sp_perf.m

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%
%  sp_perf.m - calculates single-phase induction motor performance
%              ( I1,PF,Td, Ps, efficiency ) based on equivalent 
%              circuit of Fig. 6.39.
%              Assumes F&W losses vary as nth power of speed.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;
V1=120; f=60; p=4;  % Phase voltage, frequency, poles
Rs=2.02; Xs=2.79; Xm=106.8; Rr=4.12; Xr=2.12;
Pfw=10.5; n=2.8;  % Total F&W losses at syn. speed, speed dependence
npts=100; s=linspace( 0.0001,1,npts); s=fliplr(s);
I1=zeros(1,npts); Td=I1; PF=I1; Ps=I1; eff=I1; nm=I1;
ws=2/p*2*pi*f; ns=120*f/p;   % Synchronous speed
Zs=Rs+Xs*j; Zm=0+Xm/2*j; 
for i=1:npts  % Loop to calculate torque points
ZU=Rr/2/s(i)+Xr/2*j; ZL=Rr/2/(2-s(i))+Xr/2*j;
Zf=Zm*ZU/(Zm+ZU); Zb=Zm*ZL/(Zm+ZL);
Is=V1/(Zs+Zf+Zb); I1(i)=abs(Is); nm(i)=(1-s(i))*ns;
Irf=abs(Is*Zm/(Zm+ZU)); Irb=abs(Is*Zm/(Zm+ZL));
PF(i)=cos(angle(Is)); Pin=V1*I1(i)*PF(i);
Td(i)=0.5*Irf^2*Rr/s(i)/ws-0.5*Irb^2*Rr/(2-s(i))/ws;
if Td(i)<0; Td(i)=0; end
TPs=Td(i)*(1-s(i))*ws - Pfw*(nm(i)/ns)^n;
if TPs<0; break; else;
Ps(i)=TPs; eff(i)=100*Ps(i)/Pin; end
end
subplot(2,1,1), plot(nm,Td); grid; title('Developed torque');
xlabel('Speed, rpm'); ylabel('Torque, N-m');
subplot(2,1,2), plot(nm,Ps/746); grid; title('Output power'); 
xlabel('Speed, rpm'); ylabel('Output power, hp');
figure(2);
subplot(2,1,1); plot(nm,I1); grid; title('Input current');
xlabel('Speed, rpm'); ylabel('Current, A');
subplot(2,1,2); plot(nm,eff); grid; title('Efficiency');
xlabel('Speed, rpm'); ylabel('Efficiency, %');
figure(3);
subplot(2,1,1); plot(nm,PF); grid; title('Input power factor');
xlabel('Speed, rpm'); ylabel('Power factor');