In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the rated voltage relationship.

To address off-nominal turns ratios, the relationship is represented by two series transformers:

1. Standard Per-Unit Model: This model includes all associated losses and represents the practical aspects of the transformer.
2. Ideal Transformer: This model simplifies the voltage ratio representation without considering losses.

In this combined model, shunt-exciting branches are typically neglected to simplify the analysis. However, while this approach is valid theoretically, it may not be suitable for computer programs that do not support the representation of ideal transformer windings.

An alternative modeling method involves using nodal equations to provide admittance parameters. This approach is advantageous for representing transformers with off-nominal turn ratios in computer programs. The nodal equations offer a straightforward means of incorporating the admittance parameters, making the model compatible with most simulation software.

For cases where term c is a real number, the transformer can be modeled using a pi circuit network. The pi network provides a practical and accurate representation of the transformer's behavior, particularly when dealing with off-nominal turns ratios. This model effectively captures the impedance characteristics and is compatible with most computational tools.

In conclusion, while the traditional per-unit models are effective for simplifying transformer analysis, they face limitations when dealing with off-nominal turns ratios and varying voltage bases. By employing nodal equations and pi circuit networks, engineers can develop more versatile and accurate models that are suitable for computer-based analysis. These approaches ensure that transformers with different ratings and non-standard voltage bases can be accurately represented and analyzed within complex electrical systems.