Impedance of transformer -

Table of Contents

1.1 The definition of impedance

Definition: The impedance of a transformer refers to the resistance it exerts on current when current flows through it. It consists of two parts: resistance and inductive reactance. The magnitude of impedance is usually expressed as a percentage and marked on the transformer nameplate.

constituent part:

• Resistance(R): This is the resistance part of the electrical conductor in the transformer winding, which is mainly determined by the material and length of the winding. Resistance can cause electrical energy to be lost in the form of heat energy, which is known as copper loss.

• Inductive reactance(X): This part of the impedance originates from the inductance of the winding. When alternating current passes through the winding, the inductive reactance will impede the change of current. The inductive reactance is mainly determined by the geometric structure of the windings and the leakage magnetic flux between the windings.

1.2 The expression mode of impedance

The total impedance is usually expressed in complex form and consists of the combination of resistance and inductive reactance.

Z=R+jX , Among them, j is the imaginary unit

Note: Impedance does not refer to the impedance of a single high voltage or low voltage itself, but rather the combined impedance of high voltage to low voltage, resistance and reactance, which are used to describe the impedance between windings of a transformer under a certain operating state.

For example, the impedance of a three-coil transformer:

High voltage – Low voltage

High voltage – Medium voltage

Medium voltage – low voltage

2.1 The definition of short-circuit impedance

Definition: The Short-circuit Impedance on the transformer nameplate is a very important parameter, which reflects the electrical characteristics of the transformer under short-circuit conditions. Short-circuit impedance is usually expressed as a percentage (%Z), representing the ratio of the voltage that needs to be applied to the primary winding to generate the rated current when the secondary winding of the transformer is short-circuited to the rated voltage of the primary winding.

Formulation:

Short-circuit impedance ( $Z_{short}$ ) can be expressed by the following formula:

$\%Z = \frac{V_{short}}{V_{rated}} \times 100$

Among them:

$V_{short}$ is the voltage required for the primary winding to reach the rated current when the secondary winding is short-circuited.
$V_{rated}$ is the rated voltage of the primary winding.

The significance of short-circuit impedance

2.2 The significance of short-circuit impedance

2.2.1 Limit short-circuit current

The short-circuit impedance determines the magnitude of the short-circuit current generated by the transformer when the secondary winding is short-circuited. Short-circuit current is the maximum current that can occur in a power system, and it may pose a serious threat to the safety of equipment and systems.

The greater the short-circuit impedance, the smaller the short-circuit current, which helps protect the transformer and downstream equipment from damage caused by excessive short-circuit current.

short circuit calculation

Given: The nameplate capacity of the transformer is 100MVA, the voltage is 132/11 kV, and the short-circuit impedance is 10%. Calculate the short-circuit current on both the high and low voltage sides.

$I_{short} = \frac{I_{Rated}}{Z\%}$

$I_{short}$ = short-circuit current

$I_{rated}$ = rated current

Z%= short circuit impedance

High voltage side:

$I_{Rated} = \frac{100000}{1.732 \times 132} = 437\ \text{A}$

Z%=10%

$I_{short} = \frac{437}{10\%} = 4370\ \text{A} = 4.37\ \text{kA}$

Low voltage side:

$I_{Rated} = \frac{100000}{1.732 \times 11} = 5248\ \text{A}$

Z%=10%

$I_{short} = \frac{5248}{10\%} = 52480\ \text{A} = 52.48\ \text{kA}$

2.2.2 Voltage regulation

Short-circuit impedance and voltage drop

The magnitude of the short-circuit impedance directly affects the voltage drop of the transformer. A larger short-circuit impedance means that when the transformer is under load, the voltage drop on the windings is also greater, which leads to a greater drop in the output voltage. In other words, the greater the short-circuit impedance, the worse the voltage regulation performance, because the output voltage fluctuates more when the load changes.

2.2.3 Paralleling operation

When multiple transformers operate in parallel, the magnitude of the short-circuit impedance determines the proportion of the load each transformer bears. If the short-circuit impedances of the parallel transformers are different, the load will be unevenly distributed

Transformer with low impedance

It will bear a relatively large load. This is because a smaller impedance means a smaller voltage drop, so it can transmit more current, resulting in a larger load.

Transformers with high impedance

Then it will bear a smaller load. This is because a larger impedance will generate a larger voltage drop, resulting in a smaller transmitted current and thus a smaller load.

One of the conditions for parallel operation is that the impedances of multiple transformers are the same.

Suppose there are two transformers operating in parallel:

The short-circuit impedance of transformer A is 8%.

The short-circuit impedance of transformer B is 10%.

If these two transformers operate in parallel, due to the smaller short-circuit impedance of A, it will bear a greater load than B. For instance, if the total load of the system is 1000kVA, then transformer A might bear 600kVA, while transformer B only bears 400kVA.

This uneven load distribution may lead to the following problems:

Overload: Transformers with low impedance may be overloaded, while those with high impedance may be in a light-load state.
Low efficiency: Due to uneven load distribution, the operational efficiency of the entire system may decrease.
Shortened lifespan: Transformers operating under overload conditions may experience a shortened lifespan due to thermal stress and accelerated aging.

2.2.4 Protection Settings

Short-circuit impedance has a direct impact on the setting of protective devices such as relays and circuit breakers. Protective devices usually need to be set according to short-circuit current to ensure that faults can be cut off promptly and effectively when a short circuit occurs, thereby reducing the impact on other parts of the system.

Understanding the short-circuit impedance of a transformer is helpful for designing appropriate protection Settings to ensure the safety and reliability of the system.

