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​ = 600 VIL​ = ?NZ = 8 + j6 Ωper phase

A balanced Y-connected load has an impedance of 8 + j6 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 = 8 + j6 Ω per phase
IL = A
2.Easy
ABCVL​ = 400 VIL​ = ?Z = 12 + j16 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j16 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 400 V. Find the magnitude of the line current IL.

VL = 400 VZ = 12 + j16 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VIL​ = 10 Acos φ = 0.75lagging

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 0.75 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 10 Acos φ = 0.75
P = kW
4.Medium
ABCVL​ = 400 VIL​ = ?M45 kW, η = 95%cos φ = 0.88

A three-phase induction motor delivers 45 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.88 lagging. The supply has a line-to-line voltage of 400 V. Find the line current IL.

Pout = 45 kWη = 95%cos φ = 0.88VL = 400 V
IL = A
5.Hard
P = 300 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 300 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 0.95 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 300 kWpf1 = 0.7pf2 = 0.95VL = 690 Vf = 50 Hz
QC = kvar
6.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.8 lagging from a 415 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. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.8pf2 = 0.98VL = 415 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 34.64 A
  2. 2. IL = 34.64 A
  3. 3. P = 5.196 kW
  4. 4. IL = 77.69 A
  5. 5. QC = 207.5 kvar
  6. 6. Cph = 202.2 µF

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