Transformers with Off-Nominal Turns Ratios

Per-unit models with off-nominal turns ratios are necessary when parallel transformers have different voltage ratings and selected base voltages are not proportional to the transformer's voltage ratings. Standard per-unit models assume voltage base ratios match winding voltage ratings, but this assumption fails for transformers with disparate ratings. Off-nominal models accommodate this mismatch, enabling accurate analysis of complex electrical systems with mixed transformer configurations.

An off-nominal turns ratio transformer is modeled as two transformers in series: a standard per-unit model representing losses and practical aspects, and an ideal transformer representing the voltage ratio without losses. The ideal transformer component captures the non-standard turns ratio, while the per-unit model accounts for real transformer behavior. Shunt-exciting branches are typically neglected in this simplified representation.

The off-nominal turns ratio, term c, is defined as the ratio of selected voltage bases divided by the transformer's rated voltage ratio. When chosen voltage bases satisfy a relationship involving term b and are substituted into the rated voltage relationship (term a), the resulting ratio c represents the deviation from nominal conditions. This ratio quantifies how far the selected bases deviate from the transformer's actual voltage ratings.

Series transformer models with ideal transformer windings may not be compatible with computer programs that lack support for ideal transformer representations. These programs cannot process the ideal transformer component separately. To overcome this limitation, alternative modeling approaches using nodal equations and admittance parameters provide computer-compatible representations of off-nominal turns ratio transformers.

Nodal equations provide admittance parameters that represent off-nominal turns ratio transformers without requiring ideal transformer windings. This approach is compatible with most simulation software and computational tools. The admittance parameters derived from nodal equations offer a straightforward means of incorporating transformer behavior into computer-based analysis, making complex transformer networks easier to simulate.

A pi circuit network is a practical representation used to model transformers with off-nominal turns ratios when the turns ratio is a real number. The pi network effectively captures impedance characteristics and is compatible with most computational tools. This approach provides accurate representation of transformer behavior and is particularly useful for computer-based analysis of transformers with non-standard voltage bases.

Per-unit models normalize transformer quantities to base values, eliminating the need to track actual voltage and current magnitudes. This normalization simplifies calculations and comparisons across transformers with different ratings. However, when voltage base ratios do not match winding voltage ratings, off-nominal turns ratios must be incorporated to maintain accuracy in the simplified model.