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. City lights viewed in a motion blurred exposure. ... The article on electrical energy is located elsewhere. ... A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another. ... Usually hidden to the unaided eye, the blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ... Usually hidden to the unaided eye, the blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transferred. ... Usually hidden to the unaided eye, the 60Hz blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ...

Explanation

Instantaneous and average power calculated from AC voltage and current with a unity power factor (φ=0, cosφ=1)

Instantaneous and average power calculated from AC voltage and current with a zero power factor (φ=90, cosφ=0)

Instantaneous and average power calculated from AC voltage and current with a lagging power factor (φ=45, cosφ=0.71)

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 at a given quantity of power than a circuit with a high power factor. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... It has been suggested that Electric reactance be merged into this article or section. ... Capacitors: SMD ceramic at top left; SMD tantalum at bottom left; through-hole tantalum at top right; through-hole electrolytic at bottom right. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ...

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. 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%. In the United States the term (Volt-amps) in Electrical terms, means watts. ... The watt (symbol: W) is the SI derived unit of power, equal to one joule per second. ...

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). City lights viewed in a motion blurred exposure. ... Real Power is often described as true power (or effective power) and is used by engineers to describe the actual amount of power present in a system, it is expressed in watts (W). ... The watt (symbol: W) is the SI derived unit of power, equal to one joule per second. ... Usually hidden to the unaided eye, the 60Hz blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ... Reactive power is an abstract quantity, typically used by power engineers to describe a certain type of energy flow in an electric distribution system. ...

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: In trigonometry, an ideal sine wave is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C, where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C... A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ...

If φ is the phase angle between the current and voltage, then the power factor is equal to , and:

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 as "leading" or "lagging" to show the sign of the phase angle. In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ...

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) 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, 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. Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... Capacitors: SMD ceramic at top left; SMD tantalum at bottom left; through-hole tantalum at top right; through-hole electrolytic at bottom right. ...

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 industrial and commercial customers maintain the power factors of their respective loads within specified limits or be subject to additional charges. 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, switched-mode power supplies and other devices. To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... A rectifier is one or more diodes arranged for converting alternating current (AC) to direct current (DC). ... An electric arc furnace is a system that heats the charged material by means of an electric arc. ... A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ...

A particularly important example is the millions of personal computers that typically incorporate switched-mode power supplies (SMPS) with rated output power ranging from 150W to 500W. 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. A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ...

Regulatory agencies such as the EC 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 power factor of about 0.55...0.65 only. Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ... An Active Power Factor Corrector (active PFC) is a power electronic system that controls the amount of power drawn by a load in order to obtain a Power factor as close as possible to unity. ... A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ... Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ... A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ... A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ...

To comply with current EU standard EN61000-3-2 all switched-mode power supplies with output power more than 75W must include at least passive PFC. A switched-mode power supply, or SMPS, is an electronic power supply unit (PSU) that incorporates a switching regulator - an internal control circuit that switches the load current rapidly on and off in order to stabilise the output voltage. ... Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ...

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. A digital multimeter A low cost digital multimeter An analog benchtop multimeter A multimeter or a multitester is an electronic measuring instrument that combines several functions in one unit. ... In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... The wattmeter is an electrodynamic instrument for measuring the electric power or the supply rate of electrical energy of any given circuit. ...

Mnemonics

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.

See also

• Power Factor Correction