Reactive power
Reactive power is a term of electrical engineering. In the electric power grid energy to be transferred from the producer to the consumer. In single phase or three-phase alternating current ( phase current) operated networks often flows more energy between the generator ( power plant) and an electrical load ( for example, electric machine ), as implemented in the same number of periods in the consumer. This additional energy per unit of time which does not contributes to the active power ( " actual output " ), is generally undesirable and is known as reactive power.
- 5.1 Meters
- 5.2 Single-phase
- 5.3 Three -phase network 5.3.1 Four-wire circuit with neutral
- 5.3.2 Three-wire circuit
- 5.3.3 Symmetric load
Definitions
In direct quantities defining the electrical power voltage V and current I.
When changing quantities are defined in accordance with the instantaneous value of the power of the instantaneous values of the voltage u ( t) and current i ( t). Instead of the instantaneous values are used as possible by averaging (integration) obtained, in the steady state constant terms:
- The effective values of voltage and current
- Three power ratings the effective power
- The apparent power
- The total reactive power
These definitions are general in accordance with DIN 40110-1 ( " AC quantities ").
The unit of power is the watt ( symbol ' W)., Primarily for the apparent power the volt-ampere ( symbol 'VA ) and for the reactive power, the Var ( symbol' var ) uses - In the electric power industry are in accordance with the same standard - even in DIN 1301-2 ( "Units") this applies 1 var = 1 VA = 1 W.
Another indication in DIN 40108 and DIN 40110-2 must be observed for the grid.
Sinusoidal voltages and currents
For use in the power grid are u (t ) and i ( t) change sizes with the same fundamental frequency. If they also are both sinusoidal, it may be moved to their phase angles around φ, then:
Where Q is called the displacement of reactive power or when no confusion is possible, only reactive power with | Q | = Qtot. One counts
Cause
With resistive load voltage and current have a phase gradient, the phase shift angle is φ = 0, the total energy supplied by the generator is converted to the consumer (eg as thermal or chemical energy).
In an inductive load (e.g., inductor, transformer, asynchronous ) is used by the generator power supplied to establish the magnetic field. The energy is first stored in the magnetic field, but with the periodic change in the sign of the voltage, the field is reduced again and the energy fed back into the grid. In a purely inductive load, the current of the voltage by a quarter period continues to run the phase shift angle is 90 °. The product of u and I is alternately positive and negative, the frequency of the output is twice the fundamental frequency. If the power p is negative, it means that energy is returned to the grid. The power fluctuates around its average height is zero, which indicates that energy in the grid only shuttles back and forth. However, it produces "blind " current flow. For this case, it follows
The same applies to capacitive loads (eg motors, induction motors, underground cables ), but instead of producing the magnetic an electric field which, although shifts the phase in the other direction, but otherwise the same supplies: The for assembly and disassembly of the field per transported period energy represents reactive power
The reactive power occurs generally in all coupled to the power components and the management network itself. Since in a circuit in principle, the three properties passive linear capacitance, inductance and ohmic resistance are either always present in discrete devices or as a " coating line ", is located in an AC power supply almost always before a reactive power load.
Exposure to reactive power
Follow
The power p is obtained from the mains power supply when the voltage and current have the same sign. If the signs are opposite, the power is fed back again. The feedback causes a reactive power and a reactive power, which increases with increasing reactive power requirement of the consumer. To counteract the warming of the line, larger conductor cross-sections in the supply lines as well as larger generators and transformers are needed. Heavy electrical equipment in the industry have to pay in addition to the related active energy and reactive energy for their reference. Small and private consumers, as opposed to the industry relate mainly electricity for heat generation, causing low reactive power load and are therefore and shall be exempt because of the high costs for their acquisition of the costs, and find the latter in the price of real energy (expressed in kWh) again. - In addition cause reactive load changes much larger voltage changes in the network, since the internal resistance of generators and transformers is predominantly inductive.
Underground cables provide due to the small spacing of the wires to each other at a given length, a large capacitive load represents the 11,5 km long 380 kV Transversal Berlin has a capacity of 2.2uF. To this tranship at 50 Hz, power factor must be applied of 277 A, which corresponds to a reactive power of 110 Mvar. Therefore, the reasonable maximum cable length is limited to about 70 km.
Countermeasures
Suitable measures therefore try the big energy consumers to keep the reactive power demand as low as possible. The inductive reactive power demand of an asynchronous machine can be compensated by a capacitor bank, synchronous machine or a special converter ( power factor correction ), which is referred to as reactive power compensation. The energy required for the generation of the magnetic field oscillates then no longer in the supply mains to the generator, but only between asynchronous and synchronous condenser battery or machine. Thus, the resulting current that the drive takes from the network decreases. The three curves shown are to illustrate this:
For drives with asynchronous reactive power demand is defined by the engine and largely independent of the mechanical drive power. The compensation with the help of a capacitor bank, synchronous machine or a special converter ( power factor correction ) is possible. In systems with variable reactive power demand, it is necessary that instead of a constant reactive power compensation device ( capacitor ), a controlled expansion joint is used.
