Three-Phase Transformers

Contents

Recall Three-Phase Transformer 1

Compare Three-Phase Transformer Bank and Three-Phase Transformer Unit 3

Recall Phasor Group and Connection of Three-Phase Transformer 9

Describe Open-Delta Connection 10

Describe Scott Connection 11

Recall Tap Changer in Three-Phase Transformer 12

Recall the Choice of Connections in Three-Phase Transformer 13

Recall Polarity Test of Single and Three-Phase Transformers 16

Recall Sumpner’s Test of Single and Three-Phase Transformers 17

Describe Parallel Operation of Transformers 19

Recall Proportional Load Sharing in Parallel Operation of Transformers 20

Recall Three-Phase Transformer

Definition of Three-Phase Transformer:

A three-phase transformer is a type of transformer that is designed to handle three-phase electrical power. Three-phase power is a type of AC power that consists of three separate phases, each of which is 120 degrees out of phase with each other.

Construction of Three-Phase Transformer:

A three-phase transformer consists of three separate single-phase transformers that are connected together. The three single-phase transformers are wound around a common magnetic core, which helps to reduce the size and weight of the transformer.

Each of the single-phase transformers has a primary winding and a secondary winding. The primary winding is connected to one phase of the three-phase power supply, while the secondary winding is connected to the load. The three phases of the power supply are connected to the primary windings of the three single-phase transformers, while the three secondary windings are connected to the load.

Working of Three-Phase Transformer:

The three-phase transformer works by transforming the voltage of the three-phase power supply to a voltage level that is suitable for the load. The voltage transformation is achieved by the mutual induction of the primary and secondary windings.

The primary windings of the three single-phase transformers are connected to the three-phase power supply. The three-phase power supply generates a magnetic field in the primary windings, which induces a voltage in the secondary windings. The voltage induced in the secondary windings is proportional to the number of turns in the windings and the frequency of the power supply.

The voltage level of the three-phase power supply is typically high, such as 480 volts or 240 volts. The voltage level of the load is lower, such as 120 volts or 208 volts. The transformer steps down the voltage level of the three-phase power supply to a voltage level that is suitable for the load.

Example:

A typical example of a three-phase transformer is a power transformer used in an electrical power distribution system. The transformer steps down the voltage of the high voltage transmission lines to a voltage level that is suitable for distribution to residential and commercial customers.

For example, a three-phase transformer with a primary voltage of 480 volts and a secondary voltage of 208 volts can be used to supply power to a commercial building. The transformer steps down the voltage of the three-phase power supply to a voltage level that is suitable for the building’s electrical system.

Advantages of Three-Phase Transformer:

1. Three-phase power is more efficient than single-phase power as it provides a constant power supply with no power gaps.
2. Three-phase power is more reliable than single-phase power as it provides a balanced load distribution across the three phases.
3. Three-phase transformers are smaller and lighter than single-phase transformers for the same power rating.
4. Three-phase transformers are more efficient than single-phase transformers due to the reduced amount of copper required.

Disadvantages of Three-Phase Transformer:

1. Three-phase transformers are more complex than single-phase transformers, which can make them more expensive to manufacture.
2. Three-phase transformers require a three-phase power supply, which can limit their use in some applications.
3. Three-phase transformers require a three-phase load, which can limit their use in some applications.

Applications of Three-Phase Transformer:

1. Three-phase transformers are used in electrical power distribution systems to step down the voltage of the transmission lines to a voltage level that is suitable for residential and commercial customers.
2. Three-phase transformers are used in industrial applications, such as motor drives and welding machines, where a high power output is required.
3. Three-phase transformers are used in renewable energy systems, such as wind turbines and solar panels, to step up the voltage of the generated power to a voltage level that is suitable.

Compare Three-Phase Transformer Bank and Three-Phase Transformer Unit

Three-phase transformer banks and three-phase transformer units are both used in power distribution systems to step up or step down the voltage of the power supply. However, they differ in their construction and application.

