Question

Open-circuit and short-circuit tests on a 30-KVA, 2300/230-V, 50 Hz transformer gave the following results: Open-circuit test (with measurements done on the LV side): 230 V,3.25 A,210 W Short-circuit test (with measurements done on the HV side): 46 V,13.043 A,380 W Record these values as you might need them in your subsequent calculations.

Determine the parameters of the approximate equivalent circuit of the transformer referred to the HV side from the given test results.

Answer 1

Ccalculating the equivalent circuit parameters of a transformer from open-circuit and short-circuit test results. This involves finding core loss resistance, magnetizing reactance, winding resistance, and leakage reactance, and referring these values to the high-voltage side for analysis.

Step-by-step explanation:

The parameters of the equivalent circuit of a transformer using open-circuit and short-circuit test results. From open-circuit test we can calculate the core loss component (no-load loss) and magnetizing reactance, and from short-circuit test, we find the winding resistance and leakage reactance referred to the high-voltage (HV) side.

For the open-circuit test:

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• Primary voltage (VOC) = 230 V
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• Primary current (IOC) = 3.25 A
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• Core loss (Pcore) = 210 W

For the short-circuit test:

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• Secondary voltage (VSC) = 46 V
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• Secondary current (ISC) = 13.043 A
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• Copper loss (Pcu) = 380 W

To find the equivalent circuit parameters:

1. 
   
3. We first calculate the equivalent resistance and reactance at the secondary side from the short-circuit test:
4. 
   
6. The equivalent resistance, Req, can be calculated using the power and current from the short-circuit test: Req = Pcu / ISC^2.
7. 
   
9. The total impedance, Zeq, can be derived from VSC and ISC: Zeq = VSC / ISC.
10. 
    
12. The equivalent reactance, Xeq, is then found by subtracting the square of Req from the square of Zeq and taking the square root.
13. 
    
15. To find core loss resistance, Rcore, we use Pcore and VOC: Rcore = VOC^2 / Pcore.
16. 
    
18. The magnetizing reactance, Xm, is calculated using the no-load current and the Rcore: Xm = VOC / sqrt(IOC^2 - (Pcore / VOC)^2).

These parameters form the approximate equivalent circuit of the transformer referred to the HV side. It's essential to note that power losses are considered in this equivalent circuit, which helps in the better understanding of the transformer's performance. However, the magnitude of power losses can vary with the actual operating conditions.