# What is Power Factor and Why is it Important Full Calculation

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As an electrical engineer, you should understand what is power factor is and why it is important in our field. This topic is widely known for every electrical engineer, especially those who interact with electrical grid, power, supply, and analysis.

A power factor is used to measure the effectiveness of our electrical power supply when used to supply various electrical devices. Power factor consists of active power, reactive power, and apparent power.

What are those? We will learn them one by one completely.

## What is Power Factor and Why is it Important

Power factor is a very important variable to represent the efficiency of our electrical power drawn by our electrical devices. This variable does not have a standard unit but it comes with a plain number.

Only by looking at a power factor’s value, we can predict the behavior of our electrical devices against our power grid. This value will be determined by the types of load we install to the circuit.

For a refresh, the types of load can be listed as resistive, capacitive, and inductive. Each of them can have a different effect on power efficiency.

We are going through the complete understanding of

What is power factor and why is it important

We should also learn the significance of a power factor that can improve our efficiency.

Keep in mind, while learning about power factor, we can not leave behind three important variables:

• Active power
• Reactive power
• Apparent power

Not only that, you should have understood what an electrical power is at this point. If you are not confident about your understanding about what is a power, you should read them first.

## What is a Power Factor

Power factor is the measurement of the efficiency of electrical power consumed by various electrical devices. This ranges from 0 to 1 where the power factor of 1 is the best while the power factor nearer to 0 is worse.

In other words, a power factor of 1 is the most efficient load for a system.

Power factor less than 0.8 is considered worse. The efficiency is somewhat normal but still has quite high losses in the electrical supply system. This consumes more power than it should be, looking at its produced power.

Thus, our bill should be higher. Higher power factor means good electrical utilization.

Keep in mind that this topic is only valid for AC circuits since DC circuits have zero frequency thus don’t have harmonic value. The power factor of a DC circuit is 1 where the power factor of an AC circuit ranges from 0 to 1 (0 < Cos θ < 1)

The high power factor (PF) is dreamed by every electrical circuit and utilization. But of course, this one needs more extensive analysis and strategy.

Just a quick start, the higher PF means the load is more “resistive” while the lower PF means the load is more “inductive” or “capacitive”.

## The Definition of Power Factor

The definition of power factor is

The ratio of active power (measured in W) and apparent power (measured in VA).

Since power factor forms a power triangle, we can deploy trigonometry function to calculate power factor with: Where θ is the angle between voltage (V) and current (I)

We can use the impedance to get PF by Where R is the resistance and Z is the impedance.

Observe the three graphs below to give you a better idea about the power factor. The left graph shows the best power factor (1). Where the θ is 0 degree thus cos θ is 1.

The middle graph shows the worst power factor (0). Where the θ is 90 degrees thus cos θ is 0.

The right graph shows the common power factor we can find in the field (0<PF<1) where its value varies with cos θ.

## Is the Power Factor Important?

Before learning about the power factor, we should understand why we need to learn it.

Just for a comparison, say we have an electrical motor with 100 W power. The consumed power by the motor is 125 VA.

The power of our motor is measured in W so it is the active power or working power. On the other hand, the power supported by our utility is measured in VA so it is the apparent power.

So why are those two different? Do we pay higher than we should be?

We can calculate how good our power factor (PF) is in this situation.

Before that, from now on we will use:

P = active power (W)
Q = reactive power (VAR)
S = apparent power (VA) Here we have a power factor of 0.8 or 80%.

This number means only 80% of absorbed power is fully used to supply the motor. We can say the rest 20% will be the losses or going to the reactive element (an inductor in this case).

Why do we aim for the highest power factor possible?

The power company should supply its customers with the needed apparent power (in VA) but the customer only pays for the active power (W).

Be it PF of 1 or 0.5, the customer will not suffer for any losses except for long term harmonic effects but we will ignore this for now.

On the other hand, the company will suffer if the PF is low. Since the PF is low, the amount paid by customers is less but the needed power is still delivered to them.

This is why power companies should understand and try their best to improve the power factor. The company may penalize the customer if they maintain the low PF.

Thus, high PF is beneficial for both sides.

## Why Low Power Factor is Bad

From the basic AC circuit, we know that both inductor and capacitor can cause leading and lagging current to the circuit. This is the culprit behind the low power factor. Inductor and capacitor provide reactive power in the circuit.

The higher the reactive power, the lower the active power, thus making the power factor worse.

This makes the power distribution from the utility less effective than it should be because the current is partially not delivered to power our electrical devices.

A very simple example to make you remember:

Assume that we have an electric motor of 50 kW.

With a power factor of unity (PF = 1 and Q = 0 kVAR), this motor can be supplied by a transformer with a rating of 50 kVA.

If the power factor is 70% (PF = 0.7), the transformer will supply power for both the motor and the reactive load.

From the simple equation before: We need a larger transformer at least rated for 71.4285 kVA.

Not only that, we need bigger conductors to be able to deliver high power to our place because the current delivered will be increased now.

Now you understand, not only the power factory suffers from the low PF, we as their customers have to prepare better and of course more expensive equipment to deliver necessary power and prevent any electrical fault.

## Types of Power Factor

We can find three types of power factor according to the types of load:

• Unity power factor
• Lagging power factor

For a summary, observe the comparison below:

### Unity Power Factor

Unity power factor indicates that the load in the circuit is purely resistive. Since there is no phase shift between voltage and current, the load will consume active power. Thus the reactive power (Q) will be zero.

The apparent power (S) will be equal to the active power (P).

There are no losses between the power utility such as the transformer and our load.

But do not misunderstand, we can achieve this condition using a combination of capacitors and inductors with a proper.

In case the circuit has a balance inductive and capacitive, the circuit will achieve resonance condition and can be considered as a purely resistive circuit.

Since the PF = 1 thus the phase shift (θ) between voltage and current is zero. ### Lagging Power Factor

A lagging power factor indicates that our circuit is more inductive. This is caused by an inductive load. The circuit will consume reactive power thus the circuit will have a positive reactive power (Q).

Everytime we use a higher inductive load than the capacitive load, the circuit will have a lagging power factor.

In this case, the current phase will lag the voltage phase by θ.

A pure inductive circuit will have its current lags voltage by θ = 90 degrees.  