Electrical Machine - IES Academy

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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
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