Electrical Machines (EELE 3351)

Assad Abu-Jasser, PhD Electric Power Engineering The Islamic University of Gaza ajasser@iugaza.edu.ps www.iugaza.edu.ps/ajasser

Chapter 2 Transformers

Electric Transformer Animation https://www.youtube.com/watch?v=vh_aCAHThTQ

Transformer Types and Construction Core-Type Shell-Type

The Ideal Transformer

Power in an Ideal Transformer Output Power Input Power

Impedance Transformation Through a Transformer

Ideal Transformers Circuits Analysis (Example 2.1) A generator rated at 480-V, 60-Hz is connected a transmission line with an impedance of 0.18+j0.24 Ω. At the end of the transmission line there is a load of 4+j3 Ω. If the power system is exactly as described above in Figure (a), what will the voltage at the load be? What will the transmission line losses be? Suppose a 1:10 step-up transformer is placed at the generator end of the transmission line and a 10:1 step-down transformer is placed at the load end of the line (Figure (b)). What will the load voltage be now? What will the transmission line losses be now?

Single-Phase Transformers Theory of Operation

Transformer Voltage Ratio

Transformer Current Ratio Dot Convention

Example 2.1 An ideal transformer has a 150-turn primary and 750-turn secondary. The primary is connected to a 240-V, 50-Hz source. The secondary winding supplies a load of 4 A at a lagging power factor of 0.8, Determine (a) the a-ratio, (b) the current in the primary, (c) the power supplied to the load

Transformer Equivalent Circuit Copper (I2R) Losses - Resistive heating losses Eddy current Losses - resistive heating losses in the core Hysteresis Losses - due to the magnetic domains Leakage flux - the fluxes which escape the core

Transformer Exact Equivalent Circuit

Approximate Equivalent circuits

Transformer Voltage Regulation

Transformer Phasor Diagram Simplified Voltage Regulation Calculation

Transformer Efficiency

Example 2.2 A 23-kVA, 2300/230-V, 60-Hz, step-down transformer has the following resistance and leakage-reactance values: R1=4Ω, R2=0.04Ω, X1=12Ω, and X2=0.12Ω. The equivalent core-loss resistance and the magnetizing reactance on the primary side of the transformer are 20 kΩ and 15kΩ, respectively The transformer is operating at its rated voltage and rated load. If the power factor of the load is 0.866 lagging, determine the efficiency of the transformer and plot the phasor diagram.

The Autotransformer

V-I Relations in an Autotransformer

The Autotransformer Rating

Example 2.7 A 100-VA, 120/12-V transformer is to be connected so as to form a step-up autotransformer as shown. A primary voltage of 120 V is applied to the transformer. (a) what is the secondary voltage of the transformer, (b) what is the maximum volt-ampere rating in this mode of operation?, and (c) calculate the rating advantage of this autotransformer connection over the conventional 120/12-V operation.

Three-Phase Transformer 3 Single-Phase Transformers 1 Three-Phase Transformer

3-Phase Transformer Connections

Example 2.9 A 50-kVA, 13800/208-V, ∆-Y distribution transformer has a resistance of 114.2 Ω/phase and a reactance of 800Ω/phase referred to the high voltage side. (a) what is the transformer phase impedance referred to the low voltage side, and (b) calculate the voltage regulation at full-load and 0.8 PF lagging.

End Of Chapter Two