From buses to terminals: a primer for transmission modelers

If you come from transmission optimization — MATPOWER, PowerModels.jl, PGLib-OPF ref. 13 — a bus is the electrical node: it carries a single complex voltage, KCL is one complex equation per bus, ground is the implicit reference, and there is no neutral. Even three-phase studies usually collapse to a single-phase (positive-sequence) equivalent — which is sound because transmission lines are transposed and loading is roughly balanced. Neither assumption holds on a distribution feeder, so that collapse is not available here ref. 17.

This package models distribution networks at conductor level, where that identity breaks. A bus is a physical location — a pole, a pillar, a cabinet — that hosts several terminals, one per conductor (a, b, c, n). Each terminal is its own node with its own voltage variable, KCL holds per terminal, and ground and the neutral are explicit, distinct references rather than an assumed zero ref. 1, 6. The mental shift is one sentence: a bus is a bundle of nodes, not a node.

Translation table

The Ohm's-law row is the one most likely to surprise: a distribution line is not a scalar reactance but an $n_c \times n_c$ series-impedance matrix (Carson's equations ref. 4, with the neutral as an explicit row and column), so the voltage drop on one conductor depends on the currents in all of them. The off-diagonal (mutual) terms are generally unequal — phase spacings differ — so the matrix cannot be collapsed to a transposed average without error: on the IEEE 13-node feeder, modelling one real line as transposed mis-estimates the downstream voltage unbalance by ~31% (1.50% vs 2.17%) ref. 17. See the Lines KVL constraints for the exact form.

"Why not just eliminate the neutral?"

The instinct from transmission is to fold the neutral into the phases and recover a clean per-phase model. That operation is Kron reduction ref. 10, and it is exact only when the neutral is perfectly grounded everywhere. Real LV feeders are multi-grounded through finite impedances, or grounded only at the source; under those conditions a Kron-reduced model leaves neutral and ground voltages and currents unknown and under-estimates voltage deviations ref. 6, 7. Because neutral voltage rise, neutral/ground currents, and touch-safety are precisely what distribution studies care about, this model keeps the neutral as an explicit conductor and declines the reduction. (Where a reduction is sound, it is applied deliberately and provenance-tracked — not assumed.) The grounding tutorial demonstrates all of this live — including the exact-when-pinned Kron claim, verified to the last digit.

Where you've seen this before

The terminal view is the distribution-standard one, not an invention of this package:

• OpenDSS addresses conductors with Bus.node notation — Bus1.1.2.3.4 names phases 1–3 and the neutral conductor 4 at Bus1 (node 0 is reserved for ground) ref. 9.
• PowerModelsDistribution.jl models the same structure as terminals and connections, with buses carrying one node per conductor, and supports proper four-wire (explicit-neutral) models, not only Kron-reduced ones ref. 15.

Beyond terminals: more surprises

The terminal model is the central shift, but a few further conventions will look unfamiliar to a MATPOWER/PowerModels user:

• The data model is in SI units (volts, amperes, ohms), not per-unit. There is no system MVA base in the data model; an impedance is a fixed property of a piece of equipment, independent of where it sits — which avoids the base-bookkeeping per-unit needs across voltage levels (Dommel, via Dugan ref. 16; OpenDSS likewise stores and simulates in actual volts/amps/ohms ref. 9). This is a choice about representation and is independent of the units the solver computes in: the OPF can solve directly in SI or in an internally-scaled per-unit copy (per_unit), and which one better conditions the nonlinear program is an open, instance-dependent question — see Units & scaling.
• Sequence coordinates are derived, not the network state. The symmetrical-component transform is an invertible change of coordinates for any three-phase phasor vector. What requires a cyclically symmetric network (commonly obtained from balanced/transposed parameters) is the stronger step of treating the positive-, negative-, and zero-sequence networks as decoupled ref. 17. This formulation therefore solves in phase/conductor coordinates and uses Fortescue components only as derived quantities for sequence-voltage limits. A stray $\sqrt{3}$ or phase-shift multiplier is not by itself evidence of a balanced model; the tell is whether mutual coupling and unequal conductor states have been discarded.
• The formulation is rectangular current–voltage (IVR), not power-balance polar. The decision variables are currents ($c^r, c^i$) and rectangular voltages ($v^r, v^i$); KCL is written in currents, and power is a bilinear product of the two — not $|V|\angle\theta$ with $P/Q$ bus injections ref. 1, 6. This is why opf.md is written in $c^r_{...}$ rather than $P_g$. See Variables.
• There is no slack/PV/PQ bus typing. The voltage and angle reference is a voltage source's fixed rectangular value, and that source absorbs imbalance as a current slack; generators are plain current injections, not voltage-controlled $P,|V|$ buses. See Voltage sources.

Next steps

• Data model conventions — terminal naming, voltage bounds, grounding, and how devices reference terminals.
• Optimal power flow — the variables, per-terminal KCL, and the matrix Ohm's-law constraints in full.