Power System Lab Manual 7064y
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Regency Institute of Technology: Yanam. LAB MANUAL FOR POWER SYSTEMS LAB VI Semester EEE
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
Power Systems Lab
UEE 6057 POWER SYSTEM LAB LIST OF EXPERIMENTS Page. no
Sl.no Name of the Experiment 1
PER UNIT COMPUTATION.
2
FORMATION OF BUS TTANCE MATRIX BY DIRECT INSPECTION.
3
FORMATION OF BUS TTANCE MATRIX BY SINGULAR TRANSFORMATION.
4 5
FORMATION OF BUS IMPEDANCE MATRIX. SYMMETRICAL COMPONENTS.
6
SHORT CIRCUIT FOR LL, LG AND LLG AND THREE PHASE POINTS.
7
SWING EQUATION BY STEP BY STEP METHOD.
8 9 10
DETERMINATION OF LOAD FACTOR, PEAKLOAD, AVERAGE LAOD AND DIVERSITY FACTOR. DETERMINE THE CRITICAL CLEARING ANGLE OF THE GIVEN SYSTEM USING EQUAL AREA CRITERION. ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS.
2
Remarks
Power Systems Lab
ADDITIONAL EXPERIMENTS
S.No 1 2
Name of the Experiment ECONOMIC LOAD DISPATCH INCLUDING LOSSES STUDY OF ETAP
Experiment 1 PER UNIT COMPUTATION PROBLEM: draw the reactance diagram for the power system shown in figure. Neglect resistance and use a base of 100MVA,220KV in 50Ω.
AIM: Write a MATLAB program to find the per unit values of the power system shown above. APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: %generatorG1
3
Power Systems Lab
gm1=input('enter the value of G1MVA:'); gk1=input('enter the value of G1KV:'); gx1=input('enter the value of G1X:'); %transformerT1 t1m=input('enter the value of T1MVA:'); t1kp=input('enter the value of T1KVP:'); t1ks=input('enter the value of T1KS:'); t1x=input('enter the value of T1X:'); %transmission lineTL1 tl1x=input('enter the value of TL1X:'); %transformerT2 t2m=input('enter the value of T2MVA:'); t2kp=input('enter the value of T2KVP:'); t2ks=input('enter the value of T2KVS:'); t2x=input('enter the value ofT2X:'); %generatorG2 gm2=input('enter the value of G2MVA:'); gk2=input('enter the value of G2KV:'); gx2=input ('enter the value ofG2X:'); %transmission line TL2 tl2x=input('enter the value of TL2X:'); %transformer T3 t3m=input('enter the value of T3MVA:'); t3kp=input('enter the value of T3KVP:'); t3ks=input('enter the value of T3KVS:'); t3x=input('enter the value of T3X:'); %motor mm=input('enter the value of MMVA:'); mk=input('enter the value of MKV:'); mx=input('enter the value of MX:'); %base values bm=input('enter the value of base MVA:'); bk=input('enter the value of base KV:'); gx1new=gx1*(bm/gm1)*((gk1/bk)^2); t1xnew=t1x*(bm/t1m)*((t1kp/bk)^2); bk1=bk*(t1ks/t1kp); tl1new=tl1x*(bm/(bk1^2)); bk2=bk1*(t2kp/t2ks);
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Power Systems Lab
t2xnew=t2x*(bm/t2m)*((bk/bk2)^2); gx2new=gx2*(bm/gm2)*((bk/bk2)^2); tl2new=tl2x*(bm/(bk1^2)); t3m1=3*t3m; t3kp1=1.732*t3kp; t3ks1=1.732*t3ks; bk3=bk1*(t3kp1/t3ks1); t3xnew=t3x*(bm/t3m1)*((t3kp1/bk3)^2); mnew=mx*(bm/mm)*((mk/bk3)^2); disp('the pu value of G1 is:'),gx1new disp('the pu value of T1 is:'),t1xnew disp('the pu value of TL1 is:'),tl1new disp('the pu value of T2 is:'),t2xnew disp('the pu value of T3 is:'),t3xnew disp('the pu value of M is:'),mnew disp('the pu value of TL2 is:'),tl2new disp('the pu value of G2 is:'),gx2new
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Power Systems Lab
RESULT:
Experiment -2 FORMULATION OF BUS ITTANCE MATRIX BY DIRECT INSPECTION METHOD PROBLEM:
For the Network shown in the figure formulate the Bus ittance Matrix by Direct Inspection Method 1
3
2 From BusNo 1 1 1 2 3
4
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
AIM: Write a MATLAB program to find the Bus ittance Matrix by Direct Inspection Method for the network shown above.
APPARATUS REQUIRED: 1)PERSONAL COMPUTER 2)MATLAT 6.5 VERSION 3)SIMULINK VERSION
ALGORITHM:
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Power Systems Lab
PROGRAM: zdata=[ From BusNo 1 1 1 2 3
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
]; nl=zdata(:,1);
nr=zdata(:,2); r=zdata(:,3); x=zdata(:,4); nbr=length(zdata(:,1)); nbus = max(max(nl), max(nr)); z = r + j*x;
%branch impedance
y= ones(nbr,1)./z;
%branch ittance
ybus=zeros(nbus,nbus);
% initialize Ybus to zero
for k = 1:nbr
% formation of the off diagonal elements
if nl(k) > 0 & nr(k) > 0 ybus(nl(k),nr(k)) = ybus(nl(k),nr(k)) - y(k); ybus(nr(k),nl(k)) = ybus(nl(k),nr(k)); end end for n = 1:nbus
% formation of the diagonal elements
for k = 1:nbr if nl(k) == n | nr(k) == n ybus(n,n) = ybus(n,n) + y(k); else, end end end
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Power Systems Lab
RESULT:
Experiment-3 FORMULATION OF BUS ITTANCE MATRIX BY SINGULAR TRANSFORMATION METHOD PROBLEM:
For the network shown in the figure formulate the Bus ittance Matrix by Singular Transformation method 1
2
3
4
Element 1 2 3 4 5
AIM:
From Bus 1 1 1 2 3
To bus 2 3 4 4 4
ittance 2-j6 1-j3 1-j2 1-j3 1-j6
Write a MATLAB program to find the Bus ittance Matrix by Singular Transformation method for the network shown above.
APPARATUS REQUIRED: 1)PERSONAL COMPUTER 2)MATLAT 6.5 VERSION 3)SIMULINK VERSION
ALGORITHM:
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Power Systems Lab
PROGRAM: j=sqrt(-1); ydata=[ 1 1 2 2-j*6 2 1 3 1-j*3 3 1 4 1-j*2 4 2 4 1-j*3 5 3 4 2-j*6 ]; nbr=max(ydata(:,1)); nbus=max(max(ydata(:,2),max(ydata(:,3)))); yprimitive=zeros(nbr,nbr); for i=1:nbr; yprimitive(i,i)=ydata(i,4); end a=zeros(nbr,nbus); for i=1:nbr if ydata(i,2)~=0; a(i,ydata(i,2))=1; end if ydata(i,3)~=0 a(i,ydata(i,3))=-1; end end ybus=a'*yprimitive*a
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Power Systems Lab
RESULT:
Experiment- 4 FORMATION OF BUS IMPEDANCE MATRIX PROBLEM: Write a MATLAB program to find BUS IMPEDANCE MATRIX for a given system. Whose reactance diagram is shown in the fig. All impedances are in p.u. 1
3
2
Element 1 2 3 4
4
From Bus 1 1 2 3
To bus 2 3 3 4
AIM: Write a MATLAB program to find BUS IMPEDANCE MATRIX for a given system. APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
10
ittance 1.0j 1.25j 0.25j 0.05j
Power Systems Lab
ALGORITHM:
PROGRAM: zdata=[1 1 2 1.0j 2 1 3 1.25j 3 3 4 .05j 4 3 2 .25j ]; [elements, columns]= size(zdata); zbus=0; refbusno=1; currentbusno=1; for count=1:elements [rows cols]=size(zbus); from=zdata(count,2); to=zdata(count,3); value=zdata(count,4); newbus=max(from,to); ref=min(from,to); if newbus>currentbusno & ref==refbusno zbus=[zbus zeros(rows,1) zeros(1,cols) value]; currentbusno=newbus; continue; end if newbus>currentbusno & ref~=refbusno zbus=[zbus zbus(:,ref) zbus(ref,:)
value+zbus(ref,ref)];
currentbusno=newbus; continue; end if newbus<=currentbusno & ref==refbusno zbus=zbus-1/((zbus(newbus,newbus)+value)*zbus(:,newbus)*zbus(newbus,:)); continue; end if newbus<=currentbusno & ref~=refbusno
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Power Systems Lab
zbus=zbus-1/(value+zbus(from,from)+zbus(to,to)2*zbus(from,to))*((zbus(:,from)-zbus(:,to))*(zbus(from,:)-zbus(to,:))); continue; end end disp('formation of zbus using building algorithm is'),zbus
RESULT:
Experiment -5 SYMMETRICAL COMPONENTS FOR NO LINES OPEN, ONE LINE OPEN AND TWO LINES OPEN PROBLEM: Determine the Symmetrical Components of the unbalanced three phase currents Ia= 20 ∟300 A Ib = 50 ∟2300 A Ic = 80∟1300 A For 1. No lines Open 2. One line Open (B phase open) 3. Two lines Open (A & C phases open).
