Real power

The active power P is the electric power which is available for conversion to other services ( such as mechanical, thermal, or chemical ). It appears distinct from the reactive power that is not used for this conversion.

The active power P is expressed in units of watts. At constant voltage and constant current, the active power is the product of voltage U and current I:

For variable values ​​is the active power of the DC value of the instantaneous power p.

For periodic voltages and currents over a period with the period T to transmit:

  • 2.1 Meters
  • 2.2 Single-phase
  • 2.3 Three-phase power 2.3.1 Four-wire circuit with neutral
  • 2.3.2 Three-wire circuit
  • 2.3.3 Symmetric load

Definitions when sinusoidal alternating voltage

An important application is the electrical power supply network, or three-phase network. Only this will be dealt with here. The voltage is a sinusoidal time course; Voltage and current are changing sizes with the same fundamental frequency. For this case there is indication in DIN 40108 and DIN 40110, which must be followed for this product.

Active power for sinusoidal current

Representation with time functions

The sinusoidal variation of the current occurs only when exclusively linear loads are in the network. In phase with resistive loads running voltage and current. When capacitive or inductive loads occur additionally occurs a shift of the phase angle between the course of current and voltage. Is the rms values ​​of voltage and current, the amplitudes and the phase shift angle and the angular frequency

By applying the trigonometric relationship

Follows

And with the use of the effective values

The term includes

The component of the current, which is decisive for the active power is called the active current.

Complex representation

In electrical engineering, it is common for the AC circuit analysis (ie calculation with sinusoidal alternating quantities ) carried out with the help of pointers in the complex plane, as this is much simpler than the calculation with trigonometric functions. To connect the output variables to the complex AC circuit analysis the complex apparent power S is defined that combines active and reactive power in a complex quantity. It is calculated from the product of the complex RMS value of voltage by the complex conjugate rms value of the current.

The apparent power S, ie the magnitude of the complex apparent power S, is the Pythagorean sum of the active and reactive power. The active power P is the real part, the reactive power Q of the imaginary part of the complex apparent power.

Sign questions

The conventions for counting directions of the voltages and currents through producer and consumer Bepfeilung bring it with you, that when energy flow from the producer to the consumer, the active power is positive. The picture of the time course also shows negative values ​​of p; then energy is fed back. The active power is thus less than the apparent power; but she remains positive.

In networks with multiple sources and loads can reverse the direction of the energy flow not only for fractions of a period between network segments. In view of the power used to describe this by sign inversion of the active power, so that P can have values ​​<0 sense.

Active power at nichtsinusförmigem current

When the voltage is sinusoidal, the power but not the equation is valid under the proviso that I and φ parameters of the fundamental wave of the current is. Harmonics are not included in P.

Measurements in the power supply network

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. The suitable for this purpose electro-mechanical measuring system has been replaced by electronic transmitter.

Each meter has a measuring range must not be exceeded, otherwise no margin of error is guaranteed. In addition, part of the power meter nominal values ​​of voltage and current, which may be exceeded only slightly according to the manufacturer's instructions, because otherwise the device will be damaged. This type of overload may occur entirely without exceeding the measuring range!

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 P is negative, but not a negative reading can be issued, you can help by conscious reversal of the direction in the voltage path (or rung ). At laboratory equipment, terminals on the input side is often marked with a star; Devices for permanent installation, wear a Terminal numbering according to DIN 43807; Examples see Fig.

Each power meter has a self-consumption

  • In the current path by a voltage drop (as in the current meter ),
  • The voltage circuit by a current consumption (as in the voltage measuring device).

This is to distinguish the real meter between producing and consuming active power.

Single-phase

There are two ways to connect the power meter, see related images. However, none of the circuits detects the producer or consumer - active power, but is measured

  • In the upper circuit generator voltage times current consumer,
  • In the lower circuit load voltage times current generator.

In the upper circuit preferably used the cost of the energy consumption of the meter shall be borne

  • As far as the voltage path originating by the producer,
  • As far as the current path originating by the consumer.

Three-phase power

Four-wire circuit with neutral

The most comprehensive case, the four-wire circuit with neutral and three phase conductors, as with = 230 V = 400 V and is common in the low-voltage network, in connection with any load. Any supposed to mean here: In the three phases currents with different amplitudes and different phase shifts can flow to the respective reference voltage. Then

This is measurable with three power meters or a combination device.

Three-wire circuit

Is due to the missing neutral conductor in a three -wire circuit

With

And

Shall

Where the last summand and thus disappears. In the three-wire circuit with any load so rich two power meter, if you operate in Aron circuit according to the last equation.

With

And,

Where = angle between and

And = angle between and

Information on this topic:

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.

In the three-wire circuit is to the neutral potential through a star point as shown in figure to create artificially with two resistors that are just as large as the resistance of the voltage circuit in the power meter.

Other names

All figures are in line with DIN 40110-1:1994.

Trigonometry Energy flow (ecology) Wattmeter Capacitor voltage transformer Electrical reactance
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