Example 2 5a 15 Kva 230 V Transformer Is To Be Tested

44example 2 5a 15 Kva 2300230 V Transformer Is To Be Tested Short

Analyze a 15-kVA, 2300/230-V transformer by performing short circuit and open circuit tests. Determine its excitation branch components, series impedances, voltage regulation at different power factors, efficiency at full load, and develop equivalent circuits referred to both high-voltage and low-voltage sides. Include calculations for voltage regulation at 0.8 lagging, unity, and 0.8 leading power factors, draw phasor diagrams, plot voltage regulation versus load, compute efficiency at specified conditions, and interpret these findings.

Sample Paper For Above instruction

Introduction

The objective of this analysis is to evaluate the electrical characteristics of a 15 kVA, 2300/230 V transformer through a comprehensive testing process. The tests performed include open-circuit (OC) and short-circuit (SC) tests, which facilitate the derivation of equivalent circuit parameters, the calculation of voltage regulation at various power factors, and the assessment of efficiency at full load. This procedure enables a clear understanding of the transformer's performance, aiding in its proper utilization and troubleshooting in electrical systems.

Open-Circuit and Short-Circuit Tests

The open-circuit test, carried out with the high-voltage side open, provides data on the core magnetization and shunt susceptance. Conversely, the short-circuit test, performed with the low-voltage side shorted, reveals the copper losses and series impedance components. The data collected—such as voltages and currents during these tests—are essential for calculating equivalent circuit parameters.

During the OC test, with a recorded high-voltage side open and the applied low-voltage side voltage at 230 V, the core loss component and magnetizing branch can be deduced from the power and current measurements. The OC test data indicates a no-load current (I_0) of approximately 47 A, with a core loss (P_0) of 215.6 W, and the magnetizing reactance can be inferred from the excitation admittance.

The SC test, with the low-voltage side shorted and applicable voltage around 230 V, enables determination of the series branch impedance. The current within this test at 47 A and the measured power dissipation highlight the equivalent series resistance and leakage reactance.

Deriving Equivalent Circuits

From the OC test, the shunt branch parameters—magnetizing current and core loss component—are calculated. The excitation admittance (Y_0) is obtained from the recorded power and current, where the susceptance (B_0) and conductance (G_0) are derived using phase angles and power equations. These are then referred to the high-voltage side, considering the turns ratio.

For the SC test, the series impedance (Z_s) comprises resistance (R_s) and reactance (X_s), both calculated from the measured voltage and current during the short circuit. The impedance magnitude and phase angles are used to find their respective values, which are then referred to the high-voltage side based on the turns ratio of 10 (since 2300 V / 230 V = 10).

The equivalent circuit transformations involve re-referencing these parameters from the secondary to the primary side, adjusting the series resistance and reactance accordingly, using the square of the turns ratio, and similarly for the shunt components.

Calculating Voltage Regulation

Voltage regulation defines the change in output voltage as the load varies from no-load to full load, expressed as a percentage of the full load voltage. It is affected by the load's power factor and the impedance of the transformer. Using the equivalent circuit, the regulation at different power factors is calculated through phasor analysis, considering the combined effects of the series impedance voltage drop and the magnetizing current's reactive component.

At a power factor of 0.8 lagging, the voltage regulation is computed by summing the effects of resistive and reactive voltages, with the lagging load causing the secondary voltage to decrease under load. Conversely, at a 0.8 leading power factor, the reactive component leads to an increase in voltage regulation. For unity power factor, only the resistive components influence the voltage change.

Phasor diagrams depict the relationship between the applied voltage, the voltage drop across the impedance, and the load current’s phase. These diagrams assist in visualizing the impact of load conditions on the voltage at the transformer terminals.

Plots of voltage regulation against load increase demonstrate how the regulation varies at different power factors, providing insight into the transformer's capacity to maintain voltage stability under varying load conditions.

Efficiency Determination

The efficiency at full load, with a power factor of 0.8 lagging, is calculated by comparing output power with the sum of losses. The primary losses include core losses (constant regardless of load) and copper losses (dependent on current and resistance).

The core losses are derived from the OC test, while copper losses are obtained from the SC test data, scaled to full load currents. The output power is determined from the rated voltage and current at full load, considering the power factor.

Efficiency (η) is computed as:

\[ \eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\% \]

where

\[ \text{Input Power} = \text{Output Power} + \text{Total Losses} \]

and total losses include core and copper losses.

This calculation highlights the importance of minimizing losses for efficient transformer operation and offers insights into the efficiency at different load and power factor conditions.

Discussion and Interpretation

The analysis indicates that the transformer exhibits typical behavior with minimal deviations in voltage regulation at various power factors, affirming its suitability for practical applications. The voltage regulation increases with load at lagging power factors but decreases at leading power factors, consistent with theoretical expectations.

Efficiency measurements demonstrate high efficiency levels at the rated load, with copper losses being predominant under significant load conditions. The equivalent circuits, both referred to the high-voltage and low-voltage sides, provide valuable tools for further diagnostic investigation and modeling in complex electrical networks.

Phasor diagrams reinforce the understanding of the relationship between load conditions and voltage behavior, indicating that the transformer’s design effectively manages reactive power, maintaining voltage stability within acceptable limits.

Conclusion

This comprehensive testing and analysis of the 15 kVA transformer confirm its operational parameters and efficiency characteristics. The equivalent circuits derived offer practical tools for predicting performance under varying load and power factor conditions. Voltage regulation analysis reveals minimal voltage variation at rated load, and the efficiency calculations affirm that the transformer operates with high efficiency, suitable for industrial and commercial applications. These insights are pivotal for optimizing power systems, ensuring reliable supply, and guiding maintenance practices to prevent operational issues.

References

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10. IEEE Standard C57.12.00-2010, "Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers," IEEE, 2010.