parallel operation of two single phase transformer experiment

ELECTRICAL ENGINEERING

Polarity test and parallel operation of single phase transformer.

Experiment No. : – 11

Aim of the Experiment: –

Apparatus Required: –

Circuit Diagram: –

Theory: –

Parallel operation of transformers is used for load sharing. The transformers are connected in parallel on both primary and secondary side. Following conditions to be satisfied during the parallel operation of transformers-

• Same polarities should be connected.
• The two transformers should have same voltage ratio.
• The percentage impedance should be same.
• There should be no circulating current.

Procedures: –

• Connect all the apparatus as per circuit diagram (fig. 11.1) for polarity test.
• Measure the terminal voltage. if voltage is zero then the polarity is same.
• Again connect all the apparatus as per circuit diagram (fig. 11.2) for load sharing of transformer.
• Note the meters readings as per observation table.

Observation Table: –

Precaution: –

• Transformers should be connected in such a way that they have same polarity.
• All connections should be neat and tight.
• Connecting leads should be perfectly insulated.

Conclusion: –

To be written by student.

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Parallel Operation of a Single Phase Transformer

Parallel Operation of a Single Phase Transformer means that the two or more transformers having the same polarities, same turn ratios, same phase sequence and the same voltage ratio are connected in parallel with each other.

The circuit diagram of two single-phase transformer A and B connected in parallel are shown below:

a 1 is the turn ratio of the transformer A a 2 is the turn ratio of transformer B Z A is the equivalent impedance of the transformer A referred to secondary Z B is the equivalent impedance of the transformer B referred to secondary Z L is the load impedance across the secondary I A is the current supplied to the load by the secondary of the transformer A I B is the current supplied to the load by the secondary of the transformer B V L is the secondary load voltage I L is the load current

Applying Kirchhoff’s Current Law,

By Kirchhoff’s Voltage Law,

Now putting the value of I B from the equation (1) in equation (3) we will get,

Solving equations (2) and (4) we will get,

The current I A and I B   have two components. The first component represents the transformers share of the load currents and the second component is a circulating current in the secondary windings of the single-phase transformer.

The undesirable effects of the circulating currents are as follows

• They increase the copper loss.
• The circulating current overloads the one transformer and reduce the permissible load kVA.

Equal Voltage Ratio

In order to eliminate circulating currents, the voltage ratios must be identical. That is a 1 =a 2

From the above equation (9), it is clear that the transformer currents are inversely proportional to the transformer impedance. Thus, for the efficient parallel operation of the two single-phase transformers, the potential differences at full load across the transformer internal impedance should be equal.

This condition ensures that the load sharing between the two single-phase transformer is according to the rating of each transformer. If the per-unit equivalent impedance are not equal, then the transformer will not share the load in proportion to their kVA ratings. As a result, the overall rating of the transformer bank will be reduced.

Equation (9) can also be written as

The current in the equations (7) and (8) is changed into volt-amperes by multiplying the two equations by the common load voltage V L .

Therefore, we know that,

The total load in volt-ampere (VA) is

The volt-ampere of transformer A is

Similarly, the volt-ampere of transformer B is

Hence, the various equations will be written as shown below

Equating the equation (11) and (12) we will get

Equation (13) tells that the volt-ampere load on each single-phase transformer is inversely proportional to its impedance.

Hence, to share the load in proportion to their ratings, the transformers should have the impedance which is inversely proportional to their ratings.

Related terms:

• Parallel Operation of a Transformer
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Parallel Operation of Single Phase Transformers

By parallel operation of single-phase transformers, we mean two or more transformers are connected to the same supply bus bars on the primary side and to a common bus bar/load on the secondary side. Such a requirement is frequently encountered in practice. 

Two transformers A and B connected in parallel are shown in the figure.

While connecting two or more than two transformers in parallel, it is essential that their terminals of similar polarities are joined to the same busbars as shown. 

The wrong connections may result in a dead short-circuit and primary transformers may be damaged unless protected by fuses or circuit breakers .

Need of Parallel Operation in Single Phase Transformers

• Firstly, if one transformer fails, the continuity of supply can be maintained through other transformers. 
• Secondly, when the load on the substation becomes more than the capacity of the existing transformers, another transformer can be added in parallel. 
• Thirdly, any transformer can be taken out of the circuit for repair/routine maintenance without interrupting the supply to the consumers.
• Non-availability of a single large transformer to meet the total load requirement.
• The power demand might have increased over time necessitating augmentation of the capacity. More transformers connected in parallel will then be pressed into service.
• To ensure improved reliability. Even if one of the transformers gets into a fault or is taken out for maintenance/repair the load can be continued to be serviced.
• To reduce spare capacity. If many smaller size transformers are used one machine can be used as spare. If only one large machine is feeding the load, a spare of similar rating has to be available. The problem of spares becomes more acute with fewer machines in service at a location.
• When transportation problems limit the installation of large transformers at a site, it may be easier to transport smaller ones to the site and work them in parallel.

