θ 2 = − = − = − ε x E 2 e2 e2 I2xe2 x e2 2 E 2 Magnitude of load pf, cos θ 2 = x e2 /z e2 The negative value of tan θ2 indicates that zero voltage regulation occurs when load pf is leading. For leading p.f.s. greater than x e2 /z e2 , the voltage regulation will be negative, i.e. the voltage will rise from its no load value, as the transformer load is increased. Condition for Maximum Voltage Regulation P.U. voltage regulation = εr cosθ2 + εx sinθ2 d d θ 2 (p.u.regulation) =−εsinθ +εcosθ = 0 r 2 x 2 www.iesacademy.com E-mail: iesacademy@yahoo.com Page-13 25, 1 st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290
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India’s No. 1<br />
<strong>IES</strong> <strong>Academy</strong><br />
Transformer<br />
Chapter-1<br />
The voltage regulation of a transformer can be obtained from its approximate equivalent<br />
circuit referred to primary or secondary.<br />
Approximate equivalent circuit of a 2-winding transformer, referred to secondary and the<br />
phasor diagram of the circuit for a lagging power factor load.<br />
E<br />
2<br />
= OC = OA + AB + BC( or B ' C ')<br />
= OA + AB 'cos θ<br />
2<br />
+ DB 'sinθ2<br />
= V + I r cos θ + I x sin θ<br />
2 2 e2 2 2 e2 2<br />
Thus the voltage drop in the secondary terminal voltage<br />
E − V = I r cos θ + I x sin θ<br />
= 2 2 2 e2 2 2 e2 2<br />
Per unit voltage regulation for any load current I<br />
2<br />
is<br />
E<br />
− V<br />
Ir Ix<br />
= cos θ + sin θ<br />
2 2 2 e2 2 e2<br />
2 2<br />
E2 E2 E2<br />
Ir<br />
E<br />
voltage drop across r at rated current<br />
= = p.u. equivalent resistance or p.u.<br />
Rated(=base) voltage E<br />
2 e2 e2<br />
2 2<br />
resistance drop = ε<br />
r<br />
2<br />
ε = Ir<br />
2 e2 I2r re2<br />
r<br />
E<br />
= E I<br />
=<br />
2 2 2r<br />
I2xe2<br />
Similarly, for rated current I2, let<br />
E<br />
= ε<br />
2<br />
x<br />
Ohmic lossat rated current<br />
Rated VA<br />
The per unit voltage regulation at rated current is given by ε<br />
r<br />
cosθ2 + εxsinθ2<br />
At lagging p.f., voltage regulation would be always positive.<br />
At leading p.f., E2 = OC = V2 + I2re2 cosθ2 −I2xe2sinθ 2<br />
E2 − V2 = I2re2 cos θ2 −I2xe2sinθ<br />
2<br />
∴ p.u. voltage regulation at any load current I<br />
2<br />
is given by<br />
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