TECHNICAL FIELD

[0001] The present subject matter relates, in general, to controlled switching of transformers. In particular, the present subject matter relates to controlled switching of a zig-zag transformer.

BACKGROUND

[0002] Transformers are commonly used in power systems for voltage conversion. During operation of power systems, transformers may be switched on and off, referred to as energization and de-energization, depending on various factors, such as load variation, fault detection, etc. During energization, a transformer may initially draw a large inrush current leading to a voltage drop in the power system. The inrush current generally depends on parameters such as magnetization characteristics of the core, design and connection configuration of the transformer, the residual flux in the transformer core at a preceding de energization operation of the transformer and the current instant of energization of the transformer. In order to minimize inrush currents and voltage drops during energization, a transformer is to be energized at those phase angles where residual flux matches prospective flux in each phase. This is also referred to as controlled switching. Generally, the prospective flux is obtained as an integral of the source voltage, while the residual flux is obtained as an integral of the transformer voltage measured during de-energization. These tasks are often performed by a controlled switching device (CSD), which may use the information on prospective fluxes and residual fluxes for optimal energization of a power transformer.

SUMMARY

[0003] Embodiments of the present invention provide a method for controlled switching of a zigzag transformer, a device for controlled switching of a zigzag transformer, and a computer readable storage medium comprising instructions for controlled switching of a zigzag transformer. Objectives of embodiments of the invention include accurate evaluation of controlled energization targets for transformers to be energized from grounded zigzag winding, irrespective of the secondary winding connection configuration. The evaluation of controlled energization targets is based on a residual flux value, a design of the transformer, and a connection configuration of the zigzag transformer to achieve the desired phase shift.

[0004] According to a first aspect, a method for optimized controlled switching of a zigzag transformer is provided. The method comprises obtaining an average residual flux value of a first equivalent phase of a transformer, where the first equivalent phase is associated with magnetically interdependent windings of two or more phases of the transformer. The average residual flux value of the first equivalent phase is compared with a source flux of one phase of the two or more phases associated with the first equivalent phase. Based on a comparison, a first switching pole of a circuit breaker is closed, where the first switching pole is associated with the first equivalent phase.

[0005] According to a second aspect, a device comprising a processor and a controlled switching module executable by the processor is provided. The device is configured to obtain an average residual flux value of a first equivalent phase of a transformer, where the first equivalent phase is associated with magnetically interdependent windings of two or more phases of the transformer. Further, the average residual flux value of the first equivalent phase is compared with a source flux of one phase of the two or more phases associated with the first equivalent phase. Based on the comparison, a first switching pole of a circuit breaker is closed, where the first switching pole is associated with the first equivalent phase. [0006] According to a third aspect a non-transitory computer readable medium containing program instruction that, when executed, causes the processor to perform the method for controlled switching of a transformer, is provided.

[0007] According to an implementation, the transformer is energized from a winding connected in a zig-zag configuration. [0008] According to an implementation, the source flux is derived from a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase.

[0009] According to an implementation, the magnetically interdependent windings of the transformer correspond to a series connection of a first winding of a first phase of the transformer and a second winding of a second phase of the transformer.

[0010] According to an implementation, the average residual flux value of the first equivalent phase of the transformer corresponds to an average of a residual flux in the magnetically interdependent windings.

[0011] According to an implementation, the first switching pole of the circuit breaker is closed when the average residual flux value of the first equivalent phase is equal to the source flux.

[0012] According to an implementation, the first switching pole of the first equivalent phase of the circuit breaker is closed on a rising slope of a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase when the source flux is equal to the average residual flux value.

[0013] According to an implementation, a second switching pole of the circuit breaker of a second equivalent phase is closed at a first pre-determined time after closing the first switching pole of the circuit breaker and a third switching pole of the circuit breaker of a third equivalent phase is closed at a second pre-determined time after closing the second switching pole of the circuit breaker.

