the program that is needed to do the work is power world Five Bus System Homewor

ID: 1996117 • Letter: T

Question

the program that is needed to do the work is power world

Five Bus System Homework Assignment Thanks to Prof Chen-Ching Liu and Ph.D. Candidate Madeleine Gibescu ofthe University of Washington for this problem set Download the cases needed for the Assignment (PW Simulator 5.0 or later format) A one line diagram, together with the bus and line data, of a 5-bus power system is shown below; the system will be referred to as utility A. Solve the following problems using thePowerWorld Simulator and the original data file 454 0.pwb and the one-line diagram file 454 0.pwd 1. For the power system of utility A, use the PowerWorld program to find the MVAr rating of a shunt capacitor at bus 3 that increases V3 to 1.00 p.u. Determine the effect of the capacitor bank on the line loading and total 12R losses 2. Run the original power flow for utility A. Do you find any voltage violations? (The normal range of bus voltages is assumed to be 0.95-1.05 p.u. Now suppose both transformers in this system are tap changing transformers whose taps can be varied from 0.85 to 1.15 p.u. in increments of 0.05 p.u. Determine the tap settings required to increase the voltage at bus 3 to 0.95 p.u., while causing as few high voltage violations as possible at the other buses 3. A new transformer is installed between buses 2 and 5, in parallel with the existing transformer between buses 2 and 5. The new transformer is identical to the existing transformer. The taps on both transformers are set to the nominal value, 1.0 p.u. Find the real power, reactive power and MVA supplied by each of these transformers to bus 5 4. Refer to the one-line diagram of utility A. Suppose an additional line is installed between buses 3 and 4. The line parameters of the added line are equal to those of the existing line 3-4. Determine the effects on the voltage at bus 3, line loading and total 12R losses 5. In problem 2 you already ran the power flow for utility A and detected low voltage violations Place a capacitor at bus 3 to bring the bus 3 voltage up to 0.95 p.u. Determine the size of the capacitor bank. Now suppose the line between buses 3 and 5 is removed for maintenance. Run the power flow again. s the operating condition acceptable? If not, determine the amount of load you have to shed at bus 3 in order to maintain the bus 3 voltage above 0.95 p.u. Cut the same percentage of MW and MVAr at bus 3

