Transmission & Grid calculator
Unbalanced Three-Phase Wye Load Calculator
Calculate phase currents, neutral current, neutral displacement and total power for an unbalanced wye load with connected or floating neutral.
GridBasis: RMS phasor nodal analysis
Results
- Enter values to calculate
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How to use this calculator
Different phase impedances draw different currents even from a balanced source. With a solid neutral, each branch retains its source phase-to-neutral voltage and the neutral carries the vector sum of the phase currents. Arithmetic addition of current magnitudes gives the wrong answer.
If the neutral is disconnected, the load star point moves. The branch voltages must be solved using the admittance-weighted neutral potential before dividing by each impedance. Individual branch voltages can then differ substantially, even though the source line-to-line voltages remain balanced.
Formula
VAN = VLL/√3 ∠0°; VBN = VLL/√3 ∠−120°; VCN = VLL/√3 ∠120°
Connected ideal neutral: Vn = 0; Ik = VkN/Zk; Ireturn = IA+IB+IC.
Floating neutral: Vn = (VAN/ZA + VBN/ZB + VCN/ZC)/(1/ZA+1/ZB+1/ZC); Ik = (VkN−Vn)/Zk.
Stotal = Σ [(VkN−Vn) conj(Ik)]; P = Re(Stotal); Q = Im(Stotal)
All phasors are RMS. Current flows source to load on each phase; neutral return current is defined load to source. A floating neutral has no return path, so the phase-current vector sum is zero within numerical precision.
Worked example
For 400 V line-to-line, source phase voltage is 230.9401 V. With a connected neutral and resistive branches of 10, 20 and 30 Ω, phase current magnitudes are 23.0940, 11.5470 and 7.6980 A. Neutral return magnitude is 13.8778 A, and total real power is 9.7778 kW.
Assumptions and standards
- Balanced ideal source; linear wye load; sinusoidal steady state; ABC sequence.
- Connected neutral has zero impedance; floating neutral has infinite impedance. Finite neutral/source impedance is not modeled.
- Harmonics and triplen neutral-current accumulation are not included. Negative reactance is allowed for a capacitive branch.
Calculation model checked: November 4, 2026
Frequently asked questions
Can neutral current exceed the difference between phase magnitudes?
Yes. Neutral current is a phasor sum, so both magnitudes and phase angles matter. Harmonic loads require additional analysis outside this sinusoidal model.
Can I use √3 VLL I PF for an unbalanced load?
A single line-current value does not represent a general unbalanced load. Calculate each phase complex power and add the results.
Can I use these results for final design?
Use them for preliminary design and checking. Final designs must be verified by a qualified engineer against the code edition and standards adopted where the work is installed.
Is my data sent anywhere?
No. Every calculation runs in your browser. Nothing you type is uploaded or stored on our servers.
References and further reading
Power system calculations: formulas and model guide