What is power factor

In layman’s terms, the power factor is a numerical expression of how efficiently an electric device uses electricity. Put even more simply, it is a number without a unit (dimensionless), usually but not necessarily between 0 and 1, and the lower it is, the worse is efficiency and consequently the higher are any costs associated with improving it. Lastly, power factor is, well a factor (no pun intended) only in alternating current (AC) systems, whereas in direct current (DC) it is always 1 and doesn’t need to be calculated.

However, as with anything related to electric phenomena, things are a bit more complex. For example, the power factor can in special circumstances be a negative number, meaning that the power flows from the load (consumer) to the source (producer) – more or less efficiently.

Next, low power factor of a number of large loads can lead to significant stresses in poorly dimensioned and overloaded installations and may even cause failures. Improving (raising) the power factor is therefore essential for reliable operation, although it is most often done to lower the energy costs.

But, what underlying phenomena and mechanisms contribute or in other words necessitate the calculation of a power factor? Since the answer is somewhat complex, it is prudent to first take a look at quantities that are intimately connected with the power factor – the active (P), reactive (Q) and apparent (S) power.

What is active power (P)?

Active power (P) is useful electric power that does actual work; power an electric motor within its specifications, raise the temperature of a heater to a desired level, power your office computer and lighting etc. It is expressed in watts (W) or more commonly in kilowatts (kW) and megawatts (MW).

What is reactive power (Q)?

Reactive power (Q) on the other hand is power that is transferred through the system, but doesn’t do any useful work like the active power. It oscillates between the load and the source each cycle due to the energy stored, in one form or the other (inductive, capacitive, non-linear loads), in the system. Despite this “parasitic” nature, reactive power is (Q) intractably linked to the way modern electric machinery (motors, transformers etc.) works and can be at best mitigated, but not completely eliminated.

This brings us to the phenomena that causes reactive power (Q) – phase shift between voltage and current. In an ideal situation – i.e. if the load is of purely resistive nature (e.g. large resistor without any parasitic inductance or capacitance), voltage and current change/reverse their polarity at the same time. Reactive power (Q) is in this case 0 and active power is the same as apparent power (more on that later).

In reactive loads, voltage and current are not in phase and the current either lags or precedes the voltage. This translates to some of the current that should be doing useful work (in the machine) moving to and fro through the wires, heating them.

The more reactive a load is, the larger is the phase shift between the voltage and current, the worse is the power factor, and more current is used for heating up wires and other conductors. This current is added to the current that does actual work (active power), meaning that the load uses more current from the installation/source than it (ideally) should.

Reactive power (Q) is expressed in volt-amperes reactive or vars (VAr) or kilovars (kVAr) and megavars (MVAr).

What is apparent power (S)?

Apparent power (S) is a vector sum of active and reactive power, i.e. a square root of a sum of squared active and squared reactive power. Why vector sum? Well, the three types of power form a so-called power triangle, which is a visual representation of all three in a vector space (in 2D) using vectors (a geometric object/a line of a specific length and with specific direction) and how they influence each other can’t be calculated using simple algebra. The power triangle and angle between the two sides (used in power factor calculation) can however be simply visualized with a horse and a railcar.

The horse-railcar analogy and the power triangle

Let’s pretend that the electric load is a railcar and a horse is power that pulls the railcar along the track with desired speed (i.e. electric load operates within prescribed parameters) using a long towline. If the towline is strung parallel with the direction of travel (the horse is basically walking on track in front of the railcar) then there are no losses and the entire horse’s strength is used for pulling the railcar (no reactive power, just active power). 

Though, if the towline is strung at an angle to the direction of travel, the horse has to struggle more to pull the railcar with the same speed. And the larger the angle, the more work has the horse have to put in to move the railcar. In electrical engineering terms: load uses more current to operate within desired limits. In mathematical terms, in vector space: the line that describes (vector) the direction of travel represents active power, reactive power is a vector that starts at the end of the active power vector and is perpendicular to the active power vector, and the towline is the apparent power vector (starts at the start of active power vector and ends at the end of reactive power vector).

And where is the power factor in all this? It is hidden in the angle (Φ) between the active power (P) and apparent power (S) vector. However, the actual number can only be derived through deft application of trigonometric functions.

Calculation: power factor

The power factor is equal to the cosine of the aforementioned angle. The cosine is also equal to the absolute value of active power (P) divided by apparent power (S). Quite a simple equation, but the whole process of measuring and calculating active, reactive and active power and ultimately power factor is cumbersome and inconvenient. Fortunately, modern power quality analysers (PQAs) like the MI 2893 Power Master XT or MI 2885 Master Q4 have a built-in feature that calculates the power factor at a simple press of a button. 

cos φ = |P|/|S| 

Now, a word or two about typical power factor values. For purely resistive loads, the power factor is 1 or very close to it, while for arc welding equipment it might be as low as 0.35 – most loads are however between the two extremes. Nevertheless, too many of them (particularly if they are large) in any system inevitably leads to unacceptable losses and higher costs that can only be mitigated with properly dimensioned capacitor banks. Needless to say, power quality analysers are a most helpful tool in this and other power quality improvement-related endeavours.