[0014] According to an implementation, the first pre-determined time and the second pre-determined time is determined based on a time taken for a residual flux in the second equivalent phase of the transformer and the third equivalent phase of the transformer to reach a negligible value or a time taken for a resultant flux value of the second equivalent phase and the third equivalent phase to attain a negligible asymmetry.

[0015] According to an implementation, a first terminal and a second terminal of a first phase winding, a second phase winding and a third phase winding of the transformer are interconnected to achieve a phase shift between the windings to form equivalent phases.

[0016] According to an implementation, a secondary winding of the transformer is grounded, ungrounded, or connected in a delta connection. [0017] According to an implementation, the processor is to execute the method for controlled switching of transformer.

BRIEF DESCRIPTION OF DRAWINGS

[0018] The features, aspects, and advantages of the present subj ect matter will be better understood with regard to the following description and accompanying figures. The use of the same reference number in different figures indicates similar or identical features and components.

[0019] Fig. 1 illustrates a block diagram of an electrical network including a device for controlled switching of a zigzag transformer, in accordance with an embodiment of the present subject matter.

[0020] Figs. 2(a), 2(b) and 2(c) illustrate a first example winding configuration of a zigzag grounding bank, in accordance with an embodiment of the present subject matter.

[0021] Figs. 3(a), 3(b) and 3(c) illustrate a second example winding configuration of a zigzag grounding bank, in accordance with an embodiment of the present subject matter.

[0022] Fig. 4 illustrates a graph depicting controlled energization targets for zigzag transformer with 30-degree lagging phase shift, in accordance with an embodiment of the present subject matter. [0023] Fig. 5(a) and 5(b) illustrates an example delayed closing strategy based on flux equalization and the corresponding inrush current pattern, in accordance with an embodiment of the present subject matter.

[0024] Fig. 6 illustrates a method for controlled switching of a zigzag transformer, in accordance with an embodiment of the present subject matter. DETAILED DESCRIPTION

[0025] The present subject matter relates to controlled switching of zig zag transformers. The following describes optimized controlled switching of zig zag transformers based on computing residual flux values of the transformers.

[0026] Zigzag transformers are mainly used to achieve grounding on ungrounded or delta connected systems for medium and low voltage systems. Zigzag transformers are also used to achieve a phase shift between the windings of the transformers. During no load energization of these transformers, they may be subjected to high magnetizing inrush currents that may have an impact on the grid stability. Controlled switching can be used to mitigate the inrush current.

[0027] To mitigate the effect of inrush currents, residual flux values may be determined to perform controlled switching of the transformers. The residual flux values may be evaluated from the load side voltage measurements. However, the individual phase wise energization targets, i.e., the instant at which a circuit breaker may be closed to energize the transformer considering the residual fluxes imposes challenges. This is due to the configuration of a zig-zag transformer, where, the three phases are realized with connecting two windings in series based on the phase shift to be achieved between the windings. Thus, determining individual energization target for each phase of the zigzag transformer may be a challenge. [0028] The present subject matter facilitates controlled switching of zigzag transformers. In one example, determining controlled energization targets with reference to each switching pole of the circuit breaker for zigzag transformers is performed considering residual fluxes based on an equivalent phase concept. An equivalent phase comprises two windings connected in a series connection, where each winding may be from a different phase and the two windings may be magnetically interdependent. Each equivalent phase may be associated with a switching pole of the circuit breaker. For example, if the three phases of the transformer are U, V, and W, to form a first equivalent phase of the transformer, a winding from phase U is connected to a winding from phase V in series to form a first equivalent phase. The first equivalent phase with windings from phases U and V connected in series may be connected to the first switching pole of the circuit breaker.

[0029] In operation, in one example, an average residual flux value of a first equivalent phase of a transformer is obtained. The first equivalent phase may be associated with magnetically interdependent windings of two or more phases of the transformer. Further, the average residual flux value of the first equivalent phase is compared with a source flux of one phase of the two or more phases associated with the first equivalent phase. A first switching pole of the circuit breaker is closed based on the comparison, where the first switching pole is associated with the first equivalent phase. Thus, the energization target for the first switching pole is determined based on the average residual flux value of the first equivalent phase. [0030] The present subject matter thus provides for an accurate evaluation of controlled energization targets for transformers to be energized from grounded zigzag winding side based on the residual flux impact and irrespective of the secondary winding connection configuration or any other winding other than the grounded zigzag winding.

