Power & Power factor

In simple terms power is the work done in a unit time.
Its SI unit is Watts (W). Basic equation of electric power = P = V*I

Other main expression related to voltage/ current/ power is 'rms'.This means 'root-mean-square'. This is derived by first taking square - then getting the average - and finally taking the square root for a formula representing certain electrical quantity.

Other expressions similar to rms are, average and peak values of an electrical quantity. The rms, peak & average values of a Sine wave is illustarted below.

V      = Vpk*Sin(θ)
Vrms= Vpk/(root 2)


Electric power is viewed as 3 different quantities, but related to each other.

1. Apparent power (S)
2. Active/Real power (P)
3. Reactive power (Q)

where,
S= V*I ;
P= V*I*Cos(φ)    ; φ - phase angle difference between the current and voltage waveforms
Q=V*I*Sin(φ)

It is notable that:
S^2= P^2 + Q^2   ; ^2 - square of that quantity

Technically speaking, Cos(φ) is called the 'power factor' (p.f.) of that particular electrical system.

In a nutshell, active power relates to the actual work done, while reactive power is a loss to the system - BUT it is inevitable.

As we know the power factor is Cos(φ), it's further differentiated into leading power factor and lagging power factor. Leading occurs when the current waveform leads the volatge waveform (in time/angular axis); and lagging p.f. occurs at the opposite occasion.

Here Inductors and Capacitors come into play. Whatever conductor coiled spatially provides an inductance, and whatever two electrical terminals - having an insulator (air, paper etc) in between, provides capacitance.

Both Inductors and capacitors are reactive loads. But pure capacitors offer leading power factor while pure inductors offer lagging power factor to the supply side of the system.

Normally, a power system is inductive. This is because, when it is loaded - winding in transformers, windings in induction motors make the most of the power system. Hence the inductance present in these loads would offer leading power factor to the system.
(Note: Induction motors make up very significant portion of an industrialised power system, which are used in elevators, factories, industrial pumps etc.)

But, it should be noted that - long extra high voltage transmission lines are found to be capacitive; means those offer leading power factor. Similarly it is claimed that unloaded transmission lines have a tendency to show leading power factor.

Image obtained from: www.nationalgrid.com

Technically speaking, how does a transmission line gets capacitance?
1. capacitance between every phase and earth
2. capacitance between each of the phases
3. capacitance between each phases and trees/objects etc.