# Power factor

The power factor of an AC electric power system is defined as the ratio of the real power to the apparent power.

In a purely resistive AC circuit, voltage and current waveforms are in step, changing polarity at the same instant in each cycle. Where reactive loads are present, such as capacitors or inductors, energy storage in the loads result in a time difference between the current and voltage waveforms. Since 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 higher currents to transfer a given quantity of power than a circuit with a high power factor.

Real power is the capacity of the circuit for performing work in a particular time. Due to reactive elements of the load, the apparent power, which is the product of the voltage and current in the circuit, will be equal to or greater than the real power. The reactive power is a measure of the stored energy that is reflected to the source during each alternative current cycle.

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 can be expressed as:

[itex]\frac{P}{S}[itex].

In the case of a perfectly sinusoidal waveform, P, Q and S can be expressed as vectors that form a vector triangle such that:

[itex]S^2\,\! = {P^2\,\!} + {Q^2\,\!}[itex]

If φ is the phase angle between the current and voltage, then the power factor is then equal to [itex]\left|\cos\phi\right|[itex], and:

[itex] P = S \left|\cos\phi\right| [itex]

By definition, the power factor is 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 at "leading" or "lagging" to show the sign of the phase angle.

The power factor is determined by the type of loads connected to the power system. These can be

• Resistive
• Inductive
• Capacitive

If a purely resistive load is connected to a power supply, current and voltage will change polarity in phase, 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) generate 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, only to send 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 kVA = 1 kW × 1). 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 = 5 kVA × 0.2).

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.

Energy losses in transmission lines increase with increasing current. Where a load has a power factor lower than 1, more current is required to deliver the same amount of useful energy. Power companies therefore require that customers, especially those with large loads, maintain the power factors of their respective loads within specified limits or be subject to additional charges. Energy losses in transmission lines increase with increasing current. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.

## Non-sinusoidal components

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 and other devices.

## Mnemonics

English-language power engineering students are advised to remember: "ELI the ICE man" - 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 V(Voltage), Voltage leads Current in an inductor L.es:Factor de potencia

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