Assignment 1&2 Ppt

8/21/2019 Assignment 1&2 Ppt

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PROJECTTITLE:- POWERFLOWANALYSIS

BYUSINGMATLABCOD.

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1. INTRODUCTIONANDBACKGROUND

1.1 INTRODUCTION

A power flow analysis (load-flow analysis) is a steady-

state analysis whose target is to determine

Bus voltages profile Currents

Real and reactive power flows in a system under a given

load conditions.

The load flow solution gives theNodal voltages and phase angles

The power injection at all the buses and

Power flows through interconnecting power channels2

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CONTD

In a power system each node or bus is associated with

four quantities

Magnitude of voltage

Phage angle of voltage Active power and

Reactive power

In load flow problem two out of these four quantities are

specified and remaining two is required to be determined

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CONTD

Depending on the quantities that have been specified, thebuses are classified into three categories.

1. Slack (swing) bus

2. Voltage controlled bus (P-V)

3. Load bus (P-Q)

To finish load flow analysis there are methods ofmathematical calculations which consist plenty of stepdepend on the size of system.

But this process is difficult and takes a lot of times toperform by hand.

In order to improve these difficulties, this project aimedto develop Matlab programmes for two popularly usedalgorithms in load flow analysis.

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1.2. OBJECTIVE

The objective of this paper is

To develop a computer program to solve the set of non

linear load flow equations using Gauss- Seidal and

Newton- Raphson load flow algorithm.

To evaluate the performance of these two methods.

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1.3. METHODOLOGY

Form a bus admittance matrix Ybusfor the power system

Perform nodal analysis of power system

The basic equation for power-flow analysis is derived

from the nodal analysis equations. Build flow chart of power-flow analysis technique

Develop Gauss-Seidel and Newton-Raphson power-

flow method algorithm.

Coding Gauss-Seidel and Newton-Raphson power-flowalgorithm using Matlab software.

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2. BACKGROUND

2.1 BUS ADMITTANCE MATRIX

The Ybusmatrix constitutes the models of thepassive portions of the power network.

Ybus matrix is often used in solving load flow

problems. that is Ybus(i i)

Where: Bijis the half line shunt admittance in mho.

Yijis the series admittance in mho.

Off-diagonal element in Y-bus matrix = -Yij that isYbus(i j) or Ybus(j i)

Where: Yijis the series admittance in mho.7

n

ij

j=1

Main diagonal element in Y-bus matrix= ijG B

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2.1.1.ALGORITHM

Step 1: Read the number of buses and the number

of lines of the given system.

Step 2: Read the self-admittance of each bus and

the mutual admittance between the buses.

Step 3: Calculate the diagonal element term called

the bus driving point admittance, Yiiwhich is the

sum of the admittances connected to bus i.

Step 4: The off-diagonal term called the transfer

admittance, Yijwhich is the negative of the

admittance connected from bus i to bus j.

Step 5: Check for the end of bus count and print the

computed Y-bus matrix.8

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2.2. LOADFLOWANALYSIS

Load flow study is the steady state solution of

the power system network and uses simplified

notation such as a one-line diagram and per-unit

system.

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2.3. METHODSOFLOADFLOWANALYSIS

The solution of the simultaneous nonlinear power

flow equations requires the use of iterative

techniques for even the simplest power systems.

There are many methods for solving nonlinear

equations, such as:

Gauss Seidel.

Newton-Raphson.

Fast Decoupled In this project we made use of the Gauss-Seidel

and Newton -Raphson method

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2.3.1.GAUSS-SEIDELMETHOD

Gauss-Seidel method is also known as the method

of successive displacements.

It is important to have a good approximation to the

load flow solution, which is after used as a starting

estimate (or initial guess) in the iterative procedure.

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CONTD

The 1sttask is driving the load flow equation

12

*

1

* *

1

*1

......................... 1, 2,........

1......................................................................

n

i i i ij j

j

n

i i i ii i i ij j

jj i

ni i

i ij j

jii ij i

P Q V Y V i n

P Q V Y V V Y V

P QV Y V

Y V

* *

1

* *

1

.................(1)

.......................................................................................(2)

Im .......

n

i i ii i i ij j

jj i

n

i i ii i i ij j

jj i

P RE V Y V V Y V

Q ag V Y V V Y V

...........................................................................(3)

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CONTD

At the beginning of an iterative method, a set of

values for the unknown quantities are chosen.

These are then update at each iteration.

The process continues till errors between all theknown and actual quantities reduce below a pre-

specified value.

The Gauss-Seidel method needs much iteration to

achieve the desired accuracy,

And there is no guarantee for the convergence.