Explanation / Answer

. MAIN MENU

=========

1 LOAD THE PSF 8 DATA VERIFICATIO

2 IMPORTING UTILITIES 9 LIMIT CHECKS

3 INPUT DATA PROCESSING 10 SENSITIVITY FACTORS

4 STUDY PREPARATION UTILITIES 11 EXPORTING UTILITIES

5 POWER FLOW SOLUTION 12 CLOSE THE PSF

6 NETWORK REDUCTION 13 QUIT

7 POWER FLOW SOLUTION REPORTING

ENTER MENU CHOICE: 5

*** POWER FLOW SOLUTION ***

=============================

1 AUTOMATIC SOLUTION

2 FAST DECOUPLED (XB)

3 NEWTON RAPHSON

4 FAST DECOUPLED (BX)

5 LOCALIZED SOLUTION (FD XB)

6 DC POWER FLOW SOLUTION

7 POWER FLOW SOLUTION OPTIONS

ITEM #, EXIT 3

*** START OF NEWTON RAPHSON ITERATIONS ***

ITERATION : 1 NEWTON RAPHSON UNSOLVED ABSOLUTE ERROR

-------------- BUS WITH LARGEST ERROR ------------ BUSES SUMMATION

P(P.U. MW) 0.000375 ( 30 BUS 3138. ) 0 0.0017

V(RADIANS) 0.000179 ( 70 BUS 7138. ) 8 0.0016

Q(P.U. MVAR) 0.001873 ( 120 BUS 12230. ) 0 0.0078

V(P.U. KV) 0.000210 ( 30 BUS 3138. ) 3 0.0009

ITERATION : 2 NEWTON RAPHSON UNSOLVED ABSOLUTE ERROR

-------------- BUS WITH LARGEST ERROR ------------ BUSES SUMMATION

P(P.U. MW) 0.000006 ( 160 BUS 16230. ) 0 0.0000

Q(P.U. MVAR) -0.000008 ( 170 BUS 17230. ) 0 0.0000

*** POWER FLOW SOLUTION IS REACHED IN 2 ITERATIONS ***

2. MAIN MENU

=========

1 LOAD THE PSF 8 DATA VERIFICATION

2 IMPORTING UTILITIES 9 LIMIT CHECKS

3 INPUT DATA PROCESSING 10 SENSITIVITY FACTORS

4 STUDY PREPARATION UTILITIES 11 EXPORTING UTILITIES

5 POWER FLOW SOLUTION 12 CLOSE THE PSF

6 NETWORK REDUCTION 13 QUIT

7 POWER FLOW SOLUTION REPORTING

ENTER MENU CHOICE: 9

** LOAD FLOW SOLUTION LIMIT CHECK **

====================================

1 OVERLOADED LINES OR TRANSFORMERS

2 CONTROL PARAMETERS VIOLATION

3 BUS VOLTAGE OUTSIDE SPECIFIED BAND

4 LINES ACROSS WHICH THE ANGLE EXCEEDS THE SPECIFIED VALUE

5 CHECK FOR ALL LIMITS AND VIOLATIONS

6 SORT OPTIONS

ITEM #, SPECIFY SUBSYSTEM, EXIT 1

ALL LINES TRANSFORMERS: A

*** LOAD FLOW SOLUTION LIMIT CHECK ***

1 OVERLOADED BRANCHES RATING GROUP = 1 % LOADING = 100.0

<----- FROM BUS -----> <------ TO BUS ------> MVA MVA PERCENT

NUMBER NAME NUMBER NAME CKT LOADING RATING LOADING

====== ================ ====== ================ ======== ======= ====== =======

60 BUS 6138. 100 BUS 10138. 1 175.4 175.0 100.22

3. ** LOAD FLOW SOLUTION LIMIT CHECK **

====================================

1 OVERLOADED LINES OR TRANSFORMERS

2 CONTROL PARAMETERS VIOLATION

3 BUS VOLTAGE OUTSIDE SPECIFIED BAND

4 LINES ACROSS WHICH THE ANGLE EXCEEDS THE SPECIFIED VALUE

5 CHECK FOR ALL LIMITS AND VIOLATIONS

6 SORT OPTIONS

ITEM #, SPECIFY SUBSYSTEM, EXIT 3

HI VOLTAGE LIMIT LO VOLTAGE LIMIT: L

ENTER VALUE IN PU: .99

*** LOAD FLOW SOLUTION LIMIT CHECK ***

4 BUSES WITH V < 0.990

<-------- BUS --------> <-- VOLTAGE -->

NUMBER NAME TYPE BASE KV MAG ANGLE AREA ZONE OWNER ID

====== ================ ==== ======= ======= ======= ==== ==== ================

30 BUS 3138. 1 138.00 0.9868 -26.02 10 1 BLANK

40 BUS 4138. 1 138.00 0.9888 -20.27 10 1 BLANK

90 BUS 9138. 1 138.00 0.9824 -15.83 10 1 BLANK

120 BUS 12230. 1 230.00 0.9876 -4.73 10 1 BLANK

UP DOWN SCREEN DUMP LIST TO FILE CHANGE RATING EXIT : e

4. MAIN MENU

=========

1 LOAD THE PSF 8 DATA VERIFICATION

2 IMPORTING UTILITIES 9 LIMIT CHECKS

3 INPUT DATA PROCESSING 10 SENSITIVITY FACTORS

4 STUDY PREPARATION UTILITIES 11 EXPORTING UTILITIES

5 POWER FLOW SOLUTION 12 CLOSE THE PSF

6 NETWORK REDUCTION 13 QUIT

7 POWER FLOW SOLUTION REPORTING

ENTER MENU CHOICE: 7

** LOAD FLOW SOLUTION REPORTING **

==================================

1 MISMATCH SUMMARY 11 ULTC/PS SUMMARY

2 SUBSYSTEM SUMMARY 12 SERIES COMPENSATORS

3 BUS SHUNT DATA 13 POWER FLOW SUMMARY

4 PLANT DATA 14 SECTIONALIZED BRANCHES

5 MACHINE DATA 15 STATIC TAP CHANGERS / PHASE SHIFTERS

6 AREA INTERCHANGE DATA 16 THREE WINDING TRANSFORMERS

7 TIE LINE FLOWS 17 INTERFACE FLOWS

8 BUS FLOWS 18 VOLTAGE PROFILE

9 DC CONVERTERS 19 SORT OPTIONS

10 DC FLOWS

ITEM #, SPECIFY SUBSYSTEM, EXIT 8

SUBSYSTEM BUSES PICK BUSES EXIT: p

ENTER BUS LIST FILE NAME OR BUSES TO INCLUDE OR EXCLUDE

> 60

*** SOLUTION REPORTING - BUS FLOWS ***

BUS: 60 BUS 6138.

