Home

.

Power

 

The power P dissipated by a resistance R carrying a current I with a voltage drop V is:
P = V2 / R = VI = I2R

Similarly, the power P dissipated by a conductance G carrying a current I with a voltage drop V is:
P = V2G = VI = I2 / G

The power P transferred by a capacitance C holding a changing voltage V with charge Q is:
P = VI = CV(dv/dt) = Q(dv/dt) = Q(dq/dt) / C

     The power P transferred by an inductance L carrying a changing current I with magnetic linkage Y is:
     P = VI = LI(di/dt) =
Y(di/dt) = Y(dy/dt) / L

Complex Power

When a voltage V causes a current I to flow through a reactive load Z, the complex power S is:
S = VI*   where I* is the conjugate of the complex current I.

Inductive Load
Z = R + jXL
I = IP - jIQ
cos
f = R / |Z| (lagging)
I* = IP + jIQ
S = P + jQ
An inductive load is a sink of lagging VArs (a source of leading VArs).

Capacitive Load
Z = R - jXC
I = IP + jIQ
cos
f = R / |Z| (leading)
I* = IP - jIQ
S = P - jQ
A capacitive load is a source of lagging VArs (a sink of leading VArs).

 

Three Phase Power

For a balanced star connected load with line voltage Vline and line current Iline:
Vstar = Vline / Ö
3
Istar = Iline
Zstar = Vstar / Istar = Vline / Ö3Iline
Sstar = 3VstarIstar = Ö3VlineIline = Vline2 / Zstar = 3Iline2Zstar

For a balanced delta connected load with line voltage Vline and line current Iline:
Vdelta = Vline
Idelta = Iline /
Ö3
Zdelta
= Vdelta / Idelta = Ö3Vline / Iline
Sdelta = 3VdeltaIdelta =
Ö3VlineIline = 3Vline2 / Zdelta = Iline2Zdelta

The apparent power S, active power P and reactive power Q are related by:
S2 = P2 + Q2
P = Scos
f
Q = Ssin
f
where cos
f is the power factor and sinf is the reactive factor

Note that for equivalence between balanced star and delta connected loads:
Zdelta = 3Zstar