Transformer impedance is a critical parameter in the design and operation of electrical power systems. This vital characteristic determines the short-circuit current that a transformer can withstand and influences the voltage regulation and power flow in the network.

In this blog post, we will delve into the concept of transformer impedance, its calculation, and its practical implications in the machinery industry.

What Is Transformer Impedance

Definition of Transformer Impedance

Transformer impedance is defined as the vector sum of the transformer’s winding resistance and leakage reactance. It is typically expressed as a percentage of the transformer’s rated voltage and current, known as the percentage impedance (%z). This value indicates the voltage drop across the transformer windings when the rated current flows through them.

Components: Resistance and Reactance

Transformer impedance consists of two primary components: resistance and reactance.

The resistance component arises from the inherent resistivity of the transformer windings, typically made of copper or aluminum. This resistance causes power losses in the form of heat dissipation, known as copper losses.

Reactance is the result of the interaction between the alternating current and the magnetic fields generated within the transformer. Reactance can be further divided into leakage reactance and magnetizing reactance. Leakage reactance is caused by the leakage flux that escapes the magnetic core and does not contribute to the power transfer between the primary and secondary windings. Magnetizing reactance, in contrast, is associated with the magnetizing current required to establish the magnetic flux in the core.

Percentage Impedance (%Z)

In practice, transformer impedance is often expressed as a percentage, known as percentage impedance or %Z. This value represents the ratio of the voltage drop across the transformer windings to the rated voltage of the transformer, under full-load current conditions.

To calculate the percentage impedance, the impedance voltage (the voltage required to circulate the rated current through the transformer windings) is measured and then divided by the rated voltage of the transformer. The resulting value is expressed as a percentage. For example, if a transformer has an impedance voltage of 5% and a rated voltage of 10,000 volts, the percentage impedance would be 5%.

Functions of Transformer Impedance

• Short Circuit Protection: Transformer impedance limits the fault current during short circuit conditions. By restricting the maximum fault level, it prevents damage to the transformer and other connected equipment.
• Voltage Regulation: The impedance of a transformer affects the voltage drop across the windings under load conditions. A higher impedance results in a larger voltage drop, while a lower impedance minimizes voltage variation between the primary and secondary windings.
• System Efficiency: Transformer impedance influences the overall efficiency of the electrical system. Lower impedance values reduce copper losses in the windings, leading to improved efficiency.
• Fault Current Limitation: During earth faults or other asymmetrical fault conditions, the impedance of the transformer helps restrict the fault current to manageable levels, preventing excessive stress on the electrical system components.
• Parallel Operation of Transformers: When multiple transformers operate in parallel, their impedances must be carefully matched to ensure proper load sharing and prevent circulating currents.
• System Stability: Transformer impedance contributes to the overall stability of the electrical system. It helps limit the impact of disturbances, such as sudden load changes or generator outages, by providing a measure of electrical “stiffness.”

Calculating Transformer Impedance

Short Circuit Test Method and Calculation Formula

The short circuit test is a standard method for measuring transformer impedance. In this test, the secondary winding is short-circuited while a reduced voltage is applied to the primary winding until the rated current flows through the windings. The impedance of the transformer is then calculated using the following formula:

Z = V / I

Where:

• Z is the transformer impedance in ohms
• V is the voltage applied to the primary winding during the test
• I is the rated current flowing through the windings

The impedance value obtained from this test includes both the resistance and reactance components of the transformer windings. The resistance represents the copper losses, while the reactance is due to the leakage flux between the primary and secondary windings.

How to Interpret Impedance Values on Nameplates

Transformer nameplates often display the impedance value as a percentage, known as the percent impedance or %Z. This value is the ratio of the voltage drop across the transformer windings to the rated voltage, expressed as a percentage. The percent impedance can be calculated using the following formula:

%Z = (V / V_rated) × 100

Where:

• %Z is the percent impedance
• V is the voltage drop across the transformer windings during the short circuit test
• V_rated is the rated voltage of the transformer

A lower percent impedance indicates a higher fault current and lower voltage regulation, while a higher percent impedance results in better fault current limitation and voltage regulation.

Typical Values for Different Transformer Types and Sizes

Factors Affecting Transformer Impedance

Core and Winding Arrangement

The core shape, size, and type, as well as the winding configuration, affect the leakage flux and, consequently, the leakage reactance. Efficient transformer designs often involve careful consideration of the core and winding arrangement to achieve the desired impedance levels while maintaining optimal performance.

Leakage Flux

Leakage flux refers to the magnetic flux that does not link both the primary and secondary windings of a transformer. This leakage flux contributes to the transformer’s leakage reactance, which is a component of its overall impedance. The path taken by the leakage flux depends on the transformer’s design, including the core geometry and the spacing between windings.

Material Properties

The magnetic permeability and electrical conductivity of the core material affect the transformer’s ability to efficiently transfer power and limit fault currents. Common core materials include silicon steel, ferrite, and amorphous alloys, each with its own advantages and disadvantages in terms of impedance, efficiency, and cost.

Temperature Effects

Temperature variations can cause changes in the transformer’s impedance due to the temperature-dependent properties of the core and winding materials. As the temperature increases, the electrical resistance of the windings rises, leading to an increase in the transformer’s overall impedance. This effect is more pronounced in transformers with high current densities or those operating in high-temperature environments.

High Vs. Low Impedance Transformers

High Impedance Transformers

High impedance transformers typically have an impedance range of 6-15% or higher. These transformers offer several benefits:

• Improved protection against fault currents: The higher impedance limits the maximum current that can flow during short circuit conditions, reducing the potential damage to the transformer and associated equipment.
• Better voltage regulation: High impedance transformers experience a smaller voltage drop under load, maintaining a more stable secondary voltage.
• Reduced inrush currents: The higher impedance helps limit the magnitude of inrush currents during transformer energization, minimizing stress on the system.

However, high impedance transformers also have some drawbacks:

• Increased losses: The higher winding resistance and leakage reactance lead to greater copper and core losses, reducing overall efficiency.
• Larger size and cost: To achieve higher impedance, these transformers require more turns in the windings and larger core sizes, resulting in increased dimensions and material costs.

Low Impedance Transformers

Low impedance transformers have an impedance range typically below 6%. They offer the following advantages:

• Higher efficiency: The lower winding resistance and leakage reactance result in reduced losses, leading to improved operational efficiency.
• Compact size and lower cost: With fewer turns and smaller core sizes, low impedance transformers are more compact and economical.
• Better voltage regulation under heavy loads: The lower impedance allows for better voltage regulation when supplying high current loads.

However, low impedance transformers also have some limitations:

• Higher fault current levels: The lower impedance results in higher maximum fault currents, requiring more robust protection systems and switchgear.
• Increased voltage drop: Under heavy load conditions, low impedance transformers may experience a more significant voltage drop, affecting the quality of the supply.