 Usually hidden from the unaided eye, the blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. Light is emitted twice each cycle. Power is defined as the rate of flow of energy past a given point. In alternating current circuits, voltage and current only remain in phase if the load is purely resistive. When this happens the power is said to be 'real power'. If instead the load is purely reactive (either Capacitive or Inductive), all of the power is reflected back to the generator as the phase cycles. The load is said to draw zero real power, instead it draws only 'reactive power'. If a load is both resistive and reactive, it will have both real and reactive power, resulting in total amount of power called the 'apparent power'. Image File history File links Download high resolution version (2048x1536, 707 KB) The city lights of Prince George, British Columbia, motion-blurred by waving the camera during the exposure. ...
Image File history File links Download high resolution version (2048x1536, 707 KB) The city lights of Prince George, British Columbia, motion-blurred by waving the camera during the exposure. ...
In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ...
City lights viewed in a motion blurred exposure. ...
International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...
In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...
Resistor symbols (American) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ...
The currents and voltages are forced out of synchrony by attached devices that store and release energy in different ways at different times. In AC power systems, attached loads that store energy behave like combinations of coils and capacitors. Coils store power as magnetic fields, behave something like "electrical flywheels" and delay changes in the current. Capacitors store power as electric charge, behave something like "electrical springs" and therefore advance changes in currents. An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ...
Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ...
The portion of power flow averaged over a complete cycle of the AC waveform that results in net transfer of energy in one direction is known as real power. The portion of power flow due to stored energy which returns to the source in each cycle is known as reactive power. Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ...
In reality there are losses along AC power transmission lines, meaning a purely reactive load, while drawing no real power itself, consumes power because the supplied and reflected power dissipate away on the transmission line, and energy is wasted. For this reason an AC load should be designed to have as little reactive power as possible. In most jurisdictions the power factor (percentage of apparent power that is real power) must be at least a certain percentage (typically 90%, 95% or 99%), otherwise extra charges may apply above what is recorded on a power meter, as power as been reflected back up the transmission line and wasted.
Real, reactive, and apparent power
 The apparent power is the vector sum of real and reactive power Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them): Image File history File links No higher resolution available. ...
Image File history File links No higher resolution available. ...
- Real power (P) [Unit: W - Watt]
- Reactive power (Q) [Unit: VAR - Volt-Ampere Reactive]
- Complex power (S) [Unit: VA - Volt-Ampere]
- Apparent Power (|S|) [Unit: VA]: i.e. the absolute value of complex power S.
In the diagram, P is the real power, Q is the reactive power (in this case negative), S is the complex power and the length of S is the apparent power. In mathematics, the absolute value (or modulus[1]) of a real number is its numerical value without regard to its sign. ...
The unit for all forms of power is the watt (symbol: W). However, this unit is generally reserved for the real power component. Apparent power is conventionally expressed in volt-amperes (VA) since it is the simple product of rms voltage and rms current. The IEC gave the unit for reactive power the unit symbol "var", which stands for volt-amperes reactive (since reactive power flow transfers no net energy to the load, it is sometimes called "wattless" power). Note that it does not make sense to assign a single unit to complex power because it is a complex number and it is therefore defined as a pair of two units: W and var. For other uses, see Watt (disambiguation). ...
In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...
International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...
In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...
This box: Electric current is the flow (movement) of electric charge. ...
The International Electrotechnical Commission (IEC) is an international standards organization dealing with electrical, electronic and related technologies. ...
volt-amperes reactive (VAR): In alternating-current power transmission and distribution, the product of the rms voltage and current, the apparent power, multiplied by the sine of the phase angle between the voltage and the current. ...
Understanding the relationship between these three quantities lies at the heart of understanding power engineering. The mathematical relationship among them can be represented by vectors or expressed using complex numbers,
 (where j is the imaginary unit). In mathematics, the imaginary unit (or sometimes the Latin or the Greek iota, see below) allows the real number system to be extended to the complex number system . ...
The complex value S is referred to as the complex power.
Consider an ideal alternating current (AC) circuit consisting of a source and a generalized load, where both the current and voltage are sinusoidal. If the load is purely resistive, the two quantities reverse their polarity at the same time, the direction of energy flow does not reverse, and only real power flows. If the load is purely reactive, then the voltage and current are 90 degrees out of phase and there is no net power flow. This energy flowing backwards and forwards is known as reactive power. City lights viewed in a motion blurred exposure. ...
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 is the...
Electrical resistance is a measure of the degree to which a body opposes the passage of an electric current. ...
It has been suggested that Electric reactance be merged into this article or section. ...
If a capacitor and an inductor are placed in parallel, then the currents flowing through the inductor and the capacitor oppose and tend to cancel out rather than adding. Conventionally, capacitors are considered to generate reactive power and inductors to consume it. This is the fundamental mechanism for controlling the power factor in electric power transmission; capacitors (or inductors) are inserted in a circuit to partially cancel reactive power of the load. A practical load will have resistive, inductive, and capacitive parts, and so both real and reactive power will flow to the load.
