Reactive current

The terms reactive current and active current are used in AC technology , especially in connection with the transmission of electrical energy . While the active current stands for the electrical work or the transport of electrical energy, which is converted into mechanical, thermal, chemical or other electrical energy by the consumer, the reactive current is not involved. The reactive current stands for energy that is transported but not converted in the consumer, see reactive power . This reactive current means an additional load for the lines and transformers and is generally undesirable.

For consumers with the elementary behavior of an ohmic resistance , the instantaneous value of the current intensity is proportional to the instantaneous value of the electrical voltage . This behavior is often not given in practice: While the electrical alternating voltage as an impressed voltage is almost always almost sinusoidal, the alternating current strength can be shifted over time or changed in shape ( distorted ). ${\displaystyle u}$ ${\displaystyle i}$

The sinusoidal current strength here can be thought of as a composite of an active  current strength (curve 1) and a reactive  current strength (curve 2) ${\displaystyle i}$ ${\displaystyle i_{p}}$ ${\displaystyle i_{q}}$

A description model is the division of the current intensity into two components, one of which is selected as the active current intensity proportional to the voltage . The other component, the difference to the total current, is the reactive current . ${\displaystyle i_{p}}$ ${\displaystyle i_{q}}$

${\displaystyle u\,\sim i_{p}}$

${\displaystyle i_{q}=i-i_{p}}$   or for the effective value . ${\displaystyle I_{q}={\sqrt {I^{2}-I_{p}^{2}}}}$

Are triggers of reactive current

• non-linear components , a distortion cause ( distortion reactive current ), and
• capacitive or inductive components that cause a phase shift between voltage and current ( displacement reactive current ).

Sinusoidal current and voltage curve

With sinusoidal voltage with a non-proportional sinusoidal current strength, there are times when energy is fed back. This can be seen from the fact that the performance is  negative ${\displaystyle u}$ ${\displaystyle i}$ ${\displaystyle p}$

If in a linear consumers the instantaneous values of the sinusoidal sizes and not proportional to each other, the size relative to the other is in their phase angle shifted. The only active current that contributes to energy transport is that current component that corresponds to the voltage in the phase angle. The reactive current is that current component which is shifted by 90 ° to the sinusoidal voltage. Furthermore, a distinction is made between capacitive reactive current, which leads the voltage by 90 °, and inductive reactive current, which lags the voltage by 90 °, depending on whether the reactive current is generated by capacities (capacitors or line capacitance) or inductances (inductive loads or line inductance). ${\displaystyle u}$ ${\displaystyle i}$ ${\displaystyle u={\hat {u}}\sin \omega t}$

With a phase shift angle , the current intensity can be split into ${\displaystyle \varphi }$

${\displaystyle i={\hat {\imath }}\sin(\omega t-\varphi )={\hat {\imath }}\sin \omega t\cos \varphi -{\hat {\imath }}\cos \omega t\sin \varphi =i_{p}+i_{q}\ .}$

The rms value of the current can be split into the rms value of the active current ${\displaystyle I}$

${\displaystyle I_{p}=I\cdot |{\cos \varphi }|}$

and the effective value of the reactive current strength

${\displaystyle I_{q}=I\cdot |{\sin \varphi }|\ .}$

Associated with this are the terms active power

${\displaystyle P=U\,I\cdot \cos \varphi \ ,}$

Shift reactive power (if no confusion is possible, simply reactive power)

${\displaystyle Q=U\,I\cdot \sin \varphi }$

and total reactive power

${\displaystyle Q_{\text{tot}}=U\,I_{q}={\sqrt {S^{2}-P^{2}}}=|Q|\ .}$

Stands for the apparent power . ${\displaystyle S=U\,I}$

Active current without accompanying reactive current is created, for example, by conventional heating devices. In general, active current arises with all consumers that have an ohmic component in their electrical resistance . In the low-voltage network , due to the line inductance and many inductive loads (e.g. motors , transformers , ballasts , induction ovens , i.e. coils of any kind), a considerable inductive reactive current can occur, which is required to generate magnetic fields that are built up and reduced in rhythm with the alternating voltage; the reactive current thus stands for the transport of energy that commutes between the producer and consumer. This current causes a power loss on the lines at their ohmic resistors.

For drives with asynchronous machines, the reactive power requirement is defined by the motor and largely independent of the mechanical drive power. Since the reactive current increases the current in the power grid unnecessarily, the energy supply companies charge large customers for the reactive work ("reactive power consumption") caused by the reactive current. Therefore, the bulk buyers operate devices for reactive current compensation . These are primarily capacitors that take up a capacitive reactive current which is directed in the opposite direction to the usually inductive reactive current of the consumer and which approximately cancels it.