[0031] The above and other features, aspects, and advantages of the subject matter will be better explained with regard to the following description and accompanying figures. Wherever possible, the same reference numbers are used in the drawings and the following description to refer to the same or similar parts. While several examples are described, modifications, adaptations, and other implementations are possible.

[0032] Fig. 1 illustrates a block diagram of an electrical network including a device for controlled switching of a zigzag transformer, in accordance with an embodiment of the present subject matter. An electrical network 100 comprises electrical sources 102, 104, 106 that supply power to the three phases of the network. In one example, the electrical sources 102, 104, and 106 may be power generators, such as synchronous power generators or inverter-based sources. The three electrical sources 102, 104, and 106 may supply power to the three phases of the transformer namely phase U, phase V, and phase W respectively. [0033] It will be understood that that the electrical network 100 may include a plurality of additional components or devices for monitoring, sensing, and controlling various parameters that may be associated with the network but are not shown for brevity. For example, components such as circuit breakers, sensors, current transformers, voltage transformers, loads connected to the transmission lines, shunt reactors, intelligent electronic devices IEDs, protective relays, and the like may be connected to the network. In one example, a zigzag transformer 120, alternatively referred to as transformer 120, for which the controlled switching is performed may be connected to the electrical network 100. In zigzag transformers, each phase is formed by connecting two windings in series. The windings chosen to be connected in series are based on the phase shift to be achieved between primary and secondary winding of the transformer. The secondary winding of the transformer may refer to any other winding of the transformer on which energization is not performed. It may be understood that the energization of the transformer is performed on the primary winding irrespective of the secondary winding connection, where the secondary winding of the transformer may refer to any other winding of the transformer on which energization is not performed. As all the windings are of a similar design, the induced electromagnetic force (EMF) and the residual fluxes are generally equally distributed across each winding in series.

[0034] A device 122 may receive voltage measurements associated with the transformer 120. In one example, the device 122 may be an intelligent electronic device (TED). In other examples, the device 122 may be any computing device, such as a server, a desktop device, a laptop, etc., which may receive the measurements from an IED. In an example, a protection and control unit 124 may be configured to provide a trip signal to a circuit breaker 126. In one example, the trip signal may be directly applied to start the integration of the transformer 120 or the trip signal may be derived by other methods known in the art to derive the status of the circuit breaker 126. In one example, the protection and control unit 124 may provide the trip signal to the device 122 to open the circuit breaker 126. [0035] In an example, the present subject matter may be implemented by one or more modules. The modules may be implemented as instructions executable by one or more processors. For instance, in the example where the device 122 performs the method, the modules are executed by the processors of the device 122. In case the method is implemented in part by the device 122 and in part by a server, the modules (depending on the step) will be distributed accordingly in the device 122 and the server.

[0036] In one example, the device 122 may be configured to receive input measurement signals from various measurement equipment connected to the electrical network 100, such as current transformers, potential transformers, Rogowski coils, circuit breakers or other measurement sensors. In one example, the device 122 may receive voltage measurements of the zigzag transformer 120 from a voltage measuring device (not shown in the figure). The device 122 may process the measurements obtained with the help of a processor 130. The processor 130 may be implemented as a dedicated processor, a shared processor, or a plurality of individual processors, some of which may be shared. The device 122 may comprise a memory 134, that may be communicatively connected to the processor 130. Among other capabilities, the processor 130 may fetch and execute computer- readable instructions, stored in the memory 134. In one example, the memory 134 may store a controlled switching module 136. In other examples, the controlled switching module 136 may be external to the memory 134. The memory 134 may include any non-transitory computer-readable medium including, for example, volatile memory, such as RAM, or non-volatile memory, such as EPROM, flash memory, and the like.