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Power Systems Lab
AIM:
Write a MATLAB program to find the Symmetrical Components of the unbalanced
three phase currents. For 1. No lines Open 2. One line Open (B phase open) 3. Two lines Open (A&C phases open)
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: disp ('calculation of symmetrical components:'); i=sqrt (-1); Iam=input ('enter the magnitude of Ia:'); Iad=input ('enter the angle of Ia:'); Ia =Iam*(exp (i*Iad*(pi/180))); Ia Ibm= input ('enter the magnitude of Ib:'); Ibd= input ('enter the angle of Ib:'); Ib=Ibm*(exp (i*Ibd*(pi/180))); Ib Icm=input ('enter the magnitude of Ic:'); Icd=input ('enter the angle of Ic:'); Ic=Icm*(exp(i*Icd*(pi/180))); Ic k=menu('option','1.no lines open.','2.one line open.','3.two lines open.'); if(k==1) disp('no lines open:'); end if (k==2) l=menu ('option.','1.phase A open.','2.phase B open.','3.phase C open.'); if (l==1) disp ('phase A open.') Ia=0;
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Power Systems Lab
end if(l==2) disp ('phase B open.') Ib=0; end if (l==3) disp ('phase c open.') Ic=0; end end if(k==3) m=menu('option.','1.phase A&B open.','2.phase B&C open.','3.phase C&A open.'); if (m==1) disp ('phase A&B open.') Ia=0; Ib=0; end if(m==2) disp ('phase B&C open.') Ib=0; Ic=0; end if(m==3) disp('phase C&A open') Ic=0; Ia=0; end end a=-0.5+0.866i; b=a*a; Iao=(1/3)*(Ia+Ib+Ic); Iaom=abs(Iao) Iaod=angle(Iao)*(180/pi) Ia1=(1/3)*(Ia+(a*Ib)+(b*Ic)); Ia1m=abs(Ia1) Ia1d=angle(Ia1)*(180/pi) Ia2=(1/3)*(Ia+(b*Ib)+(a*Ic)); Ia2m=abs(Ia2)
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Power Systems Lab
Ia2d=angle(Ia2)*(180/pi) Ibo=Iao; Ibom=abs(Ibo) Ibod=angle(Ibo)*(180/pi) Ib1=b*Ia1; Ib1m=abs(Ib1) Ib1d=angle(Ib1)*(180/pi) Ib2=a*Ia2; Ib2m=abs(Ib2) Ib2d=angle(Ib2)*(180/pi) Ico=Iao; Icom=abs(Ico) Icod=angle(Ico)*(180/pi) Ic1=a*Ia1; Ic1m=abs(Ic1) Ic1d=angle(Ic1)*(180/pi) Ic2=b*Ia2; Ic2m=abs(Ic2) Ic2d=angle(Ic2)*(180/pi)
RESULT:
Experiment -6 SHORT CIRCUIT STUDIES FOR LL, LG, LLG AND THREE PHASE FAULTS PROBLEM:A salient pole generator is rated 30MVA, 12.8KV and has a direct axis sub-transient reactance of 0.3p.u.The negative and zero sequence reactances are 0.25 p.u and 0.1 p.u. The neutral of generator is rapidly grounded. Determine the sub-transient currents and line-to-line voltages at the faults under sub-transient conditions. When a L-L, L-G, and LLG fault occurs at generator terminals.
AIM:
Write a MATLAB program to find fault currents and line-to-line voltages when L-L (A & B), L-G (B)and LLG (B & C) fault occurs.
15
Power Systems Lab
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: zp=input('enter +ve sequence reactance'); zn=input('enter – ve sequence reactance'); z0=input('enter 0 sequence reactance'); mva=input('enter MVA rating of generator'); kv=input('enter KV rating of generator'); x= menu('options','L-G fault','L-L fault','L-L-G fault'); ib0=mva*1000/(sqrt(3)*kv); abs(ib0); kvab=kv/sqrt(3); a=-0.5+0.866i; aa=-0.5-0.866i; if(x==1) y=menu('options','solid gnd','gnd through impedance'); if(y==1) zf=0; end if(y==2) zf=input('enter fault impedance'); end ia1=1/(zp+zn+z0+zf); ia2=ia1; ia0=ia1; ia=3*ia1; disp('fault current') fi=ia*ib0; abs(fi) va1=1-(ia1*zp); va2=(-ia2*zn);
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Power Systems Lab
va0=(-ia1*z0); va=0 vb=va0+(aa*va1)+(a*va2) vc=va0+(a*va1)+(aa*va2) end if(x==2) r=menu('option','solid gnd','gnd through impedance'); if(r==1) zf=0; end if (r==2) zf=input('fault impedance'); end ia1=1/(zp+zn+zf); t=menu('options','ab phase','bc phase','ca phase'); ia2=-ia1; ia0=0; disp('fault current') fi=(ia0+(aa*ia1)+(a*ia2))*ib0; abs(fi) va0=0; va1=1-(ia1*zp); va2=va1; if(t==1) va=va0+va1+va2 vb=va vc=abs(va0+(a*va1)+(aa*va2)) end if(t==2) va=va0+va1+va2 vb=va0+(aa*va1)+(a*va2) vc=vb end if(t==3) vb=va0+(aa*va1)+(a*va2) vc=va0+(a*va1)+(aa*va2) va=vc end
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Power Systems Lab
end if(x==3) s=menu('option','solid gnd','gnd through impedance'); if(s==1) zf=0; end if(s==2) zf=input('enter fault impedance'); end ia1=1/(zp+(zn*(z0+3*zf))/(zn+z0+3*zf)); va0=1-(ia1*zp); va1=va0; va2=va0; ia2=(-va2/zn); ia0=(-va0/z0); ia=ia1+ia2+ia3; ib=ia0+(aa*ia1)+(a*ia2); ic=ia0+(a*ia1)+(aa*ia2); disp('fault current') fi=(ib+ic)*ib0 g=menu('option','ab phase','bc phase','ca phase'); if(g==1) va=0 vb=0 vc=va0+(a*va1)+(aa*va2) end if(g==2) vb=0 vc=0 va=va0+va1+va2 end if(g==3) vc=0 va=0 vb=va0+(aa*va1)+(a*va2) end end vab=va-vb
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Power Systems Lab
vbc=vb-vc vca=vc-va vaba=vab*kvab vbca=vbc*kvab vcaa=vca*kvab disp('the actual values of line to line voltages are vaba,vbca, vcaa '); vabam=abs(vaba) vabaa=angle(vaba)*180/pi vbcam=abs(vbca) vbcaa=angle(vbca)*180/pi vcaam=abs(vcaa) vcaaa=angle(vcaa)*180/pi
RESULT:
Experiment -7 SWING EQUATION BY STEP BY STEP METHOD PROBLEM: A 3-phase 50 hertz, 50 MVA synchronous generators with 4.5 MW /MVA in steady State with input and output as 0.7 p.u. displacement angle of 30.5 degrees w.r.t. infinite bus
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Power Systems Lab
Consequent upon the occurrence of a fault. Assuming that the input power remains constant. Taking the time interval of 0.05 sec set at t=1 sec
AIM:
Write a MATLAB Program for the Solution of Swing Equation by Step by Step method.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: flag=0; x=0; y=0; omega=0; freq=input('Enter the frequency:'); h=input('Enter the inertia constant:'); pin=input('Enter the input Power:'); delta=input('Enters the electrical angle:'); it=input('enter the incremenatal time:'); M=h/(180*freq); dd=1; disp('
t
pe
pa
iomega
idelta
omega
for t=0:it:1.0 r=1; s(r)=t; r=r+1; pe=1*sin(delta*3.14/180); s(r)=pe; r=r+1; pa=pin-pe; s(r)=pa; r=r+1;
20
delta');
Power Systems Lab
iomega=pa*it/M; s(r)=iomega; r=r+1; idelta=it*omega+(it*it/2*M)*pa; s(r)=idelta; r=r+1; omega=iomega+ omega; s(r)=omega; r=r+1; x(dd)=t; y(dd)=delta; delta=idelta+delta; s(r)=delta; r=r+1; if(delta
Experiment -8
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Power Systems Lab
DETERMINATION OF AVERAGE LOAD, PEAK LOAD, LOAD FACTOR AND DIVERSITY FACTOR PROBLEM: The daily load on a power system varies as shown in the below table. Using the data compute the average load, peak load, daily load factor and draw the daily load curve. Interval, hr 12A.M – 2A.M 2 -6 6 -9 9 -12 12P.M – 2P.M 2 -4 4 -6 6 -8 8 -10 10 -11 11 -12
Load, MW 6 5 10 15 12 14 16 18 16 12 6
AIM:
Write a MATLAB program to find the average load, peak load, daily load factor and draw the daily load curve.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: data = [
0 2 6 9 12 14 16 18 20 22 23
2 6 9 12 14 16 18 20 22 23 24
P =data(:,3); dt = data(:, 2) - data(:,1); w = P'*dt;
6 5 10 15 12 14 16 18 16 12 6]; % Column array of load % Column array of demand interval % Total energy, area under the curve
22
Power Systems Lab pavg = w/sum(dt) peakvalue = max(P) lf = pavg/peakvalue*100 l=length(data); tt = [data(:,1) data(:,2)]; t = sort(reshape(tt, 1, 2*l)); pp=data(:,3); for n = 1:l p(2*n-1)=pp(n); p(2*n)=pp(n); end plot(t,P) title(‘Daily Load Curve’); xlabel('Time, hr'); ylabel('P, MW'); grid
% Average load % Peak load % Percent load factor
RESULT:
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Power Systems Lab
Experiment -9 DETERMINE THE CRITICAL CLEARING ANGLE OF THE GIVEN SYSTEM USING EQUAL AREA CRITERION PROBLEM: A synchronous machine is delivering 1.0 PU power to an infinite bus through a double circuit a transmission lion. The transient reactance of the generator is 0.3 PU reactance are given to a base of the machine rating one of the transmission lion experience a solid 3- fault at middle to ground Determine .
