Electrical Machine - IES Academy
Electrical Machine - IES Academy Electrical Machine - IES Academy
India’s No. 1 IES Academy Transformer Chapter-1 εx xe tan θ 2 = = ε r r 2 e2 re 2 i.e. cos θ 2 = z e2 Maximum voltage regulation occurs at a lagging load p.f. For max VR, lagging load p.f. angle should be equal to leakage impedance angle. The magnitude of maximum voltage regulation is equal to the p.u. value of the equivalent leakage impedance ze2 of the transformer. Transformer Losses and Efficiency There are mainly two kinds of losses (i) core losses (ii) ohmic losses Core loss PC: Core loss consists of hysteresis loss Ph and eddy current losses Pe. i.e. Pc = Ph + Pe Ph = KhfBm x Pe = Kef 2 Bm 2 The Stein Meitz constant x varies 1.5 – 2.5. ( x = 1.6, if unstated). V = √2π f N Bm Ai For a transformer number of turns N and net core area Ai are constant. Hence, P h ⎡ 1 ⎤ ⎡V ⎤ = Khf ⎢ ⎥ ⎢ 2 NA f ⎥ ⎣ π i ⎦ ⎣ ⎦ x x Ph = k hV x f 1-x 2 2 ⎡ 1 ⎤ ⎡V ⎤ Pe = Kf e ⎢ ⎥ ⎢ = kV e 2 NA f ⎥ ⎣ π i ⎦ ⎣ ⎦ 2 2 1. Hysteresis loss depends upon frequency and voltage where as eddy current loss depends only on voltage (squared). 2. Kh depends upon volume of core material & permeability of core material. Thus, permeability should be as high as possible for minimum hysteresis loss. 3. Ke depends on volume of material, resistivity and thickness of lamination By plotting PC/f against f, Pe and Ph can be calculated separately by extrapolating the graph. Ohmic losses: Ohmic losses occur in both the primary and secondary winding resistances. They should be calculated at standard operating temperature of electrical machines 75°. Apart from core loss and ohmic loss, stray load loss and dielectric loss also occur. Efficiency: The efficiency of a transformer (or any other device) is defined as the ratio of output power to input power. Thus www.iesacademy.com E-mail: iesacademy@yahoo.com Page-14 25, 1 st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290
India’s No. 1 IES Academy Efficiency η = Where I r output power input power VI cosθ cos c e 2 2 2 = 2 VI 2 2 θ 2 + P + I2 r 2 P c = total core loss, 2 2 e2 = total ohmic losses, VI 2 2 = output VA, And cos θ 2 = load p.f. The efficiency can also be expressed as Transformer Chapter-1 output power input power − losses losses η = = = 1 − input power input power input power Condition for maximum efficiency: Pc + Psc η at full load = 1 − (Rated VA) cos θ + P + P As before, maximum efficiency occurs when variable ohmic loss = Constant core loss, 2 Pc + n Psc η= 1 − 2 n(Rated VA)cos θ + P + n P As before, maximum efficiency occurs when variable ohmic loss = Constant core loss, nP = P ⇒ n= 2 c sc c Psc Above equation can now be re-written as (kV A)max ⋅ η = (n) (kVA)rated Pc + Psc η at full load = 1 − (Rated VA)cos θ + P + P At any other load current, say 2 cos θ2 η= Pc Ire cos θ 2 + + VI VI c sc www.iesacademy.com E-mail: iesacademy@yahoo.com Page-15 2 c 2 2 2 2 2 2 2 nI fl , the efficiency is given by η= 1 − 2 Pc + n Psc 2 n(Rated VA)cosθ 2 + Pc + n Psc Maximum efficiency occurs when variable ohmic loss = constant core loss, 2 P c sc sc 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 />
Efficiency η =<br />
Where<br />
I r<br />
output power<br />
input power<br />
VI cosθ<br />
cos<br />
c e<br />
2 2 2<br />
=<br />
2<br />
VI<br />
2 2<br />
θ<br />
2<br />
+ P + I2 r<br />
2<br />
P<br />
c<br />
= total core loss,<br />
2<br />
2 e2<br />
= total ohmic losses,<br />
VI<br />
2 2<br />
= output VA,<br />
And cos θ<br />
2<br />
= load p.f.<br />
The efficiency can also be expressed as<br />
Transformer<br />
Chapter-1<br />
output power input power − losses losses<br />
η = = = 1 −<br />
input power input power input power<br />
Condition for maximum efficiency:<br />
Pc<br />
+ Psc<br />
η at full load = 1 − (Rated VA) cos θ + P + P<br />
As before, maximum efficiency occurs when variable ohmic loss = Constant core loss,<br />
2<br />
Pc<br />
+ n Psc<br />
η= 1 −<br />
2<br />
n(Rated VA)cos θ + P + n P<br />
As before, maximum efficiency occurs when variable ohmic loss = Constant core loss,<br />
nP = P ⇒ n=<br />
2 c<br />
sc c<br />
Psc<br />
Above equation can now be re-written as<br />
(kV A)max ⋅ η = (n) (kVA)rated<br />
Pc<br />
+ Psc<br />
η at full load = 1 − (Rated VA)cos θ + P + P<br />
At any other load current, say<br />
2<br />
cos θ2<br />
η=<br />
Pc Ire<br />
cos θ<br />
2<br />
+ +<br />
VI VI<br />
c<br />
sc<br />
www.iesacademy.com E-mail: iesacademy@yahoo.com Page-15<br />
2<br />
c<br />
2<br />
2 2<br />
2 2 2 2<br />
nI<br />
fl<br />
, the efficiency is given by<br />
η= 1 −<br />
2<br />
Pc<br />
+ n Psc<br />
2<br />
n(Rated VA)cosθ 2<br />
+ Pc<br />
+ n Psc<br />
Maximum efficiency occurs when variable ohmic loss = constant core loss,<br />
2<br />
P<br />
c<br />
sc<br />
sc<br />
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