Short answer
Unbalanced load flow explicit neutral modelling matters on low-voltage networks with significant unbalance. A common three-wire reduction eliminates the neutral using an effectively grounded-neutral assumption. Kron reduction is a general elimination method: its accuracy depends on the retained variables and boundary conditions, and it does not inherently require every neutral node to be perfectly grounded. A four-wire model keeps the neutral as its own conductor with its impedance and its real grounding points, so neutral voltage can rise along the feeder. In an illustrative LV feeder with phase currents of 100, 60 and 40 A at unity power factor, neutral current is about 53 A; with 0.1 Ω of neutral impedance to the end, neutral voltage rises about 5.3 V, shifting phase-to-neutral voltages at customers by several volts in different directions. This changes voltage compliance results and neutral conductor loading. Models should include neutral impedance and grounding explicitly where unbalance is significant.
Two modelling approaches
| Aspect | Grounded-neutral approximation | Four-wire |
|---|---|---|
| Neutral voltage | Assumed zero | Calculated |
| Grounding | Implicit, perfect | Explicit impedances |
| Customer voltage | Phase-to-earth | Phase-to-neutral |
| Example neutral shift | 0 V | ≈ 5.3 V |
- Grounded-neutral three-wire approximation: the neutral is eliminated with its voltage treated as effectively zero; assess whether the actual grounding makes that approximation adequate. A general reduction can use different boundary assumptions.
- Four-wire: neutral kept as a conductor; grounding at transformer, services and electrodes modelled as impedances to earth.
Neutral current and voltage
Illustrative example. LV feeder end with phase currents 100 A, 60 A and 40 A at unity power factor, phases at 0°, −120°, +120°; neutral impedance from transformer to end 0.1 Ω. Values chosen for demonstration.
I_N = 100∠0° + 60∠−120° + 40∠120° ≈ 50 − j17.3 A, |I_N| ≈ 52.9 A
V_N ≈ 52.9 × 0.1 ≈ 5.3 V
Phase-to-neutral voltages at the customer are the phase voltages minus the neutral voltage, so the heavily loaded phase loses voltage while a lightly loaded one may gain. A reduced model that fixes V_N = 0 would miss these shifts.
Where it matters
| Situation | Effect of explicit neutral |
|---|---|
| High unbalance on LV | Neutral shift of several volts |
| Few grounding points | Larger neutral voltage |
| Triplen harmonics | More neutral current; see neutral-to-earth voltage |
| PV on one phase | Voltage rise on that phase increased |
| Balanced MV feeders | Small effect |
Inputs for four-wire models
- Neutral conductor size and length per segment.
- Grounding points and their resistance.
- Phase connection of each customer; see distribution transformer phase swapping.
- Transformer neutral grounding.
- Load models per phase; delta-connected loads need care; see delta-connected loads in transformer models.
Results to report
- Neutral voltage at each node.
- Phase-to-neutral voltages at customers, not only phase-to-earth.
- Neutral current against conductor rating.
- Comparison with the chosen three-wire approximation, recording its neutral and grounding assumptions.
What this article does not cover
Diagnosis of broken or high-resistance neutral faults is not covered here.
Where this reasoning stops. The example uses a single lumped neutral impedance; real networks need distributed models.
Practical takeaway
Use four-wire models with explicit neutral impedance and grounding where LV unbalance is significant, report phase-to-neutral voltages at customers, and check neutral current against ratings.
Reference framework
- W. H. Kersting, Distribution System Modeling and Analysis (four-wire line models).