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:
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.
Per-unit quantity models simplify transformer analysis compared to actual quantity models. Ideally, transformer winding is eliminated when voltage base ratios match the windings' voltage ratings.
However, selecting voltage bases is challenging for parallel transformers with different ratings.
For such cases, per-unit models with off-nominal turn ratios are developed, where selected base voltages are not proportional to the transformer's voltage ratings.
Consider a transformer with rated voltages related by the term a.
If chosen voltage bases satisfy a relationship with term b, term c is their ratio and substituted in the rated voltage relationship.
This setup can be modeled by two transformers in series: one representing the standard per-unit model with losses, and the other an ideal transformer. In this model, shunt-exciting branches are neglected for simplicity.
This model may not suit computer programs that do not accommodate ideal transformer windings.
An alternative involves nodal equations, providing admittance parameters representing off-nominal turn ratio transformers in computer programs.
For real c, a pi circuit network can be modeled.
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