Critical angle before which circuit breaker of faulted line should operate. If the stability is to be maintained. Calculate prefault, during fault, post fault operating power angle & represents then in the form of equal area criterion.
AIM: Write a MATLAB program to find the critical clearing angle of the given system using equal area criterion.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: for i=1:4 r(i)=input('enter the line reactance'); end e=input('enter the per unit value of generator voltage'); pm=input('enter the power proceeding fault'); v=input('enter the infinite bus voltage'); x1=r(1)+((r(2)*(r(3))/(r(2)+r(3)))+r(4)) pel=abs((e*v)/x1); d0=asin(pm./pel); ra=r(1)+(r(2)*r(3))/(2*(r(2)+r(3)));
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Power Systems Lab
rb=r(4)+(r(2)*r(3))/(2*(r(2)+r(3))); rc=r(3)*r(3)/4; rt=ra*rb+rb*rc+rc*ra; rab=rt./rc; rbc=rt./ra; rac=rt./rb; x2=rab pe2=abs((e*v)./x2); x3=r(1)+r(2)+r(4) pe3=abs((e*v)./x3); dm=pi-asin(pm./pe3); disp('maximum delta is'); disp(dm); x=pm*(dm-d0); y=pe3-pe2; dcr=acos((x-(pe2*cos(d0))+(pe3*cos(dm)))./y); disp(' the critical angle for the given system is'),dcr ddcr=dcr*180/pi; ddm=dm*180/pi; dd0=d0*180/pi; i=0:5:180; b=pel*sin(i*pi/180); c=pe3*sin(i*pi/180); plot(i,b,'r',i,c,'g',i,pm,'b',ddm,c,'-k',dd0,c,'-k') title(‘EQUAL AREA CRITERION’); xlabel(‘power angle delta’); ylabel(‘electrical power’);
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Power Systems Lab
RESULT:
Experiment -10(i) ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS PROBLEM: Incremental fuel costs in Rs/MW hr a plant consisting of the units are dc1/dPG1 =0.2PG1+40 dc2/dPG2 =0.2PG2+30 load varies from 40 to 250 MW. Maximum & minimum loads on each limit are 125&250 MW
AIM:
Write a MATLAB program to find load shared by two units with generation limits.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: n=2; pd=input('enter the load demand is'); alpha=[0.2 0.25]; beta=[40 30]; lamda=20; lamdaprev=lamda; eps=1; deltalamda=0.25; pgmax=[125 125]; pgmin=[20 20]; pg=100*ones(n,1); while abs(sum(pg)-pd)>eps for i=1:n pg(i)=(lamda-beta(i)./alpha(i)); if pg(i)>pgmax(i); pg(i)=pgmax(i); end if pg(i)
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Power Systems Lab lamdaprev=lamda; lamda=lamda+deltalamda; else lamdaprev=lamda; lamda=lamda-deltalamda; end end lambda=lamdaprev; disp('the final of lambda is'), lambda disp('the distribution of load shared by two units is'), pg
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Power Systems Lab
RESULT:
Experiment -10(ii) ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS PROBLEM:
The fuel cost of three thermal plants are given below C1= 500+5.3 P1+0.004 P12 C2= 400+5.5 P2+0.006 P22 C3= 200+5.8 P3+0.009 P32
P1, P2, P3 are in MW. The total element P0=800MW.Find optimal dispatch & total cost in Rs/hr.
Find optimal dispatch & total cost.
AIM:
Write a MATLAB program to find optimal dispatch & total cost without generation limits.
APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM: PROGRAM: alpha=[500 400 200]; beta=[5.3 5.5 5.8]; gamma=[0.004 0.006 0.009];, dem=800; n=input('enter the no.of plants'); for i= 1:n t1(i)=beta(i)./(2*gamma(i)); t2(i)=1./(2*gamma(i)); end
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Power Systems Lab
lamda=(dem+sum(t1))./sum(t2) for i=1:n p(i)=(lamda-beta(i))./(2*gamma(i)); end for i=1:n c(i)=alpha(i)+(beta(i)*p(i))+(gamma(i)*p(i)^2); end cost=sum(c); disp('load shared by generator 1'),p(1) disp('load shared by generator 2'),p(2) disp('load shared by generator 3'),p(3) disp('cost of generation'),cost
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Power Systems Lab
RESULT:
ADDITIONAL EXPERIMENT:1 ECONOMIC LOAD DISPATCH INCLUDING LOSSES PROBLEM: Two bus systems are shown if 100MW is transmitted from plant (1) to the load. A transmission loss of 10MW is increased. Find required generation for each plant and power required by load when the generation limits are PG1 max=PG2 max=200&PG min=0 dc1/dPG1=0.02 PG1+16 dc2/dPG2=0.04 PG2+20
AIM:
Write a MATLAB program to find required generation for each plant and power required by load with generation limits and losses.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: n=2; pd=input(‘enter the load demand is:’); alpha=[0.02 0.04]; beta=[16 20]; lamda=20; lamda prev=lamda; eps=1; delta lamda=0.25; pgmax=[200 200]; pgmin=[0 0]; b=[0.001 0;0 0];
30
Power Systems Lab pg=zeros(n,10); noofiter=0; pl=0; while abs(sum(pg)-pd-pl)>eps for i=l:n sigma=b(i,:)*pg-b(i,i)*pg(i); pg(i)=(1-beta(i)/(lamda-(2*sigma)))/(alpha(i)/lamda+2*b(i,i)); p1=pg’*b*pg; if pg(i)>pgmax(i); pg(i)=pgmax(i); end if pg(i)
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Power Systems Lab
RESULT:
ADDITIONAL EXPERIMENT -2
STUDY OF ETAP
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Power Systems Lab
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Power Systems Lab
SAMPLE EXPERIMENTS BASED ON E-TAP
Regency Institute of Technology: Yanam Department of Electrical and Electronics Engineering Exercise questions Semester: VI
Branch: EEE
Name of the Lab: power systems Lab
1.
Write a MATLAB program to find the per unit values of the power system shown below.
2.
Write a MATLAB program to determine the YBUS by Direct Inspection method for the system shown below. 1 2
34
From BusNo 1 1 1 2 3
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
Power Systems Lab
3.
3
4
Write a MATLAB program to determine the YBUS by Singular Transformation Method for the system shown below. 1
4
Element
Bus
ittance
1
1–2
2-j6
2
1–3
1- j3
3
1–4
1- j2
4
2–4
1- j3
5
3–4
2- j6
4.
