How to calculate transformer short circuit current?

To calculate the input current of a transformer, you can use the following formula based on the transformer’s power rating, input voltage, and efficiency. The input current depends on the power demand on the secondary side (load), and this can be calculated for both single-phase and three-phase transformers.

1. Single-Phase Transformer Input Current Calculation

For a single-phase transformer, the input current $I_{\text{input}}$ can be calculated using the formula:

$$I_{\text{input}} = \frac{P_{\text{out}}}{V_{\text{primary}} \times \eta}$$​​

Where:

• $I_{\text{input}}$ = Input Current (in Amperes)
• $P_{\text{out}}$ = Output Power (in Watts or VA)
• $V_{\text{primary}}$ = Primary Voltage (in Volts)
• $\eta$ = Efficiency of the transformer (expressed as a decimal)

If the efficiency is not given, it can be assumed based on typical transformer efficiency (for instance, 0.98 for a high-efficiency transformer).

2. Three-Phase Transformer Input Current Calculation

For a three-phase transformer, the input current $I_{\text{input}}$ is calculated with a similar formula but with an additional factor for three-phase power:

$$I_{\text{input}} = \frac{P_{\text{out}}}{\sqrt{3} \times V_{\text{primary}} \times \eta}$$​​

Where:

• $I_{\text{input}}$ = Input Current (in Amperes)
• $P_{\text{out}}$ = Output Power (in Watts or VA)
• $V_{\text{primary}}$ = Primary Line-to-Line Voltage (in Volts)
• $\eta$
• $\sqrt{3}$ = 1.732, a factor used for three-phase power

3. Example Calculation (Three-Phase Transformer)

Suppose you have a 500 kVA transformer, with a primary voltage of 11 kV (11,000 V) and an efficiency of 98%.

Step 1: Determine Output Power:

For a 500 kVA transformer, the power $P_{\text{out}}$ is 500,000 VA (since 1 kVA = 1,000 VA).

Step 2: Apply the Formula:

$$I_{\text{input}} = \frac{500,000}{\sqrt{3} \times 11,000 \times 0.98}$$

$$I_{\text{input}} = \frac{500,000}{1.732 \times 11,000 \times 0.98}$$

$$I_{\text{input}} = \frac{500,000}{18,577.176} \approx 26.92 \, \text{A}$$

So, the input current for the primary side of the transformer is approximately 26.92 A.

Important Notes:

• The output power $P_{\text{out}}$ is usually given in kVA or VA. To convert from kW to VA, use the apparent power formula $P_{\text{out}} = \frac{\text{kW}}{\text{power factor}}$ if necessary.
• Efficiency $\eta$
• For three-phase systems, make sure you use the line-to-line primary voltage.

This calculation helps determine how much current is drawn on the primary side of the transformer based on the output load.