Power Factor Correction – MVA Method

Another application of MVA Method is power factor correction. Consider the diagram below:

MVA_1 = sqrt{MW^2+{MVAR_1}^2} right {(1)}
MVAR_1 = sqrt{{MVA_1}^2-MW^2} right {(2)}

MVA_2 = sqrt{MW^2+{MVAR_2}^2} right {(3)}
MVAR_2 = sqrt{{MVA_2}^2-MW^2} right {(4)}

MVAR_c = {MVAR_1}-{MVAR_2} right {(5)}

where:
MW = real power
MVA1 = apparent power (before power factor correction)
MVAR1 = reactive power (before power factor correction)
MVA2 = apparent power (after power factor correction)
MVAR2 = reactive power (after power factor correction)
MVARc = Power Factor Capacitor MVAR
{theta_1} = Power Factor (before power factor correction)
{theta_2} = Power Factor (before power factor correction)

Using the above formula, find the size of power factor capacitor to improve the power factor of an industrial plant from o.80 lagging to 0.90 lagging if the maximum demand is 4.5 MW.

Solution:
theta_1 = {cos^1}(0.8) = 36.7^o
theta_2 = {cos^1}(0.9) = 25.8^o

MVAR_1 = {MW}*{sin theta_1} = {4.5}*{sin 36.7} = 2.70 MVAR
MVAR_2 = {MW}*{sin theta_2} = {4.5}*{sin 25.8} = 1.96 MVAR

MVAR_c = 2.70 - 1.96 = 0.74 MVAR

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