The power factor of an AC electric power system is defined as the ratio of the real power to
the apparent
power, and is a number between 0 and 1. Real power
is the capacity of the circuit for performing work in a particular time. Apparent
power is the product of the current and voltage of the circuit. Due to
energy stored in the load and returned to the source, or due to a non-linear
load that distorts the wave shape of the current drawn from the source, the
apparent power can be greater than the real power. Low-power-factor loads
increase losses in a power distribution system and result in increased energy
costs.
In
a purely resistive AC circuit, voltage and current waveforms are in step (or in
phase), changing polarity at the same instant in each cycle. Where reactive
loads are present, such as with capacitors or inductors,
energy storage in the loads result in a time difference between the current and
voltage waveforms. This stored energy returns to the source and is not
available to do work at the load. A circuit with a low power factor will have
thus higher currents to transfer a given quantity of real power than a circuit
with a high power factor.
Circuits containing purely resistive
heating elements (filament lamps, strip heaters, cooking stoves, etc.) have a
power factor of 1.0. Circuits containing inductive or capacitive elements (
lamp ballasts, motors, etc.) often have a power factor below 1.0. For example,
in electric lighting circuits, normal power factor ballasts (NPF) typically
have a value of (0.4) - (0.6). Ballasts with a power factor greater than (0.9)
are considered high power factor ballasts (HPF).
The significance of power factor
lies in the fact that utility companies supply customers with volt-amperes,
but bill them for watts.
Power factors below 1.0 require a utility to generate more than the minimum
volt-amperes necessary to supply the real power (watts). This increases
generation and transmission costs. For example, if the
load power factor were as low as 0.7, the apparent power would be 1.4 times the
real power used by the load. Line current in the circuit would also be 1.4
times the current required at 1.0 power factor, so the losses in the circuit
would be doubled (since they are proportional to the square of the current).
Alternatively all components of the system such as generators, conductors,
transformers, and switchgear would be increased in size (and cost) to carry the
extra current.
Good power factor is considered
to be greater than 90 to 95%. Utilities typically charge additional costs to
customers who have a power factor below some limit, which is typically 90 to
95%. Engineers are often interested in the power factor of a load as one of the
factors that affect the efficiency of power transmission.
AC power flow has the three components: real power
(P), measured in watts
(W); apparent power (S), measured in volt-amperes (VA);
and reactive
power (Q), measured in reactive volt-amperes (VAr).
The power factor is defined as:
.
In the case of a perfectly sinusoidal
waveform, P, Q and S can be expressed as vectors that form a vector triangle such that:
If Ф is the phase angle
between the current and voltage, then the power factor is equal to /cosФ/, and:
Since the units are consistent,
the power factor is by definition a dimensionless number between 0 and 1. When
power factor is equal to 0, the energy flow is entirely reactive, and stored
energy in the load returns to the source on each cycle. When the power factor
is 1, all the energy supplied by the source is consumed by the load. Power
factors are usually stated as "leading" or "lagging" to
show the sign of the phase angle, where leading indicates a negative sign.
If a purely resistive load is
connected to a power supply, current and voltage will change polarity in step,
the power factor will be unity (1), and the electrical energy flows in a single
direction across the network in each cycle. Inductive loads such as
transformers and motors (any type of wound coil) consumes reactive power with
current waveform lagging the voltage. Capacitive loads such as capacitor banks
or buried cable generate reactive power with current phase leading the voltage.
Both types of loads will absorb energy during part of the AC cycle, which is
stored in the device's magnetic or electric field, only to return this energy back
to the source during the rest of the cycle.
For example, to get 1 kW of real
power if the power factor is unity, 1 kVA of apparent power needs to be
transferred (1 kW ÷ 1 = 1 kVA). At low values of power
factor, more apparent power needs to be transferred to get the same real power.
To get 1 kW of real power at 0.2 power factor 5 kVA of apparent power needs to
be transferred (1 kW ÷ 0.2 = 5 kVA).
It is often possible to adjust
the power factor of a system to very near unity. This practice is known as power factor correction and is achieved
by switching in or out banks of inductors or capacitors. For example the inductive effect of motor loads
may be offset by locally connected capacitors.
In circuits having only
sinusoidal currents and voltages, the power factor effect arises only from the
difference in phase between the current and voltage. This is narrowly known as
"displacement power factor". The concept can be generalized to a
total, distortion, or true power factor where the apparent power includes all
harmonic components. This is of importance in practical power systems which
contain non-linear
loads such as rectifiers, some forms of electric lighting, electric arc furnaces, welding equipment, switched-mode power supplies and other
devices.
A particularly important example
is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with
rated output power ranging from 250 W to 750 W. Historically, these
very-low-cost power supplies incorporated a simple full-wave rectifier that
conducted only when the mains instantaneous voltage exceeded the voltage on the
input capacitors. This leads to very high ratios of peak-to-average input current,
which also lead to a low distortion power factor and potentially serious phase
and neutral loading concerns.
Regulatory agencies such as the EU have set harmonic limits
as a method of improving power factor. Declining component cost has hastened
acceptance and implementation of two different methods. Normally, this is done
by either adding a series inductor (so-called passive PFC) or the addition of a boost
converter that forces a sinusoidal input (so-called active PFC). For example, SMPS with passive PFC can achieve power
factor of about 0.7–0.75, SMPS with active PFC, up to 0.99, while SMPS without
any power factor correction has a power factor of only about 0.55–0.65.
To comply with current EU
standard EN61000-3-2, all switched-mode power supplies with output
power more than 75 W must include passive PFC, at least.
A typical multimeter
will give incorrect results when attempting to measure the AC current drawn by
a non-sinusoidal load and then calculate the power factor. A true RMS
multimeter must be used to measure the actual RMS currents and voltages (and
therefore apparent power). To measure the real power or reactive power, a wattmeter
designed to properly work with non-sinusoidal currents must be used.
English-language power
engineering students are advised to remember: "ELI the ICE man" or
"ELI on ICE" – the voltage E leads the current I in an inductor L,
the current leads the voltage in a capacitor C.
Or even shorter: CIVIL – in a Capacitor the I (current) leads Voltage, Voltage leads I (current) in an
inductor L.