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 = 24 + j18 Ωper phase

A balanced Y-connected load has an impedance of 24 + j18 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 = 24 + j18 Ω per phase
IL = A
2.Easy
ABCVL​ = 600 VIL​ = ?NZ = 16 + j12 Ωper phase

A balanced Y-connected load has an impedance of 16 + 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 = 16 + j12 Ω per phase
IL = A
3.Medium
ABCVL​ = 690 VIL​ = 120 Acos φ = 0.9lagging

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

VL = 690 VIL = 120 Acos φ = 0.9
P = kW
4.Medium
ABCVL​ = 480 VIL​ = ?M18.5 kW, η = 90%cos φ = 0.88

A three-phase induction motor delivers 18.5 kW of mechanical output power at full load. At this load its efficiency is 90% and its power factor is 0.88 lagging. The supply has a line-to-line voltage of 480 V. Find the line current IL.

Pout = 18.5 kWη = 90%cos φ = 0.88VL = 480 V
IL = A
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 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 0.9 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 50 kWpf1 = 0.7pf2 = 0.9VL = 400 Vf = 50 Hz
Cph = µF
6.Hard
P = 75 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 75 kW at a power factor of 0.78 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 0.98 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 75 kWpf1 = 0.78pf2 = 0.98VL = 415 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 11.55 A
  2. 2. IL = 17.32 A
  3. 3. P = 129.1 kW
  4. 4. IL = 28.1 A
  5. 5. Cph = 177.7 µF
  6. 6. Cph = 692.2 µF

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