Question 16.29: In Figure P16-28 the load voltage is |VL| = 440 V(rms) at 60......
In Figure P16-28 the load voltage is \left|\mathrm{V}_{\mathrm{L}}\right| = 440 V(rms) at 60 Hz. The load Z_{\mathrm{L}} draws an apparent power of 880 VA at a lagging power factor of 0.7. Find the value of the capacitance required to raise the power factor of the parallel combination to 0.95. Repeat for a corrected power factor of unity.
Use MATLAB to perform the calculations.
Script File
clear all
MagVL = 440;
MagSL = 880;
pf = 0.7;
% Find the average and reactive power at the load
PL = MagSL*pf;
QL = MagSL*sqrt(1-pf^2);
% Set the new power factor
disp('Correct the power factor to 0.95.')
pfc = 0.95;
% Find the new apparent power
MagSp = PL/pfc;
% Find the new reactive power
Qp = MagSp*sqrt(1-pfc^2);
% Find the required change in reactive power
QC = Qp-QL;
% Solve for the capacitance
C = -QC/2/pi/60/MagVL^2
disp('Correct the power factor to 1.')
pfc = 1;
QC = -QL;
% Solve for the capacitance
C = -QC/2/pi/60/MagVL^2
Correct the power factor to 0.95.
C =
5.8365e-006
Correct the power factor to 1.
C =
8.6106e-006
For a power factor of 0.95, the capacitance is 5.8365 µF.
For a power factor of 1, the capacitance is 8.6106 µF.