Three-Phase Transformer Bank:

A three-phase transformer bank is a group of three-phase transformers that are connected together in either a wye or delta configuration. The three-phase transformer bank is typically used to step up or step down the voltage of the power supply to a level that is suitable for distribution to residential and commercial customers.

Construction of Three-Phase Transformer Bank:

A three-phase transformer bank consists of three or more single-phase transformers that are connected together to form a three-phase transformer. The single-phase transformers are connected in either a wye or delta configuration, depending on the application.

Working of Three-Phase Transformer Bank:

The three-phase transformer bank works by transforming the voltage of the three-phase power supply to a voltage level that is suitable for the load. The voltage transformation is achieved by the mutual induction of the primary and secondary windings of the three-phase transformer bank.

Advantages of Three-Phase Transformer Bank:

1. Three-phase transformer banks are more efficient than single-phase transformers for the same power rating.
2. Three-phase transformer banks provide a balanced load distribution across the three phases, which reduces the risk of power outages.
3. Three-phase transformer banks can be easily expanded by adding additional single-phase transformers to the bank.

Disadvantages of Three-Phase Transformer Bank:

1. Three-phase transformer banks are more complex than single-phase transformers, which can make them more expensive to manufacture and maintain.
2. Three-phase transformer banks are larger and heavier than single-phase transformers for the same power rating.

Applications of Three-Phase Transformer Bank:

1. Three-phase transformer banks are used in electrical power distribution systems to step up or step down the voltage of the transmission lines to a voltage level that is suitable for residential and commercial customers.
2. Three-phase transformer banks are used in industrial applications, such as motor drives and welding machines, where a high power output is required.

Three-Phase Transformer Unit:

A three-phase transformer unit is a single transformer that is designed to handle three-phase electrical power. The transformer unit is typically used in applications where a single transformer is required to step up or step down the voltage of the power supply.

Construction of Three-Phase Transformer Unit:

A three-phase transformer unit consists of a single transformer that is wound around a common magnetic core. The transformer unit has a primary winding and a secondary winding for each phase of the three-phase power supply.

Working of Three-Phase Transformer Unit:

The three-phase transformer unit works by transforming the voltage of the three-phase power supply to a voltage level that is suitable for the load. The voltage transformation is achieved by the mutual induction of the primary and secondary windings of the transformer unit.

Advantages of Three-Phase Transformer Unit:

1. Three-phase transformer units are simpler and easier to manufacture and maintain than three-phase transformer banks.
2. Three-phase transformer units are smaller and lighter than three-phase transformer banks for the same power rating.

Disadvantages of Three-Phase Transformer Unit:

1. Three-phase transformer units are less efficient than three-phase transformer banks for the same power rating.
2. Three-phase transformer units do not provide a balanced load distribution across the three phases, which can increase the risk of power outages.

Applications of Three-Phase Transformer Unit:

1. Three-phase transformer units are used in applications where a single transformer is required to step up or step down the voltage of the power supply, such as in a single commercial or industrial building.
2. Three-phase transformer units are used in renewable energy.

Here’s a comparison between Three-Phase Transformer Bank and Three-Phase Transformer Unit in tabular form:

Aspect	Three-Phase Transformer Bank	Three-Phase Transformer Unit
Definition	A combination of multiple single-phase transformers	A single transformer unit with three-phase windings
Construction	Consists of three single-phase transformers	Consists of a single transformer with three windings
Connections	Primary and secondary windings are interconnected	Windings are interconnected within the transformer unit
Voltage Ratios	Can have different voltage ratios for each phase	Voltage ratios are the same for all three phases
Physical Size	Generally larger in size and occupies more space	Compact design and occupies less space
Fault Isolation	Each single-phase transformer can be isolated	Fault in one phase can affect the entire unit
Parallel Operation	Can be easily paralleled for increased capacity	Cannot be easily paralleled with other transformer units
Flexibility and Scalability	More flexible as individual transformers can be added or removed	Less flexible as the entire unit needs to be replaced
Cost	Generally more cost-effective due to mass production of single-phase transformers	Can be costlier due to the complexity of the design

It’s important to note that the suitability of a Three-Phase Transformer Bank or Three-Phase Transformer Unit depends on the specific application and requirements.

