Question

Q2 (Newton-Raphson Power Flow Solution with FACTS Devices Consider a two-bus system with the single-line diagram shown in Fig. 2. In the two bus system, Bus is slack bus where voltage is given: V 1.03 +j0.0 p. u. Bus 2 is a PQ bus where load power is given in p.u.. The impedance of the transmission line between bus 1 and bus 2 is 212-0.0+ j0.15 p.u. A STATCOM is connected at bus 2 through a transformer to regulate the bus 2 voltage to be 1.05 piu. The impedance of the STATCOM transformer isan-0.0 +j0.06 p. u.. Code computer programme using Newton-Raphson method to calculate power flow solution, using a convergence tolerance of sp 10-. max |VkVKEp Bus 1 Bus 2 Z12 Pd2zjOdz-0.80+j0.25 Psh jQsh 2 sh STATCOM Fig. 2 Two-bus system with STATCOMM

do it in Matlab

Answer 1

Ans:

j = sqrt(-1);
V = zeros(1.03,1.05);
S = zeros(3,1);
Mismatch = zeros(3,1);
%------------------ Base values----------------%
kVLL=345;
MVA3Ph=100;
Zbase=kVLL^2/MVA3Ph;
%%%%%%%---------- line parameters in pu/km----------%
XL_km=0.376;
RL_km= 0.037; B_km=4.5;
%---------Line Susceptances--------%
B13_Micro_Mho=4.5*200; %200 km long
B12_Micro_Mho=4.5*150; %150 km long
B23_Micro_Mho=4.5*150; %150 km long
%---------Line impedances------------%
Z13_pu=(0.0+j*0.15)*200; %200 km long
Z12_pu=(0.0+j*0.06)*150; %150 km long

%------- line impedances in per unit--------%
Z13=Z13_pu/Zbase;
Z12=Z12_pu/Zbase;

%-------- susceptances in per unit----------%
B13=B13_Micro_Mho*Zbase*10^-6;
B12=B12_Micro_Mho*Zbase*10^-6;

%---------- YBUS Creation-------------%
Y(1,1)=1/Z12 + 1/Z13;
Y(1,2)=-1/Z12;
Y(2,1)=-1/Z12;
Y(2,2)=1/Z12 + 1/Z23;

Y; % Print Y=G+jB Admittance Matrix
%----------Conductance Values------------%
G(1,1)=real(Y(1,1));
G(1,2)=real(Y(1,2));

G(2,1)=real(Y(2,1));
G(2,2)=real(Y(2,2));

%--------Susceptance Values----------%
B(1,1)=imag(Y(1,1));
B(1,2)=imag(Y(1,2));

B(2,1)=imag(Y(2,1));
B(2,2)=imag(Y(2,2));

%--------- Given Specifications in pu (Known)----------%
V1MAG=1.03;   
ANG1=0;
V2MAG=1.05;
P2sp=1.0;   
P3sp=-0.9;
Q3sp=-0.6;
% -------------Calulate ANG2, V3MAG and ANG3---------------%
% ----Solution Parameters----%
Tolerance= 0.001;
Iter_Max=25;
%----- Initialization-------%
Iter=0;
i=0;
ConvFlag=1;
delANG2=0;

%-------------- to be determined (Flat start)-----------%%%%%%%%
ANG2=0;
ANG3=0;
V3MAG=1.0;
%------------------ Start Iteration Process for N-R-----------------%
while( ConvFlag==1 && Iter < Iter_Max)
Iter=Iter+1;
i=i+1;
%%----------- update the Voltage and Angles to calculate new jacobian---%
ANG2=ANG2+delANG2;

%------- Creation of Jacobian J--------%
% ------ delP2/delANG2=J(1,1)
J(1,1) = V2MAG*(V1MAG*(B(2,1)*cos(ANG2-ANG1)-G(2,1)*sin(ANG2-ANG1))+V3MAG*(B(2,3)*cos(ANG2-ANG3)-G(2,3)*sin(ANG2-ANG3)));
%%%%--------- delP2/delANG3 = J(1,2)------------%
J(1,2)=V2MAG*V3MAG*(G(2,3)*sin(ANG2-ANG3)-B(2,3)*cos(ANG2-ANG3));
%%%%%%%------ delP2/delV3Mag = J(1,3)--------%

%%%%%%%%%%%--- delP3/delANG2 = J(2,1)---------%%%
J(2,1) = V3MAG*V2MAG*(G(3,2)*sin(ANG3-ANG2)-B(3,2)*cos(ANG3-ANG2));
%%%%%%%%%%%-------delP3/delANG3 = J(2,2)-----------------%%
J(2,2)= V3MAG*(V1MAG*(B(3,1)*cos(ANG3-ANG1)-G(3,1)*sin(ANG3-ANG1))+V2MAG*(B(3,2)*cos(ANG3-ANG2)-G(3,2)*sin(ANG3-ANG2)));
%%%%%%%%%%%----------delP3/delV3MAG = J(2,3)------%

J = [J(1,1) J(1,2) ;J(2,1) J(2,2);
%%%%%%% calculation of updated voltages with angles %%%%%%%%%%%%
V(1)= V1MAG*exp(1i*ANG1);
V(2)= V2MAG*exp(1i*ANG2);

%%%%%%%----------- Current injections at each bus based on updated voltages and angles----------%%%%%%%%%
I = Y*V;
%%%%%%%%%----------calculation of P and Q-----------%%%%%%%%%%%
S(1) = V(1)*conj(I(1));
S(2) = V(2)*conj(I(2));

%%%%%%%%%%%------------- Mistmatches--------------%%%%%%%%%%
Mismatch(1) = P2sp-real(S(2));
Mismatch(2) = P3sp-real(S(3));

%%%%%%%-------- calculate the deltaANG and deltaVMAG-----------%%%%%%%
del=inv(J)*Mismatch; % for large matrices, this mathod is bad.
% Always use LU factorization to solve this linear equation.
delANG2 = del(1);
delANG3 = del(2);

%%%%%%%%%%%----------- Calculate power flow on transmission line-------%%
P12 = real(V(1))*conj((V(1)-V(2))/Z12);

P21 = real(V(2))*conj((V(2)-V(1))/Z12);

Q12 = imag(V(1))*conj((V(1)-V(2))/Z12);

Q21 = imag(V(2))*conj((V(2)-V(1))/Z12);

P1 = real(S(1));
Q1 = imag(S(1));
P2 = real(S(2));
Q2 = imag(S(2));