Calculating SLG Fault Current in Three-Winding Transformers

Tom Garrett6 min read
Other ManufacturerTechnical ReferenceWiring & Electrical
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The HV-side single-line-to-ground (SLG) current appears higher than the LV-side current after applying the transformer turns ratio. The number that matters is not the ratio-adjusted bus total; it is the branch contribution from each source through the positive-, negative-, and zero-sequence networks at the selected fault time. A grounded wye-grounded wye transformer with a delta tertiary provides a zero-sequence path, but the transformer is not an independent energy source.

Current Path and Immediate Answer

If both wye neutrals are grounded, the transformer connects the external zero-sequence networks on its two wye sides. Generators connected on the LV side can therefore contribute to an HV-side SLG fault through the transformer. The HV grid also contributes directly from the faulted bus side.

If a wye neutral is ungrounded, zero-sequence line current cannot cross that terminal because there is no return path for three equal, in-phase currents. Positive- and negative-sequence coupling alone cannot complete an SLG circuit.

The buried delta tertiary forms a closed path for circulating zero-sequence current inside the transformer. It does not export zero-sequence line current through delta terminals. Its circulation balances zero-sequence ampere-turns and affects the transformer zero-sequence impedance used by the fault calculation.

Calling the transformer a fault-current source obscures the mechanism. The grid and generators supply energy; grounded neutral paths and winding connections determine whether their zero-sequence contributions reach the fault.

Comparison of the Available Interpretations

Interpretation What the value represents Usefulness Decision
Compare HV and ratio-adjusted LV bus totals Total SLG current calculated at two different buses Shows bus duty, but combines different source sets and sequence impedances Insufficient for identifying the source of the difference
Compare transformer branch contributions Current entering and leaving each transformer winding for one fault case Separates grid, generator, neutral, and tertiary effects Use this method
Open selected sources or grounding connections in study cases Change in fault current after removing one modeled path Confirms which network element supplies each contribution Use as a diagnostic cross-check

Recommend the branch-contribution method. Run one HV-bus fault and inspect currents in every connected branch without moving the fault. Comparing separate HV- and LV-bus fault studies changes the network seen from the fault and does not isolate transformer behavior.

Sequence-Network Physics

For a solid SLG fault, the positive-, negative-, and zero-sequence networks connect in series at the fault. In a consistent ohmic or per-unit basis, the fault current is:

is the prefault positive-sequence phase-to-neutral voltage, , , and are the sequence impedances seen from the fault, and Z_f is the fault impedance. Any grounded-neutral impedance appears in the zero-sequence network multiplied by three because the neutral carries the sum of the three phase currents.

The connection described as Yn0Yn0d has grounded wye windings and a delta tertiary. For that topology, zero-sequence current can enter a grounded wye terminal, couple magnetically through the transformer, and circulate in the delta while another grounded wye terminal participates according to the transformer model. An ungrounded wye changes the path from connected to open at that terminal.

Fault timing also changes the answer. Generator contribution begins from the modeled subtransient condition and decays as machine reactance changes. Equipment interrupting duty, momentary duty, and conductor heating therefore require values from the corresponding study time. This is current and heat, not logic: thermal stress follows the time integral of I², while peak mechanical duty depends on current asymmetry and system reactance-to-resistance ratio.

Model Checks That Decide the Case

Quantity or condition Limit or expected relationship Where to read it
Wye neutral grounding Each neutral must have an intentional return path for external zero-sequence current Transformer connection data and grounding element properties
Zero-sequence transformer impedance Must represent the three-winding core and delta-tertiary path Transformer test data or manufacturer data table
Fault location Keep one HV fault location while comparing contributions Short-circuit study scenario
Reported current type Compare like quantities: branch with branch, bus total with bus total, and the same duty time Study report headings and contribution report
Voltage basis Use line-to-line voltage ratios consistently when referring line current between windings Transformer ratings and report base settings
Source sequence data Grid and generator Z1, Z2, and Z0 must be populated for an SLG result Utility source and generator model records
Neutral impedance Include it as 3Zn in the zero-sequence path Grounding resistor, reactor, or source-neutral model

A higher HV bus total can be correct because it includes the local grid contribution plus any contribution arriving through the transformer. The corresponding LV bus total is calculated from a different fault location and may exclude the direct HV-side grid path. Even within one case, delta circulating current and a third winding mean that a simple two-winding current-ratio comparison does not describe every terminal current.

Contribution-Isolation Procedure

  1. Place one SLG fault on the selected HV bus and record the fault impedance, prefault voltage option, calculation time, and reported current convention.
  2. Confirm whether each wye neutral is grounded in the model. Record every neutral impedance and verify that the delta tertiary is represented as a closed winding rather than an external grounded source.
  3. Read the transformer branch contribution on the HV winding, the LV winding contribution from the generators, the grid-source branch contribution, and any tertiary circulating current exposed by the software.
  4. Run a comparison case with the LV generators disconnected. The decrease in HV fault current identifies the generator-side contribution transferred through the transformer.
  5. Restore the generators and run a case with the HV grid source disconnected. The remaining HV fault current identifies the contribution supplied from the LV system through the grounded-wye path.
  6. Change no other model element between cases. Compare currents on the same voltage base and at the same fault time.
  7. If the isolated contributions do not reconcile with the reported total, inspect zero-sequence transformer data, source grounding, report direction conventions, and whether the displayed values are bus totals or branch currents.

Verification and Recurring Pitfalls

Verify the result first by topology. Opening a grounded neutral should remove the external zero-sequence path through that terminal. Opening the LV sources should remove their transformer-mediated contribution. Neither test should remove the direct grid contribution to a fault located on the HV bus.

Then verify arithmetic on a single study case. Refer a branch current through the transformer only when the software values represent comparable winding line currents. Use the rated voltage ratio associated with those windings, maintain one direction convention, and account for current entering the tertiary. A ratio-adjusted LV bus total is not expected to equal the HV fault-bus total when the HV grid injects current locally.

Common errors are modeling a grounded wye as ungrounded, omitting source zero-sequence impedance, treating the delta as a grounded external terminal, mixing initial and interrupting currents, and comparing currents from faults placed on different buses. Another error is substituting positive-sequence transformer impedance for zero-sequence impedance without checking the transformer data. The delta tertiary and core construction can make that substitution materially wrong.

FAQ

How do I tell whether the grid or generators supply the SLG fault?

Keep the SLG fault on the HV bus and inspect branch contributions. Disconnect one source group per comparison case; the reduction in I_f is that group’s contribution under the unchanged fault conditions.

How do I model the buried delta tertiary for ground faults?

Represent it as the transformer’s closed delta winding with the applicable zero-sequence data. It carries internal circulating zero-sequence current but does not deliver external zero-sequence line current from delta terminals.

How do I verify a higher HV-side SLG current is valid?

Compare the HV grid branch, transformer branch, and total fault current in the same study case and at the same duty time. Confirm grounded wye neutrals, Z0 data, neutral impedance, and the report’s current basis before applying a turns ratio.

Stop changing the model when the winding grounding or zero-sequence impedance cannot be traced to transformer test data or manufacturer documentation. Escalate to the transformer manufacturer’s official support channel or the study-software provider with the one-line diagram, winding connection, grounding data, sequence impedances, fault settings, and branch-contribution report.

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