The voltages across a three phase unbalanced load are V a = 300 ∟200, Vb = 360 ∟900 and Vc=500∟-1400.Write a MATLAB program to determine the Symmetrical components of voltages.
5.
Write a MATLAB program to determine the Symmetrical components of the unbalanced three phase currents Ia = 10∟00, Ib = 12∟2300 and Ic = 10∟1300.
6.
Write a MATLAB program to determine the Symmetrical components of the unbalanced three phase currents Ia = 18∟00, Ib = 10∟-300 and Ic = 10∟300. A generating station has maximum demand of 10MW and the daily load on the station is as 2 follows
7.
3 3
TIME (hours)
LOAD (KW)
11 p.m. – 6 a.m. 6 a.m. – 8 a.m. 8 a.m. – 12 Noon 412 Noon – 1 p.m. 14p.m. – 5 p.m. 5 p.m. – 7 p.m. 7 p.m. – 9 p.m. 9 p.m. – 11 p.m.
2000 3500 8000 3000 7500 8500 10000 4500
Write a MATLAB program to determine the load factor and to draw the load curve. 8.
A residential consumer as 10 lamps of 40W each connected at his premises. His demand is as follows TIME (hours)
35
LOAD (KW)
Power Systems Lab
12 Midnight – 5 a.m. 5 a.m. – 6 p.m. 6 p.m. – 7 p.m. 7 p.m. – 9 p.m. 9 p.m. – 12 Midnight
40 No Load 320 360 160
Write a MATLAB program to determine the Average Load, Maximum Load, Load factor and to draw the load curve. 9.
The load on a power plant on a typical day as under. TIME (hours)
LOAD (KW)
12 Midnight – 5 a.m. 5 a.m. – 9 a.m. 9 a.m. – 6 p.m. 6 p.m. – 10 p.m.
20 40 80 100
10 p.m. – 12 Midnight
20
Write a MATLAB program to determine the Average Load, Maximum Load, Load factor and to draw the load curve. 10.
The fuel inputs per hour of plants 1 and 2 are given as F1 = 0.2 P12 + 40 P1 + 120 Rs per hour F2 = 0.25 P22 + 30 P2 + 150 Rs per hour Write a MATLAB program to determine the Optimal dispatch and the total cost. The demand is 180 MW. (Neglect the losses)
11.
The fuel cost functions is Rs./hs for three thermal plants are given by C1 = 0.004 P12 + 7.2 P1 + 350 C2 = 0.0025 P22 + 7.3 P2 + 500 C3 = 0.003 P32 + 6.74 P3 + 600 Where P1, P2 and P3 are in MW. The governers are set such that generators share the load equally. Neglecting line losses and generator limits, write a MATLAB program to find the total cost in Rs/hr when the total load is (PD) 450MW.
12.
The fuel cost for three thermal plants in Rs./hr are given by C1 = 0.004 P12 + 5.3 P1 + 500 C2 = 0.006 P22 + 5.5 P2 + 400 C3 = 0.009 P32 + 5.8 P3 + 200
36
Power Systems Lab Write a MATLAB program to determine the optimal dispatch and the total cost. The demand is 800 MW. (Neglect the losses) 13.
A three phase, 50Hz synchronous generator with 4.5MW/MVA in steady state with input and output as 0.7p.u. Displacement angle of 30.5 0 w.r.t. infinite bus, consequent upon the occurrence of a fault. Assuming that the input power remains constant. Write a MATLAB program to determine and swing curve by step-by-step method. Taking the time interval of ∆t=0.05 set at t=1 sec.
14.
A salient pole generator is rated 30MVA, 12.8KV and has a direct axis sub-transient reactance of 0.3p.u. The negative and zero sequence reactances are 0.25p.u. and 0.1p.u. The neutral of generator is rapidly grounded. Write a MATLAB program to determine the sub-transient currents and line-to-line voltages at the faults under sub-transient conditions.
15.
Develop a Simulink Diagram to perform the frequency duration response for automatic generation control i.e. with & without proportional integral controller. Take: Tsg = 0.4; Tt = 0.5; Tps = 20; R = 3 Ksg = 10; Kt = 0.1; K1 = 0.09; Kps = 100
16.
The symmetrical components of phase a – fault current in a 3-Φ unbalanced system are I a0 = 350 ∟900 A, Ia1 = 600 ∟-900 A and Ia2 = 250 ∟900 A. Determine the phase currents I a, Ib, & Ic .
17.
A 25 MVA, 13.2 KV alternator with solidly grounded neutral has a sub transient reactance of 0.25 p.u. The –ve & zero sequence reactances are 0.35 and 0.1 p.u. respectively. A single line to ground fault occurs at the terminals of an unloaded generator, determine the fault current and the line-to-line voltages. Neglect resistance.
18.
A power station has to meet the following demand: Group A: 200 KW between 8 AM and 6 PM Group B: 100 KW between 6 AM and 10 AM Group C: 50 KW between 6 AM and 10 AM Group D: 100 KW between 10 AM and 6 PM and then between 6 PM and 6 AM Plot the daily load curve, determine diversity factor & load factor.
19.
The incremental fuel costs for two plants are given by dF1 / dP1 = 0.1 P1 + 22 Rs / MWhr dF2 / dP2 = 0.1 P2 + 22 Rs / MWhr
37
Power Systems Lab If both the units operate at all times and maximum & minimum loads on each unit are 100 MW and 20 MW respectively. Determine the economic operating schedule of the loads of 40 MW, 60 MW, 80 MW, 120 MW, 160 MW, neglecting the transmission line losses plot the incremental cost curve.
20.
A 3-Φ, 4 wire system supplies loads which are unequally distributed in the three phases. An analysis of the current flowing in R 1 Y and B lines shows that in R line, the sequence component is 200 ∟00 A. and the –ve sequence component is 100 ∟600 A. The total observed current flowing back to the supply in the neutral conductor is 300 ∟3000 A. Calculate the currents in the three lines.
21.
A balanced star connected load takes 90A from a balanced 3-Φ 4-wire supply. If the fuses in the Y and B phases are removed, find the symmetrical components of the line currents. (a) Before the fuses are removed. (b) After the fuses are removed.
22.
One conductor of a 3-Φ line is open. The current flowing to the A – connected load through the line R is 10A. With the line current in R as reference and assuming that the line B is open, find the symmetrical components of the line currents.
23.
A 3-Phase, 10MVA, 11 KV generator with a solidly earthed neutral point supplies a feeder. The relevant impedances of the generator and feeder in ohms are as follows Generator Feeder +ve sequence impedance j 1.2 j 1.0 -ve sequence impedance j 0.9 j 1.0 Zero sequence impedance j 0.4 j 3.0 Calculate (i) Magnitude of fault current (ii) Line to neutral voltage at the generator terminal. If the LG fault occurs on the R terminal.
24.
Incremental fuel in Rs/MWhr for a plant consisting of two units are: dC1 / dPG1 = 0.2 PG1 + 40. dC2 / dPG2 = 0.25 PG2 + 30. Assume that both units are operating at all times, and total load varies from 40 MW to 250 MW, and the maximum and minimum loads on each unit are to be 125 and 20 MW respectively. Write a MATLAB program to find how will the load be shared between the units as the system load varies over the full range. What are the corresponding values of the plant incremental costs?
38
Power Systems Lab
25.
26.
27.
A two bus system is shown in the figure, if 100 MW is transmitted from plant (1) to load, a transmission loss of 10 MW is incurred. Find the required generation for each plant and the power received by the load when generation limits are PG1 max = PG2 max = 200 MW, PGi min = 0 & dC1 / dPG1 = 0.02 PG1 + 16.0 dC2 / dPG2 = 0.4 PG2 + 20.0 A two bus system is shown in the figure. If a load of 125 MW is transmitted from plant 1 to the load, a loss of 15.625 MW is incurred. Determine the generation schedule and the load demand. If the cost of received power is Rs. 24/MWhr. Solve the problem using coordination equations and the penalty factor method approach. The incremental costs of the plants are dF1 / dP1 = 0.025 P1 + 15 dF2 / dP2 = 0.05 P2 + 20 Assume that the fuel input in Rs per hour for units 1 & 2 are given by F1 = 8 P1 + 0.024 P12 + 80 F2 = 6 P2 + 0.04 P22 + 120 The maximum & minimum loads on the units are 100 MW & 10 MW respectively. Determine the minimum cost of generation when the following load is supplied.
39
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
Power Systems Lab
UEE 6057 POWER SYSTEM LAB LIST OF EXPERIMENTS Page. no
Sl.no Name of the Experiment 1
PER UNIT COMPUTATION.
