Transformer Percentage Impedance (%Z) Calculator
Use this free online tool to quickly calculate a transformer’s percentage impedance (\%Z) for power system analysis and design. Transformer impedance is a critical parameter for sizing protective devices, performing short-circuit analysis, and ensuring proper voltage regulation.
Interactive Calculator
Calculate \%Z from Short-Circuit Test
Calculate Ohmic Z from \%Z
Calculate Fault Current from \%Z
The Formula
The transformer percentage impedance is calculated using the following formula, which is derived from the short-circuit test:
$$\text{\%}Z = \frac{V_{\text{impedance}}}{V_{\text{rated}}} \times 100$$
The transformer impedance in Ohms is calculated using the percentage impedance and rated power/voltage:
$$Z_{\text{Ohmic}} = \frac{(\text{\%}Z) \times (V_{\text{rated}})^2}{100 \times S_{\text{kVA}} \times 1000}$$
The maximum short-circuit or fault current can be calculated using the transformer's percentage impedance and full load current:
$$I_{\text{sc}} = \frac{I_{\text{fl}}}{\text{\%}Z} \times 100$$
Where:
- \%Z is the percentage impedance.
- Vimpedance is the impedance voltage in Volts.
- Vrated is the rated primary voltage in Volts.
- ZOhmic is the impedance in Ohms (Ω).
- SkVA is the rated apparent power in kilo-Volt-Amperes (kVA).
- Isc is the short-circuit current in Amperes (A).
- Ifl is the full load current in Amperes (A).
Example Calculation (\%Z)
Let's calculate the percentage impedance of a transformer with a rated voltage of 11,000 V and an impedance voltage of 500 V.
-
Identify the variables:
- Vrated = 11,000 V
- Vimpedance = 500 V
-
Plug the values into the formula:
$$\text{\%}Z = \frac{500 \text{ V}}{11,000 \text{ V}} \times 100$$
-
Calculate the result:
$$\text{\%}Z = 4.545 \%$$
Therefore, the percentage impedance of this transformer is 4.545\%.
Why is Percentage Impedance Important?
Transformer impedance is a crucial value for the safety and performance of any electrical system.
- Short-Circuit Current Calculation: The impedance value directly limits the maximum short-circuit or fault current that can flow from the transformer. This is essential for sizing circuit breakers, fuses, and other protective devices.
- Voltage Regulation: A transformer's impedance causes a voltage drop when a load is applied. A lower impedance results in better voltage regulation, meaning the output voltage remains more stable under varying loads.
- System Protection: When coordinating protective relays and fuses, engineers use the transformer impedance to determine the available fault current at different points in the system.