Question

It is desired to obtain 500 VAR reactive power from 230 Vrms 50 Hz 1.5 KVAR reactor. What should be the angle of the AC to AC converter to be used? Calculate the THD of the current drawn from the mains (consider up to the 12th harmonic)?

Answer 1

14.5° ; THD % = 3.873 × 100 = 387.3%.

Step-by-step explanation:

Okay, in this question we are given the following parameters or data or information which is going to assist us in solving the question efficiently and they are;

(1). "500 VAR reactive power from 230 Vrms 50 Hz 1.5 KVAR reactor".

(2). Consideration of up to 12th harmonic.

So, let us delve right into the solution to the question above;

Step one: Calculate the Irms and Irms(12th) by using the formula for the equation below;

Irms = reactive power /Vrms = 500/230 = 2.174 A.

Irms(12th) = 1.5 × 10^3/ 12 × 230 = 0.543 A.

Step two: Calculate the THD.

Before the Calculation of the THD, there is the need to determine the value for the dissociation factor, h.

h = Irms(12th)/Irms = 0.543/ 2.174 = 0.25.

Thus, THD = [1/ (h)^2 - 1 ] ^1/2. = 3.873.

THD % = 3.873 × 100 = 387.3%.

Step four: angle AC - Ac converter

theta = sin^-1 (1.5 × 10^3/ 12 × 500) = 14.5°.