What is Power Factor (Cos ϕ) ? Cos fi or P.F Definition & Formulas

Electrical Technology

Power Factor Definitions and Formulas

In electrical engineering, power factor is only and only related to AC circuits i.e. there is no power factor (P.f) in DC circuits due to zero frequency and phase angle difference (Φ) between current and voltage.

What is Power Factor?

Power factor may be defined by three definitions and formals as follow.

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1). The Cosine of angle between Current and Voltage is called Power Factor.

P = VI Cosθ OR
Cosθ = P ÷ V I OR
Cosθ = kW ÷ kVA OR
Cosθ = True Power ÷ Apparent Power

Where:

P = Power in Watts
V = Voltages in Volts
I = Current in Amperes
W = Real Power in Watts
VA = Apparent Power in Volt-Amperes or kVA
Cosθ = Power factor

2). The ratio between Resistance and Impedance in AC Circuit is known as Power Factor.

Cosθ = R ÷ Z

Where:

R = Resistance in Ohms (Ω)
Z = Impedance (Resistance in AC circuits i.e. X_L, X_C and R known as Inductive reactance, capacitive reactance and resistance respectively) in Ohms (Ω)
Cosθ = Power factor

Impedance “Z” is the total resistance of AC Circuit i.e.

Z = √ [R² + (X_L + X_C)²]

Where:

X_L = 2πfL … L is inductance in Henry
X_C = 1 ÷ 2πfC … C is capacitance in Farads

3).The ratio between Active Power and Apparent Power in volts-amperes is called power factor.

Cosθ = Active Power ÷ Apparent Power
Cosθ = P ÷ S
Cosθ = kW ÷ kVA

Where

kW = P = Real Power in kilo-Watts
kVA = S = Apparent Power in kilo-Volt-Amperes or Watts
Cosθ = Power factor

Power Factor Formula in Three Phase AC Circuits

Power Factor Cosθ = P ÷ √3 V_L × I_L… Line Current & Voltage

Power Factor Cosθ = P ÷ √3 V_P × I_P… Phase Current & Voltage

Power Factor Triangle and Examples

Beer analogy of active or true power, reactive power, apparent power and power factor.

Chips bag analogy of true or real power, reactive power, apparent power and power factor.

Good to know:

In pure resistive circuit, power factor is unity (1) due to zero phase angle difference (Φ) between current and voltage.

In pure capacitive circuit, power factor is leading due to the lagging VARs. i.e. Voltage is lagging 90° behind the current. In other words, Current is leading 90° from voltage (Current and voltage are 90° out of phase with each others, where current is leading and voltage is lagging).

In pure inductive circuit, power factor is lagging due to the leading VARs i.e. Voltage is leading 90° from current. In other words, Current is lagging begging 90° behind the voltage (Current and voltage are 90° out of phase with each, others where voltage is leading and current is lagging).