Circulating currents in delta
Three Phase Systems · Lesson 12 · Intermediate
Purpose
Explain circulating current in a closed delta and separate legitimate zero-sequence paths from fault or mismatch conditions.
Learning objectives
- Define circulating current
- Explain triplen paths
- Identify unequal-emf causes
- Assess thermal consequences
A closed delta permits current to circulate around its loop without appearing as an equal line-current component. This can be intentional for some sequence components or harmful when driven by mismatch.
Core theory
Equal balanced fundamental phase emfs sum to zero around the delta, so they do not drive fundamental circulating current in an ideal unloaded loop.
In transformers, compatible delta windings can contain triplen/zero-sequence magnetising components instead of exporting them as line currents. This behavior depends on winding connection and system sequence paths.
Unequal ratios, vector groups, tap positions, phase displacement, source voltage, or impedance can drive large circulating currents when equipment is paralleled. Harmonics and unbalance add heating and must be assessed against declared winding duty.
| Term | Meaning | Symbol | Unit |
|---|---|---|---|
| Circulating current | Current flowing within a closed connection without an equivalent external line-current demand | Not applicable | Not applicable |
| Zero sequence | Three equal co-phasal components | Not applicable | Not applicable |
| Triplen | Odd multiple of the third harmonic | Not applicable | Not applicable |
Assumptions: Ideal symmetry; No harmonic or mismatch component.
- Phasors: Represent the three equal emfs at 0°, −120°, and +120°.
- Sum: Their vector sum around the closed loop is zero.
- Drive: With zero resultant fundamental emf, no fundamental circulating current is driven in the ideal loop.
The resultant fundamental driving voltage is 0 V.
Reasonableness check: A balanced three-phasor set closes geometrically.
- Saying delta always has circulating current
- Paralleling transformers from ratio alone
- Ignoring harmonic thermal duty
Where this appears in practice
Circulating-current assessment matters for transformer vector groups, parallel operation, delta tertiary windings, and converter interfaces.
Knowledge check
Can equal balanced fundamental emfs drive an ideal unloaded delta loop current?
No. Their phasor sum is zero; mismatch or other sequence/harmonic components are needed.
Answer: No. Their phasor sum is zero; mismatch or other sequence/harmonic components are needed.
Practical exercise
List the evidence required before two three-phase transformers may be considered for parallel operation.
Summary
- Balanced fundamentals sum to zero
- Delta provides sequence/harmonic paths
- Mismatch can create severe current
Sources and review
- IEC 60038: IEC standard voltages: IEC; 2009+A1:2021; International
- IEC 61921: Low-voltage power-factor-correction banks: IEC; 2017; International
- Harmonics and Power Quality Analysis webinar Q&A: IET; Current online guidance; United Kingdom
Editorial review date: 2026-08-22. Professional electrical review is pending.