Unbalance & open phase

Two engine products drive this page. study.unbalFlow is the three-phase unbalanced steady-state load flow (P2-01): a phase-domain, four-wire (A/B/C/N) nodal formulation, so the per-phase voltages vA/vB/vC, the neutral displacement and the neutral conductor current are all raw unknowns of the solution rather than derived guesses; element impedances stay symmetric (asymmetry inside a device is not modelled), and the unbalance degree is computed as the negative-to-positive sequence ratio and compared with the GB/T 15543-2008 limit. study.openPhaseResult (P1-04) simulates a single-phase or two-phase open conductor on the same phase-domain network by removing that conductor from the admittance matrix (with the open stub left on the energised side), verifies the zero-current condition on the open phase, and reports the resulting unbalance alarm - again against GB/T 15543-2008. Both studies converge by Newton iteration on the four-wire nodal equations.

Real low-voltage systems are never balanced: lighting, socket outlets and single-phase chargers sit on one phase. The effects - neutral current, neutral displacement, negative-sequence heating of motors and the extra loss - are invisible in a symmetric study, yet they are exactly what the utility penalises and what a motor manufacturer cites when a warranty claim is rejected. An open conductor is the extreme case of the same physics and is the fault most likely to be missed by protection.

Input = topology with per-phase loads and the open-phase definition (edge, phase, which end) plus studyOptions.enableUnbalanced3pFlow / enableOpenPhase. Chain: every node is expanded into four conductors and every branch carries the three phase impedances plus a neutral impedance with the charging susceptance; transformers are inserted through their winding connection matrix and sources and neutral earthing as Norton equivalents at the slack; the nodal equations are solved by Newton iteration, and the sequence components for the unbalance degree are obtained from the three phase voltages through the same sequence function used by the PV power-quality study. For an open phase, that conductor is simply removed from the branch and the open stub stays on the energised side. Output = study.unbalFlow (per-node per-phase voltages, neutral displacement, branch currents, summary) and study.openPhaseResult (resolved flag, breaks, zero-current verification, worst unbalance against the limit). Linkage: single-phase load placement moves the neutral current and the unbalance; transformer group and earthing decide how much of it can flow; the same unbalanced currents change the losses reported on the loss page and the negative-sequence duty that the protection function sees.