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 VIL​ = ?Z = 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 480 V. Find the magnitude of the line current IL.

VL = 480 VZ = 7 + j24 Ω per phase
IL = A
2.Easy
ABCVL​ = 480 VIL​ = ?NZ = 15 + j20 Ωper phase

A balanced Y-connected load has an impedance of 15 + j20 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 line current IL.

VL = 480 VZ = 15 + j20 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VIL​ = ?M11 kW, η = 95%cos φ = 0.85

A three-phase induction motor delivers 11 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.85 lagging. The supply has a line-to-line voltage of 400 V. Find the line current IL.

Pout = 11 kWη = 95%cos φ = 0.85VL = 400 V
IL = A
4.Medium
ABCVL​ = 400 VIL​ = 150 Acos φ = 0.9lagging

A balanced three-phase load draws a line current of 150 A from a supply with a line-to-line voltage of 400 V. The power factor is 0.9 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 150 Acos φ = 0.9
P = kW
5.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.75 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 Y. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.75pf2 = 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 0.65 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 = 75 kWpf1 = 0.65pf2 = 0.95VL = 690 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 33.26 A
  2. 2. IL = 11.09 A
  3. 3. IL = 19.66 A
  4. 4. P = 93.53 kW
  5. 5. Cph = 474.6 µF
  6. 6. Cph = 117.1 µF

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