1. Today’s Topics 1- The per unit system 2-Transformer Voltage Regulation
3- Transformer Efficiency
4- Transformer Taps
5- Transformer Rating and Related Problems

2. The Per Unit System
In power systems there are so many different elements such as
Motors, Generators and Transformers with very different sizes
and nominal values.
To be able to compare the performances of a big and a small
element, per unit system is used.
In per unit system, each electric quantity is measured as a decimal fraction of some base level
Per Unit Value =
Actual value
Base value
e.g. in a synchronous generator with 13.8 Kv as its nominal voltage,
Instead of saying the voltage is Kv, we say the voltage is 0.9 p.u.

3. How Are the Base Values Defined
For an electric element, we have : Power, Voltage, Current and Impedance
Usually, the nominal apparent power (S) and nominal voltage (V)
are taken as the base values for power and voltage
The base values for the current and impedance can be calculated

4. Example 1:
A load takes 20 A at a power factor 0.9 lead when connected to a 600 Voltage. If the base voltage and apparent power are 600 and 6000 VA, determine the variables and impedance in per unit system

5. Ideal Transformers in Per Unit Values

6. Ignore the transformer

7. Example: Given the transformer in the previous example
rated at 20 kVA, 8000/240, calculate the equivalent circuit, with per unit values

8. The equivalent circuit in per unit values
Referred to the primary or secondary

9. Transformer Voltage Regulation
Fact: As the load current is increased, the voltage (usually) drops.
Transformer voltage regulation is defined as:

10. Other useful formulas
Prefer small VR
For an ideal transformer : VR=0
Note: If there were only resistive loads, the VR would not be much large in real transformers, but because loads
normally have different power factors, VR may be considerably large in real transformers.

11. VR in real transformers

12. At unity power factor
Resistive load
At lagging power factor
Inductive load
At leading power factor
Capacitive load

14. Transformer Efficiency

16. Transformer Taps The voltage in a distribution line is not constant.
It may be 1.05 p.u. at generator terminal and 0.95 at the load side.
Depending on the place the transformer is used, we may need to adjust the transformer ratio to get similar load voltage. That’s why we need Tap
In Tap Changing Under Load (TCUL) transformer, the tap changes automatically to keep the output voltage constant

17. Transformer Rating and Related Problems
Transformers have three major ratings:
Voltage, Apparent power (current) and frequency
The parameters of equivalent circuit are given in p.u.
As long as a transformer is working under rated conditions, there should be (is) no problem
What should we consider if we want to use a transformer under de-rating conditions?

18. Voltage rating
The insulation has been designed to stand up to a particular voltage
10% increase in voltage in the linear part of B-H curve would result in 10% increase in magnetization current, but in the saturation part, the magnetization current may be unacceptable

19. Frequency rating
Exactly the same problem.
If a 60 Hz transformer is going to be used in a 50 Hz system, the applied voltage should be reduced by a factor 5/6.
Apparent power (current) rating
Each coil has limit for current magnitude and also the higher current results in higher power loss (which is converted to heat) and may damage the insulation. This has a dramatic effect on transformer life.
If the voltage rating has been reduced, the apparent power should be reduced by the same factor.

20. Current Inrush
If a transformer is switched to a system, there may be some current with large magnitude (Current Inrush), in the first few milliseconds after the switch is closed.
The reason behind the current inrush is transient

21. Transients
Transient in electrical systems is the severe changes in current and voltage after a switch is closed or opened