Selection of impedance size

3.1 The advantage of high impedance

Limit the short-circuit current

Transformers with high impedance can limit the magnitude of short-circuit current when a short circuit occurs. This helps protect the power system and equipment and reduces the impact of faults on the system.

Flexibility during parallel operation

In transformers operating in parallel, if there is a slight difference in impedance (but within a reasonable range), it is easier to distribute the load and avoid excessive concentration of the load on a single transformer due to too small impedance.

The cost may be relatively low

In some designs, increasing impedance can reduce the amount of winding material used, thereby lowering manufacturing costs.

3.2 The disadvantage of high impedance

The voltage regulation performance is poor

Transformers with high impedance will experience significant fluctuations in their output voltage when the load changes. This is unfavorable for loads that require a stable voltage, and the voltage drop is relatively large

Relatively large energy loss

Greater impedance means greater resistance and reactance, which may lead to higher energy loss and reduce the efficiency of the transformer.

3.3 Advantages of low impedance

It has good voltage regulation performance

Transformers with low impedance have smaller output voltage fluctuations when the load changes, and can provide a more stable voltage. This is very important for devices that are sensitive to voltage fluctuations, such as electronic devices and data centers, where the voltage drop is relatively small.

High efficiency

A smaller impedance means lower resistance and reactance, which usually leads to higher energy efficiency and reduces losses during operation.

3.4 Disadvantage of Low impedance

The short-circuit current is relatively large

Low impedance means that when a short circuit occurs, the current will be very large, which may cause a significant impact on the system and equipment. This requires more complex and expensive protective measures.

High manufacturing cost

Achieving low impedance usually requires the use of more materials (such as thicker wires or larger cores) and more complex manufacturing processes, which increases costs.

3.5 Compromise Choice

In practical applications, transformer designers usually need to find a balance point between the magnitudes of impedance.

This balance point depends on:

Protection requirements for power systems

If the short-circuit current needs to be strictly controlled, a design with a larger impedance may be chosen.

The voltage stability requirements of the load

If a very stable output voltage is required, a design with a smaller impedance may be chosen.

Cost consideration

On the premise of meeting performance requirements, cost is often an important decision-making factor.

4.1 Test Purpose

The Short-circuit Impedance and load loss Test is an important test for transformers, which is used to determine the short-circuit impedance (%Z) of the transformer and the load loss (i.e., copper loss) under short-circuit conditions. This test can provide important electrical characteristic information of the transformer under specific working conditions, which is helpful for verifying the design quality and performance of the transformer.

• Measure the short-circuit impedance (%Z)

Short-circuit impedance reflects the combined effect of the resistance and reactance of a transformer and is crucial for evaluating the performance of a transformer under fault conditions.

• Measure load loss

Load loss (or copper loss) is the power loss caused by winding resistance of a transformer under rated load, which can be measured through short-circuit impedance tests

4.2 Test Principle

Short-circuit impedance test involves applying a relatively low voltage to the primary winding (usually the high-voltage side) of a transformer while short-circuiting the secondary winding (usually the low-voltage side), and measuring the voltage, current and power of the primary winding at this time. Based on these measurement values, the short-circuit impedance and load loss of the transformer can be calculated.

4.3 Test Procedures

4.3.1 Test preparation

Wiring: Short-circuit the secondary side (low-voltage side) winding of the transformer and connect the primary side (high-voltage side) winding to an adjustable power supply.

Equipment preparation: Connect the measuring device to record parameters such as voltage, current and power.

4.3.2 Applied voltage

Gradually increase the voltage on the primary side from zero until the current on the primary side reaches the rated current. At this point, due to the short circuit on the secondary side, the voltage should be close to zero.

4.3.3 Measure

Voltage: Measure and record the voltage $V_{short}$ on the primary side

Current: Measure and record the current $I_{rated}$ on the primary side

Power: Measure and record the input active power P, which is mainly the load loss (copper loss) of the winding.

4.4.4 Calculation

Calculation formula of short-circuit impedance $Z_{short}$ :

$Z_{short} = \frac{V_{short}}{I_{rated}}$

Percentage short-circuit impedance(%Z):

$\%Z = \frac{V_{short}}{V_{rated}} \times 100$

Among them, $V_{rated}$ is the rated voltage of the transformer

Load loss (copper loss) refers to the measured power P.

4.4.5 Test Conditions

Tests are usually conducted at room temperature, but due to the significant influence of temperature on winding resistance, the actual measured load losses may require temperature correction.

In the test, the applied voltage is relatively low. It only needs to reach the rated current, not the rated voltage, because when the secondary winding is short-circuited, applying a lower voltage is sufficient to generate the rated current.

4.4.6 Analysis of Test Results

Short-circuit impedance value

The measured short-circuit impedance value should be consistent with the design value or the value on the nameplate. If the differences are significant, it may indicate that there are problems in the design or manufacture of the transformer.

Load loss

The measured load loss (copper loss) is used to evaluate the efficiency of the transformer under full-load conditions. This loss should be within the range specified in the design.

4.4.7 significance

The short-circuit impedance test not only verifies the design and manufacturing quality of the transformer, but also provides key data for the fault analysis of the system, the setting of protection devices, and the parallel operation of the transformer. Through this test, engineers can ensure the safety and reliability of the transformer in actual operation. In conclusion, the short-circuit impedance test is an important step to ensure that the transformer complies with the design specifications and can operate safely and efficiently.

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Product Details

Product Details

Impedance of transformer

Basic knowledge of impedance

Short circuit impedance

Selection of impedance size

Short-circuit impedance and load loss test

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