Skip to main content

Combined balanced three-phase loads

Short answer

Sum active and reactive powers: 194.5 kW, 76.3 kVAR lag. Total apparent power is 208.9 kVA. Line current at 415 V is 290.6 A. Combined power factor is 0.931 lagging.

The following balanced three phase loads are connected to a 415 V, three phase, four wire supply. (i) 160 kVA at 0.7 power factor lagging (ii) 50 kVA at 0.65 power factor leading (iii) 50 kW at unity power factor. Calculate (a) the total load in kVA (b) the line current (c) the combined power factor

Given a balanced supply of 415 V (line), three loads in parallel.

Each load as complex power S = P + jQ

  1. 160 kVA at 0.7 lag: P₁ = 160 × 0.7 = 112 kW, Q₁ = 160 × sin(45.57°) = +114.3 kVAR
  2. 50 kVA at 0.65 lead: P₂ = 50 × 0.65 = 32.5 kW, Q₂ = −50 × sin(49.46°) = −38.0 kVAR
  3. 50 kW at unity: P₃ = 50 kW, Q₃ = 0

Totals

  • P = 112 + 32.5 + 50 = 194.5 kW
  • Q = 114.3 − 38.0 = 76.3 kVAR (lagging)

(a) Total load in kVA

S = √(194.5² + 76.3²) = 208.9 kVA

(b) Line current

I_L = S/(√3 V_L) = 208 900/(1.732 × 415) = 290.6 A

(c) Combined power factor

cos φ = P/S = 194.5/208.9 = 0.931 lagging

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Basic Electrical Engineering chapter 8 questions →