Part II
THE REAL TRANSFORMER AND
DEVELOPMENT OF THE EQUIVALENT
CIRCUIT
34
The non-ideal transformer at no load
35
The non-ideal transformer at no load
a) Transformer with no load current
b) No load phasor diagram
Core Losses
37
Magnetizing Reactance
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Magnetizing Reactance
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Transformer equivalent circuit at no load
Io Io
IC
Io
I I
2
C
To
2
m
no load power factor
1
RC
gC
conductance
bm
1
Xm
susceptance
Transformer equivalent circuit at no load
41
The exciting current
• The exciting current is not sinusoidal however it is
symmetrical
• The predominant harmonic is the third. It is usually in
the order of 40% of the exciting current
• The exciting current is usually 5% of the full load
current
42
Development of the equivalent circuit
• windings resistances: each winding has some
resistance
• the resistances of the primary and secondary
windings are R1 and R2.
43
The equivalent circuit (cont’d)
• The inclusion of the winding resistances
dictates that:
– the power input must be greater than the power
output. efficiency ()<100%.
– the terminal voltage is not equal to the induced
emf, V1E1 and V2E2
44
The equivalent circuit (cont’d)
45
The equivalent circuit (cont’d)
• Each transformer winding can be replaced by
two windings:
– One winding is responsible to create the leakage
flux
– The other encircles the core (the mutual flux)
46
The equivalent circuit (cont’d)
47
The equivalent circuit (cont’d)
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The equivalent circuit (cont’d)
49
Practical Transformer Equivalent
circuit
E1
E2
N1
N2
Example (1) on the non-ideal
transformer
• A 23-kVA, 2300/230V, 60HZ transformer has
the following resistance and leakagereactance values: R14, R20.04, X112,
and X20.12.
• The transformer is operating at 75% of its
rated load. If the power factor of the load is
0.866 leading, determine the efficiency of the
transformer.
• Ignore the no load current
51
Solution
52
Solution (cont’d)
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Equivalent circuit referred to the
primary
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The phasor diagram
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Other equivalent circuits
Equivalent circuit (a): secondary impedances referred
to the primary
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Other equivalent circuits
• Equivalent circuit (b): primary impedances
referred to the secondary
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Equivalent circuit (c)
• The impedance of the parallel branch is very
high so that the voltage drop across the
parallel branch is almost equal to the input
voltage V1
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Equivalent circuit ( d )
• The impedance of the parallel branch is very
high it can be considered as an open circuit
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Equivalent circuit (e)
• The impedance of the equivalent series
inductance is very large if compared with the
equivalent series resistance, therefore the
resistances can be omitted and the circuit
reduces to:
60
Example: on the equivalent circuit
• Single phase transformer, 50kVA, 2400/240V,
60Hz, R10.75, R20.0075, Xl11, Xl20.01,
y0(on the 2400.003-j0.02)S
– Draw the equivalent circuit referred to the HV side
and referred to the LV side
– The transformer is used as a step down transformer at
the end of a feeder whose impedance is (0.5+j2).
Determine the voltage Vs at the sending end of the
feeder if the transformer delivers rated load at rated
secondary voltage and 0.8 lagging power factor.
Neglect the exciting current of the transformer.
61
Solution
62
Solution
• Similarly, the equivalent circuit referred to the
LV side is given below:
63
Solution
• The equivalent circuit of the transformer + the
feeder referred to the primary side is given
below, neglecting the exciting current of the
transformer
64
solution
65
Solution
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