2
FORMATION OF BUS TTANCE MATRIX BY DIRECT INSPECTION.
3
FORMATION OF BUS TTANCE MATRIX BY SINGULAR TRANSFORMATION.
4 5
FORMATION OF BUS IMPEDANCE MATRIX. SYMMETRICAL COMPONENTS.
6
SHORT CIRCUIT FOR LL, LG AND LLG AND THREE PHASE POINTS.
7
SWING EQUATION BY STEP BY STEP METHOD.
8 9 10
DETERMINATION OF LOAD FACTOR, PEAKLOAD, AVERAGE LAOD AND DIVERSITY FACTOR. DETERMINE THE CRITICAL CLEARING ANGLE OF THE GIVEN SYSTEM USING EQUAL AREA CRITERION. ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS.
2
Remarks
Power Systems Lab
ADDITIONAL EXPERIMENTS
S.No 1 2
Name of the Experiment ECONOMIC LOAD DISPATCH INCLUDING LOSSES STUDY OF ETAP
Experiment 1 PER UNIT COMPUTATION PROBLEM: draw the reactance diagram for the power system shown in figure. Neglect resistance and use a base of 100MVA,220KV in 50Ω.
AIM: Write a MATLAB program to find the per unit values of the power system shown above. APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: %generatorG1
3
Power Systems Lab
gm1=input('enter the value of G1MVA:'); gk1=input('enter the value of G1KV:'); gx1=input('enter the value of G1X:'); %transformerT1 t1m=input('enter the value of T1MVA:'); t1kp=input('enter the value of T1KVP:'); t1ks=input('enter the value of T1KS:'); t1x=input('enter the value of T1X:'); %transmission lineTL1 tl1x=input('enter the value of TL1X:'); %transformerT2 t2m=input('enter the value of T2MVA:'); t2kp=input('enter the value of T2KVP:'); t2ks=input('enter the value of T2KVS:'); t2x=input('enter the value ofT2X:'); %generatorG2 gm2=input('enter the value of G2MVA:'); gk2=input('enter the value of G2KV:'); gx2=input ('enter the value ofG2X:'); %transmission line TL2 tl2x=input('enter the value of TL2X:'); %transformer T3 t3m=input('enter the value of T3MVA:'); t3kp=input('enter the value of T3KVP:'); t3ks=input('enter the value of T3KVS:'); t3x=input('enter the value of T3X:'); %motor mm=input('enter the value of MMVA:'); mk=input('enter the value of MKV:'); mx=input('enter the value of MX:'); %base values bm=input('enter the value of base MVA:'); bk=input('enter the value of base KV:'); gx1new=gx1*(bm/gm1)*((gk1/bk)^2); t1xnew=t1x*(bm/t1m)*((t1kp/bk)^2); bk1=bk*(t1ks/t1kp); tl1new=tl1x*(bm/(bk1^2)); bk2=bk1*(t2kp/t2ks);
4
Power Systems Lab
t2xnew=t2x*(bm/t2m)*((bk/bk2)^2); gx2new=gx2*(bm/gm2)*((bk/bk2)^2); tl2new=tl2x*(bm/(bk1^2)); t3m1=3*t3m; t3kp1=1.732*t3kp; t3ks1=1.732*t3ks; bk3=bk1*(t3kp1/t3ks1); t3xnew=t3x*(bm/t3m1)*((t3kp1/bk3)^2); mnew=mx*(bm/mm)*((mk/bk3)^2); disp('the pu value of G1 is:'),gx1new disp('the pu value of T1 is:'),t1xnew disp('the pu value of TL1 is:'),tl1new disp('the pu value of T2 is:'),t2xnew disp('the pu value of T3 is:'),t3xnew disp('the pu value of M is:'),mnew disp('the pu value of TL2 is:'),tl2new disp('the pu value of G2 is:'),gx2new
5
Power Systems Lab
RESULT:
Experiment -2 FORMULATION OF BUS ITTANCE MATRIX BY DIRECT INSPECTION METHOD PROBLEM:
For the Network shown in the figure formulate the Bus ittance Matrix by Direct Inspection Method 1
3
2 From BusNo 1 1 1 2 3
4
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
AIM: Write a MATLAB program to find the Bus ittance Matrix by Direct Inspection Method for the network shown above.
APPARATUS REQUIRED: 1)PERSONAL COMPUTER 2)MATLAT 6.5 VERSION 3)SIMULINK VERSION
ALGORITHM:
6
Power Systems Lab
PROGRAM: zdata=[ From BusNo 1 1 1 2 3
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
]; nl=zdata(:,1);
nr=zdata(:,2); r=zdata(:,3); x=zdata(:,4); nbr=length(zdata(:,1)); nbus = max(max(nl), max(nr)); z = r + j*x;
%branch impedance
y= ones(nbr,1)./z;
%branch ittance
ybus=zeros(nbus,nbus);
% initialize Ybus to zero
for k = 1:nbr
% formation of the off diagonal elements
if nl(k) > 0 & nr(k) > 0 ybus(nl(k),nr(k)) = ybus(nl(k),nr(k)) - y(k); ybus(nr(k),nl(k)) = ybus(nl(k),nr(k)); end end for n = 1:nbus
% formation of the diagonal elements
for k = 1:nbr if nl(k) == n | nr(k) == n ybus(n,n) = ybus(n,n) + y(k); else, end end end
7
Power Systems Lab
RESULT:
Experiment-3 FORMULATION OF BUS ITTANCE MATRIX BY SINGULAR TRANSFORMATION METHOD PROBLEM:
For the network shown in the figure formulate the Bus ittance Matrix by Singular Transformation method 1
2
3
4
Element 1 2 3 4 5
AIM:
From Bus 1 1 1 2 3
To bus 2 3 4 4 4
ittance 2-j6 1-j3 1-j2 1-j3 1-j6
Write a MATLAB program to find the Bus ittance Matrix by Singular Transformation method for the network shown above.
APPARATUS REQUIRED: 1)PERSONAL COMPUTER 2)MATLAT 6.5 VERSION 3)SIMULINK VERSION
ALGORITHM:
8
Power Systems Lab
PROGRAM: j=sqrt(-1); ydata=[ 1 1 2 2-j*6 2 1 3 1-j*3 3 1 4 1-j*2 4 2 4 1-j*3 5 3 4 2-j*6 ]; nbr=max(ydata(:,1)); nbus=max(max(ydata(:,2),max(ydata(:,3)))); yprimitive=zeros(nbr,nbr); for i=1:nbr; yprimitive(i,i)=ydata(i,4); end a=zeros(nbr,nbus); for i=1:nbr if ydata(i,2)~=0; a(i,ydata(i,2))=1; end if ydata(i,3)~=0 a(i,ydata(i,3))=-1; end end ybus=a'*yprimitive*a
9
Power Systems Lab
RESULT:
Experiment- 4 FORMATION OF BUS IMPEDANCE MATRIX PROBLEM: Write a MATLAB program to find BUS IMPEDANCE MATRIX for a given system. Whose reactance diagram is shown in the fig. All impedances are in p.u. 1
3
2
Element 1 2 3 4
4
From Bus 1 1 2 3
To bus 2 3 3 4
AIM: Write a MATLAB program to find BUS IMPEDANCE MATRIX for a given system. APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
10
ittance 1.0j 1.25j 0.25j 0.05j
Power Systems Lab
ALGORITHM:
PROGRAM: zdata=[1 1 2 1.0j 2 1 3 1.25j 3 3 4 .05j 4 3 2 .25j ]; [elements, columns]= size(zdata); zbus=0; refbusno=1; currentbusno=1; for count=1:elements [rows cols]=size(zbus); from=zdata(count,2); to=zdata(count,3); value=zdata(count,4); newbus=max(from,to); ref=min(from,to); if newbus>currentbusno & ref==refbusno zbus=[zbus zeros(rows,1) zeros(1,cols) value]; currentbusno=newbus; continue; end if newbus>currentbusno & ref~=refbusno zbus=[zbus zbus(:,ref) zbus(ref,:)
value+zbus(ref,ref)];
currentbusno=newbus; continue; end if newbus<=currentbusno & ref==refbusno zbus=zbus-1/((zbus(newbus,newbus)+value)*zbus(:,newbus)*zbus(newbus,:)); continue; end if newbus<=currentbusno & ref~=refbusno
11
Power Systems Lab
zbus=zbus-1/(value+zbus(from,from)+zbus(to,to)2*zbus(from,to))*((zbus(:,from)-zbus(:,to))*(zbus(from,:)-zbus(to,:))); continue; end end disp('formation of zbus using building algorithm is'),zbus
RESULT:
Experiment -5 SYMMETRICAL COMPONENTS FOR NO LINES OPEN, ONE LINE OPEN AND TWO LINES OPEN PROBLEM: Determine the Symmetrical Components of the unbalanced three phase currents Ia= 20 ∟300 A Ib = 50 ∟2300 A Ic = 80∟1300 A For 1. No lines Open 2. One line Open (B phase open) 3. Two lines Open (A & C phases open).
