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 VZ = 16 + j12 Ωper phase

A balanced Δ-connected load has an impedance of 16 + 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 phase current Iph flowing through each impedance.

VL = 208 VZ = 16 + j12 Ω per phase
Iph = A
2.Easy
ABCVL​ = 690 VZ = 18 + j24 Ωper phase

A balanced Δ-connected load has an impedance of 18 + j24 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 = 18 + j24 Ω per phase
Iph = A
3.Medium
ABCVL​ = 400 VIL​ = 120 Acos φ = 0.92lagging

A balanced three-phase load draws a line current of 120 A from a supply with a line-to-line voltage of 400 V. The power factor is 0.92 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 120 Acos φ = 0.92
P = kW
4.Medium
ABCVL​ = 415 VIL​ = ?M110 kW, η = 95%cos φ = 0.9

A three-phase induction motor delivers 110 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.9 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 110 kWη = 95%cos φ = 0.9VL = 415 V
IL = A
5.Hard
P = 300 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 300 kW at a power factor of 0.75 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 0.92 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 300 kWpf1 = 0.75pf2 = 0.92VL = 480 Vf = 50 Hz
Cph = µF
6.Hard
P = 80 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 80 kW at a power factor of 0.75 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 0.98 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 80 kWpf1 = 0.75pf2 = 0.98VL = 415 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. Iph = 10.4 A
  2. 2. Iph = 23 A
  3. 3. P = 76.49 kW
  4. 4. IL = 179 A
  5. 5. Cph = 629.9 µF
  6. 6. Cph = 836.5 µF

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