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​ = 400 VIL​ = ?Z = 15 + j20 Ωper phase

A balanced Δ-connected load has an impedance of 15 + j20 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 = 15 + j20 Ω per phase
IL = A
2.Easy
ABCVL​ = 415 VZ = 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 415 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 415 VZ = 12 + j16 Ω per phase
Iph = A
3.Medium
ABCVL​ = 480 VIL​ = ?M110 kW, η = 90%cos φ = 0.82

A three-phase induction motor delivers 110 kW of mechanical output power at full load. At this load its efficiency is 90% and its power factor is 0.82 lagging. The supply has a line-to-line voltage of 480 V. Find the line current IL.

Pout = 110 kWη = 90%cos φ = 0.82VL = 480 V
IL = A
4.Medium
ABCVL​ = 208 VIL​ = 60 Acos φ = 0.85lagging

A balanced three-phase load draws a line current of 60 A from a supply with a line-to-line voltage of 208 V. The power factor is 0.85 lagging. Find the total real power P drawn by the load in kW.

VL = 208 VIL = 60 Acos φ = 0.85
P = kW
5.Hard
P = 50 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 50 kW at a power factor of 0.72 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 50 kWpf1 = 0.72pf2 = 0.92VL = 480 Vf = 50 Hz
QC = kvar
6.Hard
P = 120 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 120 kW at a power factor of 0.65 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 = 0.65pf2 = 0.92VL = 415 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. IL = 27.71 A
  2. 2. Iph = 20.75 A
  3. 3. IL = 179.3 A
  4. 4. P = 18.37 kW
  5. 5. QC = 26.89 kvar
  6. 6. QC = 89.18 kvar

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