Zig-Zag Reactors for Zero-Sequence Current Supply for Weak Power Systems

From 42 A to 337 A: How Zig-Zag Reactors Make Ground Faults Detectable on Weak Power Systems — A Practical Case Study

Ground Fault Protection · Renewable Energy · Power Systems

Denis Ruest, IPQDF 13.8 kV / 5 MVA islanded site IEC 60076-6 · IEC 61869-2

Introduction

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. 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, transient reactance X′d, and synchronous reactance Xd 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 — which is common practice to limit stator winding damage — 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.

The solution 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 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.

Scope

Equations are parametric — no specific voltage level is assumed in the theory sections. A fully worked numerical example using a 13.8 kV / 5 MVA islanded renewable energy site is developed in Section 4, with a downloadable calculation sheet provided for adaptation to other voltage levels. The zig-zag reactor is treated as primary electrical equipment with its own equipment tag, asset register entry, and maintenance schedule.

01 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. 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.

Fig. 1 — Air-gapped three-leg core zig-zag reactor. Each limb carries one upper and one lower half-winding from two different phases in series with opposing polarity. The air gap (dashed white break) linearises the magnetic characteristic, sets Z₀ to the specified value, and eliminates ferroresonance susceptibility on capacitive cable networks.

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.

Fig. 2 — Balanced positive-sequence load (left) vs zero-sequence ground fault (right). Under balanced conditions I_N = 0 — the reactor is transparent. During a fault all three phases carry in-phase I₀; these sum to 3I₀ at 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

02 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.

Fig. 3 — Network equivalence between the zig-zag reactor and an unloaded star-delta transformer. Both present the same sequence network: high Z₁ and Z₂, low Z₀ shunted to the reference bus.

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 kVA rating and voltage class.

2.3 Limitations of the star-delta approach

Note on using stock star-delta transformers

A star-delta transformer already on site can serve as a temporary or interim zero-sequence current source if its Z₀ produces a minimum fault current above relay pickup. It should not be assumed suitable without a full sequence network study. Additionally, an ungapped transformer core is susceptible to ferroresonance on capacitive cable networks — the purpose-built air-gapped zig-zag reactor eliminates this risk entirely.

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

03 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.

Fig. 4 — Sequence network for a single-phase-to-ground fault. The zig-zag reactor appears only in the zero-sequence network as a shunt Z₀ to the reference bus. On a weak system with large Z₁ and Z₂, lowering Z₀ has proportionally more impact on I_f.

3.2 Zero-sequence impedance — zig-zag reactor

Eq. 1

\( Z_0 = \dfrac{V^2_{LL}}{S_0} \)

Z₀ in Ω; V_LL = line-to-line voltage (V); S₀ = rated zero-sequence kVA

Eq. 2

\( z_0\,(\text{pu}) = \dfrac{S_\text{base}}{S_0} \times z_{0,\text{rated}} \)

z₀_rated as a fraction from the reactor nameplate

3.3 Zero-sequence impedance — star-delta transformer

Eq. 3

\( Z_0 = z_k \times \dfrac{V^2_{LL}}{S_\text{rated}} \)

z_k = per-unit leakage impedance from nameplate; typically 0.04–0.08 pu; fixed at manufacture

Contribution to short-circuit power

The zig-zag reactor does not contribute to three-phase short-circuit MVA. However, it materially increases the single-phase-to-ground fault current by lowering Z₀_total. This effect must be accounted for in protection coordination and equipment ratings.

04 Practical Example — 13.8 kV / 5 MVA Islanded Renewable Energy Site

Before developing the specification methodology, it is instructive to see the reactor in action on a real network. The numbers below are site-specific — a 13.8 kV / 5 MVA islanded renewable energy site with a 5 km overhead feeder. They are not universal. The specification methodology in Section 5 provides the parametric equations for any voltage and any site.