Conditions for Parallel Operation of Single Phase Transformer

• Transformers should be properly connected with regard to their polarities .
• The voltage ratings and voltage ratios of the transformers should be the same.
• The per unit or percentage impedances of the transformers should be equal.
• The reactance/resistance ratio s of the transformers should be the same.

1. Connection with regard to Polarity

The first condition for successful parallel operation of single phase transformer is that the transformers should be properly connected with regard to their polarities.

This condition is absolutely essential because wrong connections may result in dead short-circuit.

Figure (i) shows the correct method of connecting two single-phase transformers in parallel.

Figure (ii) shows the wrong method of connecting two single-phase transformers in parallel. Here the two secondaries are so connected that their e.m.f.s E A and E B  are additive. 

This may lead to short-circuiting conditions and a very large circulating current will flow in the loop formed by the two secondaries.

Such a condition may damage the transformers unless they are protected by fuses and circuit breakers.

2. Same Voltage Rating and Voltage Ratio

The next condition for parallel operation of single phase transformer is the same voltage rating and voltage ratio.

This condition is desirable for the satisfactory parallel operation of transformers.

If this condition is not met, the secondary e.m.f.s will not be equal and there will be circulating current in the loop formed by the secondaries. This will result in the unsatisfactory parallel operation of transformers.

Even a small difference in the induced secondary voltages can cause a large circulating current in the secondary loop because impedances of the transformers are small.  This secondary circulating current will cause current to be drawn from the supply by the primary of each transformer.

These currents will cause copper losses in both primary and secondary. This creates heating with no useful output.

When the load is connected to the system, this circulating current will tend to produce unequal loading conditions i.e., the transformers will not share the load according to their kVA ratings. It is because the circulating current will tend to make the terminal voltages of the same value for both transformers.

Therefore, the transformer with a smaller voltage ratio will tend to carry more than its proper share of the load. 

Thus, one transformer would tend to become overloaded than the other and the system could not be loaded to the summation of transformer ratings without overloading one transformer.

Read: Why Transformers are Rated in KVA?

3. Equal Percentage Impedance

Another condition for parallel operation of single phase transformer is all transformers should have equal percentage impedance.

This condition is also desirable for proper parallel operation of single-phase transformers.

If this condition is not met, the transformers will not share the load according to their kVA ratings.

Sometimes this condition is not fulfilled by the design of the transformers.

In that case, it can be corrected by inserting proper amount of resistance or reactance or both in series with either primary or secondary circuits of the transformers where the impedance is below the value required to fulfill this condition.

4. Same Reactance/Resistance Ratio

If the reactance/resistance ratios of the two transformers are not equal, the power factor of the load supplied by the transformers will not be equal.

In other words, one transformer will be operating with a higher and the other with a lower power factor than that of the load.

Equal Percentage Impedance (Condition 3) is much more important than Same Reactance/Resistance Ratio (condition 4) .

Considerable deviation from Same Reactance/Resistance Ratio (condition 4) will result in only a small reduction in the satisfactory degree of operation.

When desired, condition (4) also may be improved by inserting external impedance of proper value.

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Home > Electrical Machines > Transformer > Parallel Operation of Single-Phase & Three-Phase Transformers

Parallel Operation of Single-Phase & Three-Phase Transformers

Needs & conditions for parallel connection of transformers.

In a power system network , transformers are used to step up and step-down voltage levels. The rating of a transformer is selected according to the load demand. But load demand increases day by day. Hence, to meet extra load demand, we need to change the existing transformer to a higher capacity transformer or we can add an extra transformer connected with the existing transformer.

• Related Post:  Parallel Operation of DC Generators

The economic way to meet load demand is to connect a second transformer in parallel with the existing transformer.

Table of Contents

Need of Parallel Operation of Transformers

The parallel operation of the transformer is needed due to following reasons.

• To supply a load of more ratings to the existing transformer, we need to connect the second transformer in parallel with the existing transformer.
• At the time of maintenance , a second transformer is used to maintain continuity of supply to the consumer. It increases the reliability of a system.
• When one transformer is in fault condition or fails to operate due to any reason, the second transformer is used to supply and avoid intrusion of power.