12
Power Systems Lab
AIM:
Write a MATLAB program to find the Symmetrical Components of the unbalanced
three phase currents. For 1. No lines Open 2. One line Open (B phase open) 3. Two lines Open (A&C phases open)
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: disp ('calculation of symmetrical components:'); i=sqrt (-1); Iam=input ('enter the magnitude of Ia:'); Iad=input ('enter the angle of Ia:'); Ia =Iam*(exp (i*Iad*(pi/180))); Ia Ibm= input ('enter the magnitude of Ib:'); Ibd= input ('enter the angle of Ib:'); Ib=Ibm*(exp (i*Ibd*(pi/180))); Ib Icm=input ('enter the magnitude of Ic:'); Icd=input ('enter the angle of Ic:'); Ic=Icm*(exp(i*Icd*(pi/180))); Ic k=menu('option','1.no lines open.','2.one line open.','3.two lines open.'); if(k==1) disp('no lines open:'); end if (k==2) l=menu ('option.','1.phase A open.','2.phase B open.','3.phase C open.'); if (l==1) disp ('phase A open.') Ia=0;
13
Power Systems Lab
end if(l==2) disp ('phase B open.') Ib=0; end if (l==3) disp ('phase c open.') Ic=0; end end if(k==3) m=menu('option.','1.phase A&B open.','2.phase B&C open.','3.phase C&A open.'); if (m==1) disp ('phase A&B open.') Ia=0; Ib=0; end if(m==2) disp ('phase B&C open.') Ib=0; Ic=0; end if(m==3) disp('phase C&A open') Ic=0; Ia=0; end end a=-0.5+0.866i; b=a*a; Iao=(1/3)*(Ia+Ib+Ic); Iaom=abs(Iao) Iaod=angle(Iao)*(180/pi) Ia1=(1/3)*(Ia+(a*Ib)+(b*Ic)); Ia1m=abs(Ia1) Ia1d=angle(Ia1)*(180/pi) Ia2=(1/3)*(Ia+(b*Ib)+(a*Ic)); Ia2m=abs(Ia2)
14
Power Systems Lab
Ia2d=angle(Ia2)*(180/pi) Ibo=Iao; Ibom=abs(Ibo) Ibod=angle(Ibo)*(180/pi) Ib1=b*Ia1; Ib1m=abs(Ib1) Ib1d=angle(Ib1)*(180/pi) Ib2=a*Ia2; Ib2m=abs(Ib2) Ib2d=angle(Ib2)*(180/pi) Ico=Iao; Icom=abs(Ico) Icod=angle(Ico)*(180/pi) Ic1=a*Ia1; Ic1m=abs(Ic1) Ic1d=angle(Ic1)*(180/pi) Ic2=b*Ia2; Ic2m=abs(Ic2) Ic2d=angle(Ic2)*(180/pi)
RESULT:
Experiment -6 SHORT CIRCUIT STUDIES FOR LL, LG, LLG AND THREE PHASE FAULTS PROBLEM:A salient pole generator is rated 30MVA, 12.8KV and has a direct axis sub-transient reactance of 0.3p.u.The negative and zero sequence reactances are 0.25 p.u and 0.1 p.u. The neutral of generator is rapidly grounded. Determine the sub-transient currents and line-to-line voltages at the faults under sub-transient conditions. When a L-L, L-G, and LLG fault occurs at generator terminals.
AIM:
Write a MATLAB program to find fault currents and line-to-line voltages when L-L (A & B), L-G (B)and LLG (B & C) fault occurs.
15
Power Systems Lab
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: zp=input('enter +ve sequence reactance'); zn=input('enter – ve sequence reactance'); z0=input('enter 0 sequence reactance'); mva=input('enter MVA rating of generator'); kv=input('enter KV rating of generator'); x= menu('options','L-G fault','L-L fault','L-L-G fault'); ib0=mva*1000/(sqrt(3)*kv); abs(ib0); kvab=kv/sqrt(3); a=-0.5+0.866i; aa=-0.5-0.866i; if(x==1) y=menu('options','solid gnd','gnd through impedance'); if(y==1) zf=0; end if(y==2) zf=input('enter fault impedance'); end ia1=1/(zp+zn+z0+zf); ia2=ia1; ia0=ia1; ia=3*ia1; disp('fault current') fi=ia*ib0; abs(fi) va1=1-(ia1*zp); va2=(-ia2*zn);
16
Power Systems Lab
va0=(-ia1*z0); va=0 vb=va0+(aa*va1)+(a*va2) vc=va0+(a*va1)+(aa*va2) end if(x==2) r=menu('option','solid gnd','gnd through impedance'); if(r==1) zf=0; end if (r==2) zf=input('fault impedance'); end ia1=1/(zp+zn+zf); t=menu('options','ab phase','bc phase','ca phase'); ia2=-ia1; ia0=0; disp('fault current') fi=(ia0+(aa*ia1)+(a*ia2))*ib0; abs(fi) va0=0; va1=1-(ia1*zp); va2=va1; if(t==1) va=va0+va1+va2 vb=va vc=abs(va0+(a*va1)+(aa*va2)) end if(t==2) va=va0+va1+va2 vb=va0+(aa*va1)+(a*va2) vc=vb end if(t==3) vb=va0+(aa*va1)+(a*va2) vc=va0+(a*va1)+(aa*va2) va=vc end
17
Power Systems Lab
end if(x==3) s=menu('option','solid gnd','gnd through impedance'); if(s==1) zf=0; end if(s==2) zf=input('enter fault impedance'); end ia1=1/(zp+(zn*(z0+3*zf))/(zn+z0+3*zf)); va0=1-(ia1*zp); va1=va0; va2=va0; ia2=(-va2/zn); ia0=(-va0/z0); ia=ia1+ia2+ia3; ib=ia0+(aa*ia1)+(a*ia2); ic=ia0+(a*ia1)+(aa*ia2); disp('fault current') fi=(ib+ic)*ib0 g=menu('option','ab phase','bc phase','ca phase'); if(g==1) va=0 vb=0 vc=va0+(a*va1)+(aa*va2) end if(g==2) vb=0 vc=0 va=va0+va1+va2 end if(g==3) vc=0 va=0 vb=va0+(aa*va1)+(a*va2) end end vab=va-vb
18
Power Systems Lab
vbc=vb-vc vca=vc-va vaba=vab*kvab vbca=vbc*kvab vcaa=vca*kvab disp('the actual values of line to line voltages are vaba,vbca, vcaa '); vabam=abs(vaba) vabaa=angle(vaba)*180/pi vbcam=abs(vbca) vbcaa=angle(vbca)*180/pi vcaam=abs(vcaa) vcaaa=angle(vcaa)*180/pi
RESULT:
Experiment -7 SWING EQUATION BY STEP BY STEP METHOD PROBLEM: A 3-phase 50 hertz, 50 MVA synchronous generators with 4.5 MW /MVA in steady State with input and output as 0.7 p.u. displacement angle of 30.5 degrees w.r.t. infinite bus
19
Power Systems Lab
Consequent upon the occurrence of a fault. Assuming that the input power remains constant. Taking the time interval of 0.05 sec set at t=1 sec
AIM:
Write a MATLAB Program for the Solution of Swing Equation by Step by Step method.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: flag=0; x=0; y=0; omega=0; freq=input('Enter the frequency:'); h=input('Enter the inertia constant:'); pin=input('Enter the input Power:'); delta=input('Enters the electrical angle:'); it=input('enter the incremenatal time:'); M=h/(180*freq); dd=1; disp('
t
pe
pa
iomega
idelta
omega
for t=0:it:1.0 r=1; s(r)=t; r=r+1; pe=1*sin(delta*3.14/180); s(r)=pe; r=r+1; pa=pin-pe; s(r)=pa; r=r+1;
20
delta');
Power Systems Lab
iomega=pa*it/M; s(r)=iomega; r=r+1; idelta=it*omega+(it*it/2*M)*pa; s(r)=idelta; r=r+1; omega=iomega+ omega; s(r)=omega; r=r+1; x(dd)=t; y(dd)=delta; delta=idelta+delta; s(r)=delta; r=r+1; if(delta
Experiment -8
21
Power Systems Lab
DETERMINATION OF AVERAGE LOAD, PEAK LOAD, LOAD FACTOR AND DIVERSITY FACTOR PROBLEM: The daily load on a power system varies as shown in the below table. Using the data compute the average load, peak load, daily load factor and draw the daily load curve. Interval, hr 12A.M – 2A.M 2 -6 6 -9 9 -12 12P.M – 2P.M 2 -4 4 -6 6 -8 8 -10 10 -11 11 -12
Load, MW 6 5 10 15 12 14 16 18 16 12 6
AIM:
Write a MATLAB program to find the average load, peak load, daily load factor and draw the daily load curve.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: data = [
0 2 6 9 12 14 16 18 20 22 23
2 6 9 12 14 16 18 20 22 23 24
P =data(:,3); dt = data(:, 2) - data(:,1); w = P'*dt;
6 5 10 15 12 14 16 18 16 12 6]; % Column array of load % Column array of demand interval % Total energy, area under the curve
22
Power Systems Lab pavg = w/sum(dt) peakvalue = max(P) lf = pavg/peakvalue*100 l=length(data); tt = [data(:,1) data(:,2)]; t = sort(reshape(tt, 1, 2*l)); pp=data(:,3); for n = 1:l p(2*n-1)=pp(n); p(2*n)=pp(n); end plot(t,P) title(‘Daily Load Curve’); xlabel('Time, hr'); ylabel('P, MW'); grid
% Average load % Peak load % Percent load factor
RESULT:
23
Power Systems Lab
Experiment -9 DETERMINE THE CRITICAL CLEARING ANGLE OF THE GIVEN SYSTEM USING EQUAL AREA CRITERION PROBLEM: A synchronous machine is delivering 1.0 PU power to an infinite bus through a double circuit a transmission lion. The transient reactance of the generator is 0.3 PU reactance are given to a base of the machine rating one of the transmission lion experience a solid 3- fault at middle to ground Determine .