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2.3.1.1. ALGORITHM

Step 0: Formulate and Assemble Ybusin Per Unit

Step 1: Assign Initial Guesses to Unknown Voltage

Magnitudes and Angles

Step 2:For Load Buses, calculate from this equation

Where k iteration number

For voltage-controlled busses, calculate Qi byequation (4) and check limits then find by equation

(5)

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1..... 0V

( 1)

*

1

1 nk i ii ij j

jii ij i

P QV Y V

Y V

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CONTD

However, is specified for voltage-controlled

busses. So,

Step 3: Check Convergence

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( 1) * *

1

Im .................................................(4)n

k

i i ii i i ij j

jj i

Q ag V Y V V Y V

( 1)

* 1

1.............................................................(5)

nk i i

i ij jjii ij i

P QV Y V

Y V

( 1) ( 1)

,

k k

i i i calcuV V spec

( 1)k

i iV V

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CONTD

If the difference is greater than tolerance, return to

Step 2. If the difference is less than tolerance, the

solution has converged; go to Step 4.

Step 4: Find Slack Bus Power PGand QG

Step 5: Find All Line Flows16

* *

1

n

i i ii i i ij j

jj i

P RE V Y V V Y V

* *

1

Imn

i i ii i i ij j

jj i

Q ag V Y V V Y V

( )ij i j ijI V V y

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CONTD

The power loss in line (i- j) is the algebraic sum of

the power flows determined in equation (6) and (7).

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( )ji j i jiI V V y

* ........................................(7)ji j jiS V I

*.....................................................(6)ij i ijS V I

Lji ij jiS S S

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2.3.1.2. GAUSS-SEIDELMATLABCODE

Gauss-seidal matlab cod

2.3.2. NEWTON-RAPHSON METHOD

It is an iterative method which approximates the set

of non-linear simultaneous equations to a set of

linear simultaneous equations using Taylors seriesexpansion and the terms are limited to first order

approximation.

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http://c/Users/User/Desktop/power%20flow/GShttp://c/Users/User/Desktop/power%20flow/GShttp://c/Users/User/Desktop/power%20flow/GShttp://c/Users/User/Desktop/power%20flow/GShttp://c/Users/User/Desktop/power%20flow/GShttp://c/Users/User/Desktop/power%20flow/GS


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CONTD

Power flow equation

Real power in terms of Vi, , and Yij

Reactive power

Newton- Raphson matrix form:

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1

( )..........................................(8)n

i i j ij ij ij ij

j

P V V G Cos B Sin

1

( )..........................................(9)n

i i j ij ij ij ij

j

Q V V G Sin B Cos

1 2

3 4

J JP

J JQ V

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2.3.2.1. ALGORITHMNEWTON-RAPHSON

Step 1: Formulate and Assemble Ybusin Per Unit

Step 2: Assign Initial Guesses to Unknown Voltage

Magnitudes and Angles

Step 3: Compute Piand Qifor each load bus from

the Equations (8) and (9).

Step 4: Determine the Mismatch Vector for

Iteration k

20

1..... 0V

(k)

i

(k)

i

P

Q

( ) ( )k Sch k

i i iP P P

( ) ( )k Sch k

i i iQ Q Q

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CONTD

For PV buses, the exact value of Qiis not specified,

but its limits are known.

If the calculated value of Qiis within limits, only is

calculated.

If the calculated value of Qiis beyond the limits,

then an appropriate limit is imposed and is also

calculated by subtracting the calculated value of Qi

from the appropriate limit.

The bus under consideration is now treated as a

load bus.

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CONTD

Step 5: Determine the Jacobian Matrix using the

estimated value in step-2

Step 6: Obtain

Step 7: Update the voltage and angle start next

iteration cycle at step 2 with this modified value.22

1 2

3 4

J JJ

J J

( ) ( )From matrixk ki iV and

( ) (k)

i

(k)( )i

P\

Q

k

i

k

i

VJ

( 1) ( ) ( )k k k

i i i

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CONTD

Step 8: Continue until scheduled errors for all buses

are within a specified tolerance

Step 9: Find Slack Bus Power PGand QGfrom

Equation (8) and (9). Step 10: Compute Line Flows and Total Line

Losses from Equation (6) and (7)

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( 1) ( ) ( )k k ki i iV V V

( )k

iQ

( )k

iP

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2.3.2.2. NEWTON-RAPHSONMATLABCODE

Newton-raphson matlab code

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http://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NRhttp://c/Users/User/Desktop/power%20flow/NR


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4. CONCLUSION

The result of power flow study is the magnitude and

phase angle of the voltage at each bus, and the

real and reactive power flowing in each line.

This information is essential in long term

planning,

It helps in choosing the best unit commitment plan

and generation schedules to run the system

efficiently

Rate of convergence of Newton-Raphson method is

fast as compared to the Gauss -Seidal program and

also it is suitable for large size system.25

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