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 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 600 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 600 VZ = 6 + j8 Ω per phase
Iph = A
2.Easy
ABCVL​ = 400 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 400 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 400 VZ = 6 + j8 Ω per phase
Iph = A
3.Medium
ABCVL​ = 415 VIL​ = ?M11 kW, η = 93%cos φ = 0.88

A three-phase induction motor delivers 11 kW of mechanical output power at full load. At this load its efficiency is 93% and its power factor is 0.88 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 11 kWη = 93%cos φ = 0.88VL = 415 V
IL = A
4.Medium
ABCVL​ = 400 VIL​ = 30 Acos φ = 0.82lagging

A balanced three-phase load draws a line current of 30 A from a supply with a line-to-line voltage of 400 V. The power factor is 0.82 lagging. Find the total real power P drawn by the load in kW.

VL = 400 VIL = 30 Acos φ = 0.82
P = kW
5.Hard
P = 200 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 200 kW at a power factor of 0.75 lagging from a 400 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. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 200 kWpf1 = 0.75pf2 = 0.95VL = 400 Vf = 60 Hz
QC = kvar
6.Hard
P = 80 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 80 kW at a power factor of 0.78 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 0.9 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 80 kWpf1 = 0.78pf2 = 0.9VL = 415 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. Iph = 60 A
  2. 2. Iph = 40 A
  3. 3. IL = 18.7 A
  4. 4. P = 17.04 kW
  5. 5. QC = 110.6 kvar
  6. 6. QC = 25.44 kvar

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