Electrical Engineering Concepts

Question

A climate control system, a motor load, and a lightning circuit of a small warehouse establish a 20kVA power demand at 0.587 power factor lagging on a 240 V, 60 Hz supply.

a) Establish the power triangle for the load.

b) Determine the power-factor capacitor that must be placed in parallel with the load to raise the power factor to 0.865 lagging.

c) Determine the change in supply current from the uncompensated to the compensated system. Explain.

Answer 1

a) The power triangle consists of three vectors plotted on an orthoganol pair of axes. The vertical is the Imaginary and the horizontal is the Real. The Apparent power vector S, forms the hypoteneuse of a right trangle. The Real power vector P, is on the real axis, and the Imaginary power vector Q, is vertical side. The angle between S and P is the arccos of the power factor. Since it is lagging Q is negative.

b) to increase the pf the angle must be reduced by shortening Q while keeping P constant. The new angle is arccos of .8655. The angle Phi is also arctan (Q/P) thus Q = PtanPhi. Subject Qold -Qnew to find the amount of imaginary power addied. Find the impedance of this capacitor by dividing 240^2/Qchange. Note that this impedance =1/ wC and use that to calculate C.

c) the New S will be sqrt(P^2+Qnew^2) = 240*I .... find Inew and subtrract from Iold to find the change.