What is Power Factor?

Power Factor (PF) is what determines how efficiently an electrical appliance uses power.

Did you know that the power consumed by most of our AC equipment is not the same as the overall power that is supplied to it? Yep! This is even more paramount in industries with heavy 3-phase equipment.

As power is supplied to our AC equipment, a part of it is used for work while the remaining is not used. The factor that compares the used power and total supplied power is called the power factor.

Now, let’s take a look at how power factor is defined.

Definition of Power Factor

In simple terms, the power factor of an electrical appliance is defined as the ratio of power actually used by the appliance for work to the total power that the appliance draws from the mains supply. In other words, it is the measure of how effective the supplied power is used.

When power is supplied to an AC equipment, some powers are used to do work while the remaining power is unused for work.

Here is the explanation of those powers:

Active power is the power that is actually used by an appliance to do real work. It is also called real power, actual power, true power or working power. It is measured in Watt, W

Reactive power is the ‘unused’ power that helps generate magnetic fields needed by equipment like motors, transformers, and relays, to perform real work. It is measured in volt-ampere reactive, VAR

Apparent power is the total power that is supplied to the equipment. It is the vector sum of the active power and reactive power. It is measured in volt-ampere, VA.

One simple way to describe Apparent power is by using a cup of beer:

The foamy part can be referred to as reactive power (VAR). It is the part that does not quench one’s thirst for the beer.

The non-foamy part of the beer is referred to as the active power (W). It is what quenches one’s thirst for the beer.

The sum of the foamy (VAR) and non- foamy (W) part is called apparent power (VA).

Apparent power = Active power + Reactive power.

Mathematically, Power factor = Active power/Apparent power.

In other words, Power factor is defined as the ratio of active power to apparent power. Its value is commonly known to range between 0 and 1. But, it can be negative. So, in totality, it ranges between -1 and 1.

• The more the reactive power (foamy part), the less the active power (non-foamy part). Thus, the lower the power factor.
• The less the reactive power (foamy part), the more the active power non-foamy part). Thus, a higher power factor.
• As the reactive power (foamy part) reduces towards 0, the power factor increases towards 1.

Also, power factor can also be defined as the percentage of the total drawn power that is used to do work.

About Power Triangle

The power triangle is a triangle that shows the relationship between Apparent power, reactive power, and Active power in a vector space.

From the power triangle diagram above, the power factor can be defined as Cos ϕ.

Φ is called the phase angle. The phase angle is the angle between current and voltage waveform.

• The more the phase angle, the less or poorer the power factor
• As the phase angle reduces, the power factor increases.

Unit of Power Factor

Power factor does not have a unit because it is a factor that gives the ratio between active power and apparent power. It only shows how electric power is effectively used.

So, just like every other mathematical ratio, it is unitless.

However, its value ranges from -1 to 1. It can be unity, leading or lagging.

When Power factor is Unity, Leading or Lagging

The terms leading or lagging is used to determine whether the phase of the current is leading or lagging the phase of the voltage.

Unity Power factor: In a purely resistive circuit or load, the current and voltage are in same phase. So, there is a 0-degree phase angle (ϕ) difference between current and voltage.

PF = Cos ϕ

PF = Cos 0 =1

Because the power factor is 1, it is called unity power factor.

So, when the power factor is 1, VA is the same as W.

Leading Power Factor: When power factor is leading, it means current is leading the voltage by a certain angle. The kind of circuit in which current lead the voltage is called the capacitive circuit. So, a leading power factor means the load is capacitive.

If circuit’s current leads its voltage by exactly 90 degrees, the circuit is said to be purely capacitive

A capacitive circuit produces reactive power.

Lagging Power Factor: When the power factor is lagging, it means the current is lagging the voltage. A circuit in which current lags the voltage is called an inductive circuit. So, a lagging power factor means the load is inductive.

If a circuit’s current lag the voltage by exactly 90 degrees, the circuit is said to be purely inductive

An inductive load consumes reactive power.

When is the Power Factor Between 0 and 1?

The power factor value is determined by how much active or reactive power is needed by an AC circuit or load.

For power factor to be positive, the power source must be the one generating power and sending it to the load.

Apparent power is the sum of active and reactive power.

The more active power that is drawn, the less the reactive power; and in turn a better power factor.

With less active power, there will be more reactive power drawn; and in turn a poor power factor.

When power factor is 0, there is only reactive power and no active power.

