Guide to Zig-Zag Transformers

This guide provides a comprehensive overview of zigzag transformers-special-purpose winding configurations widely used for grounding, harmonic mitigation, power quality improvement, and ac-dc power conversion in modern electrical systems. The guide covers the fundamental principles of operation, technical characteristics, design considerations, comparison with alternative grounding schemes, and detailed application scenarios including system neutral grounding, harmonic cancellation, and integrated power conversion systems. The guide also includes practical considerations for selection, sizing, protection and compliance with relevant standards such as IEEE C57.105 and IEC 60076.

Modern three-phase electrical systems often operate with delta-connected transformer secondaries, which lack a natural neutral point for grounding purposes. More broadly, ungrounded three-phase systems-whether from delta configurations or other sources-present significant operational challenges, including the absence of a defined ground reference, the risk of transient overvoltages during line-to-ground faults, and difficulties in fault detection and localization. The zig-zag transformer (also known as an interconnected-star or earthing transformer) was developed to address these challenges.

A zig zag transformer is a special-purpose transformer with a winding configuration where each output is the vector sum of two phases offset by 120°. Each magnetic core limb is split into two winding sections wound in opposite directions, and the coils are interconnected across different phases to create a cancellation effect for balanced currents while allowing zero-sequence currents to flow freely through the neutral connection.

While neutral grounding is the most prominent application, zig-zag transformers have evolved into a versatile platform serving multiple functions: providing a low-impedance path for ground-fault currents, suppressing triplen harmonics, balancing load currents, and serving as an integral component in unified ac-dc power conversion systems.

2.1 Winding Configuration and Internal Connections

Although the internal arrangement may appear complicated, the operating principle is fundamentally governed by Ampere’s law-the magnetic balance across windings on the same core dictates that current flowing in one winding must be accompanied by corresponding current in the other winding on that limb.

2.2 Current Flow Analysis Under Fault Conditions

To appreciate how zero-sequence currents are enabled, consider a line-to-ground fault on one phase of an otherwise ungrounded system. The cross-connected winding arrangement creates an interdependent current propagation path. Current flowing upward from the neutral point through the bottom winding of phase A passes through the top winding of phase C onto the grid connection. This induces a corresponding current in the bottom winding of phase C, which in turn propagates to the grid through phase B. The sequence continues to involve all three phases. The critical observation is that all currents in the top windings, bottom windings, and the earth connection are in phase with one another, unambiguously identifying them as zero-sequence currents.

The sum of these zero-sequence currents across all three phases equals the total earth fault current . Under normal balanced operating conditions, the phase-shifted voltages cancel out, and only a small exciting current circulates. It is only under unbalanced conditions—such as ground faults or unbalanced loads—that zero-sequence currents can flow through the transformer.

2.3 Impedance Characteristics

Under normal operation, the zig-zag transformer presents high impedance to positive- and negative-sequence currents, making it essentially invisible to the electrical system during balanced conditions. For zero-sequence currents, however, the transformer presents low impedance, effectively short-circuiting the neutral to ground for fault currents.

Key parameters that govern zero-sequence impedance include the winding turn count, core geometry, leakage inductance between the two halves of each limb, and the magnetic properties of the core material. The ability of the iron core design to limit the flow of triple-harmonic fluxes is another unique advantage that distinguishes zig-zag configurations from other grounding schemes.

2.4 Critical Installation Requirements

A phase open-circuit condition—such as a blown fuse or loose connection—disrupts the interdependence of winding currents. With one phase disconnected, the chain of current propagation necessary for zero-sequence flow breaks, and the earthing transformer can no longer conduct earth fault current. Therefore, earthing transformers must be solidly connected to both earth and grid without intermediate mechanical switching devices that could inadvertently interrupt continuity.

Two main types of grounding transformers are used in power systems: the zig-zag (interconnected-star) transformer and the wye-delta transformer. The choice between them carries significant cost, sizing, and performance implications.

