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​ = 480 VZ = 9 + j12 Ωper phase

A balanced Δ-connected load has an impedance of 9 + j12 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 480 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 480 VZ = 9 + j12 Ω per phase
Iph = A
2.Easy
ABCVL​ = 400 VZ = 3 + j4 Ωper phase

A balanced Δ-connected load has an impedance of 3 + j4 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 400 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 400 VZ = 3 + j4 Ω per phase
Iph = A
3.Medium
ABCVL​ = 690 VIL​ = 25 Acos φ = 0.8lagging

A balanced three-phase load draws a line current of 25 A from a supply with a line-to-line voltage of 690 V. The power factor is 0.8 lagging. Find the total real power P drawn by the load in kW.

VL = 690 VIL = 25 Acos φ = 0.8
P = kW
4.Medium
ABCVL​ = 480 VIL​ = 10 Acos φ = 0.95lagging

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 0.95 lagging. Find the total real power P drawn by the load in kW.

VL = 480 VIL = 10 Acos φ = 0.95
P = kW
5.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.78 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 = 60 kWpf1 = 0.78pf2 = 0.95VL = 690 Vf = 60 Hz
Cph = µF
6.Hard
P = 80 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 80 kW at a power factor of 0.8 lagging from a 400 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. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 80 kWpf1 = 0.8pf2 = 0.98VL = 400 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. Iph = 32 A
  2. 2. Iph = 80 A
  3. 3. P = 23.9 kW
  4. 4. P = 7.898 kW
  5. 5. Cph = 52.77 µF
  6. 6. Cph = 290.2 µF

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