This document discusses the per unit system of calculation used in power systems analysis. It provides examples of calculating per unit reactance for single phase transformers and the relationship between primary and secondary sides. The key advantages of the per unit system are that it gives a clear idea of relative magnitudes, per unit impedance values are consistent regardless of rating, and circuit laws and equations are simplified. The per unit system is ideal for computerized analysis and simulation of complex power systems.

1. MIRPUR UNIVERSITY OF SCIENCE AND TECHNOLOGY (MUST), MIRPUR
DEPARMENT OF ELECTRICAL ENGINEERING

2. POWER SYSTEM ANALYSIS
EE-3653
Lecture No. 03: Per Unit System of Calcluation
Engr. Mirza Ateeq Ahmed Baig
Assistant Professor
Date: June, 2020

3. Per Unit Reactance for Single Phase Transformer
Power System Analysis 3
 The leakage resistance and reactance (in ohm) for a transformer depends whether it is
referred to Primary or Secondary. If these values are stated in per‐unit, the base power is
the rating of the transformer.
 Whereas, the referred base voltage could be from the Primary or secondary. However, the
per‐unit values for transformer is the same regardless the base voltage is taken from the
Primary or Secondary.
(Attention: If not stated what the referred side, by default, the impedance is always referred to the
lower voltage)

4. Relationship between primary and secondary side
Power System Analysis 4

5. Base values of transformer
Power System Analysis 5
In a transformer, two circuits are not directly connected but magnetically coupled.
The voltages of the windings are in the ratio of turns and currents in inverse ratio.
For the coupled circuit, we should then choose
» The same base power
» Base voltages in the ratio of turns
This will ensure Spu, Vpu, Ipu, to remain unchanged when passing through an ideal
transformer

6. Example: 04
Power System Analysis 6

7. Example: 05
Power System Analysis 7

8. Example: 05
Power System Analysis 8

9. Example: 05
Power System Analysis 9

10. Example: 05
Power System Analysis 10

11. Example: 06
Power System Analysis 11

12. Example: 06
Power System Analysis 12

13. Example: 06
Power System Analysis 13

14. Advantages of Per Unit System
Power System Analysis 14
In power system, per‐unit is used because of the following advantages:
 It gives us a clear idea of relative magnitudes of various quantities, such as
voltage, current, power and impedance.
 The per‐unit impedance of equipment of the same general type based on their own
ratings fall in a narrow range regardless of the rating of the equipment. Whereas
their impedance in ohms vary greatly with the rating.
 The per‐unit values of impedance, voltage and current of a transformer are the
same regardless of whether they are referred to the primary or secondary side.
This is a great advantage since the different voltage levels disappeared and the
entire system reduces to a system of simple impedance.

15. Advantages of Per Unit System
Power System Analysis 15
 Manufacturers usually specify the impedance of apparatus in per unit
values.
 The circuit laws are valid in per‐unit systems, and the power and
voltage equations are simplified since the factors of 3 and 3 are
eliminated in the per‐unit system.
 The per‐unit systems are ideal for the computerized analysis and
simulation of complex power problems.

16. THANKS