Modern electrical distribution networks — particularly long radial three-phase feeders supplying remote loads, rural infrastructure, or renewable energy collection systems — present a fundamental protection challenge that is often underestimated at the system design stage. As the penetration of inverter-based generation (photovoltaic, wind, battery storage) increases, the short-circuit behaviour of these networks departs significantly from the assumptions embedded in conventional overcurrent and earth fault protection philosophies.
A central statistic motivates the discussion: single-phase-to-ground faults are by far the most frequent fault type in power systems, accounting for approximately 70–80% of all recorded fault events [1,2,3]. This figure is consistent across medium-voltage (MV, 1–36 kV) and high-voltage (HV, 36–150 kV) distribution networks worldwide and has been confirmed in multiple peer-reviewed studies of 6–66 kV systems. The dominance of single-phase ground faults arises from the physical vulnerability of individual phase conductors to insulation degradation, wildlife contact, vegetation encroachment, conductor galloping, and mechanical damage — all statistically far more likely to affect one phase at a time than to produce a simultaneous multi-phase event [4].
On a long distribution feeder, this is compounded by impedance. Source impedance increases with line length, reducing available fault current at the remote end. On an inverter-dominated network, grid-following inverters typically limit their output current to 1.0–1.2 times rated current within a few milliseconds of fault inception [5]. The result: a single-phase ground fault at the far end of a long feeder may produce a fault current indistinguishable from a normal load unbalance. The earth fault relay sees no credible pickup signal, the fault persists, and the probability of escalation to a multi-phase event increases significantly.
This problem is not new to renewable energy sites. Remote communities, mining camps, offshore platforms, and rural areas supplied by diesel generators have faced the same challenge for decades. A diesel generator’s subtransient reactance X″d (the reactance governing fault current in the first few cycles), transient reactance X′d (governing the following seconds), and synchronous reactance Xd (the steady-state value) typically produce a three-phase fault current of only 5–10 times rated — already modest compared to a strong grid connection. For a single-phase-to-ground fault, which must drive current through the series combination of positive-, negative-, and zero-sequence impedances, the fault current is lower still. If the generator neutral is left unearthed or earthed through high impedance to limit stator winding damage — which is common practice — the zero-sequence impedance seen from the fault can be very large, producing a ground fault current that falls below the pickup of any conventional overcurrent relay. Remote area power supply (RAPS) engineers have managed this limitation for years, typically through careful neutral earthing schemes and sensitive voltage-based detection. The zig-zag reactor addresses it more directly and more completely, as this article describes.
The solution in both contexts is the deliberate introduction of a low zero-sequence impedance path at an appropriate point in the network — a piece of equipment that provides a stable, well-characterised ground reference and a controlled fault current magnitude, independently of the generation technology connected. Two equipment topologies accomplish this: the star-delta transformer (familiar from conventional power system practice) and the purpose-built zig-zag reactor. This article covers the operating principles of both, compares their zero-sequence impedance characteristics, and provides a complete specification methodology for the zig-zag reactor — including tap selection, capacity rating, and protection coordination.
1. The Zig-Zag Winding — Operating Principle
1.1 Winding configuration
A zig-zag winding (also termed an interconnected-star winding) subdivides each phase into two half-windings distributed across two separate limbs of a three-leg core. On each limb, one half-winding belongs to one phase and the second belongs to a different phase, connected in series with reversed polarity. The six half-windings are interconnected so that their junction points form the line terminals and their common point forms the neutral.
As a purpose-built reactor — rather than a power transformer — the unit is wound on an air-gapped three-leg core. The air gap on each limb linearises the magnetic characteristic of the core, preventing saturation under sustained fault current and making the zero-sequence impedance Z₀ predictable and stable across the full current range from no-load to maximum fault current. The gap width is the primary means by which the manufacturer sets Z₀ to the specified value.
The air gap is essential not only for controlling Z₀ but also for eliminating the nonlinear inductance that would otherwise make the reactor susceptible to ferroresonance on capacitive cable networks. An ungapped transformer used as an interim grounding unit does not have this protection — ferroresonance has been observed in practice on cable-fed 12–35 kV substations using ungapped grounding transformers. With the air-gapped core, the linear inductance cannot sustain ferroresonance regardless of the network capacitance.
1.2 Magnetomotive force cancellation and zero-sequence conduction
For positive- or negative-sequence currents, the two half-windings on each limb carry currents 120° apart — their magnetomotive forces (MMFs) partially cancel and the reactor presents high leakage impedance to the network. For zero-sequence currents (all three phases in phase), the MMFs on each limb add, the reactor conducts freely, and the sum 3I₀ returns via the neutral terminal.