[0037] In one example, a method to perform controlled switching of the zigzag transformer 120, such as a three-phase power transformer, may be performed by the processor 130 by execution of the controlled switching module 136. The transformer 120 may be energized from a winding connected in a zig-zag configuration. The controlled switching module 136 may obtain an average residual flux value of a first equivalent phase of a transformer, where the first equivalent phase is associated with magnetically interdependent windings of two or more phases of the transformer. The magnetically interdependent windings of the transformer may correspond to a series connection of a first winding of a first phase of the transformer and a second winding of a second phase of the transformer. In one example, a first terminal and a second terminal of a first phase winding, a second phase winding and a third phase winding of the transformer are interconnected to achieve a phase shift between the windings to form equivalent phases. For example, if phase U, phase V, and phase W are the three phases of the transformer, then the first equivalent phase may be formed by connecting the first winding of phase U with the second winding of phase V in a series connection. The windings may be connected in such a way that a phase shift of 30-degree, 120- degree lag or lead and the like may be formed between the windings. In one example, the secondary winding of the transformer may be grounded, ungrounded, or connected in a delta connection.

[0038] In zigzag transformers, to mitigate magnetizing inrush current, the controlled energization targets may be evaluated considering phase wise residual fluxes. In one example, to determine the residual flux in each phase of the transformer, the terminal voltage of the transformer may be obtained. The terminal voltage of the transformer may then be converted to limb voltages for each phase of the transformer by methods known in the art. The limb voltage of a first phase, a second phase, and a third phase of the transformer may be integrated to obtain the residual flux in the first phase, the second phase, and the third phase respectively. In one example, the voltage may be integrated by the controlled switching module 136 to compute the residual flux of the transformer 120. Based on the residual flux value determined in the first phase, the second phase, and the third phase of the transformer the average residual flux value may be obtained.

[0039] In one example, the average residual flux value of the first equivalent phase of the transformer may correspond to an average of a residual flux in the magnetically interdependent windings. The controlled switching module 136 compares the average residual flux value of the first equivalent phase with a source flux of one phase of the two or more phases associated with the first equivalent phase. For example, when the first equivalent phase is formed by connecting transformer windings of phase U and phase V in series, the average residual flux value of the first equivalent phase (UV) may be compared to the source flux of phase U. In another example, when the first equivalent phase is formed by connecting transformer windings of phase V and phase W in series, the average residual flux value of the first equivalent phase (VW) may be compared to the source flux of phase V. The comparison of the average residual flux value to the source flux is explained in detail with reference to Figs. 2(a) to 3(c).

[0040] Based on the comparison, a first switching pole of the circuit breaker 126 may be closed, where the first switching pole is associated with the first equivalent phase. The first switching pole of the circuit breaker is connected to the first equivalent phase formed by a series connection of a first phase winding and second phase winding, to energize the transformer. In one example, the first switching pole of the circuit breaker is closed when the average residual flux value of the first equivalent phase is equal to the source flux. In one example, the source flux may be derived from a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase. In one example, the gap voltage may be the difference in between the source voltage and a load voltage. In a scenario where the value of load voltage is zero or negligible, the gap voltage may be considered to be equal to the source voltage. Based on the application, the source flux value derived from the source voltage or the gap voltage may be compared to the average residual flux value.

[0041] In principle, there may be two points where the average residual flux value equals the source flux explained with reference to Fig. 4. Further, in order to minimize the resultant flux asymmetry in the successive operations, the first switching pole of the first equivalent phase of the circuit breaker is closed on a rising slope of a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase. The first switching pole of the circuit breaker may be closed when the source flux is equal to the average residual flux value.

