In recent times, we come across very often the question, why is the power factor 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. However, increasingly, these differences in power factor readings are really differences between power factor. Λ or PF and displacement power factor φ or DPF. Very often, there are compared, however, they are, in effect, two different measurement values and both of them are valid and make sense !

Consumer load is converting in dependency of the efficiency electrical energy to work. This electrical load is shown in a circuit diagram as resistive. 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 diagram these loads are shown as inductance and capacitance.

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

Parallel to linear loads, there are also nonlinear loads, e.g. rectifiers, computers, UPS systems, motor drives 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 hence depends on their values.

When a non linear load is connected to an AC voltage source with pure sine wave, then the current, which is caused by this load, has differing wave forms. When this current waveform is analyses by Fourier analysis, then you get a summation of sine waves with multiple frequencies of the fundamental wave, different phase shifts and different amplitudes. 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 caused by the multiplication between the current harmonics and the voltage, is called deformation reactive power.

The apparent power is the product of the RMS values of current and voltage. Apparent power is an important value for the rating of electric power distribution. Apparent power an also be calculated by this formula:

- S = apparent power [ kVA ]
- P = active power [ kW ]
- Q = displacement reactive power [ kVar ]
- D = deformation reactive power [ kVar ]

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 Λ or PF.

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 cos φ, 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 under these conditions:

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 cos φ and not the Power Factor Λ.

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

A simple example for this is:

- P = 100 kW
- Q = 50 kVar
- D = 50 kVar
- Λ ( PF ) = 0.82
- cos φ ( DPF ) = 0.89

A regulator, which is using as target Λ ( PF ) = 1.00 will switch 50 kVar and will reach cos φ ( DPF ) = 0.98 capacitive and Λ ( PF ) = 0.89 inductive.

A regulator, which is using as target Λ ( PF ) = 1.00 will switch 69 kVar and will reach cos φ ( DPF ) = 0.98 capacitive and Λ ( PF ) = 0.88 inductive

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

This example shows that it is wise to use FRANKE Elektrotechnik reactive power regulators (power factor control relays), which are using displacement reactive power Factor Λ ( PF ) is consequentially. It is intelligible, when utility companies want to reach Power Factor Λ ( PF ) = 1.000 To reduce the deformation reactive power, which is responsible for the difference between Λ ( PF ) and cos φ ( DPF ), harmonic are needed.