1.3 Sequence impedance summary
| Sequence | Impedance seen by network | Physical mechanism |
|---|---|---|
| Positive (Z₁) | High — leakage reactance only | MMFs partially cancel; no circulating path |
| Negative (Z₂) | High — approximately equal to Z₁ | Same MMF cancellation as positive sequence |
| Zero (Z₀) | Low — set by air gap design | MMFs add; reactor conducts freely; neutral provides return |
2. Comparison with the Star-Delta Transformer
2.1 Network equivalence
An unloaded star-delta transformer — whose delta secondary winding is closed on itself but feeds no external load — is electrically equivalent to a zig-zag reactor from the perspective of the upstream network. Both present high positive- and negative-sequence impedances and a low zero-sequence impedance shunted to the neutral. Both circulate zero-sequence and triplen harmonic currents internally.
2.2 Cost — the primary advantage of the zig-zag
A zig-zag reactor uses only one set of windings per phase. A star-delta unit achieving the same zero-sequence impedance needs two full winding sets. For a device whose sole function is zero-sequence current supply, the extra material represents waste. The zig-zag delivers the same zero-sequence shunt at roughly half the active material, typically translating to 40–60% lower cost at equivalent kilovolt-ampere (kVA) rating and voltage class.
2.3 Limitations of the star-delta approach
| Aspect | Star-delta (no load) | Purpose-built zig-zag reactor |
|---|---|---|
| Zero-sequence Z₀ | Fixed at manufacture; may not suit protection | Specified to target fault current |
| Ferroresonance risk | Yes — ungapped core on capacitive networks | No — air gap linearises inductance |
| Material and cost | Two full winding sets — higher cost | One winding set — 40–60% lower cost |
| Triplen harmonic filtering | Yes — circulates in delta winding | Yes — circulates in zig-zag winding |
| Tap adjustment | Not available after manufacture | Can be specified with taps |
3. Zero-Sequence Impedance and the Sequence Network
3.1 The sequence network for a single-phase-to-ground fault
For a solid phase-to-ground fault the three sequence networks are connected in series. The zig-zag reactor appears only in the zero-sequence network — it contributes nothing to Z₁ or Z₂. On a weak inverter-based or diesel-fed system where Z₁ is large, reducing Z₀ via the reactor has a proportionally larger effect on fault current than the same change would produce in a stiff grid-connected network.
3.2 Zero-sequence impedance — zig-zag reactor
In per unit (pu) on the system base:
3.3 Zero-sequence impedance — star-delta transformer
4. Specifying the Zig-Zag Reactor
4.1 Design objective
The specification starts from two boundary conditions that bracket the acceptable zero-sequence impedance:
- Minimum fault current If,min — the lowest single-phase-to-ground fault current that guarantees reliable earth fault relay operation, accounting for arc resistance and remote fault location. A sensitivity margin of 1.5–2.0 is recommended: If,min ≥ 2 × Ipickup.
- Maximum fault current If,max — the highest fault current the system can sustain without exceeding the ratings of cables, switchgear, the neutral current transformer (CT), and the reactor short-time rating.
4.2 Arc resistance and the Warrington formula
Single-phase ground faults on overhead lines and open switchgear typically involve an electric arc rather than a solid metallic contact. Arc resistance is not constant — it depends on arc current and arc length. The empirical Warrington formula gives a practical estimate:
4.3 Key equations
4.4 Worked example — 13.8 kV / 5 MVA islanded renewable energy site
Step 1 — Total positive-sequence impedance:
Step 2 — Z0 parallel combination (reactor ∥ line):
Step 3 — Fault current without reactor:
Step 4 — Fault current with reactor:
4.5 Voltage at each measurement point
The positive-sequence current I₁ = 112 A flows through the feeder producing a voltage drop at every point. Va is never 100% anywhere on the network during a fault — the depression propagates to all points including downstream of the reactor. The difference between upstream fault (F1) and downstream fault (F2) is small at Points B and C — current magnitude and direction are the reliable discriminators, not voltage.
| Point | Description | Va — F1 upstream | Va — F2 downstream | 3V₀ — F1 | 3V₀ — F2 | Ia — F1 | Ia — F2 |
|---|---|---|---|---|---|---|---|
| A | Source bus | 94.3% | 89.2% | ~2.5% small | ≈ 0 | ≈ 32 A | 112 A |
| B | Reactor bus | 87.5% | 86.1% | 1,517 V (19%) | 1,517 V (19%) | 150 A | 150 A |
| C | Load feeder | 87.5% | 86.1% | 0 | 1,149 V (14%) | ≈ 100 A load | 337 A |
| F | Fault point | 84.6% | 84.6% | — | — | — | 337 A · Va ∥ Ia (θ=0°) |
4.6 Network topology and phasor diagrams
The following connection diagram shows the 13.8 kV / 5 MVA islanded site with the three measurement points and both fault locations. The phasor grid below shows what each measurement point sees — voltages and currents — for both fault cases, including Point F (the fault point itself).
