Lecture 21 computational technique (2).pptx

per unit system

1. Computational techniques in power system

2. Per Unit System (1) Per unit system is the expression of system quantities in the fraction of defined base quantities. Calculation are simple because quantities expressed in per unit don’t change when they are referred from one side of machine to another. The per unit value of any quantity is the ratio of actual value of that quantity to the arbitrarily selected base quantity, both the actual and base quantity are of same unit.

3. Per Unit System (2) For example, if the base voltage is 220 kV is specified, then the voltage 210 kV is 210/220=0.954 pu . One major advantages of the per unit is that by properly specifying base quantities, the equivalent impedance of a transformer whether referred to primary or secondary, is the same. Another advantages of the per-unit system is that the comparison of the characteristics of the various electrical apparatus of different types and ratings is facilitated by expressing the impedances in per unit based on their ratings. When all the quantities are converted in per unit values, the different voltage levels disappear and power network involving synchronous generator, transformers and line reduces to a system of simple impedances.

4. Per Unit System (3)

5. Per Unit System (4) Now substituting first equation in second “Base impedance” is: Note that the phase and line quantities expressed in per unit are same, and the circuit laws are valid:

6. Per Unit System (5) If I L is the load current with a load impedance of Z L then per unit value of load is: The impedance of generators, transformers and motors supplied by the manufacturer are generally given in per-unit values on their own ratings. For power system anlalysis , all the impedances must be expressed in per unit values on a common base.

7. Per-unit representation of transformer (1)

8. Per-unit representation of transformer (2) and Also: Substituting this in V S : Substituting E P in this equation :

9. Per-unit representation of transformer (3) The last equation can be turned into per unit as: Dividing this equation by VSB and using the relation above we can get: Now,  

10. Per-unit representation of transformer (4) Therefore:

11. Numerical

12. Any Question ?