Leading Power Factor
What it means
A leading power factor happens when the current in an AC circuit leads the voltage. This is typical in capacitive loads like capacitor banks, synchronous condensers, or over-compensated circuits.
- Voltage and current are sinusoidal.
- Current reaches its peak before voltage.
- This indicates the presence of capacitance.
Mathematical Definition
Power Factor (PF) = cos(φ)
Where φ is the phase angle between voltage and current.
For leading power factor: φ < 0 (current leads voltage)
Using Power Values
PF = Real Power (P) / Apparent Power (S)
- P = Real power (kW)
- S = Apparent power (kVA)
Using Impedance
cos(φ) = R / Z
- R = resistance
- Z = impedance
Example
If:
- P = 8 kW
- S = 10 kVA
PF = 8 / 10 = 0.8
If the load is capacitive → 0.8 leading power factor
Key Idea
- Lagging PF → inductive load → current lags voltage
- Leading PF → capacitive load → current leads voltage
Calculation of Resistance and Capacitance
Given:
- Voltage (V) = 120 V
- Current (I) = 0.5 A
- Frequency (f) = 60 Hz
- Power Factor (cosφ) = 0.7 (leading)
Step 1: Calculate Impedance (Z)
Z = V / I = 120 / 0.5 = 240 Ω
Step 2: Calculate Resistance (R)
R = Z × cos(φ) = 240 × 0.7 = 168 Ω
Step 3: Calculate Capacitive Reactance (XC)
XC = √(Z² − R²) = √(240² − 168²) ≈ 171.5 Ω
Step 4: Calculate Capacitance (C)
C = 1 / (2Ï€f XC) = 1 / (2 × 3.1416 × 60 × 171.5) ≈ 15.5 μF
Final Results:
- Resistance (R) ≈ 168 Ω
- Capacitance (C) ≈ 15.5 μF