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Reactive load

 

Resistance and Series Reactance
The impedance Z of a reactive load comprising resistance R and series reactance X is:
Z = R + jX = |Z|
Ðf
Converting to the equivalent admittance Y:
Y = 1 / Z = 1 / (R + jX) = (R - jX) / (R2 + X2) = R / |Z|2 - jX / |Z|2

When a voltage V (taken as reference) is applied across the reactive load Z, the current I is:
I = VY = V(R / |Z|2 - jX / |Z|2) = VR / |Z|2 - jVX / |Z|2 = IP - jIQ
The active current IP and the reactive current IQ are:
IP = VR / |Z|2 = |I|cos
f
IQ = VX / |Z|2 = |I|sin
f

The apparent power S, active power P and reactive power Q are:
S = V|I| = V2 / |Z| = |I|2|Z|
P = VIP = IP2|Z|2 / R = V2R / |Z|2 = |I|2R
Q = VIQ = IQ2|Z|2 / X = V2X / |Z|2 = |I|2X

The power factor cosf and reactive factor sinf are:
cos
f = IP / |I| = P / S = R / |Z|
sinf = IQ / |I| = Q / S = X / |Z|

Resistance and Shunt Reactance
The impedance Z of a reactive load comprising resistance R and shunt reactance X is found from:
1 / Z = 1 / R + 1 / jX
Converting to the equivalent admittance Y comprising conductance G and shunt susceptance B:
Y = 1 / Z = 1 / R - j / X = G - jB = |Y|
Ð-f

When a voltage V (taken as reference) is applied across the reactive load Y, the current I is:
I = VY = V(G - jB) = VG - jVB = IP - jIQ
The active current IP and the reactive current IQ are:
IP = VG = V / R = |I|cos
f
IQ = VB = V / X = |I|sin
f

The apparent power S, active power P and reactive power Q are:
S = V|I| = |I|2 / |Y| = V2|Y|
P = VIP = IP2 / G = |I|2G / |Y|2 = V2G
Q = VIQ = IQ2 / B = |I|2B / |Y|2 = V2B

The power factor cosf and reactive factor sinf are:
cos
f = IP / |I| = P / S = G / |Y|
sinf = IQ / |I| = Q / S = B / |Y|