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​ = 208 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 208 V. Find the magnitude of the line current IL.

VL = 208 VZ = 9 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 415 VIL​ = ?NZ = 4 + j3 Ωper phase

A balanced Y-connected load has an impedance of 4 + j3 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 = 4 + j3 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VIL​ = ?M7.5 kW, η = 88%cos φ = 0.86

A three-phase induction motor delivers 7.5 kW of mechanical output power at full load. At this load its efficiency is 88% and its power factor is 0.86 lagging. The supply has a line-to-line voltage of 400 V. Find the line current IL.

Pout = 7.5 kWη = 88%cos φ = 0.86VL = 400 V
IL = A
4.Medium
ABCVL​ = 400 VIL​ = 10 Acos φ = 0.95lagging

A balanced three-phase load draws a line current of 10 A from a supply with a line-to-line voltage of 400 V. The power factor is 0.95 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 10 Acos φ = 0.95
P = kW
5.Hard
P = 120 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 120 kW at a power factor of 0.75 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 120 kWpf1 = 0.75pf2 = 0.92VL = 690 Vf = 60 Hz
QC = kvar
6.Hard
P = 100 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 100 kW at a power factor of 0.65 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 0.95 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 = 0.65pf2 = 0.95VL = 690 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 8.006 A
  2. 2. IL = 47.92 A
  3. 3. IL = 14.3 A
  4. 4. P = 6.582 kW
  5. 5. QC = 54.71 kvar
  6. 6. Cph = 561.9 µF

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