1. PRACTICAL TRANSFORMER
Electrical Power System
PRACTICAL TRANSFORMER
Wan Khairunizam
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Contents
Ideal transformer with an imperfect core
Ideal transformer with losses coupling
Primary and secondary leakage reactance
Simplifying the equivalent circuit
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Introduction
In the real world the transformers are not ideal. The winding of practical transformers have resistance and the cores are not infinitely permeable. The flux produced by the primary is not completely capture by the secondary. The iron core produces eddy-current and hysteresis losses with contributes to the temperature rise of the transformer.
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Ideal transformer with an imperfect core
The imperfection can be represented by 2 circuit elements Rm and Xm in parallel with the primary terminal.
The primary voltage Eg produces a voltage E1.
Rm represents the iron losses and produces If.
Xm is permeability of the transformer core and Im flowing through it to create Φm.
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Rm = E12 / Pm. (Power equation)
Xm = E12 / Qm. (Power equation)
Rm = resistance representing the iron losses [Ω]
Xm = magnetizing reactance of the primary winding [Ω]
E1 = primary voltage [V]
Pm = iron losses [W]
Qm = reactive power needed to set up the mutual flux Φm [var]
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The total current needed to produce the Φm in an imperfect core is equal to the phasor sum of If and Im.
It is called exciting current Io.
The peak value of the mutual flux Φm = E1 / (4.44 x f x N1)
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Ideal transformer with loose coupling
Consider transformer with a perfect core
Eg is a supply voltage. Current I1 and I2 flow in the primary and secondary. I1 / I2 = N2 / N1, I1N1 = I2N2 (Current ratio)
I2 produces mmf I2N2 and I1 produces mmf I1N1
I2N2 produces a total flux Φ2. Φ2 consist of Φm2 and Φf2 . Φm2 link to the primary but not Φf2 . Φf2 is called the secondary leakage flux.
Similar with primary, and it is called the primary leakage flux Φf1
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The combination of Φm2 and Φm1 into Φm
I2 produces mmf I2N2 and I1 produces mmf I1N1
Φf2 is created by I2N2 and Φf1 is created by I1N1
Es is induced in the secondary composed of 2 parts.
Ef2 = 4.44 x f x N2 x Φf2
E2 = 4.44 x f x N2 x Φm
Similar with primary, Ep is induced in the primary composed of 2 parts.
Ef1 = 4.44 x f x N1 x Φf1
E1 = 4.44 x f x N1 x Φm
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Primary and secondary leakage reactance-separating various induced voltage in the transformer circuit
The induced voltage in the circuit E1, Ef1, E2 and Ef2.
Ef2 is a secondary voltage drop across the reactance. (by N2)
The secondary leakage reactance Xf2 = Ef2 / I2
Ef1 is a primary voltage drop across the reactance. (by N1)
The primary leakage reactance Xf1 = Ef1 / I1
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Equivalent circuit for a practical transformer
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Resistive elements R1 and R2.
Inductive elements Xf1 and Xf2.
The load Z.
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Simplifying the Equivalent circuit for a practical transformer (Imperfect core + loose coupling)
Practical core / imperfect core
Leakage reactance
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Typical value of transformer parameters
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Analysis of equivalent circuit of practical transformer
1. At no load.
2. At full load.
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At no load X X X X
I2 is zero and I1 is also zero because T is ideal transformer.
R1 and Xf1 are so small that the voltage drop across them is negligible.
The current in R2 and X2 is also zero. The impedance could be neglected.
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Equivalent circuit at no load
N1 / N2 = a.
Is equal to the ratio of the primary to the secondary Ep / Es.
Ep / Es = N1 / N2
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At full load X Io
Ip is least 20 times larger than Io.
Io and magnetizing current could be neglected.
Impedance shifted to the primary site.
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Equivalent circuit at full load
Rp = R1 + a2R2. (Refer to impedance ratio)
Xp = Xf1 + a2Xf2. (Refer to impedance ratio)
Rp = total transformer resistance referred to the primary side
Xp = total transformer leakage reactance referred to the primary side
The combination of Rp and Xp constitute the total transformer impedance Zp
Zp = √(Rp2 + Xp2)
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Transformer above 500 kVA possess of a leakage reactance Xp that is least 5 times greater than Rp.
In such case Rp could be neglected.
Above is the equivalent circuit.
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Voltage regulation
Voltage regulation is an important attribute of the transformer.
Voltage regulation = (ENL-EFL/ EFL)*100
ENL=secondary voltage at no load
EFL= secondary voltage at full load
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Another important topics
Per unit systems of the transformer
Impedance of the transformer.
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