3.1 Sizing and Power Rating

The zig-zag arrangement offers considerably higher efficiency than the grounded wye-delta configuration. In a zig-zag transformer, each winding carries less than the line-to-ground voltage—by a factor of —enabling a lower total power rating:. By contrast, a grounded wye-delta transformer requires  for the same neutral current. This substantial difference makes zig-zag transformers approximately one-third smaller in kVA rating than wye-delta transformers for identical neutral current requirements.

Manufacturers report that zig-zag transformers offer lower cost and smaller physical footprint than wye-delta transformers for the same zero-sequence impedance specification, making them the preferred choice in most grounding applications.

3.2 Harmonic Performance

Wye-delta transformers circulate triplen harmonics (3rd, 9th, 15th, etc.) within the delta winding but do not eliminate neutral currents generated by unbalanced loads. Zig-zag transformers, by contrast, recirculate third harmonic currents from the neutral back to the load side, actively reducing harmonics on the secondary side. This is a fundamentally different mechanism from delta-wye transformers, where triplen harmonics are simply trapped within the closed delta loop.

3.3 Rated Time and Thermal Duty

Both types serve as short-time devices, typically rated for 10-second or 1-minute fault durations rather than continuous operation. ANSI/IEEE Std. 32-1972 requires a continuous rating of 3% for a 10-second rated unit, meaning the short-time rating equals approximately 33 times the continuous rating. A 1-minute rated bank carries a continuous current rating of 7%. This intermittent-duty characteristic reduces size and manufacturing cost relative to continuous-duty transformers of equivalent capacity, though careful thermal management remains essential.

4.1 Zero-Sequence Impedance

Zero-sequence impedance is arguably the most critical parameter for zig-zag transformer design. It determines both the ground-fault current magnitude and the voltage regulation under unbalanced conditions. The transformer impedance alone can limit fault current to desired levels; alternatively, an external resistor or reactor inserted in the neutral provides additional limiting capability.

4.2 Leakage Inductance and No-Load Losses

The two most important design parameters are no-load losses (hysteresis and eddy current losses) and leakage impedance. Recent advances in analytical methods and finite element modeling have enabled more precise calculation of leakage inductance in zigzag transformers, which benefits both researchers and transformer designers in optimizing this type. Leakage reactance influences the transformer’s current-limiting behavior during faults and its overall voltage regulation performance.

4.3 Short-Time and Continuous Ratings

Grounding transformers operate with distinct short-time and continuous ratings. A circuit with minimal load unbalance can be served by a transformer rated predominantly for short-duration faults rather than continuous operation. The continuous rating for a 10-second unit is typically 3% of the short-time rating, while for a 1-minute unit it is 7%. Sizing examples illustrate this principle: on a 12.47 kV system supplying a 6000 A ground-fault current, a zig-zag transformer would require a 24.9 MVA short-time rating. This intermittent rating corresponds to a continuous rating of approximately 0.75 MVA, enabling the bank to handle 180 A of neutral current continuously.

5.1 Protection Challenges

Protecting medium-voltage networks with zig-zag grounding transformers is challenging. The transformer differential unit may lack sensitivity to detect internal ground faults on the delta side due to the inherent zig-zag current limitation combined with the effects of the power transformer ratio and capacitive current contributions from MV feeders. A Restricted Earth Fault unit can enhance sensitivity, though external phase-phase-ground faults with current transformer saturation require special attention.

Conventional directional comparison units that compare the angle between ground and neutral current are unsuitable. Instead, external fault detectors that supervise transformer differential units have been proposed as effective substitutes. For neutral directional protection, conventional units comparing neutral voltage and current phase angles incorrectly activate forward fault conditions on healthy feeders; directional units based on zero-sequence impedance magnitude offer a more reliable solution.

5.2 Applicable Standards

Zig-zag transformer design, testing, and application are governed by multiple standards. IEEE C57.105-2019 describes transformer connections and configurations in three-phase electrical systems, including all combinations of delta and wye, grounded and ungrounded, T-connected, zigzag, and other special connections, covering both two-winding and auto-transformers. Other relevant standards include IEEE C57.32 for neutral grounding devices, IEC 60076-25 for neutral grounding resistors, and IS 2026/IS 5553 for testing and performance compliance.

