AC power

The apparent power, also connected load or power supply, featuring an electric load supplied or to be supplied to electrical power; this does not necessarily correspond to the information released by the consumer in the form of thermal, mechanical, or other energy performance. The apparent power S is obtained from the effective values ​​of electric current strength I and electric voltage U and is composed of the actual implementation of active power P and an additional reactive power Qtot

All three output variables are defined by equal values ​​or integrals sizes. For them there is no dependent on the time instantaneous values ​​at stationarity.

At zero reactive power, such as with DC voltage, the apparent power is the same as the amount of active power, or greater. Electrical equipment, the transmit power, such as transformers or electrical lines, corresponding to the apparent power to be transmitted must be designed.

Instead of the unit of power Watt ( unit symbol W) is the unit of volt-amperes for apparent power ( symbol 'VA ) used for the reactive power the unit Var ( symbol' var ).

• 3.1 Example: Dimmer
• 3.2 Example: half-wave rectifier

Apparent power at sinusoidal variables

For sinusoidal quantities produced displacement reactive power Q, when the phase angle of current and voltage are shifted by a φ. For the apparent power applies in this case

With

And

When an electric load or a power supply network contains linear inductors or capacitors, they require the construction of the magnetic or electric field, an electric energy which is returned to the network, however, after each half-period. The required reactive power for the field energy is shifted from the voltage by a quarter cycle or 90 °. The reactive power associated with the transport of the field energy and the conversion in the consumer real power give added geometrically apparent power.

The power and resources such as the serving generators and transformers must all be sized on the value of apparent power. This shall not apply only when a reactive current compensation limits the reactive current flow to the local consumer internal cable connections.

In the complex AC circuit analysis for the sinusoidal voltage or current course of the apparent power is defined as the magnitude of the complex apparent power S and the geometric sum of the active power P and reactive power Q. The complex apparent power is defined as the product of the complex voltage U by the complex conjugate power I *.

Apparent power at non-sinusoidal variables

The general case

In an electrical network with distorted, that is non-sinusoidal voltage or current occur harmonics. Each periodic signal can be set via the Fourier analysis into a series of individual sine waves, so-called spectral disassemble. Using the example of the current I, it consists of

• The fundamental component with the rms value I1 and the phase shift angle φ1 for voltage at the same frequency
• The harmonics with I2 and φ2, φ3 and I3, I4 and φ4, etc.

In this case, it can no longer specify a. In its place comes the power factor

As examples, in which the formulas for sine waves can not be applied, are:

• Non-linear loads, operated with a sinusoidal voltage source. For example, these include rectifiers, such as those found in power supplies. There, this produces distortions that affect the apparent power.
• Magnetic circuits with ferromagnetic core material saturation and hysteresis shows - such as coils or transformers that do not behave in particular in case of overload and distort the linear current.
• Phase angle control of delayed after each zero passage of the current switching. It comes at least with the current to a temporal shift in the fundamental and the formation of harmonics.

For further calculating the time characteristics or the frequency spectrum must be known.

What contribution does the reactive power and apparent power, can not give up. Only the inference about

Is possible.

A special case

The voltage remains frequently than impressed voltage despite non-linear load undistorted, ie U = U1. Then the equations simplify to

The reactive power can be specified in this case as consisting of two parts (see also reactive power)

With a fundamental frequency shift reactive power

And one caused by the harmonics distortion power

Problems with switches

Example: Dimmer

A circuit consists of a source with a sinusoidal voltage, a dimmer and a resistive load. This must be considered separately

The ohmic resistance R of each instantaneous value of u (t ) is proportional to i (t)

The current flows from the "ignition ", ie a delay? T to the zero crossing, until the next zero crossing and accordingly in the second half period. Used in the equations for the time range to get there on

And

So is here and there is no distortion power in spite of the distorted current. On the same result is obtained if one considers that the ohmic consumers no phase shift occurs, so that the equations in the frequency range for the fundamental and all harmonics.

In contrast to the line between the source and dimmer: Here flows the same " dim " power, but the power runs undimmed sinusoidal. So that the voltage has a higher effective value, and there is a higher apparent power with unchanged active power. This increase will be explained as a reactive power, the reactive power includes both displacement and distortion power. In this case, however, the displacement power factor can not be interpreted as signs of recovery, for there is no storing component in this example. Each distorted current is, the greater is: With increasing the delay of the ignition timing in the dimmer P becomes smaller without the - at the same time decreases the peak value of the current - by T / 4.

Example: half-wave rectifier

A similar function has a half-wave rectifier when it is used for power reduction, for example, in a coffee machine. By the rectifier, the power supply for each of a half period will be interrupted, thus halving the power. The heating plate behaves like an ohmic resistance. The source of a sinusoidal alternating voltage can be taken in a reduced amplitude and phase unchanged fundamental current plus DC and harmonic currents. Compared to the operation without rectifier, which is referred to here as the nominal condition, results

And at the outlet

Since the fundamental oscillation does not undergo any phase shift is.

Statements are made of the above calculation is not possible because of the direct current component in the apparent power. At an appropriate approach see distortion power.

Note: Since these half-wave rectification to the load current imposes a DC component, this form of power reduction is permitted only at low power. The upstream local mains transformer might otherwise be biased and thus become saturated in the worst case.