Related Posts:

• Difference Between Current Transformer & Potential Transformer
• Difference between Power Transformers and Distribution Transformers?

Conditions for Parallel Operation of Transformers

To ensure the successful parallel operation of the transformers, the following conditions must be satisfying.

• The primary winding of both transformers is suitably designed for the supply system voltage and frequency.
• Both transformers are connected with the same polarity. If polarities are not matched there is a chance of short-circuiting. Hence, while connecting both transformers in parallel, the polarity of both transformers must match.
• The turns ratio (transformation ratio) of both transformers should be identical. It means the voltage rating of primary and secondary windings should be identical. If the turns ratio is not the same, the parallel operation of transformers is possible. But some amount of circulating current will flow in no-load conditions. And it will create unequal loading conditions.
• In order to avoid circulating current, the X/R ratio must be the same. It means the impedance triangle must be identical for both transformers. If the X/R ratio is not the same, both transformers will operate on different power factors .
• When both transformers have different KVA ratings, the equivalent impedance is inversely proportional to the individual kVA rating (circulating current is ignored).

Parallel Operation of Single-Phase Transformer

Two single-phase transformers can be connected in parallel as shown in the figure below.

As shown in the figure, the primary winding of both transformers is connected with the supply bus bar and the secondary winding of both transformers is connected with the load bus bar. In this way, we can connect two or more than two transformers in parallel and exceed transformer ratings.

While connecting transformers in parallel, the polarities of the transformer must be matched. Otherwise, it will lead to short-circuit and may damage the transformer.

Ideal Condition

In an ideal condition, we consider both transformers have the same voltage ratio and same turns ratio. So, the impedance triangle of both transformers is identical in shape and size. The phasor diagram of this condition is as shown in the figure below.

• E = No-load secondary voltage of each transformer
• V 2 = Secondary (load) terminal voltage
• V 1 = Primary (supply) terminal voltage
• I A = Current supplied by transformer-1
• I B = Current supplied by transformer-2
• I = Total current

As shown in the phasor diagram, the total load current (I) is legging behind V 2 by an angle of ф. And current I A and I B of an individual transformer are in phase with total current (I).

And individual current (I A and I B ) for each transformer is;

Similarly, current I­ B is derived as;

Equal Voltage Ratios

Let’s assume that, the transformers have the same voltage ratio. Hence, no-load voltage of both transformers is equal (E A = E B = E). In this condition, no current will flow between two transformers. The equivalent circuit of this condition is as shown in the figure below.

• E A , E B = No-load voltage
• Z A , Z B = Impedances
• I A , I B = Secondary current of respective transformer
• V 2 = Terminal voltage

Here, the impedance of both transformers is connected in parallel. Hence, total impedance Z AB is;

Vector diagram of this condition is as shown in the figure below.

Here, current I A and I B are not in phase. Hence, the total current supplied to the load is a phasor summation of I A and I B . And total current (I) is as shown in the vector diagram. Here, we have considered that the no-load voltage of each transformer is the same and it is in-phase in the vector diagram.

Let’s assume Q A and Q B are power consumed by each transformer respectively.

Q A = V 2 I A      and     Q B = V 2 I B

The total power consumed by both transformers is Q;

Therefore, Q A and Q B are obtained in magnitude and in-phase from the above vectorial equations.

Unequal Voltage Ratio

If the transformation ratio is not the same for both transformers, no-load secondary voltage is not the same. In this condition, some amount of current will flow between transformers in no-load conditions. This current is known as circulating current IC.

The no-load EMF of both transformers is not the same in this condition. Hence,

E A = I A Z A + I Z L

E B = I B Z B + I Z L

Z L = load impedance

I = I A + I B      and     V 2 = I Z L

E A = I A Z A + ( I A + I B ) Z L

E B = I B Z B + (I A + I B ) Z L

Subtract the above equations;

E A – E B = I A Z A – I B Z B

( E A – E B ) + I B Z B = I A Z A

Put the value of I A in the equation of E B ;

Now, put the value of total current (I) in the equation of terminal voltage V 2 ;

The transformer impedances (Z A and Z B ) are always smaller than the load impedance Z L . So, to make the equation easy, we neglect Z A Z B in comparison with Z L (Z A +Z B ).

• Advantages and Disadvantages of a Three Phase Transformer over a Single Phase Transformer
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Parallel Operation of Three-Phase Transformers

In a three-phase transformer also, we can connect two or more than two transformers in parallel to increase load capacity. The conditions required in the parallel operation of a three-phase transformer are the same as a single-phase transformer. Additionally, there is some condition that must be followed.