Recall Phasor Group and Connection of Three-Phase Transformer

Phasor Group:

Phasor groups are used to describe the relationship between the voltage and current phasors in a three-phase power system. In a balanced three-phase power system, the three-phase voltages are equal in magnitude and are displaced by 120 degrees from each other. Similarly, the three-phase currents are equal in magnitude and are displaced by 120 degrees from each other. Phasor groups are used to identify the phase angles and sequence of the three-phase voltages and currents.

There are two phasor groups in a three-phase power system:

1. Positive Sequence: In the positive sequence, the phase sequence of the three-phase voltages and currents is ABC. The voltage phasors are displaced by 120 degrees from each other in a counter-clockwise direction. The current phasors are displaced by 120 degrees from each other in a counter-clockwise direction. The positive sequence is the normal sequence of a balanced three-phase power system.
2. Negative Sequence: In the negative sequence, the phase sequence of the three-phase voltages and currents is ACB. The voltage phasors are displaced by 120 degrees from each other in a clockwise direction. The current phasors are displaced by 120 degrees from each other in a clockwise direction. The negative sequence is the reverse sequence of a balanced three-phase power system.

Connection of Three-Phase Transformer:

Three-phase transformers can be connected in several different configurations, depending on the application. The most common connections are:

1. Delta-Delta Connection: In this connection, the primary and secondary windings of the transformer are connected in a delta configuration. The delta-delta connection is used for step-down applications, where the secondary voltage is lower than the primary voltage.
2. Wye-Wye Connection: In this connection, the primary and secondary windings of the transformer are connected in a wye configuration. The wye-wye connection is used for step-up applications, where the secondary voltage is higher than the primary voltage.
3. Delta-Wye Connection: In this connection, the primary winding of the transformer is connected in a delta configuration, while the secondary winding is connected in a wye configuration. The delta-wye connection is used for step-up applications, where the secondary voltage is higher than the primary voltage.
4. Wye-Delta Connection: In this connection, the primary winding of the transformer is connected in a wye configuration, while the secondary winding is connected in a delta configuration. The wye-delta connection is used for step-down applications, where the secondary voltage is lower than the primary voltage.

The choice of transformer connection depends on several factors, such as the voltage level of the power supply, the type of load, and the required power rating.

Describe Open-Delta Connection

An Open-Delta Connection is a three-phase transformer configuration where two transformers are connected in a delta configuration, while the third transformer is left disconnected. This type of connection is also known as V-V connection or Open-Voltage Delta Connection.

Here are some key features and examples of Open-Delta Connection:

1. Voltage Ratio: The Open-Delta Connection provides a voltage ratio of 1:1.73, which means that the phase voltage of the transformer is equal to the line voltage of the system.
2. Fault Current: The fault current capacity of the Open-Delta Connection is lower than other transformer configurations. The reason is that the fault current is limited by the two transformers that are connected in the delta configuration.
3. Advantages: The Open-Delta Connection has the advantage of being cost-effective, as it requires only two transformers instead of three. It is commonly used in situations where the load is light and the system has a low fault current.
4. Disadvantages: The Open-Delta Connection has some disadvantages, such as low fault current capacity, unbalanced voltage and current in the system, and increased stress on the two transformers that are connected in the delta configuration.

Example:

A common example of an Open-Delta Connection is in the distribution system, where the load is mostly light, and the fault current is relatively low. In such a scenario, an Open-Delta Connection is a cost-effective solution for power distribution. For instance, a 3-phase transformer bank can supply power to a 3-phase motor, which is rated below the full capacity of the transformer bank. In this case, two of the transformers are connected in delta, while the third transformer is left open.

Another example is in the case of a backup transformer. When one of the three transformers in a delta-delta configuration fails, an Open-Delta Connection can be used as a temporary backup solution while the failed transformer is being repaired or replaced. In this case, the two working transformers are connected in delta, and the third transformer is left open, providing a temporary solution until the failed transformer is replaced.

