What is power factor?

What actually is power factor? 

Or, why do we pay for AC power in kVA rather than in kilo Watts?

The answer is, as shown below, that often when we are running AC motors on board the applied voltage and the resulting current are not in phase.

The reason is that with an AC motor, there is a magnetic field that has to be established, increase to a maximum, then go back through zero, twice every mains frequency cycle. The magnetic field has some inertia and we find that it lags behind the voltage by 90 degrees – we call this reactive power, and it’s measured in kVAr (‘r’ for reactive).

(Incidentally a capacitor has a current flow which leads applied voltage, but we rarely, if ever find a leading load on board a superyacht).

Then there is the useful power we are actually delivering to the shaft of the motor to do work.

We know from our Ohm’s law module #3 that ‘Volts x Amps = Power’, but this does not take into account the current which sets up the magnetic field, so in fact from the vector diagram above we have two components of current – ‘in phase’ to develop the ‘active power’ (kW) to the motor shaft, and 90 degrees lagging kVAr reactive power to set up and reverse the magnetic field in the motor. So Volts x Amps is what we call ‘apparent power’, measured in kVA and that’s what we have to buy from the dock supply, because the current the dock supply (or our generators) have to deliver is larger than the real power current we need for our motor to do the work which is required of it.

The final point to appreciate, is that it’s convenient to express the angle ‘φ’, between the applied voltage and current as a cosine ‘cosφ’. So when the angle is zero, cosφ = 1.0. This the special case when all AC loads are non-inductive, like with the big water heaters found on superyachts. Often these can represent the biggest loads on board when at anchor, or on the dock.

[(*) For much more in-depth information and training on generator systems, see module 6 and 9 of our course: Electrical Control Systems for superyacht engineers.]