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 VIL​ = ?Z = 12 + j5 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j5 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 = 12 + j5 Ω per phase
IL = A
2.Easy
ABCVL​ = 208 VZ = 12 + j16 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j16 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 phase current Iph flowing through each impedance.

VL = 208 VZ = 12 + j16 Ω per phase
Iph = A
3.Medium
ABCVL​ = 480 VIL​ = 10 Acos φ = 0.7lagging

A balanced three-phase load draws a line current of 10 A from a supply with a line-to-line voltage of 480 V. The power factor is 0.7 lagging. Find the total real power P drawn by the load in kW.

VL = 480 VIL = 10 Acos φ = 0.7
P = kW
4.Medium
ABCVL​ = 208 VIL​ = 50 Acos φ = 0.82lagging

A balanced three-phase load draws a line current of 50 A from a supply with a line-to-line voltage of 208 V. The power factor is 0.82 lagging. Find the total real power P drawn by the load in kW.

VL = 208 VIL = 50 Acos φ = 0.82
P = kW
5.Hard
P = 250 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 250 kW at a power factor of 0.65 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 0.95 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 250 kWpf1 = 0.65pf2 = 0.95VL = 415 Vf = 60 Hz
Cph = µF
6.Hard
P = 250 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 250 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 0.92 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 250 kWpf1 = 0.8pf2 = 0.92VL = 690 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 79.94 A
  2. 2. Iph = 10.4 A
  3. 3. P = 5.82 kW
  4. 4. P = 14.77 kW
  5. 5. Cph = 1079 µF
  6. 6. Cph = 451.3 µF

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