It is important to recognize that IEEE C57.105 was originally written for distribution systems with primary voltages up to 34.5 kV, though its principles extend more broadly.

6.1 System Neutral Grounding

The primary and most widespread application of zig-zag transformers is to create a grounded neutral for ungrounded three-phase systems-particularly delta-connected transformer secondaries and ungrounded generator or inverter buses. This application serves multiple critical functions: reducing overvoltage stress on insulation during single line-to-ground faults, providing a defined ground reference for protection relaying, and enabling continuous operation during unbalanced conditions.

In photovoltaic and distributed energy resource systems, traditional inverters often lack a solid neutral connection, leading to voltage imbalances and ineffective grounding. Zig-zag transformers establish a stable, low-impedance path to ground, stabilizing the system under fault conditions. For medium-voltage networks with high-resistance grounding, zig zag grounding transformer combined with neutral grounding resistors provide fault detection sensitivity without requiring immediate trip-a configuration that offers robust protection for critical industrial processes.

The function of the Zig Zag transformers:

Wind Farms

• Provides artificial neutral point for medium-voltage collection systems (e.g., 35 kV) to enable grounding
• Offers low-impedance path for single line-to-ground faults, limiting overvoltages
• Suppresses triplen harmonics (3rd, 9th, etc.) from wind turbine converters
• Smaller and lighter than Δ-Y grounding transformers, ideal for offshore wind

Solar (PV) Systems

• Establishes a grounding reference for inverter AC side where neutral is unavailable
• Mitigates three-phase unbalance and inverter-generated harmonics
• Enhances low-voltage ride-through (LVRT) capability, preventing disconnection
• Can serve as an integrated filter inductor in PV + storage systems

Flexible interconnection devices in modern distribution networks have demonstrated the attractiveness of zig-zag transformer grounding on both medium- and low-voltage sides, outperforming large reactance grounding and midpoint grounding alternatives in comprehensive performance comparisons.

6.2 Harmonic Mitigation

Zig-zag transformers play a significant role in mitigating neutral current problems caused by non-linear loads. Three-phase four-wire distribution systems increasingly suffer from neutral conductor overloading due to the proliferation of switch-mode power supplies, variable-frequency drives, and other non-linear electronic loads. The delta-connected primary of a conventional distribution transformer only eliminates triplen harmonics under perfectly balanced load conditions; unbalanced loads still generate neutral currents.

Zig-zag transformers address this problem by providing a low-impedance path for triplen harmonics while maintaining high impedance for fundamental frequency currents. Strategically pairing delta-zigzag with delta-wye transformers can cancel both 5th and 7th harmonics, effectively achieving 12-pulse system performance. For larger systems, multiple small zig-zag transformers placed near loads keep neutral currents localized, eliminating the need for oversized neutral conductors and improving fundamental load current balance.

6.3 Integrated AC-DC Power Conversion

Beyond traditional power quality functions, zig-zag transformers have found application in unified ac-dc power conversion systems that combine grid (ac) and photovoltaic (dc) power sources. The winding leakage inductances of zig-zag transformers can be utilized as integrated boost inductances in unified ac-dc systems, reducing component count and overall system volume compared to conventional designs with separate inductors. Classical approaches with appropriate expressions of leakage inductance for windings with rectangular geometry support the design methodology.

Advanced applications include three-stage shunt zigzag double-tap low-harmonic multi-pulse rectifiers, where the zigzag transformer configuration supports power factor correction and harmonic attenuation in high-performance power electronic systems.

6.4 Laboratory and Research Facilities

Research facilities-including particle accelerators and experimental power distribution systems-have implemented zig-zag transformers as cost-effective solutions for reducing neutral currents caused by non-linear electronic loads. The relatively low cost, simplicity, ease of installation on existing distribution systems, and ability to keep neutral currents localized make zig-zag transformers attractive in experimental settings where power quality directly impacts measurement and equipment performance.

7.1 Determining Ground-Fault Current Requirements

The first step in sizing a zig-zag transformer is determining the desired ground-fault current level. Design engineers must decide whether to rely solely on the transformer’s internal zero-sequence impedance for current limitation or to insert an external resistor. For high-resistance grounding systems, fault currents are typically limited to 5–10 A for medium-voltage systems. Low-resistance systems may permit fault currents of 200 A or more.