4.1 System parameters

Site parameters — 13.8 kV / 5 MVA islanded site

Voltage: 13.8 kV · V_ph = 7,967 V | Rating: 5 MVA islanded · I_rated = 209 A | Source: inverter-based, SCR = 5 · Z1_src = 1.0 + j7.6 Ω (delta-wye transformer blocks zero-sequence back-propagation) | Feeder: 5 km overhead 70 mm² ACSR · Z1_line = 2.2 + j1.7 Ω · Z0_line = 8.0 + j5.0 Ω | Reactor: Z0_reactor = j4.5 Ω (air-gapped three-leg core) | Arc fault: Z_f = 20 Ω (conservative basis — see §4.5)

4.2 Fault current — without and with reactor

Step 1 — Total positive-sequence impedance:

Z1_total

\( = (1.0+j7.6) + (2.2+j1.7) = 3.2+j9.3\ \Omega \quad |Z_1| = 9.84\ \Omega \)

Z1 = Z2 (symmetrical)

Step 2 — Z0 parallel combination (reactor ∥ line):

Z0_total

\( = j4.5 \,\|\, (8+j5) = \dfrac{j4.5\,(8+j5)}{8+j9.5} = 1.05+j3.25\ \Omega \quad |Z_0| = 3.41\ \Omega \)

Full derivation in downloadable calc. sheet

Step 3 — Fault current without reactor:

No reactor

\( I_f = \dfrac{3 \times 7{,}967}{566.7} \approx 42\ \text{A} \quad (20\%\ \text{of rated}) \)

Z0 ≈ 500 Ω (capacitive path only) — undetectable

Step 4 — Fault current with reactor:

With reactor

\( I_f = \dfrac{3 \times 7{,}967}{70.9} = 337\ \text{A} \quad (161\%\ \text{of rated}) \quad \theta_f = 18°\ \text{lag} \)

I₁ = I₂ = I₀ = 112 A · relay at 100 A pickup: margin = 3.4×

Result

The reactor raises fault current from 42 A (20% of rated — undetectable) to 337 A (161% of rated) with a relay sensitivity margin of 3.4× at a 100 A pickup. The fault angle of 18° lag confirms that arc resistance dominates — the physical signature of a high-impedance arc fault.

4.3 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 1.4% difference in Va between upstream (F1) and downstream (F2) faults at Points B and C is indistinguishable in practice — current magnitude and direction are the reliable discriminators.

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°)

Key insight — Point B neutral CT

The neutral CT at Point B reads |3I₀| = 337 A for both fault locations — identical magnitude, only 1.4% Va difference. The only reliable discriminator at B is the direction of 3I₀ relative to 3V₀, requiring phase CTs and a VT simultaneously — not a neutral CT alone. A 59N relay at Point A detects upstream faults via 3V₀ (present for F1, ≈0 for F2). A feeder overcurrent relay at Point C detects downstream faults via Ia magnitude (337 A for F2, load-only for F1).

4.4 Network topology and phasor diagrams

Fig. 5 — Network topology for the 13.8 kV / 5 MVA islanded site. Point A measures 3V₀ — discriminates upstream vs downstream. Point B measures 3I₀ direction — requires phase CTs and VT. Point C measures Ia magnitude — discriminates downstream faults. F1 and F2 show both fault locations; Zf = 20 Ω in both cases.

Fig. 6 — Complete 2×4 phasor grid (Zf = 20 Ω, Z0_reactor = j4.5 Ω, I_f = 337 A). Rows: Points A · B · C · F. Columns: upstream fault F1 · downstream fault F2. The Point F row shows Va and Ia exactly in phase (θ = 0°) — the physical signature of a purely resistive arc fault.