VOLTAGE : 1.0017 PU ( 138.2 kV) -20.67

BUS NUM NAME AREA CKT MW MVAR MVA TAP

======== ================ ==== ======== ======== ======== = ======== ========

LOAD 136.00 28.00 138.85

SW SHUNT 0.00 100.33 100.33

TO 100 BUS 10138. 10 1 -128.63 -107.64 167.73

TO 20 BUS 2138. 10 1 -7.37 -20.69 21.96

UP DOWN NEXT BUS PREVIOUS BUS SCREEN DUMP LIST TO FILE EXIT : e

SUBSYSTEM BUSES PICK BUSES EXIT: p

ENTER BUS LIST FILE NAME OR BUSES TO INCLUDE OR EXCLUDE

> 100

*** SOLUTION REPORTING - BUS FLOWS ***

BUS: 100 BUS 10138.

VOLTAGE : 1.0132 PU ( 139.8 kV) -16.15

BUS NUM NAME AREA CKT MW MVAR MVA TAP

======== ================ ==== ======== ======== ======== = ======== ========

LOAD 195.00 40.00 199.06

TO 120 BUS 12230. 10 1 -234.48 60.92 242.27 1.0000LK

TO 110 BUS 11230. 10 1 -235.99 52.21 241.70 1.0000LK

TO 80 BUS 8138. 10 1 69.77 -3.74 69.87

TO 60 BUS 6138. 10 1 130.95 -131.80 185.80

TO 50 BUS 5138. 10 1 74.76 -17.59 76.80

UP DOWN NEXT BUS PREVIOUS BUS SCREEN DUMP LIST TO FILE EXIT : e

5. ** LOAD FLOW SOLUTION REPORTING **

==================================

1 MISMATCH SUMMARY 11 ULTC/PS SUMMARY

2 SUBSYSTEM SUMMARY 12 SERIES COMPENSATORS

3 BUS SHUNT DATA 13 POWER FLOW SUMMARY

4 PLANT DATA 14 SECTIONALIZED BRANCHES

5 MACHINE DATA 15 STATIC TAP CHANGERS / PHASE SHIFTERS

6 AREA INTERCHANGE DATA 16 THREE WINDING TRANSFORMERS

7 TIE LINE FLOWS 17 INTERFACE FLOWS

8 BUS FLOWS 18 VOLTAGE PROFILE

9 DC CONVERTERS 19 SORT OPTIONS

10 DC FLOWS

ITEM #, SPECIFY SUBSYSTEM, EXIT 4

*** SOLUTION REPORTING - PLANT DATA ***

=======================================

1 ALL PLANTS

2 ON LINE PLANTS

3 PLANTS AT VAR LIMIT WITH UNEQUAL VAR LIMITS

4 PLANTS WITH UNSCHEDULED REACTIVE POWER

5 PLANTS CONTROLLING A REMOTE BUS

6 PLANTS WITH RESERVE REACTIVE POWER

ITEM #, EXIT 1

*** SOLUTION REPORTING ***

10 PLANTS

PLANT BUS MACHINES

NUM NAME TYPE I/S O/S MW MVAR QMAX QMIN

======== ================ ==== ======== ======== ======== ======== ========

R 10 BUS 1138. 2 4 0 134.70 41.53 280.00 -50.00

R 20 BUS 2138. 2 4 0 187.00 30.50 140.00 -100.00

R 70 BUS 7138. 2 3 0 165.00 91.63 280.00 0.00

R 130 BUS 13230. 3 3 0 337.53 170.64 540.00 -300.00

R 150 BUS 15230. 2 6 0 185.00 40.36 310.00 -55.00

R 160 BUS 16230. 2 1 0 155.00 106.41 280.00 -55.00

R 180 BUS 18230. 2 1 0 400.00 100.73 200.00 -90.00

R 210 BUS 21230. 2 1 0 400.00 25.25 200.00 -90.00

R 220 BUS 22230. 2 6 0 300.00 -80.55 696.00 -560.00

R 230 BUS 23230. 2 3 0 660.00 33.34 310.00 -125.00

UP DOWN OTHER SCREEN SCREEN DUMP LIST TO FILE EXIT :e