7.2 Calculating kVA Rating

For a given neutral current ( ) and system line-to-ground voltage (), the short-time kVA rating for a zig-zag transformer is:

The continuous rating must also be specified. For a 10-second device, the continuous rating equals 3% of the short-time rating, while a 1-minute device requires 7%.

7.3 Application Considerations

Unlike conventional power transformers, grounding transformers are intermittent-duty devices. Their ability to withstand high fault currents for short durations enables significant cost reduction compared to an equivalently rated continuous-duty transformer. However, designers must verify that the thermal withstand capability matches the expected clearing time of upstream protection devices. Grounding transformers can be specified for solid grounding or for use with an external neutral grounding resistor-the latter offering flexibility in controlling ground-fault current magnitude.

7.4 Installation and Commissioning

Proper field installation is critical for reliable operation. Pre-commissioning activities should include insulation resistance testing, winding ratio verification, and phase-shift validation. Neutral path integrity must be thoroughly verified-interruption of any phase connection to the grid can render the earthing function inoperative. Commissioning tests should validate that the transformer presents low zero-sequence impedance while maintaining high positive- and negative-sequence impedance under normal operating conditions.

For 50 Hz or 60 Hz operation, enclosures must satisfy environmental requirements for indoor or outdoor installation, typically with ventilated Type 3R enclosures for outdoor use.

8.1 Phase Continuity Sensitivity

A fundamental limitation of zig-zag transformers is their dependence on all three phases being connected. The absence of a single phase connection to the grid breaks the interdependent winding current propagation, eliminating the ability to conduct earth fault current. This sensitivity mandates reliable phase connections and argues against inserting switching devices that could inadvertently create open-circuit conditions.

Unlike standalone protective devices, zig-zag earthing transformers must remain in service continuously while the three-phase power source is active. If the grounding transformer is lost, a single line-to-ground fault can cause high phase-to-neutral voltages on unfaulted phases, and load unbalances may lead to neutral shifts and overvoltages.

8.2 Saturation Under DC Injection

In modern power systems, DC current injection-whether from grid-connected inverters, geomagnetic disturbances, or other sources-can cause grounding transformer core saturation. Saturation reduces the transformer’s effectiveness in providing a low-impedance ground path and may lead to overheating. Special precautions in design or additional monitoring may be required for systems with significant DC content.

8.3 Fault Detection Complexity

Protection engineers must recognize that conventional differential relays may be inadequate for internal ground-fault detection with zig-zag transformers. Specialized protection schemes-including Restricted Earth Fault units, external fault detectors, and magnitude-based directional units-may be required for comprehensive protection coverage.

Zig-zag transformers are critical enabling components for modern three-phase electrical systems. By providing a low-impedance path for zero-sequence currents while presenting high impedance to positive- and negative-sequence components, they bridge the gap between ungrounded delta/wye systems and the safety and operational benefits of grounded neutral operation.

Key takeaways include:

• Construction: Six half-windings cross-connected between phases on a three-limb core
• Operating principle: Ampere-turn balance enables zero-sequence current flow while canceling balanced currents
• Primary application: Neutral grounding for ungrounded three-phase systems (delta-fed or generator systems)
• Performance advantages: Higher efficiency and smaller size than wye-delta grounding transformers
• Secondary applications: Harmonic mitigation (especially triplen harmonics), load balancing, integrated ac-dc conversion
• Design considerations: Sizing based on short-duration fault ratings (10 sec or 1 min), continuous 3%–7% capacity
• Protection requirements: Specialized schemes required; conventional differential protection may be insufficient
• Critical installation: Solid phase connections to grid essential; no switching devices in grounding path

The selection between a zig-zag and a wye-delta grounding transformer ultimately depends on the specific requirements of the system: fault current limitation needs, available budget and space, harmonic mitigation requirements, and the desire for auxiliary power availability. For most grounding applications, the zig-zag transformer’s superior efficiency, smaller footprint, and better harmonic performance make it the preferred choice for new installations.