Distortion reactive power

The distortion power is a term used in electrical engineering and describes a special form of reactive power , which in change - or three-phase systems by nonlinear caused consumers. In addition to the standardized designation used here, the terms distortion power , harmonic reactive power or harmonic reactive power also appear in the literature .

General

Power supply networks are almost always operated with sinusoidal alternating voltage . In the case of linear electrical components such as ohmic resistors or so-called reactive resistances, the current also has a sinusoidal profile. If the current and voltage are sinusoidal, there is no distortion reactive power. There can only be distortion reactive power if a non-sinusoidal current or a non-sinusoidal voltage is present. In the case of electrical loads that generate distortion reactive power, a sinusoidal voltage (provided by the supply network) and a distorted, non-sinusoidal current can usually be assumed.

The cause of the non-sinusoidal current and the distortion reactive power are non-linear electrical assemblies, such as rectifiers in power supplies , inverters or even magnetic components that show magnetic saturation phenomena. These assemblies cause distortion to non-sinusoidal alternating currents. Their course can be represented by a Fourier series as a sum of the fundamental oscillation and harmonics . These harmonics of the current in combination with the sinusoidal mains voltage result in a proportion of the total reactive power.

The harmonics that occur are almost always undesirable because they put a load on the network and cannot do any work on the consumer. They are also often the cause of electromagnetic interference. The use of power factor correction filters can reduce the proportion of harmonics.

In addition to the distortion reactive power, displacement reactive power can occur.

calculation

Relationship between the various performance data

The real power is the power that is able to do work on a consumer, for example a rotary movement against a torque in the case of an electric motor or the temperature increase in an electric heater. In systems subject to harmonics, real power results only from the vibration components of current and voltage that are proportional to one another. If the voltage has no harmonic components, overall harmonics do not contribute anything to the active power (see also under active current ). ${\displaystyle P}$

Only the fundamental oscillation of the current thus generates active power and, if necessary, displacement reactive power with the (fundamental oscillation of) voltage . This occurs when the two oscillations are shifted in phase . The fundamental oscillation apparent power is the Pythagorean sum of active power and displacement reactive power: ${\displaystyle Q}$ ${\displaystyle S_{1}}$

Vector diagram of active power , displacement reactive power and distortion reactive power ${\displaystyle P}$ ${\displaystyle Q}$ ${\displaystyle D}$

${\displaystyle S_{1}={\sqrt {P^{2}+Q^{2}}}\ .}$

In addition to the apparent power, a third component is the distortion reactive power from the harmonics. If the rms value of the voltage, the rms value of the fundamental current, and etc. are the rms values ​​of the harmonic currents, then the total current and the distortion reactive current can be expressed as ${\displaystyle D}$ ${\displaystyle U}$ ${\displaystyle I_{1}}$ ${\displaystyle I_{2},\;I_{3},\;I_{4}}$ ${\displaystyle I}$ ${\displaystyle I_{\mathrm {v} }}$

${\displaystyle I={\sqrt {\sum _{i=1}^{\infty }I_{i}^{2}}}\quad }$ and ${\displaystyle \quad I_{\mathrm {v} }={\sqrt {\sum _{i=2}^{\infty }I_{i}^{2}}}}$

and the distortion reactive power as

${\displaystyle D=UI_{\mathrm {v} }=U\cdot {\sqrt {\sum _{i=2}^{\infty }I_{i}^{2}}}\,.}$

The total reactive power - not explicitly shown in the figure - results from the displacement reactive power and the distortion reactive power to ${\displaystyle Q_{\mathrm {ges} }}$

${\displaystyle Q_{\mathrm {ges} }={\sqrt {Q^{2}+D^{2}}}\,.}$

In the general case, the total apparent power is given by ${\displaystyle S}$

${\displaystyle S=U\cdot I={\sqrt {P^{2}+Q^{2}+D^{2}}}\,.}$

The illustration shows the phasor diagram with the needles for the various services.

The quantities and are measurable, see RMS measurement , active power measurement , reactive power measurement . ${\displaystyle U,\,I,\,P}$ ${\displaystyle Q}$

Connection with the distortion factor

The distortion factor or harmonic content of a variable affected by harmonics is a measure of the distortion and the proportion of distortion reactive power in electrical systems. The distortion factor describes the ratio of the Pythagorean sum of the effective values ​​of the harmonic spectrum to the Pythagorean sum of the effective values ​​of the entire spectrum including the fundamental component . The distortion reactive power can be determined with the distortion factor ${\displaystyle k}$ ${\displaystyle I}$ ${\displaystyle I_{2},I_{3},I_{4},\dots }$ ${\displaystyle I_{1},I_{2},I_{3},I_{4},\dots }$ ${\displaystyle I_{1}}$

${\displaystyle k={\frac {\sqrt {\sum _{i=2}^{\infty }I_{i}^{2}}}{\sqrt {\sum _{i=1}^{\infty }I_{i}^{2}}}}={\frac {\sqrt {I_{2}^{2}+I_{3}^{2}+I_{4}^{2}+\dots }}{\sqrt {I_{1}^{2}+I_{2}^{2}+I_{3}^{2}+I_{4}^{2}+\dots }}}}$

and express the apparent power by

${\displaystyle D=k\cdot S\,.}$

The fundamental harmonic content is sometimes mentioned as an alternative to the harmonic content . Numerical data of this size are often of little help with regard to the proportion of the distortion reactive power, since, for example, the range  = 0 ... 14% for the fundamental vibration content is covered by the range 100 ... 99%. ${\displaystyle D/S}$

Examples

• In the case of linear reactances such as ideal capacitors or inductors , there is no distortion reactive power , only the displacement reactive power .
• If you switch to an ohmic load resistor, e.g. B. a heating plate, a diode in series , the source of a sinusoidal alternating voltage is taken from the source of a fundamental current and direct current and harmonic currents. In addition to the active power, distortion reactive power also occurs at the source. Quantitative conclusions based on the distortion factor are not possible because of the direct current component in the apparent power.

