Intro - When power systems engineers refer to "transformers", we're almost always talking about a particular subset: 2-winding transformers. These devices have a single input and a single output. However, transformers aren't limited to two windings. In fact, there can be any number of windings! Aside from 2-winding transformers, 3-winding transformers are the next most common.
Figure 1: Transformer One-Line Symbols
Modeling - Modeling a 3-winding transformer is more complicated than their 2-winding counterpart. Figure 2 below shows the added challenges. While normal 2-winding transformers can be modeled in per-unit as a single impedance, a three-winding transformer must be modeled as three-individual impedances.
Figure 2: Equivalent Per-Unit Circuit Models of 2 and 3-Winding Transformers
Moreover, the values of these three impedances in the 3-winding model are often less physically meaningful than the 2-winding case. It's possible your model could have a negative branch impedance!
For a 2-winding transformer, we can determine the percent impedance by shorting one winding and increase voltage until the full-load current is reached. The percent impedance is equal to the percent of the voltage that was applied to reach full load. For a 3-winding transformer, the process is much less straightforward.
For starters, the primary, secondary, and tertiary of a 3-winding transformer may all possess different apparent power ratings. This means impedances must be carefully referenced to the correct apparent power base to avoid confusion. For example, 12% impedance at 50 MVA is very different from 12% impedance at 200 MVA. There is no standard or convention on what power base should be referenced, so it's necessary to communicate clearly with manufacturers on ratings.
Second, the impedances used in the 3-winding model can't be measured directly because they don't really correspond to something physical. They're simply parameters used to get an equivalent circuit. What we CAN measure (and what is normally specified) is the impedance between windings (e.g. Zhx, Zhy, Zxy). These impedances can be tested in just the same way as the 2-winding transformer. We just leave one of the windings open and perform our short circuit tests. Later, this data has to be interpreted to get the correct circuit model.
Practical Considerations - So, why would we want to use a 3-winding transformer? What are the advantages over a 2-winding transformer? Well, for starters:
Reduced Cost. Instead of having two separate devices, only one larger transformer is needed. This can be a considerable material savings, in terms of the transformer itself and through the reduction in surrounding equipment (e.g. breakers and switches). Moreover, this can reduce logistical requirements of getting two transformers to a project.
Space Savings. With only one transformer to locate, distances required for firewall/separation between units are no longer an issue. On sites that are constrained for space, this may be a major project benefit.
Cross-Feeds. 3-winding transformers can be particularly useful where cross-feeds are going to be utilized in the system, such as with two alternate sources. In this case, the three-winding transformers would normally only have power flowing through their primary and secondary winding. The tertiary winding would serve as a backup to provide power to another load. This design makes use of the above two benefits while maintaining redundancy. When, 3-winding transformers are used for cross-feeds, the impedance between secondary and tertiary windings becomes much less of a concern.
Figure 3: Cross-Feeds with 3-Winding Transformers
Of course, there are drawbacks to 3-winding transformers as well:
Complicated design. 3-winding transformers may require elaborate designs to make everything work. The concept of "typical" impedances doesn't really apply to three-winding transformers. The construction of the transformer makes a big impact on impedances, so careful communication with the manufacturer is a must. Additionally, even when impedances are favorable, voltage regulation can be a challenge. Coupling between windings means that increased load draw by the secondary winding will reduce voltage on the tertiary winding and vice-versa. Elaborate tap-changing devices may be required to make voltage regulation work.
Reduced resiliency. When a single transformer is used instead of two, the system is no longer as resilient. A failure of one winding will likely require the entire unit to be taken out of service. This means power flowing between the other two windings will be lost. If separate transformers were used, this would not have necessarily been the case.
Conclusion - 3-winding transformers are great...when you can make them work. In many cases, engineers, clients, or end users may not feel comfortable with 3-winding transformers. When 3-winding transformers are permitted, they offer potential space and cost savings that can streamline projects and help meet budgets.