I am struggling to understand what’s behind each electrical parameter.

# Could you explain what kW, kVAR, kVA and PF really mean?

In AC circuit analysis, both voltage and current vary sinusoidally with time. The presence of reactive elements like inductors and capacitors directly impact the current wave by shifting it with respect to voltage wave (φ), see below.

Power is the rate at which energy is consumed by an electrical load or produced by a generator, and the value of instantaneous power is obtained by multiplying instantaneous voltage with instantaneous current.

Instantaneous power varies with time sinusoidally, so we generally look at the average power within a given time frame, for example the period of the sinusoidal wave. The average power is calculated as:

P = Vrms x Irms x cosφ (W)

*with*

*Vrms = RMS Voltage = Vm/√2*

*Irms = RMS Current = Im/√2*

*Vm and Im the maximum values of the sinusoidal voltage and current*

This average power formula is the basis to calculate the power consumed by the load over longer periods, for example your monthly electric energy bills are based on this power calculation. Note that the average power is also called ‘Real’, ‘True” or ‘Active’ power within the industry, and is measured in Watts (W).

In ideal inductors and capacitors, voltages are respectively 90° ahead and behind the phase of the current, meaning that ideal inductors and capacitors do not, on average, take active power from the circuit (cosφ=0). Current is instead used to charge a capacitor, or to create the magnetic field around a coil, as opposed to creating heat or lifting loads.

In real-world environments where resistors, inductors and capacitors are all combined within complex machines, the power that is wasted and not used to do work on the load is represented by the Reactive Power, calculated as:

Reactive Power = Vrms x Irms x sinφ (VAR)

Note that the Reactive Power is also called ‘Wattless’ power within the industry, and is measured in VAR (VoltAmpereReactive).

Apparent power represents the power that is supplied to the circuit (voltage multiplied by all the current that flows in it), and is measured in volt-amperes (VA). Apparent Power is calculated as follows:

Apparent power = Vrms x Irms (VA)

The power factor is defined as the ratio between Active Power and Apparent Power:

Power Factor = Active Power / Apparent Power

The relationship between Apparent Power (S), Active Power § and Reactive Power (Q) is often expressed as a vector-sum definition, which shows how each of them evolves based on whether the electrical load is resistive, inductive or capacitive.

There is one main difference between single-phase and three-phase electrical systems. The instantaneous single phase power is sinusoidal. In a balanced three-phase system, each phase instantaneous power is pulsating, but the three pulsating power waves are 120 degrees displaced from each other. At such, at any instant of time the total of these three instantaneous power waves is a constant which is 3 x Vrms x Irms x cosφ. As a result, the total power consumed in a three-phase balanced system is not pulsating, which is a very desirable pattern for rotating machines requiring high-starting torque.

More theory can be found at [1].