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​ = 415 VIL​ = ?Z = 20 + j15 Ωper phase

A balanced Δ-connected load has an impedance of 20 + j15 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 = 20 + j15 Ω per phase
IL = A
2.Easy
ABCVL​ = 690 VIL​ = ?Z = 24 + j18 Ωper phase

A balanced Δ-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 690 V. Find the magnitude of the line current IL.

VL = 690 VZ = 24 + j18 Ω per phase
IL = A
3.Medium
ABCVL​ = 690 VIL​ = ?M55 kW, η = 91%cos φ = 0.86

A three-phase induction motor delivers 55 kW of mechanical output power at full load. At this load its efficiency is 91% and its power factor is 0.86 lagging. The supply has a line-to-line voltage of 690 V. Find the line current IL.

Pout = 55 kWη = 91%cos φ = 0.86VL = 690 V
IL = A
4.Medium
ABCVL​ = 400 VZ = 15 + j20 Ωper phase

A balanced Δ-connected load with an impedance of 15 + j20 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 400 V. Find the total real power P absorbed by the load in kW.

VL = 400 VZ = 15 + j20 Ω per phase
P = kW
5.Hard
P = 120 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 120 kW at a power factor of 0.72 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 120 kWpf1 = 0.72pf2 = 0.92VL = 415 Vf = 60 Hz
QC = kvar
6.Hard
P = 120 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 120 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 0.98 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 120 kWpf1 = 0.7pf2 = 0.98VL = 400 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. IL = 28.75 A
  2. 2. IL = 39.84 A
  3. 3. IL = 58.8 A
  4. 4. P = 11.52 kW
  5. 5. QC = 64.54 kvar
  6. 6. QC = 98.06 kvar

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