Three identical single-phase transformers can be configured to form a three-phase transformer connection, which involves high-voltage and low-voltage windings. The high-voltage windings are denoted by capital letters A-B-C, while the low-voltage windings are labeled with lowercase letters a-b-c, representing their respective phases. This notation helps distinguish between the high and low voltage sides of the transformer.
In the per-unit equivalent circuit of a grounded Y-Y three-phase transformer, base quantities are essential for simplifying analysis. The base complex power is common across the system, and the voltage base ratio corresponds to the ratio of the rated line-to-line voltages of the transformer. These base quantities ensure consistency and facilitate comparison across different components and systems.
For balanced currents in the transformer, the neutral currents are zero. Consequently, there are no voltage drops across neutral impedances. This results in a per-unit equivalent circuit that resembles a single-phase ideal transformer, simplifying the analysis and understanding of the three-phase system.
To derive the necessary relations for a single-phase three-winding transformer, the equations from two-winding transformers are extended. These relations can be expressed in both actual and per-unit measures, ensuring they conform to the per-unit equivalent circuit model. This extension is crucial for accurately representing the practical behavior of three-winding transformers.
In a practical three-winding transformer circuit, external series impedances and shunt admittance branches are significant factors. These elements are typically evaluated through an open-circuit test. When one winding of the three-winding transformer is open, the transformer behaves like a two-winding transformer. This characteristic, along with standard short-circuit tests, is utilized to determine the per-unit leakage impedances of the transformer. The shunt admittance branches, however, are often neglected for simplification.
The results of short-circuit tests yield per-unit leakage impedances, which represent the series impedance elements in the transformer's equivalent circuit. By focusing on these per-unit series impedances and neglecting shunt admittance branches, the equivalent circuit can be simplified, providing a clearer understanding of the transformer's performance.
In conclusion, these methods and simplifications effectively model and analyze the complex behavior of three-winding transformers in three-phase systems. This approach ensures that the equivalent circuit accurately represents both the ideal and practical characteristics of the transformer, facilitating efficient design and operation within electrical systems.
Three identical single-phase transformers form a three-phase connection with high-voltage and low-voltage terminals configured across all four winding types.
Base quantities for a grounded Y-Y transformer's per-unit equivalent circuit include a common base complex power and a voltage base ratio matching the ratio of rated line-to-line voltages.
Balanced currents in this transformer yield zero neutral currents, making its per-unit equivalent circuit similar to a single-phase ideal transformer.
Extending two-winding transformer equations gives the relations needed for a single-phase three-winding transformer.
These relations, written in actual and per-unit measures, satisfy the per-unit equivalent circuit.
The practical three-winding transformer circuit includes external series impedance and shunt admittance branches evaluated via an open-circuit test.
With one winding open, the three-winding transformer acts like a two-winding one. Standard short-circuit tests evaluate per-unit leakage impedances, further simplified by neglecting the shunt admittance branches.
Finally, per-unit series impedances are derived from the leakage impedances.
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