EXPERIMENT 5 LOAD FLOW ANALYSIS - I: SOLUTION OF LOAD FLOW AND RELATED PROBLEMS

USING GAUSS-SEIDEL METHOD

AIM: (i) To understand, the basic aspects of steady state analysis of power systems that are

required for effective planning and operation of power systems.

(ii) To understand, in particular, the mathematical formulation of load flow model in complex form and a simple method of solving load flow problems of small sized system using Gauss-Seidel iterative algorithm

SOFTWARE REQUIRED The software required is Matlab 7.5 THEORETICAL BACKGROUND

Need For Load Flow Analysis

Load Flow analysis, is the most frequently performed system study by electric utilities. This analysis is performed on a symmetrical steady-state operating condition of a power system under “normal” mode of operation and aims at obtaining bus voltages and line / transformer flows for a given load condition. This information is essential both for long term planning and next day operational planning. In long term planning, load flow analysis, helps in investigating the effectiveness of alternative plans and choosing the “best” plan for system expansion to meet the projected operating state. In operational planning, it helps in choosing the “best” unit commitment plan and generation schedules to run the system efficiently for the next day’s load condition without violating the bus voltage and line flow operating limits.

Load flow analysis is the most frequently performed system study by electric utilities. This analysis is performed on a symmetrical steady-state operating condition of a power system under ‘normal’ mode of operation and aims at obtaining bus voltages and line/transformer flows for a given load condition. This information is essential both for long term planning and next day operational planning. In long term planning, load flow analysis helps in investigating the effectiveness of alternative plans and choosing the ‘best’ plan for system expansion to meet the projected operating state. In operational planning, it helps in choosing the ‘best’ unit commitment plan and generation schedules to run the system efficiently for them next day’s load condition without violating the bus voltage and line flow operating limits.

The Gauss seidal method is an iterative algorithm for solving a set of non- linear algebraic

equations. The relationship between network bus voltages and currents may be represented by either loop equations or node equations. Node equations are normally preferred because the number of independent node equation is smaller than the number of independent loop equations.

The network equations in terms of the bus admittance matrix can be written as, busbusbus VYI (1) For a n bus system, the above performance equation can be expanded as,

n

p

nnnpnn

pnpppp

np

np

n

p

V

V

VV

YYYY

YYYY

YYYYYYYY

I

I

II

2

1

21

21

222212

111211

2

1

(2)

where n is the total number of nodes. Vp is the phasor voltage to ground at node p. Ip is the phasor current flowing into the network at node p. At the pth bus, current injection:

n

pqq

qpqpppn

qqpq

npnpppppp

VYVYVY

VYVYVYVYI

11

2211 .........................

(3)

npVYIY

Vn

pqq

qpqppp

p ,....2;1

1

(4)

At bus p , we can write Pp – jQp = pp IV

Hence, the current at any node p is related to P, Q and V as follows:

p

ppp V

jQPI

)( ( for any bus p except slack bus s) (5)

Substituting for Ip in Equation (4),

npVYV

jQPY

Vn

pqq

qpqp

pp

ppp .....,2;1

1*

(6)

Ip has been substituted by the real and reactive powers because normally in a power system these quantities are specified. In case of PV bus,

1)(1 .|| ki

specifiedi

ki VV

)sin.(cos|| 11)(1 k

iki

specifiedi

ki VV

Acceleration factor: ( To speed up the convergence, the node voltage (Vi(k+1)) of the succeeding iteration can be modified(accelerated) by multiplication factor called as Acceleration factor.

ki

kii VVV 1

i

ki

ki VVV .1

Algorithm: Step 1: Read the input data. Step 2: Find out the admittance matrix. Step 3: Choose the flat voltage profile 1+j0 to all buses except slack bus. Step 4: Set the iteration count p = 0 and bus count i = 1. Step 5: Check the slack bus, if it is the generator bus then go to the next step otherwise go to next step 7. Step 6: Before the check for the slack bus if it is slack bus then go to step 11 otherwise go to next step. Step 7: Check the reactive power of the generator bus within the given limit. Step 8: If the reactive power violates a limit then treat the bus as load bus. Step 9: Calculate the phase of the bus voltage on load bus Step 10: Calculate the change in bus voltage of the repeat step mentioned above until all the bus voltages are calculated. Step 11: Stop the program and print the results

