What is the Impedance of a Transformer Short Circuit?
The impedance of a transformer short circuit, also formally known as transformer short-circuit impedance or impedance voltage, is the equivalent series impedance of the transformer windings when viewed from one set of terminals with the other set short-circuited.
Based on industry definitions, transformer short-circuit impedance:
- Refers to the equivalent series impedance Zk=Rk+jXk.
- This impedance is measured between terminals in a pair of windings.
- It is determined at the transformer's rated frequency and a specified reference temperature (typically 75°C or 85°C for power transformers).
Essentially, when a transformer is under short-circuit conditions (one winding shorted), this impedance is what limits the current flow. It represents the total opposition to current within the transformer itself under this specific condition.
Components of Short-Circuit Impedance (Zk)
The short-circuit impedance Zk is a complex value composed of two main parts:
- Rk (Equivalent Resistance): This represents the combined resistance of the primary and secondary windings, referred to the same side. It accounts for the power loss due to heating in the windings (I²R losses).
- Xk (Equivalent Reactance): This is the more significant component and represents the combined leakage reactance of the primary and secondary windings, referred to the same side. Leakage reactance is due to the magnetic flux that does not link both the primary and secondary windings.
$$ Z_k = R_k + jX_k $$
Where:
- $ Z_k $ is the total equivalent short-circuit impedance.
- $ R_k $ is the equivalent series resistance.
- $ X_k $ is the equivalent series reactance.
- $ j $ is the imaginary unit ($\sqrt{-1}$).
The magnitude of the short-circuit impedance is calculated as $|Z_k| = \sqrt{R_k^2 + X_k^2}$.
Importance of Transformer Short-Circuit Impedance
Knowing the transformer's short-circuit impedance is crucial for several reasons:
- Fault Current Calculation: It is the primary factor determining the maximum current that will flow through the transformer during a downstream short circuit. This is vital for selecting appropriate protective devices (fuses, circuit breakers). A lower impedance results in higher fault current.
- Voltage Regulation: While primarily related to load impedance, the transformer's internal impedance contributes to voltage drop under load.
- Transformer Design and Testing: Manufacturers design transformers to have specific impedance values, and the short-circuit test is a standard procedure to verify this value and assess the transformer's ability to withstand mechanical forces during faults.
The short-circuit impedance is often expressed as a percentage (%) of the transformer's rated impedance (calculated from rated voltage and power). This percentage impedance value is a common specification found on transformer nameplates.
In summary, the impedance of a transformer short circuit is not a single universal value but is defined by the equivalent series impedance Zk=Rk+jXk between windings at rated frequency and reference temperature, which limits the fault current during a short circuit.
