Fault
Transformer
More transformer data
Utility source
More source data
Per unit on the transformer rating. Prefault 1.0 per unit, no load. Angles are referred to the source phase A voltage.
Three-line diagram
Line width follows current. Click a set of CTs, the windings or the fault to see its phasors.Scroll sideways to see the whole diagram.
Sequence networks
Per unit. The fault connects the three networks at their F and N terminals.Phasors
Try it: drag three phasors and see their sequence parts
Drag the tips of a, b and c. Any three phasors can be split into a balanced positive set, a balanced negative set and a zero set that is the same in all three phases.
I0 = (Ia + Ib + Ic) / 3 · I1 = (Ia + a·Ib + a²·Ic) / 3 · I2 = (Ia + a²·Ib + a·Ic) / 3 · a = 1∠120°
How this works
The tool solves one radial system: a utility source, a two-winding transformer and a fault at the high-side or low-side bus. It uses symmetrical components (Fortescue, 1918). The three sequence networks are built in per unit on the transformer rating. They are connected at the fault as the fault type requires, and the sequence currents are turned back into phase currents at every point in the diagram.
- Source: a Thevenin equivalent with Z1 = Z2 from the three-phase short-circuit MVA and X/R, and Z0 = (Z0/Z1)·Z1 when the source neutral is grounded. An ungrounded source has no zero-sequence path.
- Transformer: leakage impedance Z1 = Z2 = %Z at the given X/R, and Z0 = (Z0/Z1)·Z1. A resistor in a grounded neutral appears as 3R in the zero-sequence network: the neutral carries 3I0 while the per-phase network carries I0, so the drop 3I0·R is drawn as 3R.
- Zero-sequence path by connection: grounded wye – grounded wye passes zero sequence straight through. A grounded wye with a delta gives a path to the reference on the wye side only: zero-sequence current circulates in the delta and never reaches the lines on the delta side. Seen from its own terminals, a delta or an ungrounded wye gives no path.
- Phase shift: IEEE C57.12.00 (C57.12.01 for dry-type) requires the low side of delta-wye and wye-delta transformers to lag the high side by 30°; in IEC 60076-1 notation these are Dyn1 and YNd1. Positive-sequence quantities shift by −30° from high side to low side and negative-sequence quantities by +30°. Dyn11 is the reverse. YNyn0 has no shift.
- Fault: prefault voltage 1.0 per unit and no load current. Zf is in each phase to a common point for a three-phase fault, from the phase to ground for L-G, between the phases for L-L, and from the joined phases to ground for L-L-G.
- Directions: source currents toward the high-side bus, high-side CT currents into the transformer, low-side CT currents out of the transformer, fault currents into the fault. Winding currents are drawn into the polarity dot on the high side and out of it on the low side, so the two windings of a unit are in phase.
Left out on purpose: line capacitance (the small charging current in an ungrounded system), load current, motor and generator contribution on the low side, DC offset and decrement, three-winding transformers, and the zero-sequence flux path of a three-legged core. A wye-wye transformer here behaves like a bank of single-phase units.
Checking: the solver was compared with an independent phase-by-phase circuit model of the same system for every combination of connection, neutral grounding, source grounding, fault location, fault type and phase, with and without fault impedance.
References: C. L. Fortescue, “Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks,” AIEE Transactions, vol. 37, pp. 1027–1140, 1918. J. L. Blackburn, Symmetrical Components for Power Systems Engineering, 1993. IEEE Std C57.12.00-2021, angular displacement of three-phase transformers. IEEE Std 551-2006 (Violet Book), short-circuit calculations. IEC 60076-1:2011, vector group notation.
For learning and quick checks. For design work, confirm results with a full short-circuit study.