Power Factor

What Is Power Factor?

AC power has factors to consider. Effective values ​​are used for voltage and current. As in AC Power there is a phase difference between voltage and current. 

For example, there is a power factor that indicates the ratio of power consumption. 

AC power P is the effective value of voltage and current V, I.The phase difference between them θ  and It is expressed by the following formula.

P = V I cos θ Watt

AC power has 3 types:

1. Active power P
2. Reactive power Q
3. Apparent power S  

So I will explain each of them next.

Relationship between active power, Reactive power, apparent power and explanation.

Active power P, Reactive power Q, Apparent power S  and phase θ.

The relationship is as shown in the following figure.

                                                                Power Triangle

The relationship between active power, reactive power, apparent power is expressed by the following formula.

S^ 2 = P ^2 + Q^2

S=√ P^2 +

 Q^2

What is active power?

Active power is P Expressed in units [W].

P=VI cosθ Unit is Watt

The power is

P=VI cosθ

This is the power actually consumed by the load 

 (power consumption) and is called "active power".

When we simply call power, we mean this active power.

Cos θ this is called a power factor. It is represented by

 cos 0= 1 , cos 90= 0.

Since it is a value from 0 to 1, it is usually multiplied by 100 and expressed as a percentage.

 Power factor (%)= P/ V I × 100 [ % ]

What is reactive power?

Current with 90 ° phase difference from voltage I sin θ and voltage V.The product of is called reactive power.

This reactive power is the power that is not actually consumed by the load as electrical energy.

Reactive power is Q Expressed in units [var ].

Q = V I sin θ [var].

Q = V I √ 1 − cos 2 θ [var] 

It is caused by inductive Reactance or Capacitive reactance due to electrostatic capacitance, such as an electric motor (motor) connected to a load.

What is apparent power?

Simply alternating voltage V and current I. The product of V, I is called apparent power. It is the electric power sent from the power supply. Apparent power is S Expressed in units [VA]  

S=VI [VA] 

what is power factor

There is an AC circuit as shown.

When the load of 20W was connected to the AC power supply, the actual power measured by the watt meter was 25W.

Active power P[W]

The actual power consumed by the load.

Reactive power Q[var]

It is the power that does not consume power.

Apparent power S[VA]

The electric power sent from the power supply.

Thus, not all of the power delivered is consumed by the load.

In the above example, the reactive power is

25−20=5

It seems to happen, but AC power does not.

Active power P

Reactive power Q

Apparent power S

 Have the following relationships:

S^2=P^2+Q^2

Because there is a relationship

25^2=20^2+Q^2 From Q=√25^2−20^2=15

It will be.

That's why, the power factor of the above circuit is

Power factor =20/25 =0.8

It is represented by

Power factor calculation formula

Power factor is apparent power S Is active power P It shows the ratio of active power is P=S Cos θ=VI cosθ

Because it is [W]

Cosθ= P/S is. Cosθ

This is called the power factor.

Electric Power=PS=P√P^2+Q^2

It is represented by.

cos 0°=1, cos 90°=0

Since it is a value from 1 to 0, it is usually multiplied by 100 and expressed as a percentage.

Difference between delayed power factor and advanced power factor

As is the case with the phase, it is very difficult to understand the delay and the advance. It can be seen as a delay or a lead depending on how the standards are taken.

There was a delay and progress in power factor, and I was very confused myself. It is easy to understand if you think as follows.

Delay power factor

Reactive power when the delay power factor Q becomes positive. Active power P Becomes positive.

Q/P>0

Thatswhy, the power factor will be delayed.

This can be seen by looking at the inductive reactance being greater than the capacitive reactance.

Power factor

Reactive power when lead power factor Q Will be negative. Active power P Becomes positive. Q/ P < 0 Therefore, it will be a power factor. This can be seen by looking at the inductive reactance being less than the capacitive reactance. 

Exercises 

Example 1

 Find the power factor and power in the series circuit of resistance and coil as shown.

 Way of thinking

Calculate the impedance of the circuit and output the flowing current. Once the impedance and current are determined, the power factor and power can be calculated.

<Answer>

Z=8+j6 Z=|Z|=√8^2+6^2=√(64+36)=√100=Ten[Ω]

I=E/Z=100/10=10[A]

 Power factor cosθ=R/Z=8/10=0.8→80[%]

Electricity P=EI cosθ=100×10×0.8=800 [W]

Example 2

A load with a power consumption of 120 W and a power factor of 60% is connected to a 100 V AC power supply.

Find the current flowing in the circuit.

Example 2

Power consumption is equal to active power, so active power P = V I Cos θ.

<Answer>

Active power P = V I cos θ

Than 120 = 220 × I × 0.6

= 120 /(220× 0.6) = 0.909 [A]