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Lec-2: Electrical Machines, B.Sc. Electrical Engineering Engr. Riaz Ahmad Rana, Assistant Professor, FOE, UCP

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Ideal & Practical Transformers Lecture Objectives

Losses, Efficiency & Voltage Regulation Shifting of Parameters Equivalent Circuits IDEAL TRANSFORMER Ideal transformer is practically nothing but its study provides useful tool in the analysis of a practical transformer.

1. Winding resistances (RCharacteristics

1 & R22. Winding reactance (X

) = Zero 1 & X2

3. Copper and core losses = Zero ) = Zero

4. Leakage flux = Zero 5. Zero voltage regulation = Zero 6. Input = output 7. Efficiency = 100 %

1. Winding resistances (RPRACTICAL TRANSFORMER

1 & R22. Winding reactance (X

) Zero 1 & X2

3. Copper and core losses Zero ) Zero

4. Leakage flux Zero 5. Zero voltage regulation Zero 6. Input output 7. Efficiency 100 % TRANSFORMER LOSSES Losses of transformer appear in the form of heat in core and windings.

Hysteresis Loss (PhAssociated with magnetization & demagnetization of the core during each half cycle of the flux.

)

Laminations of core increase the resistance by decreasing the thickness of core which in turn decreases the eddy current (i.e., Ie = E / R) and eddy current loss. Iron loses known as constant losses because applied voltage, frequency, core volume, core thickness and flux density remains constant at all loads.

Eddy current Loss (Pe) Induced emf in core sets up eddy current in core and hence eddy current losses occur.


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Leakage Flux Loss Flux leaking from core to air produces self-inductance in coils which is loss.

Resistive heating losses in the primary and secondary windings of the transformer.

Copper Losses

Proportional to square of the current flowing in the windings.

About 90 % of the total losses. Known as variable losses because they are different

at different loads.

Copper losses depend on current and iron losses depend on voltage and no other losses occur in transformer. Therefore total losses depend on Volt Ampere (VA).

Why transformer power in KVA instead of KW?

Losses do not depend on angle between volt and current. It means it is independent of power factor.

Electrical power on either side of transformer is constant (V1I1 = V2I2

), so there is no need of power factor which is only required to compensate losses.

TRANSFORMER EFFICIENCY

ALL-DAY EFFICIENCY


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Due to the resistance and reactance of the windings, voltage drop takes place in the transformer. Accordingly the output voltage under load conditions is different from the output voltage under no-load condition.

VOLTAGE REGULATION

The voltage regulation of a transformer is defined as the difference between the secondary voltages at no-load and the secondary voltages at load expressed as % age of the no-load voltage.

% age VR = [V2, NL - V2, FL] x 100 / V2, NL Voltage Regulation Up If the voltage drop is divided by V2,L, then the voltage regulation is known as voltage regulation up. % age VR Up = [V2,NL _ V2,FL] x 100 / V2, L Voltage Regulation Down If the voltage drop is divided by V2, NL, then the voltage regulation is known as voltage regulation up. % age VR Down = [V2,NL -V2,FL ] x 100 / V2,NL

It is possible to transfer resistance, reactance and impedance in a transformer from one winding to other to simplify the calculations.

SHIFTING OF PARAMETERS (RESISTANCE, REACTANCE, IMPEDANCE, VOLTAGE & CURRENT)

When the parameters are transferred from secondary to primary side, then the parameters are called referred to primary side parameters (Ro1, Xo1, Zo1

When the parameters are transferred from primary to secondary side, then the parameters are called referred to secondary side parameters (Ro

) and the circuit is called referred to primary circuit.

2, Xo2, Zo2

) and the circuit is called referred to secondary circuit.

4


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5

12

POINTS TO REMEMBER When secondary parameters like R2, X2 and Z2 are

transferred to primary side, multiply them by a2or 1 / k2.

When primary parameters like R1, X1 and Z1 aretransferred to secondary side, multiply them by1 / a2 or k2.

Secondary voltage V2 becomes a V2 in the primaryside and primary voltage V1 becomes V1 / a in thesecondary side.

Secondary current I2 becomes I2 / a in the primaryside and primary current I1 becomes I1 a in thesecondary side.

Circuital representation of of transformer parts and parameters that makes analysis easy.

EXACT EQUIVALENT CIRCIT


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Copper losses are modelled by placing resistors in primary and secondary windings.

Leakage elements are modelled by inductance or inductance.

Excitation branch of core may consist of RC and XC. Working current (heat generating current) is associated with RC and magnetization current (field generating current) is associated with XC

Exact equivalent circuits referred to primary (a) and secondary sides (b) are modelled as:

of core.

No-load current Io is only 1 3 % of the rated primary current and may be neglected without any serious error.

APPROXIMATE EQUIVALENT CIRCUIT

Equivalent circuit with out excitation branch is called app. equivalent circuit.

Approximate equivalent circuits without excitation branch, referring to primary and secondary sides are shown as:

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