4.7 Arc resistance sensitivity
The following table shows how fault current varies with arc resistance for this system. The calculation is iterative for the Warrington cases — R_arc depends on I_f which depends on R_arc. Design is always based on the highest arc resistance (lowest fault current) — if the relay operates at 337 A it will certainly operate at 624 A or 815 A.
| Z_f (Ω) | Scenario | I_f (A) | % rated | Margin at 100 A pickup |
|---|---|---|---|---|
| 0 | Bolted fault | 815 | 390% | ×8.2 |
| 5 | Warrington — 0.3 m arc (converged) | 624 | 299% | ×6.2 |
| 10 | Warrington — 0.5 m arc approx. | 472 | 226% | ×4.7 |
| 20 | Design basis — conservative | 337 | 161% | ×3.4 ← governs specification |
| 40 | Long arc / resistive ground | 216 | 103% | ×2.2 |
| 80 | Extreme — near detection limit | 125 | 60% | ×1.25 ← at pickup boundary |
4.8 Downloadable calculation sheet
A complete step-by-step calculation sheet covering all equations, the full voltage table, the arc resistance sensitivity analysis, and an adaptation template for other voltage levels is available for download:
Download calculation sheet (.docx)5. Tap Selection and Adjustment Over Time
5.1 Rationale
Renewable energy and remote power sites are not static: generation capacity is added in phases, grid connection impedances change as the upstream network reinforces, and protection settings are refined with operational experience. Each change alters Z₁ and Z₂ and shifts the ground fault current that a fixed-Z₀ reactor produces. Specifying taps at the outset provides field-adjustable Z₀ without equipment replacement.
Tap changes must be made off-load and de-energised using an off-circuit tap changer. On-load tap changing is not appropriate for grounding reactors whose operating duty is intermittent rather than continuous.
5.2 Fault current and reactor loading at each tap
5.3 Representative tap schedule
| Tap | Z₀ (rel. to nominal) | I_f | S(tap) | I²t check |
|---|---|---|---|---|
| 1 (max Z₀) | 1.20 × Z₀,nom | I_f,min | S_min | ≥ I²t_rated |
| 2 | 1.10 × Z₀,nom | I_f,2 | S_2 | ≥ I²t_rated |
| 3 (nominal) | Z₀,nom | I_f,nom | S_nom | ≥ I²t_rated |
| 4 | 0.90 × Z₀,nom | I_f,4 | S_4 | ≥ I²t_rated |
| 5 (min Z₀) | 0.80 × Z₀,nom | I_f,max | S_max | Most onerous — governs rating |
6. Protection — Neutral CT, Relay Coordination, and Thermal Rating
6.1 Neutral current transformer
A current transformer (CT) installed on the neutral-to-ground connection of the zig-zag reactor measures the zero-sequence fault current 3I₀ during a ground fault and carries negligible current under balanced conditions.
| Parameter | Requirement | Standard |
|---|---|---|
| Primary rating | I_CT ≥ I_f,max at lowest tap (Eq. 9 at tap 5) | IEC 61869-2 |
| Accuracy class | Class 5P or 10P for protection | IEC 61869-2 |
| Accuracy limit factor (ALF) | I_CT × ALF ≥ I_f,max — CT must not saturate during maximum fault current | IEC 61869-2 |
| Dynamic rating | I_peak = k√2 × I_f,max where k = DC offset factor (1.5–2.5 depending on X/R ratio of Z₀) | IEC 61869-2 |
| Burden | CT burden ≤ rated burden at specified accuracy class | IEC 61869-2 |
6.2 Earth fault relay coordination
The earth fault relay on the neutral CT operates as a definite-time or inverse definite minimum time (IDMT) overcurrent element. Its pickup current Ipickup and time multiplier setting (TMS) must satisfy:
- Sensitivity: Ipickup ≤ If,min / 2 — sensitivity margin of 1.5–2.0 recommended.