In the high-voltage network , capacitive reactive current occurs due to the capacitance of the lines, but this is largely compensated for in the low-voltage network. In underground cables, however, the reactive current component has a limiting effect on the realizable cable length.

Non-sinusoidal current curve

In the case of non-sinusoidal or "distorted" alternating current, which occurs with non-linear loads such as power converters despite sinusoidal voltage, the description model must be extended to the sinusoidal fundamental and its harmonics with integer multiples of the mains frequency. The current components with harmonics are collectively referred to as harmonic current or distortion current. With sinusoidal mains voltage, they also do not cause any energy transfer on average over time. This means that the distortion current is another form of reactive current. ${\displaystyle i_{d}}$

If the current component with the frequency -fold higher than the basic frequency is denoted by, the result is ${\displaystyle n}$ ${\displaystyle i_{n}}$

${\displaystyle u=u_{1}}$   (because only fundamental is present)

${\displaystyle i_{d}=i-i_{1}}$   or for the effective value ${\displaystyle I_{d}={\sqrt {I^{2}-I_{1}^{2}}}={\sqrt {I_{2}^{2}+I_{3}^{2}+\cdots }}\ .}$

The effective value of the total alternating current strength results from the Pythagorean sum of the fundamental oscillation current strength and harmonic current strengths

${\displaystyle I={\sqrt {I_{1}^{2}+I_{2}^{2}+I_{3}^{2}+\cdots }}={\sqrt {\sum _{n=1}^{\infty }I_{n}^{2}}}\ .}$

Only the active component of the fundamental oscillation current is of the total current intensity

${\displaystyle i_{p1}=i-i_{q1}-i_{d}}$

in the real power,

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

In addition to the reactive power of the fundamental oscillation

${\displaystyle Q_{1}=U\,I_{1}\cdot \sin \varphi _{1}}$

the distortion current causes the distortion reactive power

${\displaystyle Q_{d}=U\,I_{d}}$

and together the total reactive power

${\displaystyle Q_{\text{tot}}={\sqrt {Q_{1}^{2}+Q_{d}^{2}}}={\sqrt {S^{2}-P^{2}}}\ .}$

Non-sinusoidal voltage curve

In this case, which is less important for electrical energy transmission but is significant for switched-mode power supplies, the following applies to the entire active current

${\displaystyle I_{p}={\sqrt {\sum _{n=1}^{\infty }I_{pn}^{2}}}}$

and the total reactive current

${\displaystyle I_{q}={\sqrt {\sum _{n=1}^{\infty }I_{qn}^{2}}}={\sqrt {I^{2}-I_{p}^{2}}}}$

Measurement of active and reactive current

In the case of sinusoidal current, the controlled rectifier is suitable for measuring the active current (in the usual range ) , the arithmetically averaged output voltage of which is proportional to ${\displaystyle -\pi /2<\varphi <\pi /2}$

${\displaystyle I\cdot \cos \varphi }$

is. In addition to the current, the measuring device must be supplied with the reference voltage. If the current is distorted, the result will be influenced by odd harmonics.

With a voltage shifted by + 90 ° or -90 ° to the reference voltage (selected so that the averaged output voltage becomes positive), the corresponding

${\displaystyle I\cdot |{\sin \varphi }|}$

measurable.

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The reactive current strength is referred to as being orthogonal to the voltage and the active current strength . The orthogonality of the functions and is the background for the Pythagorean sum of the rms values . ${\displaystyle i_{q}}$ ${\displaystyle u}$ ${\displaystyle i_{p}}$ ${\displaystyle i_{p}(t)}$ ${\displaystyle i_{q}(t)}$ ${\displaystyle I^{2}=I_{p}^{2}+I_{q}^{2}}$

All components of the current strength that meet the condition are generally referred to as orthogonal to the voltage . ${\displaystyle u}$ ${\displaystyle i_{k}}$ ${\displaystyle \int \limits _{0}^{T}u\cdot i_{k}\,\mathrm {d} t=0}$

• Example 1: The current component is too orthogonal . ${\displaystyle u={\hat {u}}_{1}\sin \omega t}$ ${\displaystyle i_{1}={\hat {\imath }}_{1}\cos \omega t}$

The two quantities are sinusoidal and of the same frequency, but differ in the phase angle by 90 °. This example covers the displacement reactive current.

• Example 2: The current components are too orthogonal if , both integer ≥ 1. ${\displaystyle u={\hat {u}}_{m}\sin m\omega t}$ ${\displaystyle i_{n}={\hat {\imath }}_{n}\sin(n\omega t+\varphi _{n})}$ ${\displaystyle m\neq n}$

The two quantities are sinusoidal, but differ in frequency by a rational factor ≠ 1. This example covers the distortion reactive current.

Individual evidence

1. ↑ ^{a b c d} DIN 40110-1 (1994): "Alternating current quantities"