In the recent years, there is very often this question, as to why the powerfactor which is shown by a power factor control relay different from the power-factor which is shown by the utility meter.

For this effect, there are different reasons possible, e.g. measuring on different places. Very often, these differences in power-factor are differences between power-factor ? or PF and displacement power-factor cosf or DPF.

Very often, there are compared two different measuring values and both of them are making sense.

ACTIVE POWER, REACTIVE POWER, APPARENT POWER
Consumer load is converting depending on the efficiency of the electrical energy to work. This electrical load is shown in a circuit diagram as a resistor. In practical use, there is parallel to this resistive load or active load some other load, which is called reactive load.

Reactive load is used to build up electric and magnetic fields. In a circuit diagrams these loads are shown as inductance and capacitance. Inductances are causing a lagging of the current, because current flow is only possible after the voltage has built up the magnetic field. Capacitances are causing a leading current, because the current flow has to charge the capacitance. These characteristics are causing a displacement between voltage and current, when inductances or capacitances are in an electric circuit.

Resistive, capacitive and inductive load are linear loads. In a coordinate system with voltage and current axis, you can see the linear load as a line. The current depends from voltage with a fix factor.

Parallel to linear loads, there are also non-linear loads, e.g. rectifiers, computers, UPS-systems, motordrives or transformers which are used in saturation. In a coordinate system with voltage and current axis, you can see non-linear loads as curves with breaks and jumps. The relation between voltage and current depends on their values.

When a non-linear load is connected to an AC-voltage source with pure sinewave, then the current which is caused by this load has differing wave form.

When this current wave-form is analysed by Fourier-analysis, then you get a summation of sinewaves with multiple frequencies of the fundamental wave, different phaseshifts and different amplitude. These wave forms are called harmonics.

For the calculation of the power, these wave forms of all the voltages and current waves must be multiplied. Real power is only created by the parts of the voltages and currents with the same frequency. The value of the real power depends on the amplitude and the phase-shift of the two waves. In systems with (almost) sine-wave voltage, like it is in the real grid, only the fundamental wave of the current is important for calculation of real power.

The reactive voltage, which is caused by the phase-shift between voltage and fundamental wave of the current, is called displacement reactive power. The reactive power, which is cause by the multiplication between the current harmonics and the voltage, is called deformation reactive power.


 S= apparent power (kVA)
P= active power (kW)
Q= displacement reactive power (kvar)
D= deformation reactive power (kvar)

COMPARISON POWER FACTOR ? (PF) - DISPLACEMENT POWER FACTOR COSf (DPF)
The power factor shows which part of the apparent power, which is loading the distribution, is the active or real power. This factor is called Power Factor with the sign ? or PF.

The formula for calculating the Power Factor is:

The mean value for Power Factor can be calculated by using this formula:

This calculation is used in utility meters for calculating the mean value of Power Factor in a period of time. Because reactive power compensation with capacitors cannot compensate deformation reactive power and because deformation reactive power was not so important in the past, the cosf, which is calculated from the phase-shift of the fundamental waves of current and voltage, is used instead of the Power Factor.

This value can be calculated from the power with the following formula:

The deformation reactive power is not used in this calculation.

REACTIVE POWER COMPENSATION
Reactive power compensation is used to use the capacity of electric distribution systems in the optimal way. This saves energy and it saves investment costs for the grid. A common used way for reactive power compensation is the compensation of displacement reactive power by using capacitors.

Very often, these capacitors are controlled by a reactive power regulator. To get a correct function of this regulator, then it is necessary that the controlled variable is the displacement reactive power, because switching capacitors has only a direct influence to this. The target for compensation has to be the cosf and not the Power Factor ?.

If a reactive power regulator is compensating to Power Factor ?, then you will get problems like overcompensation of the displacement reactive power or hunting.

A simple example for this is:
P = 100kW; Q = 50kvar; D = 50kvar; cosf (DPF) = 0.89 ? (PF) = 0.82

A regulator, which is using target cosf (DPF) = 0.89, will switch 50kvar, will reach cosf (DPF) = 1.00 and ? (PF) = 0.89

A regulator, which is using ? (PF) = 0.82, will switch 69kvar, will reach cosf (DPF) = 0.98 and ? (PF) = 0.88.

This example is showing, that by using target ? (PF) more installed capacitors are necessary and a worse result of compensation is achieved compared by using cosf (DPF) as target.

This example shows that it's wise to use BELUK reactive power regulators (power factor control relays), which are using displacement reactive power as control variable. The showing of cosf (DPF) instead of ? (PF) is also possible on these devices.

It's intelligible, when utility companies want to reach Power Factor ? (PF) = 1.000. To reduce the deformation reactive power, which is responsible for the difference between ? (PF) and cosf (DPF), harmonic filters are needed.

[Michael Reith is General Manager, BELUK GmbH, Germany]

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