[0042] In one example, a second switching pole of the circuit breaker 126 of a second equivalent phase may be closed at a first pre-determined time after closing the first switching pole of the circuit breaker 126. Similarly, a third switching pole of the circuit breaker 126 of a third equivalent phase may be closed at a second pre determined time after closing the second switching pole of the circuit breaker. Thus, the closing of the second switching pole and the third switching pole of the circuit breaker may be implemented using a delayed closing strategy to energize the transformer. The delayed closing strategy may be based on a flux equalization principle in the second and third switching poles. The principle of flux equalization has been explained in detail with reference to Fig. 5(a). In one example, the first pre-determined time and the second pre-determined time are determined based on a time taken for a residual flux in the second equivalent phase of the transformer and the third equivalent phase of the transformer to reach a negligible value. In another example, the first pre-determined time and the second pre-determined time may be determined based on a time taken for an asymmetry in the resultant flux values that are caused due to the residual flux values in the second equivalent phase and the third equivalent phase of the transformer being reduced to a minimum value. For example, the first pre-determined time and the second pre-determined time may be any one of one power cycle, one and half power cycle, or two power cycles. [0043] Further, the device 122 may comprise an output interface 138 to communicate the results obtained from the controlled switching module 136, for example, to a server. The output interface 138 may include a variety of computer- readable instructions-based interfaces and hardware interfaces that allow interaction with other communication, storage, and computing devices, such as network entities, web servers, databases, and external repositories, and peripheral devices. In one example, the residual flux values, the energization targets, voltage and current measurements, and the like may be viewed on a display connected to the output interface 138 or integrated with the device 122.

[0044] Thus, the present subject matter facilitates the accurate evaluation of controlled energization targets for transformers to be energized from grounded zigzag winding irrespective of the secondary winding connection configuration based on residual flux impact. Various example scenarios where the teachings of the present subject matter may be applied are explained with reference to Figs. 2(a) to 3(c).

[0045] Figs. 2(a), 2(b) and 2(c) illustrate a first example winding configuration of a zigzag grounding bank, in accordance with an embodiment of the present subject matter. The windings of the transformer chosen to be connected in series are based on the phase shift to be achieved between the primary winding and the secondary winding of the transformer. In a first example, a winding configuration of a zigzag grounding bank to achieve a phase shift of 30-degree lagging is described. In this example, the three phases are considered to be U, V, and W, with a sequence of phase rotation as explained below. However, other sequences for phase rotation are possible.

[0046] Fig. 2(a) illustrates a zigzag grounding bank configuration to achieve a phase shift of 30-degree lagging. For the sake of discussion, a three-limb transformer is considered as an example to illustrate the method of controlled switching. However, other transformer configurations with different phase shifts are possible. As discussed above, the windings of the transformer are magnetically interdependent. In one example, a three limbed transformer with limbs LI, L2, and L3 may be considered, where, the first limb LI of the transformer comprises winding WU split into two halves as winding W 1 and winding W4, the second limb L2 of the transformer comprises winding WV split into two halves as winding W2 and winding W5, and the third limb of the transformer L3 comprises winding WW split into two halves as winding W3 and winding W6. A first terminal of windings Wl, W2, and W3 are connected to the three terminals of phase U, phase V, and phase W respectively. Further, a second terminal of winding Wl is connected in series to a first terminal of winding W5, a second terminal of winding W2 is connected in series to a first terminal of winding W6, a second terminal of winding W3 is connected in series to the first terminal of winding W4, and a second terminal of windings W4, W5, and W6 are connected to a neutral point to form a zigzag transformer to achieve a phase shift of 30 degree lag. Fig. 2(b) illustrates a phasor diagram of a zigzag transformer with a 30-degree lag and Fig. 2(c) illustrates the voltage in winding Wl lagging the voltage in phase U by 30 degrees. [0047] As shown in Figs. 2(a) and 2(b) the winding W1 of phase U and winding W5 from the phase V phase are connected in series to form a first equivalent phase that maybe connected to a first switching pole of the circuit breaker 126. Similarly, winding W3 from of phase W and winding W4 of phase U phase are connected in series to form a second equivalent phase that maybe connected to a second switching pole of the circuit breaker 126 and winding W2 from the phase V and the winding W6 from the phase W phase are connected in series to form a third equivalent phase that maybe connected to a third switching pole of the circuit breaker 126.

