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​ = ?NZ = 9 + j12 Ωper phase

A balanced Y-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 600 V. Find the magnitude of the line current IL.

VL = 600 VZ = 9 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 415 VIL​ = ?Z = 18 + j24 Ωper phase

A balanced Δ-connected load has an impedance of 18 + j24 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 = 18 + j24 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VZ = 3 + j4 Ωper phase

A balanced Δ-connected load with an impedance of 3 + j4 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 415 V. Find the total real power P absorbed by the load in kW.

VL = 415 VZ = 3 + j4 Ω per phase
P = kW
4.Medium
ABCVL​ = 480 VIL​ = 50 Acos φ = 0.9lagging

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

VL = 480 VIL = 50 Acos φ = 0.9
P = kW
5.Hard
P = 100 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 100 kW at a power factor of 0.78 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 100 kWpf1 = 0.78pf2 = 0.92VL = 690 Vf = 50 Hz
QC = kvar
6.Hard
P = 200 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 200 kW at a power factor of 0.78 lagging from a 415 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 = 0.78pf2 = 0.92VL = 415 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 23.09 A
  2. 2. IL = 23.96 A
  3. 3. P = 62 kW
  4. 4. P = 37.41 kW
  5. 5. QC = 37.63 kvar
  6. 6. Cph = 1391 µF

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