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 spec
40	Long arc / resistive ground	216	103%	×2.2
80	Extreme — near detection limit	125	60%	×1.25 ← at pickup boundary

A complete step-by-step calculation sheet covering all equations, the full voltage table, arc resistance sensitivity analysis, and an adaptation template for other voltage levels:

Download calculation sheet (.docx)

4.5 Arc resistance sensitivity

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 spec
40	Long arc / resistive ground	216	103%	×2.2
80	Extreme — near detection limit	125	60%	×1.25 ← at pickup boundary

4.6 Reactor placement and protection consequences

The two fault locations in this example illustrate why reactor placement has direct consequences for protection. For a downstream fault (F2), the feeder overcurrent relay at Point C operates cleanly on 337 A — selective, fast, no additional equipment needed beyond a standard neutral CT and earth fault relay. For an upstream fault (F1) on the 5 km feeder between source and reactor, the neutral CT detects the same fault current but there is no dedicated breaker on that upstream section to operate selectively. The reactor detects the fault but cannot isolate it without tripping the entire source.

This is the fundamental consequence of placing the reactor away from the source: the section of feeder between source and reactor is inherently harder to protect selectively, and the longer that section is, the greater its fault exposure. Placing the reactor as close to the source as the network topology permits is therefore the recommended approach — it minimises the length of the unprotected upstream section and keeps the protection scheme simple.

When site constraints force the reactor further from the source — geographic limitations, retrofit of an existing network, a remote load bus that must be served — selective protection of the upstream section requires additional equipment: a directional earth fault relay (ANSI 67N) at the reactor bus, a supplementary VT for the 3V₀ reference, and ideally a recloser or sectionaliser on the upstream feeder. This additional protection comes with additional cost. The two installation cases and their respective protection philosophies are examined in detail in Section 7.

4.7 Downloadable calculation sheet

A complete step-by-step calculation sheet covering all equations, the full voltage table, arc resistance sensitivity analysis, and an adaptation template for other voltage levels:

Download calculation sheet (.docx)

05 Specifying the Zig-Zag Reactor

5.1 The air gap — what you specify and what you do not

The air gap width is not a user-specified parameter and is not standardised by IEC 60076-6 or any other norm. The purchaser specifies only the required zero-sequence impedance Z₀ in ohms (or in per unit on the system base), and the manufacturer determines the gap geometry needed to achieve it. IEC 60076-6 defines the impedance tolerance (typically ±10%) and the test methods — gap width is an internal manufacturing variable.

The relationship governing the gap is:

Gap

\( L = \dfrac{\mu_0 \, N^2 \, A}{g} \quad \Rightarrow \quad Z_0 = \omega L \)

μ₀ = 4π×10⁻⁷ H/m · N = turns · A = core cross-section (m²) · g = total gap length (m)

The manufacturer solves for g given the specified Z₀, the core geometry, and the number of turns. For a typical 13.8 kV reactor with Z₀ = j4.5 Ω, gap widths fall in the range of 5–25 mm per limb depending on core dimensions — but this figure never appears on the purchaser’s specification sheet. What does appear, and what must be verified during factory acceptance testing, is the measured zero-sequence impedance at rated current.

What to put in your specification

Specify Z₀ in ohms and its tolerance (±10% per IEC 60076-6 is standard). Do not specify gap width — this constrains the manufacturer unnecessarily and adds no protection value. The impedance test at factory acceptance is the correct verification method.

5.2 Design objective

The specification starts from two boundary conditions that bracket the acceptable zero-sequence impedance:

Minimum fault current I_f,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: I_f,min ≥ 2 × I_pickup.
Maximum fault current I_f,max — the highest fault current the system can sustain without exceeding the ratings of cables, switchgear, the neutral CT, and the reactor short-time rating.

5.3 Arc resistance and the Warrington formula

Single-phase ground faults on overhead lines 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:

Eq. 4

\( R_\text{arc} = \dfrac{28{,}730 \times L}{I_f^{1.4}} \)

L = arc length in metres; I_f = fault current in amperes; R_arc in ohms

Arc resistance — design basis

For a 0.3 m arc at 337 A, Warrington gives R_arc ≈ 7–10 Ω. This article uses Z_f = 20 Ω — a conservative value implying a longer arc (≈ 0.6–0.8 m) or a deliberate safety margin. Specify for the worst-case arc resistance — the relay will certainly also operate for shorter, lower-impedance arcs. The arc resistance sensitivity table in §4.5 shows the full operating envelope.