The apparent power is the product of voltage and current. Apparent power is handy for sizing of equipment or wiring. However, adding the apparent power for two loads will not accurately give the total apparent power unless they have the same displacement between current and voltage.
Power factor -
Main article: Power factor Power factor measures the efficiency of an AC power system. Power factor is the real power per unit of apparent power. (pf = Wh/VAh) A power factor of one is perfect, and 99% is good. Where the waveforms are purely sinusoidal, the power factor is the cosine of the phase angle (φ) between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as "cosφ" for this reason. 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. ...
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. ...
Power factor equals 1 when the voltage and current are in phase, and is zero when the current leads or lags the voltage by 90 degrees. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle, where leading indicates a negative sign. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents in a practical system will produce higher losses and reduce overall transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power transfer.
Purely capacitive circuits cause reactive power with the current waveform leading the voltage wave by 90 degrees, while purely inductive circuits cause reactive power with the current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out.
Reactive power flow In power transmission and distribution, significant effort is made to control the reactive power flow. This is typically done automatically by switching inductors or capacitor banks in and out, by adjusting generator excitation, and by other means. Electricity retailers may use electricity meters which measure reactive power to financially penalise customers with low power factor loads. This is particularly relevant to customers operating highly inductive loads such as motors at water pumping stations. Power line redirects here. ...
Electricity retailing is the final process in the delivery of electricity from generation to the consumer. ...
Power meter redirects here. ...
Unbalanced polyphase systems While real power and reactive power are well defined in any system, the definition of apparent power for unbalanced polyphase systems is considered to be one of the most controversial topics in power engineering. Originally, apparent power arose merely as a figure of merit. Major delineations of the concept are attributed to Stanley's Phenomena of Retardation in the Induction Coil (1888) and Steinmetz's Theoretical Elements of Engineering (1915). However, with the development of three phase power distribution, it became clear that the definition of apparent power and the power factor could not be applied to unbalanced polyphase systems. In 1920, a "Special Joint Committee of the AIEE and the National Electric Light Association met to resolve the issue. They considered two definitions: The practical coil circuits were the prototypes for the modern transformers William Stanley, Jr. ...
Marconi Wireless Station in Somerset, New Jersey in 1921 Charles Proteus Steinmetz (April 9, 1865 – October 26, 1923) was an American mathematician and electrical engineer. ...
In electrical engineering, three-phase electric power systems have at least three conductors carrying voltage waveforms that are 2π/3 radians (120°,1/3 of a cycle) offset in time. ...
Polyphase can refer to: a polyphase system in electrical engineering a polyphase filter in signal processing Category: ...
 that is, the quotient of the sums of the real powers for each phase over the sum of the apparent power for each phase. that is, the quotient of the sums of the real powers for each phase over the magnitude of the sum of the complex powers for each phase.
The 1920 committee found no consensus and the topic continued to dominate discussions. In 1930 another committee formed and once again failed to resolve the question. The transcripts of their discussions are the lengthiest and most controversial ever published by the AIEE (Emanuel, 1993). Further resolution of this debate did not come until the late 1990s.
Basic calculations using real numbers A perfect resistor stores no energy, and current and voltage are in phase. Therefore there is no reactive power and P = S. Therefore for a perfect resistor:
For a perfect capacitor or inductor on the other hand there is no net power transfer, so all power is reactive. Therefore for a perfect capacitor or inductor:
Where X is the reactance of the capacitor or inductor. It has been suggested that Electric reactance be merged into this article or section. ...
If X is defined as being positive for an inductor and negative for a capacitor then we can remove the modulus signs from Q and X and get. Mathematical meanings Especially in British/European usage, the modulus of a number is its absolute value. ...
Multiple frequency systems Since an RMS value can be calculated for any waveform, apparent power can be calculated from this.
For real power it would at first appear that we would have to calculate loads of product terms and average all of them. However if we look at one of these product terms in more detail we come to a very interesting result.
however the time average of a function of the form cos(ωt + k) is zero provided that ω is nonzero. Therefore the only product terms that have a nonzero average are those where the frequency of voltage and current match. In other words it is possible to calculate real (average) power by simply treating each frequency separately and adding up the answers.
Furthermore, if we assume the voltage of the mains supply is a single frequency (which it usually is), this shows that harmonic currents are a bad thing. They will increase the rms current (since there will be non-zero terms added) and therefore apparent power, but they will have no effect on the real power transferred. Hence, harmonic currents will reduce the power factor.
Harmonic currents can be reduced by a filter placed at the input of the device. Typically this will consist of either just a capacitor (relying on parasitic resistance and inductance in the supply) or a capacitor-inductor network. An active power factor correction circuit at the input would generally reduce the harmonic currents further and maintain the power factor closer to unity. Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ...
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