Question

How do you calculate the Short-Circuit Impedance of a power transformer in AC systems?

Answer 1

Calculating the short-circuit impedance of a power transformer in an AC system involves determining the impedance that the transformer presents to the flow of fault current when a short circuit occurs on its secondary side. The short-circuit impedance is essential for assessing the performance of the transformer during fault conditions and for the design of protective devices. Here's a step-by-step guide on how to calculate the short-circuit impedance:

Identify the transformer data: Gather the necessary data about the transformer, such as its rated power (in VA or kVA), rated primary and secondary voltage (in volts), and the transformer's voltage regulation, if available.

Determine the transformer impedance voltage: The impedance voltage is the percentage of the rated voltage that appears across the transformer impedance when the rated current flows through it. You can typically find this information in the transformer's nameplate or datasheet. If the impedance is given as a percentage, you can directly use it. Otherwise, you'll need to convert the impedance to a percentage by using the formula:

Impedance % = (Impedance in ohms / Rated Secondary Voltage) x 100

Calculate the short-circuit impedance: To calculate the short-circuit impedance, use the following formula:

Short-Circuit Impedance (in ohms) = (Impedance % / 100) x Rated Secondary Voltage

Optionally, convert the impedance to per-unit: To make comparisons with other equipment easier, you can express the short-circuit impedance in per-unit values. The per-unit impedance is calculated as follows:

Short-Circuit Impedance (in per-unit) = Short-Circuit Impedance (in ohms) / Base Impedance

The base impedance is usually the rated secondary voltage divided by the base apparent power (kVA). Commonly, the base apparent power is chosen to be the rated kVA of the transformer.

Remember that the short-circuit impedance is typically a relatively small value, often expressed in percentage or per-unit, as it represents the ratio of voltage drop to fault current. During a short circuit, the impedance limits the fault current magnitude, affecting the fault level and the protection coordination in the power system.

Please note that this calculation assumes a balanced three-phase fault scenario. For more accurate results and to consider other fault types, a more detailed analysis using the transformer's per-phase impedance values and symmetrical components may be necessary. Additionally, some transformer manufacturers provide short-circuit impedance data directly, making the calculation step unnecessary in those cases.