imported>WikiSysop at 07:39, 5 December 2011

2011-12-05T07:39:12Z

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[[Wirkleistung]]

[[:en:{{PAGENAME}}]]

<math>S_{{eff}}= U_eff * I_eff </math>

[[Symbol::S_eff]]

==Real, reactive, and apparent powers==
[[Image:Cmplxpower.svg|thumb|right|250px|The complex power is the vector sum of real and reactive power. The apparent power is the magnitude of the complex power.   '''Real power''' ('''P''')   '''Reactive power''' ('''Q''')   '''Complex power''' ('''S''')   '''Apparent Power''' ('''|S|''')   '''Phase of Current''' ('''φ''') ]]

In a simple [[alternating current]] (AC) circuit consisting of a source and a linear load, both the current and voltage are [[sine wave|sinusoidal]]. If the load is purely [[resistive]], the two quantities reverse their polarity at the same time. At every instant the product of voltage and current is positive, indicating that the direction of energy flow does not reverse. In this case, only real power is transferred.

If the loads are purely [[Electrical reactance|reactive]], then the voltage and current are 90 degrees out of phase. For half of each cycle, the product of voltage and current is positive, but on the other half of the cycle, the product is negative, indicating that on average, exactly as much energy flows toward the load as flows back. There is no net energy flow over one cycle. In this case, only reactive energy flows—there is no net transfer of energy to the load.

Practical loads have resistance, inductance, and capacitance, so both real and reactive power will flow to real loads. Power engineers measure apparent power as the magnitude of the vector sum of real and reactive power. Apparent power is the product of the [[root-mean-square]] of voltage and current.

Engineers care about apparent power, because even though the current associated with reactive power does no work at the load, it heats the wires, wasting energy. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work.

Another consequence is that 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 (the same [[power factor]]).

Conventionally, capacitors are considered to generate reactive power and inductors to consume it. If a capacitor and an inductor are placed in parallel, then the currents flowing through the inductor and the capacitor tend to cancel rather than add. 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 'consumed' by the load.

Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to differentiate between them):

* '''Real power''' (''P'') or '''active power'''<ref> ''IEEE 100 : the authoritative dictionary of IEEE standards terms.-7th ed.'' ISBN 0-7381-2601-2, page 23</ref>: watt [W]
* '''Reactive power''' (''Q''): [[volt-ampere reactive]] [VAR]
* '''Complex power''' (''S''): volt-ampere [VA]
* '''Apparent Power''' (|''S''|), that is, the [[absolute value]] of complex power ''S'': [[volt-ampere]] [VA]
*'''Phase of Voltage Relative to Current''' (''φ''), the angle of difference (in degrees) between voltage and current; Current lagging Voltage (Quadrant I Vector), Current leading voltage (Quadrant IV Vector)

In the diagram, ''P'' is the real power, ''Q'' is the reactive power (in this case positive), ''S'' is the complex power and the length of ''S'' is the apparent power.

Reactive power does not transfer energy, so it is represented as the imaginary axis of the vector diagram. Real power moves energy, so it is the real axis.

The unit for all forms of power is the [[watt]] (symbol: W), but this unit is generally reserved for real power. Apparent power is conventionally expressed in [[Volt-ampere|volt-amperes]] (VA) since it is the product of [[root mean square|rms]] [[voltage]] and rms [[electric current|current]]. The unit for reactive power is expressed as var, which stands for [[Volt-ampere reactive|volt-amperes reactive]]. Since reactive power transfers no net energy to the load, it is sometimes called "wattless" power. It does, however, serve an important function in [[electrical grid]]s.

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, ''S'' = ''P'' + j''Q'' (where j is the [[imaginary unit]]).

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AC power - Revision history

imported>WikiSysop at 07:39, 5 December 2011