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POWER SYSTEM

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POWER FLOW ANALYSIS

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Introduction

Load Flow Analysis/Power Flow Analysis are one ofthe most important aspects of power system planning

and operation.

The load flow gives us the sinusoidal steady state ofthe entire system - voltages, real and reactive power

generated and absorbed and line losses.

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Cont.

The objective of Power Flow Analysis is to obtain thevoltage magnitudes and angles at each bus in thesteady state.

This is rather important as the magnitudes of the busvoltages are required to be held within a specifiedlimit.

Once the bus voltage magnitudes and their angles are

computed using the load flow, the real and reactivepower flow through each line can be computed.

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Cont.

The steady state power and reactive power

supplied by a bus in a power network are

expressed in terms of nonlinear algebraicequations. We therefore would require iterative

methods for solving these equations.

Newton-Raphson method

Gauss-Seidel method

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Bus Admittance Matrix

A power system network can be converted into anequivalent impedance diagram. This diagram forms

the basis of power flow (or load flow) studies and

short circuit analysis. Bus admittance matrix (also known as Ybus matrix)

and bus impedance matrix (also known as Zbusmatrix). These two matrices are related by

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FormationofBus Admittance Matrix

Consider the voltage source VSwith a source

(series) impedance of ZSas shown in below Fig (a).

Using Norton's theorem this circuit can be replaced

by a current source ISwith a parallel admittance ofYSas shown in Fig.(b).

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Cont.

The relations between the original system and the

Norton equivalent are

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Cont.

Consider the 4-bus power system shown belowfigure. Let Zij, i = 1, ..., 4 and j = 1, ... , 4 denote the

line impedance between buses i and j .

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Where,Z11 =j(XG1 +XT1 ) andZ22 =j(XG2 +XT2 ).

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Cont.

In this figure the nodes with the node voltages of V1 to V4indicate the buses 1 to 4 respectively. Bus 0 indicates the

reference node that is usually the neutral of the Y-

connected system.

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Cont.

The impedance diagram is converted into an equivalentadmittance diagram. In this diagram Yij= 1/ Zij, i = 1,..., 4 and j

= 1, ... , 4. The voltage sources EG1 and EG2are converted into

the equivalent current sources I1 and I2respectively using the

Norton's theorem discussed before.

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Cont.

To determine the voltage-current relationships of thenetwork. It is to be noted that this relation can be written in

terms of the node (bus) voltages V1 to V4 and injected

currents I1 and I2as follows

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or

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Cont.

Consider node (bus) 1 that is connected to the nodes 2 and3. Then applying KCL at this node we get

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Cont.

In a similar way application of KCL at nodes 2, 3 and 4results in the following equations

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Cont.

Combining equation I1 to I4 we get

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Cont.

In general the format of the Ybus matrix for an n -

bus power system is as follows

It is to be noted that Ybus is a symmetric matrix

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Problem 1

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Problem 2

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HE END

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