5.4 Key equations

Eq. 5

\( I_f = \dfrac{3\,V_\text{ph}}{Z_1 + Z_2 + Z_{0,\text{total}} + 3Z_f} \)

V_ph = V_LL / √3; Z_f = arc resistance; all impedances in Ω

Eq. 6

\( Z_{0,\text{design}} = \dfrac{3\,V_\text{ph}}{I_{f,\text{target}}} – Z_1 – Z_2 – 3Z_f \)

Target Z₀ from desired fault current — includes arc resistance term

Eq. 7

\( S_0 = 3 \times \dfrac{V_n}{\sqrt{3}} \times I_{f,\text{max}} \)

Reactor kVA rating — short-time duty at maximum fault current

Eq. 8

\( I^2_{f,\text{max}} \times t_c \leq I^2t_\text{rated} \)

Short-time withstand — use backup protection clearing time as worst case

06 Tap Selection and Adjustment Over Time

6.1 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.

6.2 Fault current and reactor loading at each tap

Eq. 9

\( I_f(\text{tap}) = \dfrac{3V_\text{ph}}{Z_1 + Z_2 + Z_0(\text{tap}) + 3Z_f} \)

Z₀(tap) varies with tap position; Z_f = arc resistance

Eq. 10

\( S(\text{tap}) = 3 \times V_\text{ph}(\text{tap}) \times I_f(\text{tap}) \)

Verify against rated kVA at every tap position

Eq. 11

\( I^2_f(\text{tap}) \times t_c \leq I^2t_\text{rated} \)

Must be satisfied at every tap position — most onerous governs

Critical design rule — reactor capacity at all tap positions

The reactor must be rated for the highest fault current across all tap positions. The tap producing the lowest Z₀ produces the highest fault current and imposes the most severe thermal and mechanical duty. Equations 9–11 must be evaluated at every tap position before finalising the rating.

6.3 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

07 Protection — Neutral CT, Relay Coordination, and Thermal Rating

7.1 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 (k = 1.5–2.5 depending on X/R of Z₀)	IEC 61869-2
Burden	CT burden ≤ rated burden at specified accuracy class	IEC 61869-2

7.2 Earth fault relay coordination

The earth fault relay on the neutral CT operates as a definite-time or IDMT overcurrent element. Its pickup current I_pickup and time multiplier setting (TMS) must satisfy:

Sensitivity: I_pickup ≤ I_f,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 I_pickup above worst-case load unbalance.

7.3 Thermal rating and short-time duty

Eq. 12

\( I^2_{f,\text{max}} \times t_{c,\text{backup}} \leq I^2t_\text{rated} \)

Use backup protection clearing time — the governing worst case per IEC 60076-6

7.4 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

08 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 (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.

Reactor vs voltage-based detection — the key distinction

The voltage-based approach is a passive detection scheme — it observes a consequence of the fault but cannot influence the fault current. The zig-zag reactor is an active zero-sequence current source — it creates the fault current that makes overcurrent protection viable, enables feeder-level selectivity, and gives circuit breakers something meaningful to interrupt. As demonstrated in the worked example (Section 4), the reactor raises fault current from 42 A (undetectable) to 337 A with a 3.4× relay margin, while the voltage depression at Point A provides complementary discrimination between upstream and downstream faults via 3V₀.

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. 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. Wiley-IEEE Press, 2011.
IEC 60076-6:2007, Power Transformers — Part 6: Reactors. IEC, Geneva, 2007.
IEC 61869-2:2012, Instrument Transformers — Part 2: Additional Requirements for Current Transformers. IEC, Geneva, 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. | IPQDF.com | March 2026

Companion Article

The grounding method selection for any system using a zig-zag reactor — whether solidly grounded, ungrounded, or HRG — is covered in depth in: The Complete Engineering Guide to System Grounding: Ungrounded, Solidly Grounded, and High-Resistance Grounded Systems — including transformer configuration compatibility, sequence network mathematics, protection philosophy, and a complete HRG retrofit worked example at 480 V.