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​ = 690 VZ = 8 + j6 Ωper phase

A balanced Δ-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 690 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 690 VZ = 8 + j6 Ω per phase
Iph = A
2.Easy
ABCVL​ = 690 VZ = 6 + j8 Ωper phase

A balanced Δ-connected load has an impedance of 6 + j8 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 phase current Iph flowing through each impedance.

VL = 690 VZ = 6 + j8 Ω per phase
Iph = A
3.Medium
ABCVL​ = 415 VIL​ = ?M45 kW, η = 92%cos φ = 0.86

A three-phase induction motor delivers 45 kW of mechanical output power at full load. At this load its efficiency is 92% and its power factor is 0.86 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 45 kWη = 92%cos φ = 0.86VL = 415 V
IL = A
4.Medium
ABCVL​ = 690 VIL​ = ?M90 kW, η = 94%cos φ = 0.82

A three-phase induction motor delivers 90 kW of mechanical output power at full load. At this load its efficiency is 94% and its power factor is 0.82 lagging. The supply has a line-to-line voltage of 690 V. Find the line current IL.

Pout = 90 kWη = 94%cos φ = 0.82VL = 690 V
IL = A
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 480 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 = 120 kWpf1 = 0.75pf2 = 0.95VL = 480 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 0.65 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 0.95 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.65pf2 = 0.95VL = 480 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. Iph = 69 A
  2. 2. Iph = 69 A
  3. 3. IL = 79.13 A
  4. 4. IL = 97.7 A
  5. 5. QC = 66.39 kvar
  6. 6. Cph = 580.6 µF

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