Describe Scott Connection

1. Voltage Ratio: The Scott Connection provides a voltage ratio of 1:1, which means that the phase voltage of the transformer is equal to the line voltage of the system.
2. Phase Shift: The Scott Connection provides a phase shift of 30 degrees between the primary and secondary windings. This phase shift is necessary to convert the three-phase system into a two-phase system or vice versa.
3. Advantages: The Scott Connection has the advantage of providing a balanced two-phase system from an unbalanced three-phase system. It is commonly used in situations where two-phase motors or equipment are used in a three-phase system.
4. Disadvantages: The Scott Connection has some disadvantages, such as increased complexity in design and higher cost due to the requirement for an additional transformer.

Example:

A common example of the Scott Connection is in the railway industry, where two-phase motors are used to power trains. In many cases, a three-phase power supply is available, and a Scott Connection is used to convert the three-phase power into two-phase power for the two-phase motors. The Scott Connection provides a balanced two-phase system that is suitable for powering the two-phase motors.

Another example is in the oil and gas industry, where two-phase equipment is used in a three-phase system. The Scott Connection can be used to convert the three-phase power into two-phase power for the two-phase equipment. This can include pumps, compressors, and other equipment that is designed to run on a two-phase power supply.

In conclusion, the Scott Connection is a useful transformer connection that is used to convert a three-phase system into a two-phase system or vice versa. It provides a balanced two-phase system from an unbalanced three-phase system and is commonly used in situations where two-phase motors or equipment are used in a three-phase system.

Recall Tap Changer in Three-Phase Transformer

At the end of this learning outcome, learners should be able to recall the function and working principle of tap changer in a three-phase transformer.

Detailed Notes:

A transformer is an electrical device used to transfer electrical energy from one circuit to another through electromagnetic induction. A three-phase transformer is a transformer that has three separate primary and secondary windings, each connected to a different phase of a three-phase electrical system. The tap changer is a component of a three-phase transformer that allows the number of turns on the secondary winding to be changed.

The function of a tap changer is to regulate the output voltage of the transformer. It does this by altering the number of turns in the secondary winding. A tap changer is particularly useful when the load on the transformer changes. If the load on the transformer increases, the voltage on the secondary side of the transformer will drop. By increasing the number of turns on the secondary winding, the voltage can be brought back to the desired level.

There are two types of tap changers: on-load tap changers and off-load tap changers. On-load tap changers (OLTCs) allow for the transformer’s voltage to be adjusted while the transformer is in operation. This is particularly useful when the transformer is supplying a load, and the load changes. OLTCs can be operated automatically or manually. Automatic OLTCs use a control circuit to adjust the voltage based on the load conditions. Manual OLTCs require an operator to physically change the tap.

Off-load tap changers (OLTCs), on the other hand, require the transformer to be taken offline before the taps can be changed. This type of tap changer is less common because it is less convenient than an on-load tap changer. However, it is still useful in situations where the transformer is not supplying a load, such as during maintenance or repair.

Example:

Consider a three-phase transformer with a rated voltage of 480 volts and a rated capacity of 150 kVA. The transformer is connected to a load that draws 100 kVA. Initially, the transformer is connected to a tap that gives a secondary voltage of 460 volts. However, due to changes in the load, the voltage drops to 450 volts. To bring the voltage back to the desired level, the tap changer can be used to increase the number of turns on the secondary winding. This will increase the voltage on the secondary side of the transformer until it reaches the desired level.

Recall the Choice of Connections in Three-Phase Transformer

Learning Outcome:

At the end of this learning outcome, learners should be able to recall the different types of connections used in three-phase transformers and understand the advantages and disadvantages of each type.

Detailed Notes:

Three-phase transformers are used to transfer electrical power from a three-phase source to a load. These transformers can be connected in several different ways, with each type having its advantages and disadvantages. The most common types of connections in three-phase transformers are Delta (Δ) and Wye (Y) connections.

