Modelling of Power System Elements

Introduction

Electrical power get transmitted to very long distance using Extra High Voltage. Voltage equal and exceeding 66kV is called EHV. Thus in transmission system most faults causes due to insulation failure. This insulation failure causes heavy current flow through elements of power system for which the elements are not designed and other adverse effects. Hence it becomes necessary to protect the power system by disconnecting the faulty element using protection system and circuit breaker.

To save the power system during this fault it is necessary to design the protection system and circuit breakers correctly. Also it is necessary to adopt the protection system properly by settings its’ parameter correctly. And for this it is necessary to have precise estimate of these fault currents and other system parameters during fault.

Modelling of Power System Elements

Every part of power system under consideration for modeling consists of various elements. Main elements of the power system are-

1)  Synchronous Generators

2)  Transformers

3)  Transmission Lines

4)  Part of power system beyond current scope of modeling - Grid

For engineering calculations such as load flow and fault calculations it is necessary to model the above said power system elements with its equivalent electrical circuit. While modeling the power system; transformer and transmission line can be represented as an impedance (simplest form). Whereas synchronous generator and grid can be represented by a voltage source in series with an impedance. Here we will discuss how to model them for fault current calculations

Synchronous Generators: - Representation of synchronous generator changes depending upon time frame under consideration after inception of fault. The overall series reactance for synchronous generator is not constant but varies with time after inception of fault. Synchronous generator can be represented by a voltage source in series with an impedance equivalent to armature reaction and armature leakage reactance. Just after fault it is Sub-transient reactance (    ) from 0.1 sec to 3.0 sec after fault it is transient reactance (    ) and after that it is steady state reactance (    ). For deciding breaker current interruption rating sub-transient reactance needs to be used while for transient stability study transient reactance to be used.

Here subscript d stands for direct axis reactance. There are two reactance for synchronous generator a) Direct axis b) Quadrature axis and for cylindrical rotor type these both are equal, most of our synchronous generators are cylindrical rotor type. Moreover even for salient pole type synchronous though the direct and quadrature axis reactance are different; but as during fault current lags voltage by nearly 90⁰ hence effect of quadrature axis reactance is negligible.  Hence for fault current calculations synchronous generators can be represented simply by   =  in series with a constant voltage source.

Transmission Lines: - From available data of conductor used for the transmission line and spacing it’s impedance per kilometer length can be calculated. Also it is generally made available by the Corporate Office. After multiplying this known impedance per kilometer by length of the line we get the series impedance of the transmission line. Generally resistance of transmission line is very less as compared to its reactance and thus for fault calculations resistance is neglected and transmission line is represented by equivalent reactance only.

Transformer: -For transformer this impedance is equivalent to winding resistance in series with transformer leakage reactance. For fault calculations resistance is neglected and transformer is represented by equivalent leakage reactance only.

Grid: - The part of power system which is beyond our current scope of modelling can be shown as single impedance in series with single source (Thevnin’s equivalent impedance in series with equivalent source). Where

 =  

(for details see section – Formula for calculating 3-Ph fault current)

The modeling can be best explained through an example. Next page Fig-1 shows a representative power system whereas Fig-2 shows its’ equivalent circuit.

Here in Fig-2 we have not shown any numerical values and during further discussion the procedure for finding out these values will be explained. 

PU Representation of power system

In power system multiple voltage level exists hence it is customary to represent element impedances numerically using percentage values (Percent Value = PU valuex100). Because once an element represented by its’ percentage value the value remains same either referred from HV side or LV side of the transformer. Any power system can be represented fully by four quantities viz. MVA and kV at busses and current through elements and impedances of those elements. If the power system is to be represented by pu quantities above mentioned quantities are to be divided by respective base values. thus

These quantities are so related that selection of any two quantities defines other two quantities. Generally MVA and kV are selected as base quantities and base current and base impedance get defined as

For DC Circuit we know P = V*I = V*V/R = V²/R Thus R = V²/P thus for AC circuit 

OR simple to remember