Reactive Power and Compensation Solution Basics For Students

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Why we don’t like reactive power

The total power, the so-called apparent power, of a transmission network is composed of active and reactive power (Figure 1). While the power consumers connected into supply transform the active power into active energy, the reactive energy pertaining to the reactive power is not consumed. The reactive power at the consumer side is merely used for building up a magnetic field, for example, for operating electric motors, pumps, or transformers.

Reactive Power and Compensation Solutions Basics For Students
Reactive Power and Compensation Solutions Basics For Students (photo credit:

Reactive power is generated when power is drawn from the supply network and then fed back into the network with a time delay.

This way it oscillates between consumer and generator. This constitutes an additional load on the network and requires greater dimensioning in order to take up the oscillating reactive power in addition to the active power made available. As a consequence, less active power can be transported.

Composition of the total power of a transmission grid
Figure 1 – Composition of the total power of a transmission grid

Reactive power has zero average value because it pulsates up and down, averaging to zero. Reactive power is measured as the maximum of the pulsating power over a cycle. It can be positive or negative, depending on whether current peaks before or after voltage.

By convention, reactive power, like real power, is positive when it is “supplied” and negative when it is “consumed”. Consuming reactive power lowers voltage magnitudes, while supplying reactive power increases voltage magnitudes.

Solution with compensation //

With a reactive power compensation system with power capacitors directly connected to the low voltage network and close to the power consumer, transmission facilities can be relieved as the reactive power is no longer supplied from the network but provided by the capacitors (Figure 2).

Principle of reactive power compensation using low voltage power capacitors
Figure 2 – Principle of reactive power compensation using low voltage power capacitors

Transmission losses and energy consumption are reduced and expensive expansions become unnecessary as the same equipment can be used to transmit more active power owing to reactive power compensation.

Determination of capacitor power

A system with the installed active power P is to be compensated from a power factor cos φ1 to a power factor cos φ2. The capacitor power necessary for this compensation is calculated as follows:

Qc = P · (tan φ1 – tan φ2)

Compensation reduces the transmitted apparent power S (see Figure 3). Ohmic transmission losses decrease by the square of the currents.

Power diagram for a non-compensated (1) and a compensated (2) installation
Figure 3 – Power diagram for a non-compensated (1) and a compensated (2) installation

Reactive power estimate

For industrial plants that are still in a configuring stage, it can be assumed by approximation that the reactive power consumers are primarily AC induction motors working with an average power factor cos φ ≥ 0.7. For compensation to cos φ = 0.9, a capacitor power of approximately 50 % of the active power is required:

Qc = 0.5 · P

In infrastructural projects (offices, schools, etc.), the following applies:

Qc = 0.1 to 0.2 · P

Calculation of the reactive power

(Based on the electricity bill)

For installations which are already running, the required capacitor power can be determined by measuring. If active and reactive work meters are available, the demand of capacitor power can be taken from the monthly electricity bill.

tan φ = reactive work / active work

For identical meter operating times in the measurement of reactive and active work //

tan φ = reactive power Q / active power P with
tan φ = √(1 – cos2 φ) / cos φ

The compensation power Qc matching the active power P can be calculated for a desired value of cos φ2.

Qc  = Q1 – Q2 = P · F

In this case F = tan φ1 – tan φ2

To simplify the calculation of Qc, Table 1 states the conversion factors F when a measured cos φ1 is to be compensated in order to attain a power factor cos φ2 in operation.

Conversion factors F for phase angle adjustments
Table 1 – Conversion factors F for phase angle adjustments

3 main types of compensation //

Capacitors can be used for single, group, and central compensation. These types of compensation will be introduced in the following //

Single compensation

In single compensation, the capacitors are directly connected to the terminals of the individual power consumers and switched on together with them via a common switching device. Here, the capacitor power must be precisely adjusted to the respective consumers. Single compensation is frequently used for induction motors (Figure 4).

Single compensation
Figure 4 – Single compensation

Single compensation is economically favourable for:

  • Large individual power consumers
  • Constant power demand
  • Long ON times
Here, load is taken off the feeder lines to the power consumers. A continuous adjustment of the capacitor power to its reactive power demand is not possible, however.

Group compensation

With group compensation, each compensation device is assigned to a consumer group. Such a consumer group may consist of motors or discharge lamps, for example, which are connected into supply together through a contactor or switch. In this case, special switching devices for connecting the capacitors are not required either (Figure 5).

Group compensation
Figure 5 – Group compensation

Group compensation has the same advantages and disadvantages as single compensation.

Central compensation

Reactive power control units are used for central compensation, which are directly assigned to a switchgear unit, distribution board, or sub-distribution board and centrally installed there. Control units contain switchable capacitor branch circuits and a controller which acquires the reactive power present at the feed-in location.

Central compensation
Figure 6 – Central compensation

If it deviates from the set-point, the controller switches the capacitors on or off step by step via contactors.

The capacitor power is chosen in such a way that the entire installation reaches the desired cos φ (Figure 6). Central compensation is recommended in case of:

  • Many small power consumers connected into supply
  • Different power demands and varying ON times of the power consumers

References //

  • Planning of Electric Power Distribution by SIEMENS
  • Principles for Efficient and Reliable Reactive Power Supply and Consumption by Federal Energy Regulatory Commission

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About Author


Edvard Csanyi

Edvard - Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry fascilities. Professional in AutoCAD programming. Present on