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​ = 208 VIL​ = ?Z = 12 + j9 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j9 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 208 V. Find the magnitude of the line current IL.

VL = 208 VZ = 12 + j9 Ω per phase
IL = A
2.Easy
ABCVL​ = 415 VIL​ = ?Z = 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 415 V. Find the magnitude of the line current IL.

VL = 415 VZ = 8 + j6 Ω per phase
IL = A
3.Medium
ABCVL​ = 480 VIL​ = 50 Acos φ = 0.88lagging

A balanced three-phase load draws a line current of 50 A from a supply with a line-to-line voltage of 480 V. The power factor is 0.88 lagging. Find the total real power P drawn by the load in kW.

VL = 480 VIL = 50 Acos φ = 0.88
P = kW
4.Medium
ABCVL​ = 415 VIL​ = 25 Acos φ = 0.75lagging

A balanced three-phase load draws a line current of 25 A from a supply with a line-to-line voltage of 415 V. The power factor is 0.75 lagging. Find the total real power P drawn by the load in kW.

VL = 415 VIL = 25 Acos φ = 0.75
P = kW
5.Hard
P = 50 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 50 kW at a power factor of 0.7 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 0.9 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 50 kWpf1 = 0.7pf2 = 0.9VL = 480 Vf = 60 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 690 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. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 150 kWpf1 = 0.8pf2 = 0.95VL = 690 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 24.02 A
  2. 2. IL = 71.88 A
  3. 3. P = 36.58 kW
  4. 4. P = 13.48 kW
  5. 5. Cph = 308.5 µF
  6. 6. Cph = 117.4 µF

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