Open-Circuit and Short-Circuit Tests for Transformers

Transformer testing is crucial for determining their equivalent circuit parameters and efficiency. The Open-Circuit (OC) test and Short-Circuit (SC) test are fundamental tests performed on transformers to achieve these objectives. These tests help us understand the transformer's behavior under no-load and full-load conditions, respectively.

The Open-Circuit (OC) Test

The Open-Circuit test, also known as the No-Load test, is performed on the high-voltage (HV) side of the transformer. The low-voltage (LV) side is kept open-circuited. This test primarily determines the core losses (iron losses) and the magnetizing branch parameters (resistance $R_0$ and reactance $X_0$ ) of the transformer's equivalent circuit. A wattmeter, ammeter, and voltmeter are connected to the HV side.

OC test reveals core losses and magnetizing parameters.

By applying rated voltage to the HV side with the LV side open, we measure the input power, voltage, and current. This input power is almost entirely due to core losses, as the secondary current is zero.

The equivalent circuit during the OC test consists of the series impedance ( $R_1 + jX_1$ ) and the parallel magnetizing branch ( $R_0 || jX_0$ ). Since the LV side is open, the current drawn from the HV side is very small, primarily flowing through the magnetizing branch. Therefore, the voltage drop across the series impedance ( $R_1 + jX_1$ ) is negligible. The power measured by the wattmeter ( $P_{OC}$ ) is approximately equal to the core losses ( $P_{core}$ ). The current measured by the ammeter ( $I_{OC}$ ) is the no-load current. From these measurements, we can calculate $R_0$ and $X_0$ .

Which side of the transformer is typically used for the Open-Circuit test, and what primary parameters does it help determine?

The Open-Circuit test is performed on the high-voltage (HV) side, and it helps determine core losses and the magnetizing branch parameters ( $R_0$ and $X_0$ ).

The Short-Circuit (SC) Test

The Short-Circuit test is performed on the low-voltage (LV) side of the transformer. The high-voltage (HV) side is short-circuited. This test is used to determine the winding losses (copper losses) and the series parameters ( $R_{eq}$ and $X_{eq}$ ) of the transformer's equivalent circuit. A wattmeter, ammeter, and voltmeter are connected to the HV side, and a low voltage is applied to the HV side to circulate rated current in the windings.

SC test reveals winding losses and series impedance.

By short-circuiting the LV side and applying a reduced voltage to the HV side until rated current flows, we measure the input power, voltage, and current. This input power is almost entirely due to copper losses in the windings.

In the SC test, the applied voltage is significantly lower than the rated voltage because the impedance of the transformer is low. The current flowing is the rated current. The power measured by the wattmeter ( $P_{SC}$ ) is approximately equal to the total copper losses ( $P_{cu}$ ) at rated current. The voltage measured by the voltmeter ( $V_{SC}$ ) is the short-circuit voltage, and the current measured by the ammeter ( $I_{SC}$ ) is the rated current. From these values, we can calculate the equivalent resistance ( $R_{eq}$ ) and equivalent leakage reactance ( $X_{eq}$ ) referred to the HV side.

Feature	Open-Circuit Test	Short-Circuit Test
Side Tested	High Voltage (HV)	Low Voltage (LV) shorted, HV side tested
Purpose	Determine core losses ( $P_{core}$ ) and magnetizing parameters ( $R_0, X_0$ )	Determine winding losses ( $P_{cu}$ ) and series parameters ( $R_{eq}, X_{eq}$ )
Applied Voltage	Rated Voltage	Reduced Voltage (to circulate rated current)
Load Condition	No Load	Full Load (effectively)
Dominant Losses	Core Losses (Iron Losses)	Copper Losses (Winding Losses)

The equivalent circuit of a transformer can be simplified for analysis. The Open-Circuit test isolates the parallel branch representing the core losses and magnetizing reactance ( $R_0$ and $X_0$ ). The Short-Circuit test effectively deactivates the parallel magnetizing branch due to the low applied voltage and focuses on the series impedance ( $R_1+R_2$ and $X_1+X_2$ ). The diagram shows how these components relate to the transformer's actual winding and core.

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The results from these two tests are combined to form the approximate equivalent circuit of the transformer, which is then used to predict its performance characteristics like voltage regulation and efficiency.

Calculating Equivalent Circuit Parameters

From the OC test readings ( $V_{OC}, I_{OC}, P_{OC}$ ): $P_{core} = P_{OC}$ $R_0 = V_{OC}^2 / P_{OC}$ $Z_0 = V_{OC} / I_{OC}$ $X_0 = \sqrt{Z_0^2 - R_0^2}$

From the SC test readings ( $V_{SC}, I_{SC}, P_{SC}$ ): $P_{cu} = P_{SC}$ $R_{eq} = P_{SC} / I_{SC}^2$ $Z_{eq} = V_{SC} / I_{SC}$ $X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2}$

How are the equivalent resistance (

R_{eq}

) and equivalent leakage reactance (

X_{eq}

) calculated from the Short-Circuit test results?

$R_{eq} = P_{SC} / I_{SC}^2$ and $X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2}$ , where $Z_{eq} = V_{SC} / I_{SC}$ .

Learning Resources

Open Circuit and Short Circuit Test on Transformer(blog)

Provides a detailed explanation of both tests, including circuit diagrams and calculations, with a focus on practical understanding.

Transformer Open Circuit and Short Circuit Test(blog)

A GATE-focused resource explaining the purpose, procedure, and calculations for OC and SC tests, ideal for exam preparation.

Transformer Tests: Open Circuit Test and Short Circuit Test(blog)

Explains the fundamental concepts behind the OC and SC tests, their significance, and how they help in analyzing transformer parameters.

Transformer Equivalent Circuit Parameters(blog)

Details how the parameters obtained from OC and SC tests are used to construct the transformer's equivalent circuit.

Transformer Testing (Open Circuit and Short Circuit Test)(video)

A visual explanation of the OC and SC tests, demonstrating the setup and the interpretation of readings, beneficial for practical understanding.

Transformer Open Circuit Test (No Load Test)(video)

Focuses specifically on the Open-Circuit test, explaining its procedure, the instruments used, and the derivation of parameters.

Transformer Short Circuit Test(video)

A dedicated video explaining the Short-Circuit test, its methodology, and the calculation of series parameters.

Transformer Equivalent Circuit(wikipedia)

Provides a comprehensive overview of transformer equivalent circuits, including the role of parameters derived from OC and SC tests.

Electrical Machines - Transformer(video)

NPTEL lectures on electrical machines, likely covering transformer testing in detail as part of the power systems and machines curriculum.

GATE Electrical Engineering - Power Systems and Machines(documentation)

Official syllabus for GATE Electrical Engineering, which confirms the importance of transformer testing within the Power Systems and Machines section.