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 = 24 + j7 Ωper phase

A balanced Δ-connected load has an impedance of 24 + j7 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 = 24 + j7 Ω per phase
Iph = A
2.Easy
ABCVL​ = 600 VIL​ = ?NZ = 12 + j5 Ωper phase

A balanced Y-connected load has an impedance of 12 + j5 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 = 12 + j5 Ω per phase
IL = A
3.Medium
ABCVL​ = 690 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 690 V. The power factor is 0.9 lagging. Find the total real power P drawn by the load in kW.

VL = 690 VIL = 50 Acos φ = 0.9
P = kW
4.Medium
ABCVL​ = 415 VIL​ = 75 Acos φ = 0.95lagging

A balanced three-phase load draws a line current of 75 A from a supply with a line-to-line voltage of 415 V. The power factor is 0.95 lagging. Find the total real power P drawn by the load in kW.

VL = 415 VIL = 75 Acos φ = 0.95
P = kW
5.Hard
P = 200 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 200 kW at a power factor of 0.72 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 200 kWpf1 = 0.72pf2 = 0.92VL = 480 Vf = 60 Hz
QC = kvar
6.Hard
P = 50 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 50 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 0.9 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 50 kWpf1 = 0.78pf2 = 0.9VL = 690 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. Iph = 19.2 A
  2. 2. IL = 26.65 A
  3. 3. P = 53.78 kW
  4. 4. P = 51.21 kW
  5. 5. QC = 107.6 kvar
  6. 6. QC = 15.9 kvar

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