- Selectivity: Grade with downstream feeder earth fault relays — grading margin ≥ 0.3–0.4 s for definite-time.
- Stability under load unbalance: Long feeders with single-phase loads may produce a standing 3I₀ component. Set Ipickup above worst-case load unbalance.
6.3 Thermal rating and short-time duty
6.4 Protection checklist
| Item | Parameter to specify | Governing reference |
|---|---|---|
| Neutral CT primary rating | I_CT ≥ I_f,max at lowest tap | Eq. 9 at tap 5 |
| CT accuracy class | 5P or 10P | IEC 61869-2 |
| CT accuracy limit factor | I_CT × ALF ≥ I_f,max | IEC 61869-2 |
| CT dynamic rating | I_peak = k√2 × I_f,max | IEC 61869-2 |
| Relay pickup | I_pickup ≤ I_f,min / 2 | Sensitivity margin 1.5–2.0 |
| Relay grading | t_grading ≥ 0.3 s above downstream feeder relay | Protection coordination study |
| Reactor I²t withstand | I²_f,max × t_c,backup ≤ I²t_rated | IEC 60076-6; Eq. 12 |
| Tap-by-tap I²t check | Eq. 9–11 at all tap positions | Most onerous tap governs |
7. Alternative Approach — Voltage-Based Detection Without a Reactor
Installing a zig-zag reactor creates zero-sequence fault current by design. Before the reactor exists — or on a system where the reactor has not yet been specified — there is essentially no zero-sequence current to measure on a weak network. Under these conditions, conventional overcurrent-based earth fault protection cannot operate reliably.
If a reactor is not installed, the only viable detection method is voltage-based. A single-phase-to-ground fault on an unearthed or high-impedance earthed network causes a voltage unbalance that is measurable even when the fault current is negligible. Two instrument transformer arrangements provide this signal:
The first uses a voltage transformer (VT) connected in open-delta (also called broken-delta) on the secondary, with the primary windings connected star to earth. The open-delta secondary voltage is the zero-sequence voltage 3V₀. Under balanced conditions 3V₀ is zero. During a single-phase fault it rises — on a solidly unearthed system it can approach the full phase-to-phase voltage. A voltage relay monitoring the open-delta output can initiate an alarm or a timed trip.
The second arrangement uses a star-connected VT with the neutral brought out, allowing 3V₀ to be measured directly as the neutral point displacement from earth potential.
Both arrangements detect that a fault exists somewhere on the network. They do not identify which feeder is faulted and they provide no directional information. Tripping on voltage displacement alone disconnects the entire busbar.
In practice, the most robust protection scheme for a weak remote system combines both: the zig-zag reactor to establish a defined zero-sequence current source, and a 3V₀ measurement at the source bus (Point A) to provide the reference signal for the directional earth fault element (ANSI 67N). The phasor grid in Fig. 6 illustrates the complete picture — 3V₀ at Point A is ~2.5% for an upstream fault and ≈0 for a downstream fault, providing the upstream/downstream discrimination that the neutral CT at Point B cannot resolve alone.
References
- Wu, Z. et al., “Single-phase grounding fault types identification based on multi-feature transformation and fusion,” Sensors, vol. 22, no. 9, p. 3521, 2022. https://doi.org/10.3390/s22093521
- Liu, J. et al., “The classification model for identifying single-phase earth ground faults in the distribution network jointly driven by physical model and machine learning,” Frontiers in Energy Research, 2022. https://doi.org/10.3389/fenrg.2022.919041
- Song, G. et al., “Faulty feeder detection for single-phase-to-ground fault in resonant grounding system based on transition resistance estimation,” Electric Power Systems Research, 2025. https://doi.org/10.1016/j.epsr.2025.110655
- Elprocus, “Types of faults in electrical power systems and their effects,” 2021. Available: https://www.elprocus.com/what-are-the-different-types-of-faults-in-electrical-power-systems/
- Teodorescu, R., Liserre, M., and Rodríguez, P., Grid Converters for Photovoltaic and Wind Power Systems. Chichester: Wiley-IEEE Press, 2011.
- IEC 60076-6:2007, Power Transformers — Part 6: Reactors. Geneva: International Electrotechnical Commission, 2007.
- IEC 61869-2:2012, Instrument Transformers — Part 2: Additional Requirements for Current Transformers. Geneva: International Electrotechnical Commission, 2012.
- Warrington, A.R.C., “Reactance Relays Negligibly Affected by Arc Impedance,” Electrical World, September 1931.
Content drafted with AI assistance and validated by the author based on 30 years of experience in the Power Quality and Power Systems field.