Question 16.26: The two loads in Figure P16-25 draw apparent powers of |S1| ......
The two loads in Figure P16-25 draw apparent powers of \left|\mathrm{S}_1\right| = 16 kVA at a lagging power factor of 0.8 and \left|\mathrm{S}_2\right| = 25 kVA at unity power factor. The voltage across the loads is 3.8 kV and the line has an impedance of Z_{\mathrm{W}} = 5 + j26 Ω per wire. Find the apparent power produced by the source and the rms value of the source voltage.
Use MATLAB to perform the calculations.
Script File
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MagS1 = 16e3;
pf1 = 0.8;
MagS2 = 25e3;
pf2 = 1;
VL = 3.8e3;
ZW = 5+26j;
% Find the complex power in each load
S1 = MagS1*(pf1+j*sqrt(1-pf1^2));
S2 = MagS2*(pf2+j*sqrt(1-pf2^2));
% Find the load current
MagIL = abs(S1+S2)/abs(VL);
% Find the power in the line
SW = 2*MagIL^2*ZW;
% Find the total complex power
Ss = S1+S2+SW;
% Find the apparent source power
MagSs = abs(Ss)
% Find the rms value of the source voltage
MagVs = MagSs/MagIL
MagSs =
41.6762e+003
MagVs =
4.0608e+003
The apparent power produced by the source is 41.6762 kVA.
The rms value of the source voltage is 4.0608 kV.