Three-phase power and motor current

Introduction

Every electrical question on board starts with the power triangle: how many kilowatts does the load take, how many kVA does the generator see, how many amps flow in the cable, and what does the power factor do to each. This calculator works the triangle in three directions: from a measured current and power factor to the powers, from a known load to the current, and from a motor nameplate (shaft output, efficiency, power factor) to the full-load and starting current. It also sizes the capacitor bank to raise the power factor and shows the generator kVA the load draws.

It is for marine and plant electricians, engineers sizing feeders and generators, and students learning three-phase power.

Formulas

Power triangle (V line-to-line for three-phase, I line current):

Three-phase:  S = √3 V I,    Single-phase:  S = V I,    DC:  P = V I
P = S cos φ,   Q = S sin φ = √(S² − P²),   φ = acos(pf)

Current from power:

I = P / (√3 V cos φ)   (three-phase),   I = P / (V cos φ)   (single-phase),   I = P / V   (DC)

Motor from nameplate:

P_in = P_shaft / η,   I_FL = P_in / (√3 V cos φ),   losses = P_in − P_shaft
I_start = k × I_FL,   S_start = √3 V I_start

Power-factor correction:

Q_c = P (tan φ₁ − tan φ₂),   I_after = P / (√3 V cos φ₂)

Generator apparent power drawn = S.

• η — motor efficiency at rated load; k — starting current multiple (DOL 6–8, star-delta ≈ 1/3 of that, soft starter 2–4, VFD 1–1.5)

Assumptions and limitations

• Balanced sinusoidal three-phase loads with line quantities; star or delta makes no difference to the formulas. Unbalance and harmonics from drives change the currents and are not modelled.
• Displacement power factor at the fundamental; the sign of Q (lagging/leading) is not tracked.
• Nameplate efficiency and power factor hold at rated load only; at part load the power factor of an induction motor drops and the current falls less than the load.
• Starting current is the locked-rotor value as a multiple of full-load current at an assumed power factor of 0.3; the actual value is on the nameplate (I_A/I_N) or in IEC 60034-12.
• Capacitor sizing is for the fundamental and the entered active power; harmonic resonance and over-correction at light load need a separate study.
• Generator sizing for motor starting depends on the permitted voltage dip and the generator's sub-transient reactance, not just the starting kVA.

Worked example

A 30 kW, 400 V, 4-pole IE3 motor with nameplate efficiency 92 % and power factor 0.85, started direct on line (7 × I_N).

1. Electrical input: 30 / 0.92 = 32.6 kW; losses 2.6 kW (heat in the motor).
2. Full-load current: 32 609 / (√3 × 400 × 0.85) = 55.4 A — the catalogue figure for motors of this class is 55–57 A.
3. Apparent power 38.4 kVA, reactive power 20.2 kvar, phase angle 31.8°.
4. Starting: 7 × 55.4 = 388 A, about 269 kVA at a starting power factor of 0.3. A 400 kVA generator with this load would see a voltage dip of the order of the starting kVA over its rating times its sub-transient reactance — on the limit of the usual 15–20 %, which is why larger motors on ships use star-delta, soft starters or sequential starting.
5. Correcting the running power factor to 0.95 needs 32.6 × (tan 31.8° − tan 18.2°) = 9.5 kvar and reduces the line current to 49.5 A.

From a measured current instead: 400 V, 50 A, cos φ 0.85 → 34.6 kVA, 29.4 kW, 18.2 kvar.

FAQ

Related calculators

• Cable sizing and voltage drop — the feeder for the current found here.
• Generator load, kVA and fuel — generators supplying this load.
• Battery capacity and runtime — DC loads and emergency supplies.
• Pump and fan affinity laws — the shaft power the motor must deliver.