Sequence Fault Visualizer

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, so a delta-delta bank passes no zero sequence in either direction.
• 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 and Dd0 have no shift.
• Feeders and cable capacitance: each feeder on the low-side bus is its capacitance to ground per phase (length × µF per mile), lumped at the bus; its series impedance is left out. The capacitance is a shunt in all three sequence networks (phase-to-ground capacitance, so C1 = C2 = C0), and its charging current flows before the fault. Leaving out the feeders' series impedance for the capacitance is fair: a feeder's capacitive reactance to ground is thousands of ohms against an ohm or two in series. Feeder 1's trunk and lateral to the fault are modeled (below). On an ungrounded system the capacitance is the only return path for ground current: a bolted fault draws about 3ωC0·V_LN, the faulted feeder's CT sees the charging current of all the other feeders, and each healthy feeder's CT sees its own, in the opposite direction. The direction shown at each feeder CT is the sign of the zero-sequence reactive power, Im(3V0·3I0*), the quantity a sin φ (varmetric) directional ground element uses; it is shown only when the low side has no grounded neutral.
• Feeder 1 line: a trunk and a lateral, each 4-wire multigrounded (the neutral grounded continuously, so its effect is folded into Z0 by Kron reduction) or 3-wire unigrounded (earth return only, back to the substation ground). On a 4-wire section the neutral carries about 46 % of the ground current (|zn/znn| for this line) and the earth about 58 %; they add as phasors. With discrete ground rods instead of continuous grounding, the neutral's share rises toward the fault. On a 3-wire section the whole ground current crosses the conductor's contact resistance to earth and the substation grid resistance: include them in Zf. Line capacitance stays lumped at the bus.
• Fault surfaces: typical currents for a conductor down on each surface on a 12.5 kV feeder (7.2 kV to ground), from IEEE PSRC Working Group D15, High Impedance Fault Detection Technology (1996), turned into a resistance. Real high-impedance faults arc, flicker and change; the tool shows their steady 60 Hz equivalent.
• Voltage rise and arresters: the highest unfaulted-phase voltage to ground during a ground fault, at the fault and at the bus; the coefficient of grounding at the fault location (the highest unfaulted-phase voltage for the worst single or double line-to-ground fault there, fault resistance swept, divided by the line-to-line voltage), which is 80 % or less on an effectively grounded system (IEEE C62.92.1); and the approximate test X0/X1 ≤ 3 and R0/X1 ≤ 1, which assumes R1 is small against X1. For the arrester, the continuous voltage (1.05 × V_LN) must not exceed MCOV, and the temporary overvoltage, COG × 1.05 × V_LL, as a multiple of MCOV, must sit under the manufacturer's TOV curve for the fault clearing time (IEEE C62.22). The suggested rating is 1.05 × V_LN on an effectively grounded system and, conservatively, 1.05 × V_LL otherwise. Ratings shown are the IEEE C62.11 distribution ratings, for 2.4 to 34.5 kV systems. On an ungrounded system a ground fault can stay on until it is found, so MCOV is usually chosen at least equal to the line-to-line voltage; a fault through some resistance can even lift the leading unfaulted phase a little above line-to-line voltage (to about 1.82 per unit in this lossless model, a coefficient of grounding near 105 %).
• Fault: prefault voltage 1.0 per unit at the source 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: capacitance on the high side and of the bus, transformer and surge capacitors; cable insulation losses (so feeder 3I0 angles come out exactly ±90°, where real relays need some angle margin); series impedance of the feeders other than feeder 1; arcing and restriking transients, which can reach several per unit on an ungrounded system; grounded-wye VTs and capacitor banks, which add their own zero-sequence path; cross-country faults on two feeders; 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. W. H. Kersting, Distribution System Modeling and Analysis, Example 4.1. IEEE PSRC Working Group D15, High Impedance Fault Detection Technology, 1996. IEEE Std C62.92.1 (effective grounding), IEEE Std C62.22 (arrester application), IEEE Std C62.11 (arrester ratings).

For learning and quick checks. For design work, confirm results with a full short-circuit study.