The reactive power within a regional power grid can be compensated by a phase shifter.
The parallel circuit of capacitance and inductance for this purpose can also be viewed as a resonant circuit, with appropriate design of the 50 Hz and having its resonant frequency reactive current is blocked. An example is shown under reactive power compensation.
Non-sinusoidal currents
With sinusoidal voltage and non-sinusoidal currents can occur. This is for all non -linear loads, such as converters in power electronics or inductors, the magnetically saturate, the case. Non-sinusoidal currents can occur without power factor correction and power adapters. See also current flow angle.
In such a current is a sum of sinusoidal components of different frequency; it includes not only the fundamental component even harmonic components. If we denote by the rms value of the fundamental, with, ... the effective values of the harmonics, then for the active power
Only the parameters of the fundamental wave of the current is of importance; Harmonics do not affect P. In contrast, in the apparent and reactive power go all harmonics in the result.
The total reactive power
A shift of reactive power in the fundamental frequency
And a distortion power in the harmonics
Results
The mechanical reactive power meter work such as active power meter and record it ( at least yet sinusoidal voltage) Q1, but not Qtot.
Multiphase system
In the first picture above it is evident that a sinusoidal voltage and resistive load, the instantaneous power although it has no negative instantaneous values , but fluctuates. It thus occurs on average ( real power ), and a power fluctuation which in this case is, however, no reactive power.
In the transition to the balanced three- phase system, the active power tripled. Because of the elimination of the return conductor ( there are only 3 required instead of 6 conductor ) increase the feed losses only by a factor of 1.5. This saving of feed losses can be explained by the fact that in the symmetric -loaded three-phase system, the total power is constant in time, so no power swings averaging occurs.
Case of unbalanced load occur in the neutral conductor to additional losses, they are the time course of total power superimposed as swinging. This effect can be described by unbalance reactive power.
Measurements in the power supply network
This section is limited to the case that the voltage and current are sinusoidal.
Meters
A power meter having a current path, and a voltage path. He multiplies the instantaneous values of voltage and current, averaged over the instantaneous values of the product and is therefore in accordance with the definition of active power as an active energy meter. For power measurement, the device is also suitable when the voltage at the voltage path is shifted by 90 ° relative to the voltage across the load, and that
- When I lags compared to U, then USpg.pfad lagging,
- If I precedes over U, then USpg.pfad voreilend.
The picture shows the voltage to be applied to the voltage path as dashed pointer in the complex plane.
If both voltages have the same rms value is measured
In the single-phase circuit is an art to the phase shift required, such as the bumblebee circuit which generates two lossy coil and a resistor at a fixed frequency, a shift of 90 °.
Rotate 90 ° -shifted voltages or in vector representation rotated by 90 ° voltages are directly available in the undistorted three-phase network with neutral. For example, is lagging by 90 °. However, it is. A resistor or a voltage converter, the voltage can however be reduced by a factor of; depending on the circumstances, the result can also be corrected by calculation.
To sign - correct measurement is to ensure proper connection, which is to be specified by proper circuit diagrams. For the control case, within this article, in accordance with DIN 43807, consistently adhered to:
- If positive energy flow in the current path from left to right
- And positive energy flow in the voltage path from bottom to top.
If the measurement leads to a negative value, but not a negative reading can be issued, you can help yourself through conscious reversal of the direction in the voltage path (or rung ). On further explanations under the heading of active power reference is made.
Single-phase
The conventional circuit corresponding to the circuit for active power measurement, except that the current must be shifted by the voltage circuit relative to the voltage by 90 °.
Three-phase network
Four-wire circuit with neutral
The most comprehensive case, the four-wire circuit with neutral and three phase conductors, as he = 230 V or 400 V = U12 is common in the low-voltage network with U1N, in connection with any load. Any supposed to mean here: In the three phases currents with different amplitudes and different phase shift angles can flow to the respective reference voltage. Thus, the reactive power can be measured with three power meters or a combination device. The equivalent circuit for the measurement of inductive reactive power is the image. What is to be measured, namely
Is measurable with the lagging by 90 ° voltages than
Three-wire circuit
Is due to the missing neutral conductor in a three -wire circuit
As the article for the active power is shown, you can see a stream here, count out, and it comes with two power meters in from Aron. The accompanying picture shows the measurement circuits for active and reactive power. Both are suitable for any load. The bill for the active power results
To connect the trailing 90 ° tensions in the three-wire circuit, the neutral potential through a star point as shown in figure is artificially creating a resistance that is equal to the resistance of the voltage circuit in the power meters. Since the rotated voltages are smaller by a factor here, the measured values must be increased by the factor ( with voltage converter or by calculation ), and it results in
Where = angle between and
And = angle between and.
The individual scores of the two instruments have no intuitive meaning, not even in sign. If it is less than 30 °, the second term is negative; a correct connection for real in sign measuring is required.
Balanced load
For symmetrical loads, use only enough of a power meter for the power reference by one of the outer conductor. The total power is of three times.
It is with the rotated voltage