Name: modeling parallel transformers with base mismatch
Uploaded: 2024-11-21T14:54:19.000Z
Duration: 1 min 25 s
Channel: JoVE

Per-unit quantity models simplify transformer analysis compared to actual quantity models. Ideally, transformer winding is eliminated when voltage base ratios match the windings&#39; 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&#39;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.

transformers with off-nominal turns ratios

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&#8217;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:
<ol>
	<li>Standard Per-Unit Model: This model includes all associated losses and represents the practical aspects of the transformer.</li>
	<li>Ideal Transformer: This model simplifies the voltage ratio representation without considering losses.</li>
</ol>
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&#39;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.

Transformers with Off-Nominal Turns Ratios

Per-unit quantity models simplify transformer analysis compared to actual quantity models. Ideally, transformer winding is eliminated when voltage base ...

transformers-with-off-nominal-turns-ratios

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Electrical Engineering

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modeling parallel transformers with base mismatch

Parallel transformers can be modeled with per-unit values even when the chosen voltage bases do not match the transformer ratings. This case creates an off-nominal turns ratio, which means the base voltages are not proportional to the rated voltages. To handle that mismatch, the transformer voltage relation is adjusted by using the ratio of the selected bases.

One way to represent the transformer is as two series transformers. The first is the standard per-unit model, which includes the associated losses and keeps the practical transformer behavior. The second is an ideal transformer, which shows only the voltage ratio and ignores losses. In this combined model, the shunt-exciting branches are usually left out to keep the analysis simpler.

This two-transformer approach is useful in theory, but it may not work well in computer programs that cannot represent ideal transformer windings. For that reason, another method uses nodal equations to build admittance parameters. These equations make it easier to include transformers with off-nominal turns ratios in simulation software.

When the ratio is a real number, the transformer can also be modeled with a pi circuit network. A pi network is a practical circuit model that captures impedance behavior. It is especially useful for off-nominal turns ratios and fits well with many computational tools. Together, these methods extend per-unit analysis so transformers with different ratings and non-standard voltage bases can be modeled more accurately.

Modeling Parallel Transformers with Base Mismatch

modeling-parallel-transformers-with-base-mismatch

the ideal transformer

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equivalent circuits for practical transformers

equivalent-circuits-for-practical-transformers

Modeling Transformer Losses with Equivalent Circuits

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three-winding transformers

Three-Winding Transformer Models

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Parallel transformers can be modeled with per-unit values even when the chosen voltage bases do not match the transformer ratings. This case creates an off-nominal turns ratio, which means the base voltages are not proportional to the rated voltages. To handle that mismatch, the transformer voltage relation is adjusted by using the ratio of the selected bases. One way to represent the transformer is as two series transformers. The first is the standard per-unit model, which includes the...

key terms and concepts

Learn how per-unit models handle parallel transformers when voltage bases do not match ratings, using ideal transformers, nodal equations, and pi networks.

Modeling Parallel Transformers with Base Mismatch | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

Modeling Parallel Transformers with Base Mismatch

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