Delta Connection:

In the delta connection, the three-phase windings are connected in a triangular shape. The primary and secondary windings are connected in series. The primary delta connection provides a higher level of phase-to-phase voltage output than the wye connection. The primary delta connection is useful when the primary voltage is high, but the load is small. The delta connection also provides better protection against phase loss.

Advantages:

• The delta connection provides a higher level of phase-to-phase voltage output.
• The delta connection is useful when the primary voltage is high, but the load is small.
• The delta connection provides better protection against phase loss.

Disadvantages:

• The delta connection does not provide a neutral point, which can be a disadvantage in some applications.
• The delta connection can be difficult to ground, which can pose safety issues.

Wye Connection:

In the wye connection, one end of each of the three-phase windings is connected together to form a neutral point. The primary and secondary windings are also connected in series. The wye connection provides a lower level of phase-to-phase voltage output than the delta connection. The wye connection is useful when the load is large but the primary voltage is low.

Advantages:

• The wye connection provides a neutral point, which is useful in many applications.
• The wye connection is easier to ground than the delta connection.
• The wye connection is useful when the load is large but the primary voltage is low.

Disadvantages:

• The wye connection provides a lower level of phase-to-phase voltage output than the delta connection.
• The wye connection does not provide as much protection against phase loss as the delta connection.

Example:

Consider a three-phase transformer that is rated at 480 volts and 225 kVA. The transformer is connected to a three-phase source with a voltage of 480 volts and a load that draws 100 kVA. If the transformer is connected in a wye configuration, the phase-to-phase voltage output will be 480 volts divided by the square root of 3 (1.73), which is approximately 277 volts. If the transformer is connected in a delta configuration, the phase-to-phase voltage output will be 480 volts. In this example, if the load is small, the delta connection may be the better choice as it will provide a higher level of voltage output. However, if the load is large, the wye connection may be more suitable as it provides a neutral point and is easier to ground.

Recall Polarity Test of Single and Three-Phase Transformers

Learning Outcome:

At the end of this learning outcome, learners should be able to recall the concept of transformer polarity and understand how to conduct polarity tests on single and three-phase transformers.

Transformer Polarity:

Transformer polarity is the relationship between the directions of the current flow and the magnetic fields produced by the transformer. The polarity of a transformer is essential in determining the direction of current flow, voltage drop, and the phase sequence. A transformer with reversed polarity will produce a negative voltage drop across its secondary winding when connected to a load.

Polarity Test of Single-Phase Transformer:

A single-phase transformer has two windings, primary and secondary. To conduct a polarity test of a single-phase transformer, the primary winding is connected to an AC voltage source, and the secondary winding is left open. A voltmeter is then used to measure the voltage across each of the primary windings. The voltage readings should be equal, indicating that the transformer has the correct polarity. If the voltage readings are not equal, the transformer’s polarity is reversed, and the primary winding’s connections should be swapped.

Polarity Test of Three-Phase Transformer:

A three-phase transformer has three windings, primary and two secondary. To conduct a polarity test of a three-phase transformer, the primary winding is connected to an AC voltage source, and each secondary winding is left open. The voltage across each of the primary windings is measured using a voltmeter. The voltage readings should be equal and have the same phase sequence. The phase sequence of the secondary windings can be determined by connecting a phase sequence meter to each of the secondary windings. If the phase sequence is not the same, the transformer’s polarity is reversed, and the primary winding’s connections should be swapped.

Example:

Consider a single-phase transformer with primary and secondary voltages of 480 V and 120 V, respectively. To conduct a polarity test, the primary winding is connected to a 480 V AC source, and the secondary winding is left open. A voltmeter is used to measure the voltage across each of the primary windings. If the voltage readings are equal, then the transformer has the correct polarity. If the voltage readings are not equal, the connections on the primary winding are swapped.

