# Power factor calculator and correction capacitor

Before jumping directly to the power factor calculator lets first understand what is power factor, how to calculate it and why it is important to calculate.

## What is Power factor ?

to understand what is power factor we first needs to understand some of its related terms like real power, apparent power and total power.

### Real power or active power or True power or Kw

Real power or an active power is the power which is actually consumed by the AC loads such as AC Motors, AC generators. This power is also called as active power and it is measured in terms of kW and denoted by P.

This is the power that is consumed by any Resistor in an AC electrical circuit which also includes inductors and capacitors along with resistors and that is the reason why this power corresponds to DC power.

In an AC electrical circuit there is a phase shift between voltage and current due to which all the power is not utilized completely and to make a phase shift as minimum as possible capacitors are used for inductive loads and generators.

### Reactive power or kVAr

Reactive power is the amount of power that is utilized by the AC components such as inductors and capacitors this power is usually not transferred to the output load. The amount of phase shift decides the value of reactive power more the phase shift more the reactive power, This power is measured in terms of kVAr and denoted by Q. Unlike active power this power is consumed reactance of the circuit that is AC resistance of inductors and capacitors.

### Apparent power or kVA

This is the amount of power that is drawn from AC supply by any AC electrical network. This power is the combination of both active and reactive power and is measured in terms of kVA and denoted by S. Apparent power is the product of the RMS (root mean square) values of voltage and current and is the vector sum of P and Q.

### Power Triangle

With the help of power triangle it is easier to understand the relation between active, reactive, and apparent power. As in the AC electrical network phase shift (angle between current and voltage) comes into picture therefore the relation between the kVA, kW, kVAr is not a linear relation but instead it is a vector relation and must follow vector rule of addition.

As it is clear from the power triangle that apparent power (VA) is the highest value and distributed between active (W) and reactive power (VAR) and the power factor formula can be derived from the power triangle itself.

power factor is the angle between Apparent power and Real power which is denoted by phi (Φ) and is sometimes referred to as power factor angle.

### Power factor formula

Power factor (p.f) = Cos(Φ) = Real power/Apparent power = W/VA

simple Pythagoras theorem is also applicable to find the relation between power S, P, Q is S² = P² + Q²

## Why power factor is important ?

Power factor is an expression of energy efficiency. It is usually expressed as a percentage—and the lower the percentage, the less efficient power usage is.

PF expresses the ratio of true power used in a circuit to the apparent power delivered to the circuit. A 96% power factor demonstrates more efficiency than a 75% power factor. PF below 95% is considered inefficient in many regions.

power factor also gives an idea that how much percentage of the drawn power is actually used by the loads, hence idea of power factor is very useful for designing the AC circuits.

## Power Factor Calculator

This calculator for power factor evaluation can be used for both single and three phase power. Input the known values of given variables use P1 = P2 and Q1 = Q2.

### Power Factor calculation

Total kVA (S)

Total kW (P)

Reactive power (Q) in kVAr

Power Factor p.f when kW is known

Power Factor p.f when Q – kVAr is known

kVAr to be reduced after adding correction capacitor

New kVAR

New kVAR

Voltage

frequency

Correction capacitor value

Formula Power factor calculation for Single phase is given as

Vrms*Irms*1 = S, P1=P2=P, Q1=Q2=Q. Q(VAR) = √(|S(VA)|2 – P(W)2)

Cos(phi) = P/S and S² = P² + Q² , Sin(phi) = Q/S

for three phase use SQRT(3) = 1.73205, S = Vrms*Irms*1.73205 rest of the calculation remains same, the voltage in three phase is often given in line to line so to convert it into line to neutral SQRT(3) as a multiplication factor whereas current is the line current.

when the the real power is same as apparent power that 0 reactive power than it is said to have unity power factor and can be confirmed by this calculator.

## Power factor correction capacitor

For many inductive loads such as Motors and generators and in industrial loads we see that power factor becomes poor and it causes too much for the owners therefore we need to correct and improve this factor. Correction of the power factor can be done by adding a capacitor in parallel to the each phase supply so to do that we need to know the capacitance value that needs to be added.

### Formula for correction capacitor

for single phase use this derivation to calculate the value of capacitor

p.f1 = cos(phi) = P in watts/S in VA

S = Vrms*Irms

Q1 (VAR) = SQRT(S^2 – P^2)

S2 (corrected VA) = P (in watts)/pf2 (corrected one)

Q2 (corrected VAR) = SQRT(S2^2 – P^2)

extra Q to be removed = Q1 – Q2 = Qc

Qc = 2*pi*f*V*V*C

C = Qc/(2*pi*f*V*V)

for three phase use this derivation to calculate

pf1 = P1/(3*V*I)

Q1 = SQRT(S1^2 – P1^2)

S2 = P1/pf2

Q2 = SQRT(S2^2 – P1^2)

Qc = Q1 – Q2

C = Qc/(2*pi*f*V*V)