What is the short-circuit impedance of a transformer?

Simple Definition

The short-circuit impedance (often denoted as Zₛₜ or Zₖ) is the impedance a transformer presents when its secondary winding is short-circuited and a reduced voltage is applied to the primary winding just enough to cause the rated current to flow in both windings.

It is one of the most critical parameters of a transformer, defining its performance under load and fault conditions.

Key Points Explained

1. What It Represents

Think of the short-circuit impedance as a measure of the transformer's internal "opposition" to the flow of current. It is the vector sum of the transformer's resistance (R) and leakage reactance (X). In most power transformers, the reactive component (X) is significantly larger than the resistive component (R).

Resistance (R): Comes from the DC resistance of the copper or aluminum windings.

Leakage Reactance (X): Arises because not all magnetic flux produced by the primary winding links with the secondary winding. Some flux "leaks" and doesn't contribute to energy transfer.

2. How It's Expressed

It is almost always expressed as a percentage (%Z). This is also known as the impedance voltage.

Percent Impedance (%Z): The percentage of the rated primary voltage that must be applied to the primary winding to cause rated current to flow in the secondary winding when it is short-circuited.

Example:
A 1000 kVA transformer with a 5% impedance.

Its rated primary voltage is, say, 11,000 V.

To get the rated current to flow with the secondary shorted, you would only need to apply 5% of 11,000 V = 550 V to the primary.

Therefore, its short-circuit impedance is 5%.

3. How It's Determined

It is found via the Short-Circuit Test (or "Impedance Test"):

The secondary terminals are short-circuited with a heavy-duty conductor.

A low, variable voltage is applied to the primary terminals.

This voltage is gradually increased until the rated current flows in both the primary and secondary windings.

The voltage applied at this point (V_sc) is measured. %Z = (V_sc / V_rated) × 100%

This test is performed at the factory and the %Z value is marked on the transformer's nameplate.

 

Why is it So Important?

1. Fault Current Limitation

This is its most crucial role. During a short-circuit fault on the secondary side, the current wants to become extremely high (theoretically infinite). The short-circuit impedance is the only thing that limits this fault current.

Lower %Z: Allows higher fault currents. This can be dangerous as it imposes enormous mechanical and thermal stress on the transformer and the connected switchgear (circuit breakers, fuses).

Higher %Z: Limits the fault current to a safer, more manageable level.

2. Voltage Regulation

The impedance causes a voltage drop within the transformer when it is loaded.

Lower %Z: Means less internal voltage drop, leading to better voltage regulation (the secondary voltage stays closer to the rated voltage as load changes).

Higher %Z: Means a larger internal voltage drop, leading to poorer voltage regulation (the secondary voltage sags more as load increases).

3. Parallel Operation

For two or more transformers to share a load efficiently in parallel, their %Z values must be matched very closely. If they are not, one transformer (with the lower %Z) will try to carry more than its share of the load, potentially leading to its overload and failure.

 

Summary in a Table

Feature	Low %Z Transformer	High %Z Transformer
Fault Current	Higher, more severe	Lower, less severe
Voltage Drop	Lower	Higher
Voltage Regulation	Better	Poorer
Cost & Size	Generally larger and more expensive for the same rating	Can be slightly smaller
Common Use	Distribution networks (where good voltage regulation is key)	Large power plants, substations (where fault current limitation is critical)

Other Names

You might hear it referred to by several names, all meaning essentially the same thing:

Impedance Voltage

Leakage Impedance

Percent Impedance (%Z)

In conclusion, the short-circuit impedance is a fundamental design parameter that represents the transformer's internal opposition to current flow. It is a critical factor for determining the transformer's behavior during faults, its voltage performance under load, and its ability to operate in parallel with other units.