Consider a three-phase transformer with primary and secondary voltages of 480 V and 240 V, respectively. To conduct a polarity test, the primary winding is connected to a 480 V AC source, and each secondary winding is left open. A voltmeter is used to measure the voltage across each of the primary windings. If the voltage readings are equal and have the same phase sequence, the transformer has the correct polarity. If the phase sequence is not the same, a phase sequence meter can be connected to each of the secondary windings to determine the phase sequence. If the polarity is reversed, the primary winding’s connections are swapped.

Recall Sumpner’s Test of Single and Three-Phase Transformers

Learning Outcome:

At the end of this learning outcome, learners should be able to recall the concept of Sumpner’s test and understand how to conduct it on single and three-phase transformers.

Sumpner’s Test:

Sumpner’s test is a method of determining the efficiency and regulation of a transformer. The test involves the parallel connection of two identical transformers, one as a load transformer and the other as a compensating transformer. The load transformer is connected to a source of power, and the compensating transformer is connected in parallel with the load transformer with its primary winding connected to the secondary winding of the load transformer.

Sumpner’s Test of Single-Phase Transformer:

To conduct Sumpner’s test on a single-phase transformer, two identical transformers are required. One transformer is connected to a source of power, and the other transformer is connected in parallel with the load transformer. The secondary winding of the load transformer is connected to the primary winding of the compensating transformer. A wattmeter is used to measure the power consumed by the load transformer, and a voltmeter and ammeter are used to measure the voltage and current of the compensating transformer’s primary winding.

Sumpner’s Test of Three-Phase Transformer:

To conduct Sumpner’s test on a three-phase transformer, three identical transformers are required. The primary windings of the three transformers are connected in parallel, and the secondary windings of the transformers are connected in a star configuration. The load is then connected to one of the secondary windings of the transformers, and the other two secondary windings are connected in series with the primary windings of two identical compensating transformers. A wattmeter is used to measure the power consumed by the load transformer, and voltmeters and ammeters are used to measure the voltage and current of the primary windings of the compensating transformers.

Example:

Consider a single-phase transformer with a rated power of 5 kVA and a rated voltage of 240 V on the primary side and 120 V on the secondary side. To conduct Sumpner’s test, two identical transformers are connected in parallel. The secondary winding of the load transformer is connected to the primary winding of the compensating transformer. A wattmeter is used to measure the power consumed by the load transformer, and a voltmeter and ammeter are used to measure the voltage and current of the compensating transformer’s primary winding.

Suppose the power consumed by the load transformer is 4.5 kW, and the voltage and current of the compensating transformer’s primary winding are 240 V and 18.75 A, respectively. The efficiency of the transformer can be calculated as follows:

Efficiency = (Power output / Power input) x 100%

Power output = 5 kVA x 0.8 (80% of the rated power) = 4 kW

Power input = Power output + Power losses = 4 kW + 0.5 kW (measured power consumption of the compensating transformer) = 4.5 kW

Efficiency = (4 kW / 4.5 kW) x 100% = 88.89%

Consider a three-phase transformer with a rated power of 15 kVA and a rated voltage of 480 V on the primary side and 240 V on the secondary side. To conduct Sumpner’s test, three identical transformers are connected in parallel. The load is connected to one of the secondary windings of the transformers, and the other two secondary windings are connected in series with the primary windings of two identical compensating transformers.

Describe Parallel Operation of Transformers

Learning Outcome:

At the end of this learning outcome, learners should be able to describe the concept of parallel operation of transformers and understand the precautions that need to be taken when connecting transformers in parallel.

Parallel Operation of Transformers:

Parallel operation of transformers is a method of increasing the power capacity of a power system by connecting two or more transformers in parallel. The parallel connection of transformers is achieved by connecting the primary and secondary windings of the transformers in parallel. When transformers are connected in parallel, the total power capacity of the system is increased, and the load can be shared between the transformers.