Flowchart:

Yes

Read the input data values

Start

Form Y Bus matrix

Set flat voltage profile 1+j0 except slack bus

Set iteration count, p=0

Set the bus count, i = 1

Check for slack bus

Check for Gen bus

It is a load bus calculate

n

jkik

j

kkik

i

ii

ii

pical VYVY

VjQP

YV

1

1

1*

1 1

Calculate

pk

n

ikik

pk

i

kik

pi VYVYipQ V 1

1

1

*1 Im

Check

min1 QQ p

i

Set Qi=Qi min

Check

max1 QQ p

i

Set Qi=Qi max

A

Y

No

Yes

No

No

No

Yes

Yes

D

E

C

B

RESULT: The given set of load flow equations for a given power system were solved using Gauss-Seidal method and verified using Matlab 7.5.

Treat this as gen bus & calculate Vpi

n

ik

pkik

i

k

pkik

i

i

ii

pi VYVY

VjQP

YV

1

1

1

1*

1 1

Calculate the change in voltage 1 piV

Increment the bus count

Check ni

Check 1p

iV

Print the result

Stop

Increment iteration count P = P+1

Yes

Yes

No

No

B

E

D

C

A

1 2

3

-j3

-j4 -j5

Problems:1 A three bus power system is shown. (Refer book Power System Analysis by K.B. Hemalatha, S.T. Jayachrista – Page no: 4.11) The relevant p.u line admittances are indicated on the diagram and bus data are given in table.

Determine the voltages at buses 2 and 3 after1st iteration using Gauss – Seidal method. Take the acceleration factor α = 1.6. clc clear all busdata=[1 1 1.02 0 0 0 0 0 0 0 2 3 1 0 0.25 0.15 0.5 0.25 0 0 3 3 1 0 0 0 0.6 0.3 0 0]; linedata=[ 1 2 0 -3i 1 3 0 -4i 2 3 0 -5i]; fb=linedata(:,1); tb=linedata(:,2); r=linedata(:,3); x=linedata(:,4); y=r+x; nbus=max(max(fb),max(tb)); nbranch=length(fb); ybus=zeros(nbus,nbus); for i=1:nbranch m=fb(i); n=tb(i); ybus(m,m)=ybus(m,m)+y(i); ybus(n,n)=ybus(n,n)+y(i); ybus(m,n)=-y(i); ybus(n,m)=ybus(m,n); end ybus bus=busdata(:,1); type=busdata(:,2); v=busdata(:,3); th=busdata(:,4);

Bus no Type Generation Load Bus voltage PG QG PL QL V

1 Slack - - - - 1.02 0o 2 PQ 0.25 0.15 0.5 0.25 - - 3 PQ 0 0 0.6 0.3 - -

genmw=busdata(:,5); genmvar=busdata(:,6); loadmw=busdata(:,7); loadmvar=busdata(:,8); qmin=busdata(:,9); qmax=busdata(:,10); p=genmw-loadmw; q=genmvar-loadmvar; vprev=v; toler=1; dv=0; iteration=1; while(toler>0.1) for i=2:nbus sumyv=0; for k=1:nbus if i~=k sumyv=sumyv+(ybus(i,k)*v(k)); end end if(type(i)==2) q(i)=-imag(conj(v(i)))*(sumyv+bus(i,i)*v(i)); if(q(i)>qmax(i) ||q(i)<qmin(i)) if q(i)<qmin(i) q(i)=qmin(i); else q(i)=qmax(i); end type(i)=3; end end v(i)=(1/ybus(i,i))*((p(i)-j*q(i))/conj(v(i))-sumyv); dv(i)=v(i)-vprev(i); v(i)=vprev(i)+(1.6*dv(i)); if type(i)==2 v(i)=pol2cart(abs(vprev(i)),angle(v(i))); end end iteration=iteration+1; toler=max(abs(abs(v)-abs(vprev))); vprev=v; end iteration; v OUTPUT: ybus = 0 - 7.0000i 0 + 3.0000i 0 + 4.0000i 0 + 3.0000i 0 - 8.0000i 0 + 5.0000i 0 + 4.0000i 0 + 5.0000i 0 - 9.0000i v = 1.0200 0.9920 - 0.0500i 0.9538 - 0.1511i