Transformers are commonly specified and ordered based on a few key parameters, including the primary and secondary voltages, the apparent power rating, and the positive sequence impedance. There's another impedance that significantly affects design though, the zero sequence impedance.
Sequence impedances aren't unique to transformers, they are part of a system known as "symmetrical components" that analyzes the way electrical systems perform in response to three types of phase rotation. Sequence impedances are only applicable for three-phase systems and are used to help analyze the behavior of the system under asymmetrical conditions. In other words, think of sequence impedances as a way to understand things like line-to-ground faults.
There are three types of sequence impedances. The first is positive sequence, Z1. Positive sequence impedance is the impedance seen when a voltage with a positive phase sequence (spaced 120 degrees apart and rotating A to B to C phase) is applied. Many times, the "positive sequence" part is left out and we simply call these values the impedance. There is also a negative sequence impedance, Z2. Negative sequence is spaced just like positive sequence but with a reversed rotation (A to C to B phase). Many simple devices like transformers and cables have the same positive sequence impedance as negative sequence impedance. The last of the sequence impedances is zero sequence, Z0. The zero sequence impedance is quite different from positive and negative. Zero sequence describes the impedance seen when three voltages that are all in-phase with one another are applied to a system. The image below helps summarize the phase rotation of the voltages associated with the three different sequence impedances.
Visualization of the Voltage Phasors for All Three Sequences
As mentioned previously, the sequence impedances of a network are used to determine unbalanced fault currents (like a line-to-ground fault). The exact workings of this analysis are beyond the scope of this article, but suffice to say that the zero sequence impedance is essential.
The reason that the zero sequence impedance of a transformer can be so challenging to understand for power systems engineers is that it is determined by the core construction of the transformer itself. At the larger side, the transformer zero sequence impedance is the same as the positive sequence impedance (Z0 = Z1). At the smaller side, the transformer zero sequence impedance is about 80% of the positive sequence impedance (Z0 = .8 Z1)
Why does this range in zero sequence impedances occur? Consider the diagram below of a simple three-phase transformer core. When zero sequence voltage is passed through the coils (of either the primary or secondary), the magnetic flux inside the iron core will be unidirectional and will not sum to zero at the top or bottom of the core like it normally would. This imbalance means that the flux must now circulate outside of the core to complete its path per Ampere's Law. This new pathway will offer a high reluctance, the equivalent of resistance for magnetic flux, and lead to a reduced magnetic flux linkage. Consequently, with a lower magnetic flux linkage, the back-emf becomes lower and current will flow more readily.
Core-Type Transformer with Black Lines Showing Flux Direction for Zero Sequence Voltage
It seems complicated, but the summary is that a high reluctance path in the transformer core leads to a low impedance. From a practical perspective, even knowing this fact doesn't help much. It's best to consult with transformer manufacturers in advance to understand the expected zero-sequence impedance based on construction.
Winding configurations matter too. Delta windings act as a short for zero sequence on their side of the transformer. This means that a delta winding makes it difficult for zero sequence current to pass from the primary through to the secondary of the transformer. Zero sequence voltages create circulating currents in a transformer's delta windings because of the triangular connections. Solidly grounded wye windings offer a low impedance path for the zero sequence current since the current can flow through the ground connections of the transformer. If both sides of a wye-wye transformer are grounded, zero sequence current can pass from the primary to the secondary. An ungrounded wye prevents the flow of zero sequence current entirely by not offering a viable path. In reality, the tank of the transformer can act as another path for zero sequence flux, but the zero sequence impedance from the tank is usually very high. The diagram below shows how the zero sequence network is affected by the winding configuration. Please note that the primary and secondary are interchangeable.
Winding Diagrams for Transformer Zero Sequence Networks
Everything discussed above is conceptual, and the intricacies of transformer design mean that no assumptions should be made about zero sequence impedances without first consulting the manufacturer. Testing for zero sequence impedances is not always performed, so be sure assumptions are always well-documented and reasonable.