Critical angle before which circuit breaker of faulted line should operate. If the stability is to be maintained. Calculate prefault, during fault, post fault operating power angle & represents then in the form of equal area criterion.
AIM: Write a MATLAB program to find the critical clearing angle of the given system using equal area criterion.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: for i=1:4 r(i)=input('enter the line reactance'); end e=input('enter the per unit value of generator voltage'); pm=input('enter the power proceeding fault'); v=input('enter the infinite bus voltage'); x1=r(1)+((r(2)*(r(3))/(r(2)+r(3)))+r(4)) pel=abs((e*v)/x1); d0=asin(pm./pel); ra=r(1)+(r(2)*r(3))/(2*(r(2)+r(3)));
24
Power Systems Lab
rb=r(4)+(r(2)*r(3))/(2*(r(2)+r(3))); rc=r(3)*r(3)/4; rt=ra*rb+rb*rc+rc*ra; rab=rt./rc; rbc=rt./ra; rac=rt./rb; x2=rab pe2=abs((e*v)./x2); x3=r(1)+r(2)+r(4) pe3=abs((e*v)./x3); dm=pi-asin(pm./pe3); disp('maximum delta is'); disp(dm); x=pm*(dm-d0); y=pe3-pe2; dcr=acos((x-(pe2*cos(d0))+(pe3*cos(dm)))./y); disp(' the critical angle for the given system is'),dcr ddcr=dcr*180/pi; ddm=dm*180/pi; dd0=d0*180/pi; i=0:5:180; b=pel*sin(i*pi/180); c=pe3*sin(i*pi/180); plot(i,b,'r',i,c,'g',i,pm,'b',ddm,c,'-k',dd0,c,'-k') title(‘EQUAL AREA CRITERION’); xlabel(‘power angle delta’); ylabel(‘electrical power’);
25
Power Systems Lab
RESULT:
Experiment -10(i) ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS PROBLEM: Incremental fuel costs in Rs/MW hr a plant consisting of the units are dc1/dPG1 =0.2PG1+40 dc2/dPG2 =0.2PG2+30 load varies from 40 to 250 MW. Maximum & minimum loads on each limit are 125&250 MW
AIM:
Write a MATLAB program to find load shared by two units with generation limits.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM:
PROGRAM: n=2; pd=input('enter the load demand is'); alpha=[0.2 0.25]; beta=[40 30]; lamda=20; lamdaprev=lamda; eps=1; deltalamda=0.25; pgmax=[125 125]; pgmin=[20 20]; pg=100*ones(n,1); while abs(sum(pg)-pd)>eps for i=1:n pg(i)=(lamda-beta(i)./alpha(i)); if pg(i)>pgmax(i); pg(i)=pgmax(i); end if pg(i)
26
Power Systems Lab lamdaprev=lamda; lamda=lamda+deltalamda; else lamdaprev=lamda; lamda=lamda-deltalamda; end end lambda=lamdaprev; disp('the final of lambda is'), lambda disp('the distribution of load shared by two units is'), pg
27
Power Systems Lab
RESULT:
Experiment -10(ii) ECONOMIC LOAD DISPATCH NEGLECTING LOSSES WITH & WITHOUT GENERATION LIMITS PROBLEM:
The fuel cost of three thermal plants are given below C1= 500+5.3 P1+0.004 P12 C2= 400+5.5 P2+0.006 P22 C3= 200+5.8 P3+0.009 P32
P1, P2, P3 are in MW. The total element P0=800MW.Find optimal dispatch & total cost in Rs/hr.
Find optimal dispatch & total cost.
AIM:
Write a MATLAB program to find optimal dispatch & total cost without generation limits.
APPARATUS REQUIRED: 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK TOOL
ALGORITHM: PROGRAM: alpha=[500 400 200]; beta=[5.3 5.5 5.8]; gamma=[0.004 0.006 0.009];, dem=800; n=input('enter the no.of plants'); for i= 1:n t1(i)=beta(i)./(2*gamma(i)); t2(i)=1./(2*gamma(i)); end
28
Power Systems Lab
lamda=(dem+sum(t1))./sum(t2) for i=1:n p(i)=(lamda-beta(i))./(2*gamma(i)); end for i=1:n c(i)=alpha(i)+(beta(i)*p(i))+(gamma(i)*p(i)^2); end cost=sum(c); disp('load shared by generator 1'),p(1) disp('load shared by generator 2'),p(2) disp('load shared by generator 3'),p(3) disp('cost of generation'),cost
29
Power Systems Lab
RESULT:
ADDITIONAL EXPERIMENT:1 ECONOMIC LOAD DISPATCH INCLUDING LOSSES PROBLEM: Two bus systems are shown if 100MW is transmitted from plant (1) to the load. A transmission loss of 10MW is increased. Find required generation for each plant and power required by load when the generation limits are PG1 max=PG2 max=200&PG min=0 dc1/dPG1=0.02 PG1+16 dc2/dPG2=0.04 PG2+20
AIM:
Write a MATLAB program to find required generation for each plant and power required by load with generation limits and losses.
APPARATUS REQUIRED : 1) PERSONAL COMPUTER 2) MATLAT 6.5 VERSION 3) SIMULINK VERSION
ALGORITHM:
PROGRAM: n=2; pd=input(‘enter the load demand is:’); alpha=[0.02 0.04]; beta=[16 20]; lamda=20; lamda prev=lamda; eps=1; delta lamda=0.25; pgmax=[200 200]; pgmin=[0 0]; b=[0.001 0;0 0];
30
Power Systems Lab pg=zeros(n,10); noofiter=0; pl=0; while abs(sum(pg)-pd-pl)>eps for i=l:n sigma=b(i,:)*pg-b(i,i)*pg(i); pg(i)=(1-beta(i)/(lamda-(2*sigma)))/(alpha(i)/lamda+2*b(i,i)); p1=pg’*b*pg; if pg(i)>pgmax(i); pg(i)=pgmax(i); end if pg(i)
31
Power Systems Lab
RESULT:
ADDITIONAL EXPERIMENT -2
STUDY OF ETAP
32
Power Systems Lab
33
Power Systems Lab
SAMPLE EXPERIMENTS BASED ON E-TAP
Regency Institute of Technology: Yanam Department of Electrical and Electronics Engineering Exercise questions Semester: VI
Branch: EEE
Name of the Lab: power systems Lab
1.
Write a MATLAB program to find the per unit values of the power system shown below.
2.
Write a MATLAB program to determine the YBUS by Direct Inspection method for the system shown below. 1 2
34
From BusNo 1 1 1 2 3
To BusNo. 2 3 4 4 4
R in P.U 0.05 0.10 0.20 0.10 0.05
X in P.U 0.15 0.30 0.40 0.30 0.15
Power Systems Lab
3.
