Unbalanced Three-Phase Load Calculator
Find total power, overall power factor, and neutral current for an unbalanced three-phase load from each phase's own voltage, current, and phase angle.
⚡ What is an Unbalanced Three-Phase Load?
An unbalanced three-phase load has different voltage, current, or phase angle on each of its three phases, unlike a balanced load where all three are identical. In this case, total power cannot use the simple sqrt(3) x VL x IL shortcut, instead, each phase's power is computed individually and summed: P_total = Pa + Pb + Pc, and similarly for reactive power.
Electrical engineers analyze unbalanced loads whenever single-phase loads (lighting, small appliances, unevenly sized equipment) are distributed across the three phases of a building or industrial feeder, since real-world loads are rarely perfectly balanced. A key additional result in this case is the neutral current, the current the fourth (neutral) conductor must carry, found as the vector (phasor) sum of the three phase currents.
A common point of confusion is expecting neutral current to be some simple average or difference of the phase currents. It is actually a full phasor (vector) sum, each phase current has both a magnitude and an angle (relative to its own phase voltage's standard 0, -120, or +120 degree reference), and only when a load is perfectly balanced do these three phasors cancel exactly to zero.
This calculator sums each phase's individual real and reactive power into total power and overall power factor, and separately computes the resulting neutral current from the full phasor addition of the three phase currents.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Moderately Unbalanced Office Feeder
A: 230V/10A/20°, B: 230V/15A/30°, C: 230V/8A/10°
Example 2 — Perfectly Balanced Check (Neutral Current = 0)
A: 230V/20A/0°, B: 230V/20A/0°, C: 230V/20A/0°
Example 3 — Heavily Unbalanced Residential Feeder
A: 240V/12A/25°, B: 235V/18A/35°, C: 220V/6A/15°
❓ Frequently Asked Questions
🔗 Related Calculators
What is an unbalanced three-phase load?
An unbalanced three-phase load has different impedance, and therefore different current magnitude and/or phase angle, on each of its three phases, unlike a balanced load where all three phases are identical. This commonly happens when single-phase loads are unevenly distributed across the three phases of a supply.
How is total power calculated for an unbalanced load?
Total real power is simply the sum of each phase's individual real power, P_total = Pa + Pb + Pc, where each Pa = Va x Ia x cos(phi_a). The same summing approach applies to reactive power, Q_total = Qa + Qb + Qc, since power (unlike apparent power) always adds algebraically across phases.
Why can't I just use sqrt(3) x V x I for an unbalanced load?
The sqrt(3) x VL x IL formula assumes all three phases carry identical current at the same phase angle, exactly what makes a load balanced. An unbalanced load has different current and/or angle on each phase, so total power must be found by summing each phase's own power individually, not through the single balanced-load shortcut formula.
What is neutral current and why does it appear in an unbalanced system?
Neutral current is the current that flows in the fourth (neutral) conductor of a three-phase four-wire system, found as the vector (phasor) sum of the three phase currents. In a perfectly balanced system, the three currents cancel exactly and neutral current is zero, any imbalance in current magnitude or phase angle leaves a nonzero resultant that the neutral conductor must carry.
How is neutral current calculated from the three phase currents?
Each phase current is expressed as a phasor (magnitude and angle), referenced to its own phase voltage's standard angle (0, -120, or +120 degrees) minus its own phase angle. The three phasors are added as vectors (summing real and imaginary parts separately), and the magnitude of that vector sum is the neutral current.
Why is overall power factor computed differently than a simple average?
Overall power factor is PF = P_total / S_total, where S_total = sqrt(P_total^2 + Q_total^2), using the combined power triangle across all three phases. This is not the same as averaging the three individual phase power factors, since power factor depends on the ratio of total real to total apparent power, not an arithmetic mean.
What causes an unbalanced three-phase load in practice?
Common causes include unevenly distributed single-phase loads (lighting circuits, single-phase appliances) across the three phases of a building's supply, an unequal fault or partial equipment failure on one phase, or intentionally different loads connected to each phase without load-balancing during design.
What problems does an unbalanced load cause?
An unbalanced load increases neutral conductor current and losses, can cause voltage imbalance that stresses three-phase motors (reducing efficiency and lifespan), and may trip protective devices calibrated for balanced conditions. Rebalancing loads across phases is the standard mitigation.
Can this calculator model a three-phase system with no neutral conductor?
The neutral current result assumes a four-wire (star with neutral) system where a physical neutral conductor exists. In a three-wire (no neutral) system, phase currents must sum to zero by Kirchhoff's current law regardless of balance, and any apparent imbalance instead shows up as a shifted neutral point voltage rather than a neutral current.
What units does this calculator use?
Each phase's voltage is entered in volts, current in amperes, and phase angle in degrees. Total power results are shown in watts (real), volt-amperes-reactive (reactive), and volt-amperes (apparent), with neutral current shown in amperes.