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​ = 690 VZ = 6 + j8 Ωper phase

A balanced Δ-connected load has an impedance of 6 + j8 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 690 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 690 VZ = 6 + j8 Ω per phase
Iph = A
2.Easy
ABCVL​ = 208 VZ = 7 + j24 Ωper phase

A balanced Δ-connected load has an impedance of 7 + j24 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 = 7 + j24 Ω per phase
Iph = A
3.Medium
ABCVL​ = 690 VIL​ = 120 Acos φ = 0.95lagging

A balanced three-phase load draws a line current of 120 A from a supply with a line-to-line voltage of 690 V. The power factor is 0.95 lagging. Find the total real power P drawn by the load in kW.

VL = 690 VIL = 120 Acos φ = 0.95
P = kW
4.Medium
ABCVL​ = 690 VIL​ = 12 Acos φ = 0.88lagging

A balanced three-phase load draws a line current of 12 A from a supply with a line-to-line voltage of 690 V. The power factor is 0.88 lagging. Find the total real power P drawn by the load in kW.

VL = 690 VIL = 12 Acos φ = 0.88
P = kW
5.Hard
P = 200 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 200 kW at a power factor of 0.7 lagging from a 480 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.92 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 200 kWpf1 = 0.7pf2 = 0.92VL = 480 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 0.72 lagging from a 400 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 = 150 kWpf1 = 0.72pf2 = 0.9VL = 400 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. Iph = 69 A
  2. 2. Iph = 8.32 A
  3. 3. P = 136.2 kW
  4. 4. P = 12.62 kW
  5. 5. Cph = 1642 µF
  6. 6. Cph = 1192 µF

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