3
4
Write a MATLAB program to determine the YBUS by Singular Transformation Method for the system shown below. 1
4
Element
Bus
ittance
1
1–2
2-j6
2
1–3
1- j3
3
1–4
1- j2
4
2–4
1- j3
5
3–4
2- j6
4.
The voltages across a three phase unbalanced load are V a = 300 ∟200, Vb = 360 ∟900 and Vc=500∟-1400.Write a MATLAB program to determine the Symmetrical components of voltages.
5.
Write a MATLAB program to determine the Symmetrical components of the unbalanced three phase currents Ia = 10∟00, Ib = 12∟2300 and Ic = 10∟1300.
6.
Write a MATLAB program to determine the Symmetrical components of the unbalanced three phase currents Ia = 18∟00, Ib = 10∟-300 and Ic = 10∟300. A generating station has maximum demand of 10MW and the daily load on the station is as 2 follows
7.
3 3
TIME (hours)
LOAD (KW)
11 p.m. – 6 a.m. 6 a.m. – 8 a.m. 8 a.m. – 12 Noon 412 Noon – 1 p.m. 14p.m. – 5 p.m. 5 p.m. – 7 p.m. 7 p.m. – 9 p.m. 9 p.m. – 11 p.m.
2000 3500 8000 3000 7500 8500 10000 4500
Write a MATLAB program to determine the load factor and to draw the load curve. 8.
A residential consumer as 10 lamps of 40W each connected at his premises. His demand is as follows TIME (hours)
35
LOAD (KW)
Power Systems Lab
12 Midnight – 5 a.m. 5 a.m. – 6 p.m. 6 p.m. – 7 p.m. 7 p.m. – 9 p.m. 9 p.m. – 12 Midnight
40 No Load 320 360 160
Write a MATLAB program to determine the Average Load, Maximum Load, Load factor and to draw the load curve. 9.
The load on a power plant on a typical day as under. TIME (hours)
LOAD (KW)
12 Midnight – 5 a.m. 5 a.m. – 9 a.m. 9 a.m. – 6 p.m. 6 p.m. – 10 p.m.
20 40 80 100
10 p.m. – 12 Midnight
20
Write a MATLAB program to determine the Average Load, Maximum Load, Load factor and to draw the load curve. 10.
The fuel inputs per hour of plants 1 and 2 are given as F1 = 0.2 P12 + 40 P1 + 120 Rs per hour F2 = 0.25 P22 + 30 P2 + 150 Rs per hour Write a MATLAB program to determine the Optimal dispatch and the total cost. The demand is 180 MW. (Neglect the losses)
11.
The fuel cost functions is Rs./hs for three thermal plants are given by C1 = 0.004 P12 + 7.2 P1 + 350 C2 = 0.0025 P22 + 7.3 P2 + 500 C3 = 0.003 P32 + 6.74 P3 + 600 Where P1, P2 and P3 are in MW. The governers are set such that generators share the load equally. Neglecting line losses and generator limits, write a MATLAB program to find the total cost in Rs/hr when the total load is (PD) 450MW.
12.
The fuel cost for three thermal plants in Rs./hr are given by C1 = 0.004 P12 + 5.3 P1 + 500 C2 = 0.006 P22 + 5.5 P2 + 400 C3 = 0.009 P32 + 5.8 P3 + 200
36
Power Systems Lab Write a MATLAB program to determine the optimal dispatch and the total cost. The demand is 800 MW. (Neglect the losses) 13.
A three phase, 50Hz synchronous generator with 4.5MW/MVA in steady state with input and output as 0.7p.u. Displacement angle of 30.5 0 w.r.t. infinite bus, consequent upon the occurrence of a fault. Assuming that the input power remains constant. Write a MATLAB program to determine and swing curve by step-by-step method. Taking the time interval of ∆t=0.05 set at t=1 sec.
14.
A salient pole generator is rated 30MVA, 12.8KV and has a direct axis sub-transient reactance of 0.3p.u. The negative and zero sequence reactances are 0.25p.u. and 0.1p.u. The neutral of generator is rapidly grounded. Write a MATLAB program to determine the sub-transient currents and line-to-line voltages at the faults under sub-transient conditions.
15.
Develop a Simulink Diagram to perform the frequency duration response for automatic generation control i.e. with & without proportional integral controller. Take: Tsg = 0.4; Tt = 0.5; Tps = 20; R = 3 Ksg = 10; Kt = 0.1; K1 = 0.09; Kps = 100
16.
The symmetrical components of phase a – fault current in a 3-Φ unbalanced system are I a0 = 350 ∟900 A, Ia1 = 600 ∟-900 A and Ia2 = 250 ∟900 A. Determine the phase currents I a, Ib, & Ic .
17.
A 25 MVA, 13.2 KV alternator with solidly grounded neutral has a sub transient reactance of 0.25 p.u. The –ve & zero sequence reactances are 0.35 and 0.1 p.u. respectively. A single line to ground fault occurs at the terminals of an unloaded generator, determine the fault current and the line-to-line voltages. Neglect resistance.
18.
A power station has to meet the following demand: Group A: 200 KW between 8 AM and 6 PM Group B: 100 KW between 6 AM and 10 AM Group C: 50 KW between 6 AM and 10 AM Group D: 100 KW between 10 AM and 6 PM and then between 6 PM and 6 AM Plot the daily load curve, determine diversity factor & load factor.
19.
The incremental fuel costs for two plants are given by dF1 / dP1 = 0.1 P1 + 22 Rs / MWhr dF2 / dP2 = 0.1 P2 + 22 Rs / MWhr
37
Power Systems Lab If both the units operate at all times and maximum & minimum loads on each unit are 100 MW and 20 MW respectively. Determine the economic operating schedule of the loads of 40 MW, 60 MW, 80 MW, 120 MW, 160 MW, neglecting the transmission line losses plot the incremental cost curve.
20.
A 3-Φ, 4 wire system supplies loads which are unequally distributed in the three phases. An analysis of the current flowing in R 1 Y and B lines shows that in R line, the sequence component is 200 ∟00 A. and the –ve sequence component is 100 ∟600 A. The total observed current flowing back to the supply in the neutral conductor is 300 ∟3000 A. Calculate the currents in the three lines.
21.
A balanced star connected load takes 90A from a balanced 3-Φ 4-wire supply. If the fuses in the Y and B phases are removed, find the symmetrical components of the line currents. (a) Before the fuses are removed. (b) After the fuses are removed.
22.
One conductor of a 3-Φ line is open. The current flowing to the A – connected load through the line R is 10A. With the line current in R as reference and assuming that the line B is open, find the symmetrical components of the line currents.
23.
A 3-Phase, 10MVA, 11 KV generator with a solidly earthed neutral point supplies a feeder. The relevant impedances of the generator and feeder in ohms are as follows Generator Feeder +ve sequence impedance j 1.2 j 1.0 -ve sequence impedance j 0.9 j 1.0 Zero sequence impedance j 0.4 j 3.0 Calculate (i) Magnitude of fault current (ii) Line to neutral voltage at the generator terminal. If the LG fault occurs on the R terminal.
24.
Incremental fuel in Rs/MWhr for a plant consisting of two units are: dC1 / dPG1 = 0.2 PG1 + 40. dC2 / dPG2 = 0.25 PG2 + 30. Assume that both units are operating at all times, and total load varies from 40 MW to 250 MW, and the maximum and minimum loads on each unit are to be 125 and 20 MW respectively. Write a MATLAB program to find how will the load be shared between the units as the system load varies over the full range. What are the corresponding values of the plant incremental costs?
38
Power Systems Lab
25.
26.
27.
A two bus system is shown in the figure, if 100 MW is transmitted from plant (1) to load, a transmission loss of 10 MW is incurred. Find the required generation for each plant and the power received by the load when generation limits are PG1 max = PG2 max = 200 MW, PGi min = 0 & dC1 / dPG1 = 0.02 PG1 + 16.0 dC2 / dPG2 = 0.4 PG2 + 20.0 A two bus system is shown in the figure. If a load of 125 MW is transmitted from plant 1 to the load, a loss of 15.625 MW is incurred. Determine the generation schedule and the load demand. If the cost of received power is Rs. 24/MWhr. Solve the problem using coordination equations and the penalty factor method approach. The incremental costs of the plants are dF1 / dP1 = 0.025 P1 + 15 dF2 / dP2 = 0.05 P2 + 20 Assume that the fuel input in Rs per hour for units 1 & 2 are given by F1 = 8 P1 + 0.024 P12 + 80 F2 = 6 P2 + 0.04 P22 + 120 The maximum & minimum loads on the units are 100 MW & 10 MW respectively. Determine the minimum cost of generation when the following load is supplied.
39
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