Precautions for Parallel Operation:

When connecting transformers in parallel, certain precautions need to be taken to ensure the safe and efficient operation of the system. The following are some of the precautions that need to be taken:

1. Same rating: Transformers that are connected in parallel should have the same rating and voltage ratio. If transformers with different ratings or voltage ratios are connected in parallel, it can cause unbalanced loading, and the transformers may not operate efficiently.
2. Same polarity: Transformers that are connected in parallel should have the same polarity. If transformers with opposite polarities are connected in parallel, it can cause a short circuit and damage the transformers.
3. Same phase angle: Transformers that are connected in parallel should have the same phase angle. If transformers with different phase angles are connected in parallel, it can cause circulating currents and increase losses in the system.
4. Impedance matching: The impedance of the transformers should be matched to avoid circulating currents and to ensure that the transformers share the load equally.

Example:

Consider two transformers with the same rating of 5 MVA and a voltage ratio of 33 kV/11 kV. To connect the transformers in parallel, the primary windings of both transformers are connected in parallel, and the secondary windings of both transformers are connected in parallel.

Suppose the load connected to the system is 8 MVA. The load will be shared equally between the two transformers, with each transformer supplying 4 MVA of power. The load sharing is achieved by ensuring that the voltage drop across the transformers is the same.

If the transformers have different impedances, it can cause circulating currents between the transformers. To avoid circulating currents, the transformers’ impedance should be matched. This can be achieved by using impedance matching transformers or by adjusting the transformer tap settings.

In conclusion, parallel operation of transformers is a useful method of increasing the power capacity of a power system. However, certain precautions need to be taken when connecting transformers in parallel to ensure the safe and efficient operation of the system.

Recall Proportional Load Sharing in Parallel Operation of Transformers

Learning Outcome:

At the end of this learning outcome, learners should be able to recall the concept of proportional load sharing in parallel operation of transformers and understand the methods used to achieve proportional load sharing.

Proportional Load Sharing:

When two or more transformers are connected in parallel, it is important to ensure that the load is shared equally between the transformers. Proportional load sharing refers to the method of sharing the load between the transformers in proportion to their respective ratings.

Proportional load sharing is important because it ensures that the transformers operate efficiently and that the system is not overloaded. When transformers are not sharing the load proportionally, it can lead to unbalanced loading and inefficiencies in the system.

Methods to Achieve Proportional Load Sharing:

There are several methods used to achieve proportional load sharing in parallel operation of transformers. The following are some of the methods:

1. Impedance Matching: Impedance matching can be used to ensure that the transformers share the load proportionally. By matching the impedance of the transformers, circulating currents can be minimized, and the transformers can share the load equally.
2. Auto-Transformer: An auto-transformer can be used to ensure proportional load sharing. An auto-transformer is a transformer that has a single winding with multiple taps. By connecting the transformers to the taps of the auto-transformer, the voltage can be adjusted to ensure that the transformers share the load equally.
3. Star-Delta Connection: Star-delta connection can be used to ensure proportional load sharing. In a star-delta connection, the transformers are connected in a star configuration on the primary side and a delta configuration on the secondary side. By adjusting the tap settings on the transformers, the voltage can be adjusted to ensure that the transformers share the load proportionally.
4. Auxiliary Transformers: Auxiliary transformers can be used to ensure proportional load sharing. Auxiliary transformers are used to provide additional voltage to the system. By adjusting the voltage of the auxiliary transformers, the voltage across the main transformers can be adjusted to ensure that the transformers share the load proportionally.

Example:

Consider two transformers with the same rating of 10 MVA and a voltage ratio of 33 kV/11 kV. The primary windings of both transformers are connected in parallel, and the secondary windings of both transformers are connected in parallel.

If the load connected to the system is 15 MVA, the load will be shared proportionally between the two transformers. Each transformer will supply 7.5 MVA of power. The load sharing is achieved by ensuring that the voltage drop across the transformers is the same.

To achieve proportional load sharing, the impedance of the transformers should be matched. This can be achieved by using impedance matching transformers or by adjusting the transformer tap settings.

In conclusion, proportional load sharing is important in parallel operation of transformers to ensure the safe and efficient operation of the system. There are several methods used to achieve proportional load sharing, including impedance matching, auto-transformers, star-delta connection, and auxiliary transformers.