eee 3233 pfa
TRANSCRIPT
-
8/9/2019 EEE 3233 PFA
1/18
POWER SYSTEM
EEE 3233
1
POWER FLOW ANALYSIS
-
8/9/2019 EEE 3233 PFA
2/18
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.
2
-
8/9/2019 EEE 3233 PFA
3/18
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.
3
-
8/9/2019 EEE 3233 PFA
4/18
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
4
-
8/9/2019 EEE 3233 PFA
5/18
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
5
-
8/9/2019 EEE 3233 PFA
6/18
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).
6
-
8/9/2019 EEE 3233 PFA
7/18
Cont.
The relations between the original system and the
Norton equivalent are
7
-
8/9/2019 EEE 3233 PFA
8/18
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 .
8
Where,Z11 =j(XG1 +XT1 ) andZ22 =j(XG2 +XT2 ).
-
8/9/2019 EEE 3233 PFA
9/18
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.
9
-
8/9/2019 EEE 3233 PFA
10/18
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.
10
-
8/9/2019 EEE 3233 PFA
11/18
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
11
or
-
8/9/2019 EEE 3233 PFA
12/18
Cont.
Consider node (bus) 1 that is connected to the nodes 2 and3. Then applying KCL at this node we get
12
-
8/9/2019 EEE 3233 PFA
13/18
Cont.
In a similar way application of KCL at nodes 2, 3 and 4results in the following equations
13
-
8/9/2019 EEE 3233 PFA
14/18
Cont.
Combining equation I1 to I4 we get
14
-
8/9/2019 EEE 3233 PFA
15/18
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
15
-
8/9/2019 EEE 3233 PFA
16/18
Problem 1
16
-
8/9/2019 EEE 3233 PFA
17/18
Problem 2
17
-
8/9/2019 EEE 3233 PFA
18/18
HE END
18