CODES: 1.) CODE FOR TAKING BUS DATA

(busdata.m)

% Returns Initial Bus datas of the system... function busdt = busdatas() % Type.... %

1 - Slack Bus.. % 2 - PV Bus.. % 3 - PQ Bus.. % |Bus | Type | Vsp | theta | PGi | QGi | PLi | QLi |

busdat14 = [1 1 1.00 0 0 0 100 0 ; 2 2 1.01 0 250 0 200 100 ; 3 3 1.00 0 0 0 300 100 ;]; busdt = busdat14; 2.) CODE FOR TAKING LINE DATA

(linedatas.m) % Returns Line datas of the system... function linedt = linedatas() % | From | To | R | X | B/2 | % | Bus | Bus | pu | pu | pu |

linedat14 = [1 2 0.01 0.05 0 1 3 0.015 0.05 0 2 3 0.015 0.05 0 ]; linedt = linedat14;

3.) CODE FOR BUILDING Y-BUS MATRIX (ybusmatrix.m)

Program to for Admittance And Impedance Bus Formation....

function Y = ybusmatrix() % Returns Y

linedata = linedatas(); % Calling Linedatas..

. fb = linedata(:,1); % From bus number..

. tb = linedata(:,2); % To bus number...

r = linedata(:,3); % Resistance, R...

x = linedata(:,4); % Reactance, X..

b = linedata(:,5); % Ground Admittance

, B/2... z = r + i*x; % z matrix..

. y = 1./z; % To get inverse of each element..

. b = i*b;% Make B imaginary...

nb = max(max(fb),max(tb)); % No. of buses...

nl = length(fb); % No. of branches..

. Y = zeros(nb,nb); % Initialise YBus... % Formation of the Off Diagonal Elements... for

k = 1:nl Y(fb(k),tb(k)) = Y(fb(k),tb(k)) - y(k); Y(tb(k),fb(k)) = Y(fb(k),tb(k));

end %

Formation of Diagonal Elements.... for m = 1:nb

for n = 1:nl

if fb(n) == m Y(m,m) = Y(m,m) + y(n) + b(n);

elseif

tb(n) == m Y(m,m) = Y(m,m) + y(n) + b(n);

end

%Y; % Bus Admittance Matrix %

Z = inv(Y); % Bus Impedance Matrix

4.) CODE FOR THE NEWTON-RAPHSON ITERATIONS (main.m) %

Program for Newton-Raphson Load Flow Analysis..

nbus=3; Y = ybusmatrix(); % Calling ybusmatrix.m to get Y-Bus Matrix..

busd = busdatas(); % Calling busdatas..

BMva = 100; % Base MVA..

bus = busd(:,1); % Bus Number..

type = busd(:,2); % Type of Bus 1-Slack, 2-PV, 3-PQ..

V = busd(:,3); % Specified Voltage..

del = busd(:,4); % Voltage Angle..

Pg = busd(:,5)/BMva; % PGi..

Qg = busd(:,6)/BMva; % QGi..

Pl = busd(:,7)/BMva; % PLi..

Ql = busd(:,8)/BMva; % QLi..

P = Pg - Pl; % Pi = PGi - PLi..

Q = Qg - Ql; % Qi = QGi - QLi..

Psp = P; % P Specified..

Qsp = Q; % Q Specified..

G = real(Y); % Conductance matrix..

B = imag(Y); % Susceptance matrix..

pv = find(type == 2 | type == 1); % PV Buses.

. pq = find(type == 3); % PQ Buses.

. npv = length(pv); % No. of PV buses..

npq = length(pq); % No. of PQ buses.. T

ol = 1; Iter = 1;

while (Tol > 1e-5) % Iteration starting..