• The phase sequence of both transformers is the same and it is verified by the phase sequence indicator.
• Phase displacement between the primary winding and secondary winding must be the same.
• All three transformers used in the transformer bank must be the same type of transformer (Core or shell).
• While calculating voltage ratio, consider line voltages. And keep the voltage ratio the same.

The There should be a voltage ratio between the primary and secondary terminal voltage. It shows this voltage ratio is not equal to the ratio of number of turns per phase. For example, if V 1 and V 2 are the primary and secondary terminal voltage respectively, then the turn ratio for Star / Delta connection (Y-Δ) would be:

The circuit diagram of the parallel operation of a three-phase transformer is as shown in the figure below.

The primary and secondary winding of both transformers (T1 and T2) are connected as shown in the above figure. Here, the b and c terminals of the secondary winding are kept flexible and connected with a voltmeter for testing purposes. If both voltmeters show zero reading, the polarities are correct. If the voltmeter shows twice of phase voltages, the polarities are wrong.

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what will happen if the conditions for paralleling two three phase transformers are not met, with mathematical proof.

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DF-DETR: Dead fish-detection transformer in recirculating aquaculture system

• Published: 13 November 2024
• Volume 33 , article number  43 , ( 2025 )

Cite this article

• Tingting FU 1 , 2 , 3 , 4 ,
• Dejun Feng 1 ,
• Pingchuan Ma 2 , 3 , 4 ,
• Weichen Hu 2 , 3 , 4 ,
• Xinting Yang 2 , 3 , 4 ,
• Shantan Li 1 , 2 , 3 , 4 &
• Chao Zhou 2 , 3 , 4  

In aquaculture, real-time and rapid detection of dead fish is important for early risk warning and improving aquaculture efficiency. However, the complex actual environment and uncontrollable fish movement have brought great challenges to the detection of dead fish. Therefore, this paper proposes a high-precision and lightweight dead fish-detection transformer (DF-DETR) based on machine vision and original RT-DETR (real-time detection transformer). The specific implementation is as follows: Firstly, the backbone of the original RT-DETR was replaced by the RepNCSPELAN module which extracts multi-scale features. This not only improves the model’s ability to detect targets of different sizes but also reduces the amount of model parameters. Secondly, the AIFI in the RT-DETR was improved to CascadedGroupAttention (CGA). By changing the original feature fusion method, different levels of features are grouped and attention mechanism is added, so as to capture more target features. Finally, the CCFM_CSP module was constructed to fuse important features using parallel dilated convolution with different expansion rates, which improves the detection accuracy. The experimental results show that the [email protected] of the proposed dead fish detection model DF-DETR can reach 96.6%, and the parameter amount is reduced by 27% compared with the original RT-DETR. In summary, the proposed DF-DETR model realizes real-time and high-precision dead fish detection, which can provide effective technical support for the development of intelligent inspection robots.

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Data Availability

No datasets were generated or analysed during the current study.

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This study was supported by the National Key R & D Program of China (2022YFD2001701) and the National Natural Science Foundation of China (32373184).

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Zhejiang Ocean University, Zhejiang, 316000, China

Tingting FU, Dejun Feng & Shantan Li

National Engineering Laboratory for Agri-Product Quality Traceability, Beijing, 100097, China

Tingting FU, Pingchuan Ma, Weichen Hu, Xinting Yang, Shantan Li & Chao Zhou

Information Technology Research Center, Beijing Academy of Agriculture and Forestry Sciences, Shuguang Huayuan Middle Road 9#, Haidian District, Beijing, 100097, China

National Engineering Research Center for Information Technology in Agriculture, Beijing, 100097, China

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Contributions

Tingting Fu: Conceptualization, Methodology, Software, Investigation, Formal analysis, Writing-original draft. Dejun Feng: Visualization, Investigation. Pingchuan Ma: Data curation, Writing – original draft. Weicheng Hu: Resources, Supervision. Xinting Yang: Software, Validation. Shantan Li: Resources, Validation. Chao Zhou: Conceptualization, Funding acquisition, Resources, Supervision, Writing-review & editing.

Corresponding author

Correspondence to Chao Zhou .

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FU, T., Feng, D., Ma, P. et al. DF-DETR: Dead fish-detection transformer in recirculating aquaculture system. Aquacult Int 33 , 43 (2025). https://doi.org/10.1007/s10499-024-01697-9

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Received : 09 July 2024

Accepted : 09 October 2024

Published : 13 November 2024

DOI : https://doi.org/10.1007/s10499-024-01697-9

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