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 = 12 + j9 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j9 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 = 12 + j9 Ω per phase
Iph = A
2.Easy
ABCVL​ = 600 VIL​ = ?NZ = 7 + j24 Ωper phase

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

VL = 600 VZ = 7 + j24 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VIL​ = 12 Acos φ = 0.75lagging

A balanced three-phase load draws a line current of 12 A from a supply with a line-to-line voltage of 415 V. The power factor is 0.75 lagging. Find the total real power P drawn by the load in kW.

VL = 415 VIL = 12 Acos φ = 0.75
P = kW
4.Medium
ABCVL​ = 415 VIL​ = ?M7.5 kW, η = 94%cos φ = 0.88

A three-phase induction motor delivers 7.5 kW of mechanical output power at full load. At this load its efficiency is 94% and its power factor is 0.88 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 7.5 kWη = 94%cos φ = 0.88VL = 415 V
IL = A
5.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.65 lagging from a 480 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 Δ. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.65pf2 = 0.98VL = 480 Vf = 60 Hz
Cph = µF
6.Hard
P = 100 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 100 kW at a power factor of 0.7 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 0.9 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 100 kWpf1 = 0.7pf2 = 0.9VL = 690 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. Iph = 32 A
  2. 2. IL = 13.86 A
  3. 3. P = 6.469 kW
  4. 4. IL = 12.61 A
  5. 5. Cph = 222.4 µF
  6. 6. Cph = 358.3 µF

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