P = zeros(nbus,1);

Q = zeros(nbus,1); % Calculate P and Q for i = 1:nbus

for k = 1:nbus

P(i) = P(i) + V(i)* V(k)*(G(i,k)*cos(del(i)-del(k)) + B(i,k)*sin(del(i)-del(k)));

Q(i) = Q(i) + V(i)* V(k)*(G(i,k)*sin(del(i)-del(k)) - B(i,k)*cos(del(i)-del(k)));

end

% Calculate change from specified value

dPa = Psp-P;

dQa = Qsp-Q; k = 1;

dQ = zeros(npq,1);

for i = 1:nbus

if type(i) == 3 dQ(k,1) = dQa(i);

k = k+1; end

end

dP = dPa(2:nbus);

M = [dP; dQ]; % Mismatch Vector % Jacobian % J1 - Derivative of Real Power Injections with Angles..

J1 = zeros(nbus-1,nbus-1);

for i = 1:(nbus-1)

m = i+1;

for k = 1:(nbus-1)

n = k+1;

if n == m for n = 1:nbus

J1(i,k) = J1(i,k) + V(m)* V(n)*(-G(m,n)*sin(del(m)- del(n)) + B(m,n)*cos(del(m)-del(n)));

end

J1(i,k) = J1(i,k) - V(m)^2*B(m,m);

else J1(i,k) = V(m)* V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));

end

% J2 - Derivative of Real Power Injections with V..

J2 = zeros(nbus-1,npq);

for i = 1:(nbus-1) m = i+1;

for k = 1:npq n = pq(k);

if n == m for n = 1:nbus

J2(i,k) = J2(i,k) + V(n)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));

end

J2(i,k) = J2(i,k) + V(m)*G(m,m);

else

J2(i,k) = V(m)*(G(m,n)*cos(del(m)-del(n)) + B(m,n)*sin(del(m)-del(n)));

end

% J3 - Derivative of Reactive Power Injections with Angles.. J3 = zeros(npq,nbus-1); for i = 1:npq m = pq(i);

for k = 1:(nbus-1) n = k+1;

if n == m for n = 1:nbus

J3(i,k) = J3(i,k) + V(m)* V(n)*(G(m,n)*cos(del(m)- del(n)) + B(m,n)*sin(del(m)-del(n)));

end

J3(i,k) = J3(i,k) - V(m)^2*G(m,m); else J3(i,k) = V(m)* V(n)*(-G(m,n)*cos(del(m)-del(n)) - B(m,n)*sin(del(m)-del(n)));

end

% J4 - Derivative of Reactive Power Injections with V..

J4 = zeros(npq,npq);

for i = 1:npq

m = pq(i);

for k = 1:npq n = pq(k);

if n == m

for n = 1:nbus

J4(i,k) = J4(i,k) + V(n)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));

end

J4(i,k) = J4(i,k) - V(m)*B(m,m);

else J4(i,k) = V(m)*(G(m,n)*sin(del(m)-del(n)) - B(m,n)*cos(del(m)-del(n)));

end

J = [J1 J2; J3 J4]; % Jacobian Matrix..

X = inv(J)*M; % Correction Vector

dTh = X(1:nbus-1); % Change in Voltage Angle..

dV = X(nbus:end); % Change in Voltage Magnitude..

% Updating State Vectors..

del(2:nbus) = dTh + del(2:nbus); % Voltage Angle..

k = 1;

for i = 2:nbus

if type(i) == 3 V(i) = dV(k) + V(i); % Voltage Magnitude..

k = k+1;

end

Iter = Iter + 1;

Tol = max(abs(M)); % Tolerance..

end

loadflow(nbus,V,del,BMva); % Calling Loadflow.m..

5.) CODE FOR THE PRINTING THE LOADFLOW SOLUTION (loadflow.m)

% Program for Bus Power Injections, Line & Power flows (p.u)...

function [Pi Qi Pg Qg Pl Ql] = loadflow(nb,V,del,BMva) Y = ybusmatrix(); % Calling Ybus program..

lined = linedatas(); % Get linedats..

busd = busdatas(); % Get busdatas.

. Vm = pol2rect(V,del); % Converting polar to rectangular.

