Three-phase power worksheet with answers

Free printable Three-phase power worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ABCVL​ = 600 VZ = 20 + j15 Ωper phase

A balanced Δ-connected load has an impedance of 20 + j15 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 600 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 600 VZ = 20 + j15 Ω per phase
Iph = A
2.Easy
ABCVL​ = 600 VIL​ = ?NZ = 20 + j15 Ωper phase

A balanced Y-connected load has an impedance of 20 + j15 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 600 V. Find the magnitude of the line current IL.

VL = 600 VZ = 20 + j15 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VNZ = 12 + j5 Ωper phase

A balanced Y-connected load with an impedance of 12 + j5 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 400 V. Find the total real power P absorbed by the load in kW.

VL = 400 VZ = 12 + j5 Ω per phase
P = kW
4.Medium
ABCVL​ = 415 VNZ = 24 + j7 Ωper phase

A balanced Y-connected load with an impedance of 24 + j7 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 415 V. Find the total real power P absorbed by the load in kW.

VL = 415 VZ = 24 + j7 Ω per phase
P = kW
5.Hard
P = 250 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 250 kW at a power factor of 0.75 lagging from a 690 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.98 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 250 kWpf1 = 0.75pf2 = 0.98VL = 690 Vf = 50 Hz
QC = kvar
6.Hard
P = 60 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 60 kW at a power factor of 0.72 lagging from a 480 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.95 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 60 kWpf1 = 0.72pf2 = 0.95VL = 480 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. Iph = 24 A
  2. 2. IL = 13.86 A
  3. 3. P = 11.36 kW
  4. 4. P = 6.613 kW
  5. 5. QC = 169.7 kvar
  6. 6. QC = 38.11 kvar

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