Power Factor
In AC circuits, the power factor is the
ratio of the real power that is used to do
work and the apparent power that is supplied to
the circuit.
The power factor can get values in the
range from 0 to 1.
When all the power is reactive power
with no real power (usually inductive load) - the power factor is 0.
When all the power is real power with no
reactive power (resistive load) - the power factor is 1.
The power factor is equal to the real or
true power P in watts (W) divided by the apparent power |S| in volt-ampere
(VA):
PF = P(W) / |S(VA)|
PF - power factor.
P - real power in watts
(W).
|S| - apparent power - the
magnitude of the complex power in volt⋅amps (VA).
For sinusoidal current, the power factor
PF is equal to the absolute value of the cosine of the apparent power phase
angle φ (which is also is
impedance phase angle):
PF = |cos φ|
PF is the power factor.
φ is the apparent power
phase angle.
The real power P in watts (W) is equal
to the apparent power |S| in volt-ampere (VA) times the power factor PF:
P(W) = |S(VA)| × PF = |S(VA)| × |cos φ|
When the circuit has a restrictive impedance load, the real power P is equal to the apparent power |S| and the
power factor PF is equal to 1:
PF(restrictive load) = P / |S| = 1
The reactive power Q in volt-amps
reactive (VAR) is equal to the apparent power |S| in volt-ampere (VA) times the
sine of the phase angle φ:
Q(VAR) = |S(VA)| × |sin φ|
Single phase circuit calculation from real power meter
reading P in kilowatts (kW), voltage V in volts (V) and current I in amps (A):
PF = |cos φ| = 1000 × P(kW) / (V(V) × I(A))
Three phase circuit calculation from
real power meter reading P in kilowatts (kW), line to line voltage VL-L in volts (V) and
current I in amps (A):
PF = |cos φ| = 1000 × P(kW) / (√3 ×
VL-L(V) × I(A))
Three phase circuit calculation from
real power meter reading P in kilowatts (kW), line to line neutral VL-N in volts (V) and
current I in amps (A):
PF = |cos φ| = 1000 × P(kW) / (3 ×
VL-N(V) × I(A))
Power factor
correction
Power factor correction is an adjustment
of the electrical circuit in order to change the power factor near 1.
Power factor near 1 will reduce the
reactive power in the circuit and most of the power in the circuit will be real
power. This will also reduce power lines losses.
The power factor correction is usually
done by adding capacitors to the load circuit, when the circuit has inductive
components, like an electric motor.
Power factor
correction calculation
The apparent power |S| in volt-amps (VA)
is equal to the voltage V in volts (V) times the current I in amps (A):
|S(VA)| = V(V) × I(A)
The reactive power Q in volt-amps
reactive (VAR) is equal to the square root of the square of the apparent power
|S| in volt-ampere (VA) minus the square of the real power P in watts (W) (Pythagorean
Theorem):
Q(VAR) = √(|S(VA)|2 - P(W)2)
The reactive power Q in volt-amps reactive (VAR) is
equal to the square of voltage V in volts (V) divided by the reactance Xc:
Q(VAR) = V(V)2 / XC = V(V)2 / (1 / (2πf(Hz)·C(F))) = 2πf(Hz)·C(F)·V(V)2
So the power factor correction capacitor in Farad (F)
that should be added to the circuit in parallel is equal to the reactive power
Q in volt-amps reactive (VAR) divided by 2π times the frequency f in Hertz (Hz)
times the squared voltage V in volts (V):
C(F) = Q(VAR) / (2πf(Hz)·V(V)2)
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