AC power
From Biocrawler, the free encyclopedia.
- This article deals with power in AC systems. See Mains electricity for information on utility supplied AC power.
Power is defined as the rate of flow of energy past a given point. In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power flow that, averaged over a complete cycle of the ac waveform, results in net transfer of energy in one direction is known as real power. That portion of power flow due to stored energy that returns to the source in each cycle, is known as reactive power.
Mostly this article will concentrate on single frequency systems. Unfortunately unlike voltage and current power cannot be calculated by superposition of calculations at the various frequency components due to the fact its calculation invovles the square of voltage or current.
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Real, reactive, and apparent power
Engineers use three types of power to describe energy flow in a system:
Real power (P)
Reactive power (Q)
apparent power (S sometimes |S| when regarded as the modulus of complex power)
In the diagram, P is the real power Q is the reactive power (in this case negative) the length of S is the apparent power.
The unit for all forms of power is the watt (symbol: W), in practice however this is generally reserved for the real power component. The SI unit for reactive power is the voltampere which is given the special name "var" (symbol: var) in IEC 60027-1. The combination of real and reactive power is expressed in volt-amperes (VA).
Understanding the relationship between these three quantities lies at the heart of understanding power engineering. The mathematical relationship between them is a vector and is typically expressed using complex numbers
S = P + jQ (where j is the imaginary unit)
This complex value S is often 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 there is only real power flowing. If the load is purely inductive or capacitive then the voltage and current are 90 degrees out of phase (for a capacitor current leads voltage for an inductor current lags voltage) and there is no net power flow. This energy flowing backwards and forwards is known as reactive power. If a capacitor and an inductor are placed in parallel then the currents caused by the inductor and the capacitor are 180 degrees out of phase with each other and therefore partially cancel out rather than adding to each other. Conventionally capacitors are considered to generate reactive power and inductors to consume it. In reality the load is likely to have resistive inductive and capactive parts and so both real and reactive power will flow to the load. The apparent power is the result of a nieve calculaution of power from the voltage and current that is simply multiplying the rms voltage and the rms current. Apparent power is handy for rough sizing of generators or wiring especially when the power factor is close to 1. However adding the apparent power for two loads will not give the total apparent power unless the two loads have the same phase difference between voltage and current.
Power Factor
The ratio between real power and apparent power in a circuit is called the Power factor. Where the waveforms are purely sinusoidal, the power factor is the cosine of the phase angle between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as " cos φ" for this reason.
Power factor equals unity (1) when the voltage and current is in phase, and is zero when the current leads or lags the voltage by 90 degrees. Power factor must be specified as leading or lagging. 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 may produce higher losses and reduce over all transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power transfer.
Capacitive circuits cause reactive power with the current waveform leading the voltage wave by 90 degrees, while 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. By convention, capacitors are said to generate reactive power whilst inductors are said to consume it (this probably comes from the fact that most real life loads are inductive and so reactive power has to be supplied to them from power factor correction capacitors).
In power transmission and distribution, significant effort is made to control the reactive power flow. This is typically done automatically by switching in/out inductors or capacitor banks, 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 (especially larger customers).
Basic calculations using real numbers
for a perfect resistor there is no energy stored 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 capcitor or inductor.
where X is the reactance of the capacitor or inductor and is defined as being positive for an inductor and negetive for a capacitor.
more generally using phasors/complex numbers
in this section overline will be used to indicate phasor or complex quantities and letters with no annotation will be considered the magnitude of those quantities.
say we have a series cuircuit with some resistance and some reactance. From what has been said before we can make up the expression
which simplifies to
but the complex impedance Z is simply
so
however I2=I I*</sub> (multiplying a complex number by its conjugate squares its magnitude and makes its angle 0) and V=I Z so
