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.

transformatoren met afwijkende nominale wikkelverhoudingen

In scenario's met parallelle transformatoren met uiteenlopende waarden moet bij het ontwikkelen van per-unit modellen off-nominale windingsverhoudingen geacommodeerd worden. Deze situatie doet zich voor wanneer de geselecteerde basisspanningen niet proportioneel zijn aan de spanningswaarden van de transformator. We beschouwen een transformator waarbij de nominale spanningen gerelateerd zijn door de term a. Als de gekozen spanningsbases voldoen aan een relatie met term b, wordt term c gedefinieerd als de verhouding van deze bases. Deze verhouding wordt vervolgens gesubstitueerd in de nominale spanningsrelatie.

Om de nominale wikkelverhoudingen aan te pakken, wordt de relatie weergegeven door twee serietransformatoren:

<ol style="padding-left: 35px; margin: 0;">
 <li>Standaardmodel per unit: Dit model omvat alle bijbehorende verliezen en vertegenwoordigt de praktische aspecten van de transformator.</li>
 <li>Ideale transformator: Dit model vereenvoudigt de weergave van de spanningsverhouding zonder rekening te houden met verliezen.</li>
</ol>

In dit gecombineerde model worden shunt-exciterende takken doorgaans verwaarloosd om de analyse te vereenvoudigen. Hoewel deze aanpak theoretisch geldig is, is deze mogelijk niet geschikt voor computerprogramma's die de weergave van ideale transformatorwikkelingen niet ondersteunen.

Een alternatieve modelleringsmethode omvat het gebruik van knooppuntvergelijkingen om admittance parameters te leveren. Deze aanpak is voordelig voor het weergeven van transformatoren met off-nominale draaiverhoudingen in computerprogramma's. De knooppuntvergelijkingen bieden een eenvoudige manier om de admittance parameters op te nemen, waardoor het model compatibel is met de meeste simulatiesoftware.

Voor gevallen waarin term c een reëel getal is, kan de transformator worden gemodelleerd met behulp van een pi-circuitnetwerk. Het pi-netwerk biedt een praktische en nauwkeurige weergave van het gedrag van de transformator, met name bij het omgaan met off-nominale windingsverhoudingen. Dit model legt de impedantiekarakteristieken effectief vast en is compatibel met de meeste rekenhulpmiddelen.

Al met al, hoewel de traditionele per-unit modellen effectief zijn voor het vereenvoudigen van transformatoranalyse, hebben ze tekortkomingen met het omgaan van off-nominale wikkelverhoudingen en variërende spanningsbases. Door gebruik te maken van knooppuntvergelijkingen en pi-circuitnetwerken kunnen ingenieurs veelzijdigere en nauwkeurigere modellen ontwikkelen die geschikt zijn voor computergebaseerde analyse. Deze benaderingen zorgen ervoor dat transformatoren met verschillende waarden en niet-standaard spanningsbases nauwkeurig kunnen worden weergegeven en geanalyseerd binnen complexe elektrische systemen.

Transformatoren met afwijkende nominale wikkelverhoudingen

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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Transformers with Off-Nominal Turns Ratios

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

Transformer Core Flux and Turn Ratio

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Modeling Transformer Losses with Equivalent Circuits

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transformers with off-nominal turns ratios

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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