Power factor

This article explains the electrotechnical term power factor, other meanings under power factor (work study) .

As power factor (also: active power factor ) is known in the electrical engineering , the ratio of the amount of real power to apparent power . The ratio is expressed in the following formula: ${\displaystyle P}$  ${\displaystyle S}$

Measuring device in the machine hall of the Zollern colliery

${\displaystyle {\text{Leistungsfaktor}}=\lambda ={\frac {|P|}{S}}}$

The power factor can be between 0 and 1: ${\displaystyle 0\leq \lambda \leq 1}$

Active factor

Power indicator diagram and phase shift angle for sinusoidal voltages and currents in the complex plane

Only with sinusoidal currents and voltages is the active factor defined from the ratio . It is equal to the cosine of the phase shift angle , see adjacent graphic. ${\displaystyle {\tfrac {P}{S}}}$  ${\displaystyle \varphi }$

${\displaystyle {\text{Wirkfaktor}}={\frac {P}{S}}=\cos \varphi }$

The amount of the active factor is defined as the shift factor .

In addition to the fundamental oscillation , non-sinusoidal quantities also contain harmonics for which no uniform phase shift angle can be specified. Then the power factor can not be specified as an active factor . Harmonics are to be expected, especially in power supplies with conventional bridge rectifiers , switched-mode power supplies and loads that contain semiconducting or magnetic components with non-linear characteristics . ${\displaystyle \lambda }$ ${\displaystyle \cos \varphi }$

In order to show the characteristics of the load, the correct designation of the reactive power flow direction must be ensured (clear designations are "overexcited" and "underexcited", whereas the sole designation "inductive" or "capacitive" is ambiguous).

meaning

In power supply facilities, the highest possible power factor is sought to avoid transmission losses. In the ideal case it is exactly 1, but practically only about 0.95 (inductive). In motor systems with asynchronous machines, there is a risk of self-excitation if the reactive power is fully compensated. In addition, a capacitive power factor would lead to overvoltages on the insulation of lines and electrical consumers. Energy supply companies often prescribe a power factor of at least 0.9 for their customers. If this value is not reached, the related reactive work will be billed separately. However, this does not matter for private households. Systems for reactive power compensation are used to increase the power factor . Also, photovoltaic systems must be from 1 January 2012 in Germany in a position depending on the size one to underexcited between 0.9 or 0.95 drive up overexcited in order depending on the requirements of the network operator , the local mains voltage to stabilize. ${\displaystyle \cos \varphi }$

Power factor with non-linear loads

In spite of the sinusoidal alternating voltage, a non-sinusoidal or “ distorted ” alternating current often occurs due to non-linear loads . The apparent power

${\displaystyle S=U\cdot I}$

is given by the rms values ​​of the voltage and the total current strength consisting of the fundamental and harmonics . In the case of a sinusoidal voltage, only the active component of the fundamental oscillation of the current is included in the active power, see active current . With the rms value of the fundamental and its phase shift angle is ${\displaystyle U}$ ${\displaystyle I}$ ${\displaystyle I_{1}}$ ${\displaystyle \varphi _{1}}$

${\displaystyle P=U\cdot I_{1}\cdot \cos \varphi _{1}\,.}$

Together with the fundamental content of the current intensity or its distortion factor , the power factor can also be specified as ${\displaystyle g={\tfrac {I_{1}}{I}}}$ ${\displaystyle k={\tfrac {\sqrt {I^{2}-I_{1}^{2}}}{I}}}$

${\displaystyle \lambda ={\frac {|P|}{S}}={\frac {I_{1}}{I}}\cdot |{\cos \varphi _{1}}|=g\cdot |{\cos \varphi _{1}}|={\sqrt {1-k^{2}}}\cdot |{\cos \varphi _{1}}|\,.}$

Individual evidence

1. ↑ ^{a b c} DIN 40110-1: 1994: AC quantities
2. ↑ IEC 60050, see DKE German Commission for Electrical, Electronic and Information Technologies in DIN and VDE: Internationales Electrotechnical Dictionary - IEV . at 131-11-46
3. ↑ VDE application rule " VDE-AR-N 4105 application rule: 2018-11 " "Generation systems on the low-voltage network", "Minimum technical requirements for connection and parallel operation of generation systems on the low-voltage network".