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​ = 415 VIL​ = ?NZ = 16 + j12 Ωper phase

A balanced Y-connected load has an impedance of 16 + j12 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 415 V. Find the magnitude of the line current IL.

VL = 415 VZ = 16 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 600 VZ = 8 + j6 Ωper phase

A balanced Δ-connected load has an impedance of 8 + j6 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 = 8 + j6 Ω per phase
Iph = A
3.Medium
ABCVL​ = 400 VIL​ = 100 Acos φ = 0.8lagging

A balanced three-phase load draws a line current of 100 A from a supply with a line-to-line voltage of 400 V. The power factor is 0.8 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 100 Acos φ = 0.8
P = kW
4.Medium
ABCVL​ = 415 VIL​ = ?M7.5 kW, η = 95%cos φ = 0.84

A three-phase induction motor delivers 7.5 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.84 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 7.5 kWη = 95%cos φ = 0.84VL = 415 V
IL = A
5.Hard
P = 75 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 75 kW at a power factor of 0.72 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 0.95 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 75 kWpf1 = 0.72pf2 = 0.95VL = 690 Vf = 50 Hz
Cph = µF
6.Hard
P = 150 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 150 kW at a power factor of 0.8 lagging from a 415 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.9 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 150 kWpf1 = 0.8pf2 = 0.9VL = 415 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 11.98 A
  2. 2. Iph = 60 A
  3. 3. P = 55.43 kW
  4. 4. IL = 13.08 A
  5. 5. Cph = 318.5 µF
  6. 6. Cph = 204.6 µF

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