. Del = 180/pi*del; % Bus Voltage Angles in Degree...

fb = lined(:,1); % From bus number..

. tb = lined(:,2); % To bus number...

nl = length(fb); % No. of Branches..

Pl = busd(:,7); %

PLi.. Ql = busd(:,8); %

QLi.. Iij = zeros(nb,nb);

Sij = zeros(nb,nb);

Si = zeros(nb,1); % Bus Current Injections..

I = Y*Vm; Im = abs(I);

Ia = angle(I); %Line Current Flows..

for m = 1:nl

p = fb(m);

q = tb(m);

Iij(p,q) = -(Vm(p) - Vm(q))*Y(p,q);%

Y(m,n) = -y(m,n).. Iij(q,p) = -Iij(p,q);

end Iij = sparse(Iij);

Iijm = abs(Iij);

Iija = angle(Iij);

% Line Power Flows..

for m = 1:nb

for n = 1:nb

if m ~= n Sij(m,n) = Vm(m)*conj(Iij(m,n))*BMva;

end

Sij = sparse(Sij);

Pij = real(Sij);

Qij = imag(Sij); % Line Losses..

Lij = zeros(nl,1); for m = 1:nl

p = fb(m); q = tb(m); Lij(m) = Sij(p,q) + Sij(q,p); end Page | 19 Lpij = real(Lij); Lqij = imag(Lij); % Bus Power Injections.. for i = 1:nb for k = 1:nb Si(i) = Si(i) + conj(Vm(i))* Vm(k)*Y(i,k)*BMva; end end Pi = real(Si); Qi = -imag(Si); Pg = Pi+Pl; Qg = Qi+Ql; disp('##################################################################### ####################'); disp('--------------------------------------------------------------------- --------------------'); disp(' Newton Raphson Loadflow Analysis '); disp('--------------------------------------------------------------------- --------------------'); disp('| Bus | V | Angle | Injection | Generation | Load |'); disp('| No | pu | Degree | MW | MVar | MW | Mvar | MW | MVar | '); for m = 1:nb disp('----------------------------------------------------------------- ------------------------'); fprintf('%3g', m); fprintf(' %8.4f', V(m)); fprintf(' %8.4f', Del(m)); fprintf(' %8.3f', Pi(m)); fprintf(' %8.3f', Qi(m)); fprintf(' %8.3f', Pg(m)); fprintf(' %8.3f', Qg(m)); fprintf(' %8.3f', Pl(m)); fprintf(' %8.3f', Ql(m)); fprintf(' '); end disp('--------------------------------------------------------------------- --------------------'); fprintf(' Total ');fprintf(' %8.3f', sum(Pi)); fprintf(' %8.3f', sum(Qi)); fprintf(' %8.3f', sum(Pi+Pl)); fprintf(' %8.3f', sum(Qi+Ql)); fprintf(' %8.3f', sum(Pl)); fprintf(' %8.3f', sum(Ql)); fprintf(' '); disp('--------------------------------------------------------------------- --------------------'); disp('##################################################################### ####################'); disp('--------------------------------------------------------------------- ----------------'); disp(' Line FLow and Losses '); disp('--------------------------------------------------------------------- ----------------'); disp('|From|To | P | Q | From| To | P | Q | Line Loss |'); disp('|Bus |Bus| MW | MVar | Bus | Bus| MW | MVar | MW | MVar |'); for m = 1:nl p = fb(m); q = tb(m); disp('----------------------------------------------------------------- --------------------'); fprintf('%4g', p); fprintf('%4g', q); fprintf(' %8.3f', full(Pij(p,q))); fprintf(' %8.3f', full(Qij(p,q))); Page | 20 fprintf(' %4g', q); fprintf('%4g', p); fprintf(' %8.3f', full(Pij(q,p))); fprintf(' %8.3f', full(Qij(q,p))); fprintf(' %8.3f', Lpij(m)); fprintf(' %8.3f', Lqij(m)); fprintf(' '); end disp('--------------------------------------------------------------------- ----------------'); fprintf(' Total Loss '); fprintf(' %8.3f', sum(Lpij)); fprintf(' %8.3f', sum(Lqij)); fprintf(' '); disp('--------------------------------------------------------------------- ----------------'); disp('##################################################################### ################');

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