However, a solution is possible by calculating the Fourier coefficients. If the current flowing without the diode is denoted by, the coefficients can be used to calculate: ${\displaystyle I_{0}}$

${\displaystyle I_{\mathrm {gl} }={\frac {\sqrt {2}}{\pi }}I_{0}\;;\qquad I_{1}={\frac {1}{2}}I_{0}\;.}$ No other odd harmonics occur.

${\displaystyle I_{2}={\frac {1}{\pi }}{\frac {2}{1\cdot 3}}I_{0}\;;\quad I_{4}={\frac {1}{\pi }}{\frac {2}{3\cdot 5}}I_{0}\;;\quad I_{6}={\frac {1}{\pi }}{\frac {2}{5\cdot 7}}I_{0}\;;\quad \ldots }$

${\displaystyle I_{\mathrm {v} }^{2}=I_{2}^{2}+I_{3}^{2}+\dotsb =0{,}0473\;I_{0}^{2}}$

${\displaystyle I^{2}=I_{\mathrm {gl} }^{2}+I_{1}^{2}+I_{2}^{2}+I_{3}^{2}+\dotsb }$ ${\displaystyle =0{,}4999\;I_{0}^{2}\;;}$theoretically exactly see under apparent power . ${\displaystyle ={\frac {1}{2}}\;I_{0}^{2}\;,}$

${\displaystyle {\frac {D^{2}}{S^{2}}}={\frac {I_{\mathrm {v} }^{2}}{I^{2}}}=0{,}0946;\quad D=30{,}8\,\%\cdot S}$

• For distortion reactive power when using a dimmer, see also under Apparent power.

Harmonic components for different consumers

The following table lists various loads and their harmonic distribution without filtering when operated with sinusoidal AC voltage. The harmonic currents are specified relative to the fundamental oscillation of the current. In general, the following applies: The higher the harmonic components in the current, the higher the distortion reactive power of the consumers concerned.

Cause of harmonic currents and distortion reactive power

root cause	curve	Exemplary consumer	${\displaystyle I_{n}/I_{1}}$ in %
			n = 2	n = 3	n = 4	n = 5	n = 7
No. There are no harmonics		Heating plate	0	0	0	0	0
magnetic saturation		Transformer with undersized core	0	25 ... 55	0	8… 30	2… 10
Gas discharge, glow discharge		Fluorescent lamp	1… 2	8… 20	0	2… 3	1… 2
Half-wave rectifier with resistive load without smoothing capacitor		Halving the power of thermal devices such as hair dryers	42	0	8th	0	0
Half-wave rectifier with capacitive and ohmic load, with smoothing capacitor		Simple miniature power supplies for entertainment electronics	70 ... 90	40 ... 60	30 ... 50	25 ... 50	12… 25
Full wave rectifier with capacitive and ohmic load, with smoothing capacitor		Power supplies in PCs, printers, monitors, TVs	0	65 ... 80	0	50 ... 70	25… 35

Effects

Particularly in the consumer goods sector, there has been an increase in consumers in recent years who have a rectifier on the mains side and thus generate distortion reactive power. These include B. Energy-saving lamps and power packs for computers , chargers for batteries, monitors , TV sets , etc. A remedy is a power factor correction filter (PFC), usually designed as a so-called active power factor correction filter.

Since the distortion reactive power has to be transferred from the network, there is greater stress on the electrical supply network and interference such as flicker . In contrast to the currents of the fundamental oscillation, the currents of the harmonics, which can be divided by three, in the neutral conductor of a three-phase alternating current network do not cancel each other out, but add up. This concerns in the standard European network frequency in particular, the third harmonic at 150 Hz and the ninth harmonic of 450 Hz of 50 Hz. This may, in particular if the neutral conductor with markedly smaller cross section than the external conductor is carried out to an inadmissibly high current load on Neutral conductor come.

The limit values ​​of the harmonic components in percent relative to the nominal voltage in public low-voltage networks (230 V between outer conductor and neutral conductor) and in the medium-voltage network (between any two outer conductors with 10 kV or 20 kV) are defined as:

Measured curve of the AC mains voltage at a transformer station based on a large number of non-linear small consumers. The flattening of the voltage in the area of ​​the maximum values ​​is clearly visible. The sinusoidal curve in light red for comparison

Limit values ​​according to DIN EN 50160

Odd harmonics				Straight harmonics
Not multiples of 3		Multiples of 3
order	% U nominal	order	% U nominal	order	% U nominal
5	6.0%	3	5.0%	2	2.0%
7th	5.0%	9	1.5%	4th	1.0%
11	3.5%	15th	0.5%	6 ≤ n ≤ 24	0.5%
13	3.0%	21st	0.5%
17th	2.0%
19th	1.5%
23	1.5%
25th	1.5%

literature

• Flosdorff, Hilgarth: Electrical energy distribution , Teubner Verlag, 2003, ISBN 3-519-26424-2
• Budeanu, Constantin: Puissances reactives et fictives 1927

Individual evidence

1. ↑ ^{a b c d} DIN 40 110-1: 1994; "Alternating currents - two-wire circuits"
2. ^ R. Gretsch: Harmonics in power supply networks ; Course documents "Voltage quality" at the Technical Academy Esslingen, 2001
3. ↑ DIN EN 61000-3-2, Electromagnetic Compatibility (EMC) - Part 3-2: Limit values ​​for harmonic currents (device input current <16 A per conductor), German version EN 61000-3-2: 2000