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Three-Phase Unbalanced Load · Neutral Point Displacement and Neutral Line Current

One phase load changes in a three-phase four-wire system, demonstrating neutral point displacement and neutral line current changes.
Voltage/current phasor diagrams update in real time, intuitively presenting the unbalanced effect.

Three-Phase Load Parameters

50 Ω
10 Ω200 Ω
50 Ω
10 Ω200 Ω
50 Ω
10 Ω200 Ω
0°
-90° (Capacitive)90° (Inductive)
Phase Voltage \(V_{\text{phase}}\) 220 V (RMS)
Frequency \(f\) 50 Hz

Three-Phase Currents

\(I_A\)
4.40 A
0°
\(I_B\)
4.40 A
-120°
\(I_C\)
4.40 A
120°

Neutral Point Analysis

Neutral Displacement Voltage \(V_{NN'}\) 0.00 V
\(V_{NN'}\) Angle 0°
Neutral Line Current \(I_N\) 0.00 A
\(I_N\) Angle --

\(V_{NN'}\) is the neutral point displacement voltage (calculated) without a neutral line

Voltage/Current Phasor Diagram

V_A V_B V_C I_A I_B I_C I_N

Arrow length represents RMS magnitude and direction represents phase angle. Current phasors are scaled by 50 to share the voltage scale; labels retain their actual values. \(V_{NN'}\) is shown as a purple dashed line.

Voltage and Neutral Line Current Waveforms

V_A I_A I_N

Theoretical Basis

In a three-phase four-wire system, neutral current \(I_N = I_A + I_B + I_C\) (phasor sum).
When load is balanced, \(I_N = 0\); when unbalanced, \(I_N \neq 0\).
Without a neutral line (three-phase three-wire), the neutral displacement voltage is:
\(V_{NN'} = \frac{V_A Y_A + V_B Y_B + V_C Y_C}{Y_A + Y_B + Y_C}\) where \(Y = 1/Z\) is admittance.

Characteristic Interpretation

The neutral line forces the load neutral point potential to equal the supply neutral point, keeping each phase load voltage symmetric.
If the neutral line breaks, unbalance causes severe voltage deviation across phases (some phases over-voltage, some under-voltage).
Adjust Phase A load to observe: I_A changes in the phasor diagram, I_N appears, V_NN' deviates from the origin.