Three loads are connected in parallel cross a 1-phase, 1200 V, 50 Hz supply.

Load 1: Capacitive load, 10 kW and 40 kVAR

Load 2: Inductive load, 35 kW and 120 kVAR

Load 3: Resistive load of 15 kW

What is the total complex power of the circuit?

Concept:

Complex Power of an AC circuit is given as:

\(P = V \times {I^*}\)

P = complex power

V = Voltage

I* = Conjugate of current

For lagging loads, the current lags the voltage by an angle ϕ.

Voltage = V∠0°

Current = I∠-ϕ°

Complex power = VI* = (V∠0°) (I∠ϕ°)

= VI cos ϕ + VI sin ϕ = P + jQ

For leading loads, current leads the voltage by an angle ϕ.

Voltage = V∠0°

Current = I∠ϕ°

Complex power = VI* = (V∠0°) (I∠-ϕ°)

= VI cos ϕ – VI sin ϕ = P – jQ

Calculation:

Load 1: Capacitive load, 10 kW and 40 kVAR

P₁ = (10 – j40) kVA

Load 2: Inductive load, 35 kW and 120 kVAR

P₂ = (35 + j120) kVA

Load 3: Resistive load of 15 kW

P₃ = 15 kW

Total power (P) = P₁ + P₂ + P₃

= 10 – j40 + 35 + j120 + 15

= (60 + j80) kVA