When power factor is 1, there is only active power and no reactive power

Can Power Factor be Negative or More Than 1?

Greater-than-1 power factor: For the value of power factor to be 1, the phase angle between current and phase must be 0. That is, Cos0 =1. So, for power factor to be greater than 1, the phase angle must be less than 0. And that is not possible

The phase angle only varies between 0 and 90 degrees.

Also, for power factor to be greater than 1, active power (useful power) must be more than Apparent power (Total power). But apparent power cannot be more than active power.

Hence, Power factor can not be greater than 1.

Negative Power factor: Power is generated from a source while it is consumed by loads. Normally, power flows from source to load. So, power factor is normally positive.

But when a load, which is supposed to consume power, generates power and sends it to the power system, power becomes negative. As a result, power factor becomes negative.

So, the signs of power factor all depend on the direction of power.

For example, if a generator, which is suppose to generate power, consumes power, it is said to be receiving negative power. Therefore, it is said to be of negative power factor.

Importance of Power Factor

Power factor is important because it determines how much of the total supplied power is effectively used by a circuit or load. The value of power factor is between -1 and 1. When power factor is less than 1, more power is supplied than is needed, and as a result, more current flows through the circuits wiring.

For example, if an inductive load (like refrigerator), with a power factor of 0.6, is rated 100W, the power source will have to supply more than the 100W. So, the amount of supplied power required to provide the load with 100W will be = 100/0.6 = 166.7KVA. The more power is supplied, the more the current flow through the cables. Thus, more losses

But when power factor is 1 (like in resistive load), no extra power is required to deliver a certain power. For example, if a resistive load (that is, PF =1) is rated 100W, a supply of 100VA will be enough to provide the 100W. No need for extra power.

Power Factor is the Reason Why Transformers are Rated in KVA

The commonly known reason for rating transformers in KVA, and not KW, is that the copper losses in a transformer are dependent on current while iron loss is dependent on voltage.

That might be correct but that is not the whole story.

A transformer transfers power from one AC circuit to one or more circuits. Its rating determines much power it can output to loads connected to it.

The circuits or loads that are connected to a transformer are mostly inductive and resistive loads.

If an inductive load (like a motor) is connected to a transformer, more power will be supplied to it than it uses to do work. This is because power factor is always less than 1 for an inductive circuit or load. And the reason it is less than 1 is that inductive loads need reactive power (extra unused power)

The more inductive loads or circuits are connected to a transformer, the more extra unused power it needs to supply.

Since, some of the connected loads (like inductive loads) to transformer need extra power called reactive power, to function, transformers are rated to factor in those needed extra power.

For example, if an inductive load like a motor, with a power factor of 0.8, is rated 100W, the total power from the transformer required to supply the 100W would be 125VA. That is 100/0.8 = 125VA.

So, because of the power factor of loads connected to transformers, transformers have to be rated in KVA. It is the KVA that sums up the reactive power and active power.

Power Factor Penalty

Utility companies charge customers based on the active power they consume. But it gets to some point that consumers are charged some extra.

For efficient use of power, equipment should draw mostly active power (W). When equipment draws more reactive power (lowering power factor) from the power system, it limits the amount of active power that can be delivered by the line; causing voltage drops; and generating more power line and transformer losses.

All these losses are not initially factored in the electricity bills. So, extra charges are issued to consumers involved in this lowering power factor.

Residential areas are not usually issued extra charges because it is assumed that the reactive power they draw Is negligible.

The reactive power drawn by Industrial and commercial customers is not negligible. So, a contract is drawn between the customers and the utility companies to indicate that when their power factor falls below a certain value (e.g 90%), the customers will pay an agreed extra charge called the power factor penalty charge.

Power factor penalty charges varies from country to country.

Power Factor is Related to AC and not DC Circuits.

In a DC circuit, the voltage and current are always in phase, as there are no reactive components. So, one can say a DC circuit does not have a power factor or power factor is always 1. That is, W is always the same as KVA.

In AC circuits, the voltages and currents are not always in phase, as there is a reactive component. That difference in phase angle between current and voltage is what leads to power factor.

Key points

• Power factor is the ratio of active power to apparent power
• Power factor is applicable to AC circuits and not DC circuits.
• Apparent power is the vector sum of active and reactive power.
• Power triangle shows the relationship between active, reactive and apparent power.
• Power factor can be unity, leading or lagging.