1 Answer
The short-circuit test in a transformer is performed to determine the transformer’s impedance and to calculate its copper losses (the losses due to the resistance of the windings). This test is conducted on the low-voltage side of the transformer, and the high-voltage side is shorted. Here’s the step-by-step procedure, along with the readings you would typically obtain.
### **Procedure:**
1. **Connect the Transformer:**
- The transformer is connected to a variable AC supply on the low-voltage (LV) side.
- The high-voltage (HV) side is shorted, meaning the HV terminals are connected together with a conductor of negligible resistance.
2. **Apply the Test Voltage:**
- A low voltage (usually a small percentage of the rated voltage) is applied to the LV side of the transformer.
- The voltage is gradually increased, and you measure the current flowing through the transformer on the LV side.
3. **Measure the Current and Voltage:**
- The current is measured using an ammeter, and the voltage is measured using a voltmeter across the low-voltage side of the transformer.
- At the same time, the power (or input power) is measured using a wattmeter.
4. **Record the Readings:**
- Record the following readings:
- **Voltage (V_sc)**: The applied voltage on the low-voltage side.
- **Current (I_sc)**: The current that flows during the short-circuit test.
- **Power (P_sc)**: The power consumed by the transformer during the test.
5. **Adjust the Voltage:**
- Increase the applied voltage until the rated current for the short circuit test is achieved. Usually, this current is a small fraction (like 5-10%) of the rated full-load current.
### **Readings Obtained:**
- **V_sc (Short-Circuit Voltage):** This is the voltage applied to the low-voltage side when the transformer is under short-circuit conditions. It is typically quite small (a few percent of the rated voltage).
- **I_sc (Short-Circuit Current):** This is the current that flows when the transformer is short-circuited. It should be close to the rated current of the transformer, depending on the voltage applied.
- **P_sc (Power Losses or Copper Losses):** The power loss measured during the short-circuit test is the sum of the copper losses in both windings of the transformer. These losses depend on the current flowing through the windings and their resistance.
### **Calculations:**
From the data obtained, you can calculate the following:
1. **Impedance of the Transformer (Z):**
The impedance can be calculated using Ohm’s law:
\[
Z = \frac{V_{sc}}{I_{sc}}
\]
Where:
- \( Z \) is the total impedance of the transformer.
- \( V_{sc} \) is the short-circuit voltage.
- \( I_{sc} \) is the short-circuit current.
2. **Resistance and Reactance:**
The measured power loss during the test is primarily due to the resistance of the transformer windings. You can use the following formula to calculate the equivalent resistance \( R_{eq} \):
\[
R_{eq} = \frac{P_{sc}}{I_{sc}^2}
\]
Where:
- \( P_{sc} \) is the short-circuit power loss.
- \( I_{sc} \) is the short-circuit current.
The reactance \( X_{eq} \) can be found using the impedance and resistance:
\[
X_{eq} = \sqrt{Z^2 - R_{eq}^2}
\]
3. **Copper Losses:**
The copper losses during the short-circuit test are given by the power \( P_{sc} \) measured during the test.
### **Conclusion:**
The short-circuit test helps in determining the internal impedance of the transformer and the copper losses. This is important for assessing the efficiency of the transformer and for designing protection systems like fuses and circuit breakers.
### **Procedure:**
1. **Connect the Transformer:**
- The transformer is connected to a variable AC supply on the low-voltage (LV) side.
- The high-voltage (HV) side is shorted, meaning the HV terminals are connected together with a conductor of negligible resistance.
2. **Apply the Test Voltage:**
- A low voltage (usually a small percentage of the rated voltage) is applied to the LV side of the transformer.
- The voltage is gradually increased, and you measure the current flowing through the transformer on the LV side.
3. **Measure the Current and Voltage:**
- The current is measured using an ammeter, and the voltage is measured using a voltmeter across the low-voltage side of the transformer.
- At the same time, the power (or input power) is measured using a wattmeter.
4. **Record the Readings:**
- Record the following readings:
- **Voltage (V_sc)**: The applied voltage on the low-voltage side.
- **Current (I_sc)**: The current that flows during the short-circuit test.
- **Power (P_sc)**: The power consumed by the transformer during the test.
5. **Adjust the Voltage:**
- Increase the applied voltage until the rated current for the short circuit test is achieved. Usually, this current is a small fraction (like 5-10%) of the rated full-load current.
### **Readings Obtained:**
- **V_sc (Short-Circuit Voltage):** This is the voltage applied to the low-voltage side when the transformer is under short-circuit conditions. It is typically quite small (a few percent of the rated voltage).
- **I_sc (Short-Circuit Current):** This is the current that flows when the transformer is short-circuited. It should be close to the rated current of the transformer, depending on the voltage applied.
- **P_sc (Power Losses or Copper Losses):** The power loss measured during the short-circuit test is the sum of the copper losses in both windings of the transformer. These losses depend on the current flowing through the windings and their resistance.
### **Calculations:**
From the data obtained, you can calculate the following:
1. **Impedance of the Transformer (Z):**
The impedance can be calculated using Ohm’s law:
\[
Z = \frac{V_{sc}}{I_{sc}}
\]
Where:
- \( Z \) is the total impedance of the transformer.
- \( V_{sc} \) is the short-circuit voltage.
- \( I_{sc} \) is the short-circuit current.
2. **Resistance and Reactance:**
The measured power loss during the test is primarily due to the resistance of the transformer windings. You can use the following formula to calculate the equivalent resistance \( R_{eq} \):
\[
R_{eq} = \frac{P_{sc}}{I_{sc}^2}
\]
Where:
- \( P_{sc} \) is the short-circuit power loss.
- \( I_{sc} \) is the short-circuit current.
The reactance \( X_{eq} \) can be found using the impedance and resistance:
\[
X_{eq} = \sqrt{Z^2 - R_{eq}^2}
\]
3. **Copper Losses:**
The copper losses during the short-circuit test are given by the power \( P_{sc} \) measured during the test.
### **Conclusion:**
The short-circuit test helps in determining the internal impedance of the transformer and the copper losses. This is important for assessing the efficiency of the transformer and for designing protection systems like fuses and circuit breakers.