[0048] In an example, for the zigzag transformer with 30-degree phase shift lag to be energized from the grounded zigzag winding side, the residual fluxes of phase U and phase V may be averaged, i.e., the residual flux associated to the limb of winding W1 of phase U and the residual flux associated to the limb of winding W5 of phase V may be averaged to obtain the average residual flux value of the first equivalent phase ( UV). The averaged residual flux value may be referred to as the average residual flux value of the first equivalent phase (U and V). Consequently, the energization target for the first switching pole connected to phase U of the circuit breaker 126 is evaluated considering the aforesaid average residual flux. The optimum target for closing the first switching pole U of the circuit breaker associated with the first equivalent phase UV may be when the source side flux for the first switching pole U equals the average residual flux value of the first equivalent phase UV. For the second equivalent phase (WU) and the third equivalent phase (VW) the delayed closing strategy may be applied. In one example the delayed closing strategy may be based on the principle of flux equalization, where, the residual flux values may be neglected. In one example, the second switching pole W connected to the second equivalent phase may be switched at a gap voltage peak followed by the third switching pole V connected to the third equivalent phase, at least 1 ms later, to maintain the U-W-V switching sequence. The target for closing the second switching pole W is considered when the resultant flux for phase W equals the source side flux neglecting the residual flux effect. In one example, the sequence for the closing of the first, second, and third switching pole of the circuit breaker may be in accordance with the switching sequence desired.

[0049] Figs. 3(a), 3(b) and 3(c) illustrate a second example winding configuration of a zigzag grounding bank, in accordance with an embodiment of the present subject matter. The windings of the transformer chosen to be connected in series are based on the phase shift to be achieved between the primary winding and the secondary of the transformer. In a second example, a winding configuration of a zigzag grounding bank to achieve a phase shift of 30-degree lead is described. In this example, the three phases are considered to be U, V, and W, with a sequence of phase rotation as explained below. However, other sequences for phase rotations are possible.

[0050] Fig. 3(a) illustrates a zigzag grounding bank configuration to achieve a phase shift of 30-degree leading. For the sake of discussion, a three-limb transformer is considered as an example to illustrate the method of controlled switching. However, other transformer configurations with different phase shifts between the primary winding and the secondary winding are possible. As discussed above, the windings of the transformer are magnetically interdependent. In one example, a three limbed transformer with limbs LI, L2, and L3 may be considered, where the first limb LI of the transformer comprises winding WU split into two halves as winding W1 and winding W4,the second limb L2 of the transformer comprises winding WV split into two halves as winding W2 and winding W5, and the third limb of the transformer L3 comprises winding WW split into two halves as winding W3 and winding W6. A first terminal of windings Wl, W2, and W3 are connected to the three terminals of phase U, phase V, and phase W respectively. Further, a second terminal of winding Wl is connected in series to a first terminal of winding W6, a second terminal of winding W2 is connected in series to a first terminal of winding W4, a second terminal of winding W3 is connected in series to the first terminal of winding W5, and a second terminal of windings W4, W5, and W6 are connected to a neutral point to form a zigzag transformer to achieve a phase shift of 30 degree lead. [0051] Fig. 3(b) illustrates a phasor diagram of a zigzag transformer with a 30-degree lag and Fig. 3(c) illustrates the voltage in winding W 1 leading the voltage in phase U by 30 degrees.

[0052] As shown in Figs. 3(a) and 3(b) the winding W1 of phase U and winding W6 from the phase W phase are connected in series to form a first equivalent phase that maybe connected to a first switching pole of the circuit breaker 126. Similarly, W3 from of phase W and winding W5 of phase V are connected in series to form a second equivalent phase and winding W2 from the phase V and the winding W4 from the phase U phase are connected in series to form a third equivalent phase. The second equivalent phase may be connected to a second switching pole W of the circuit breaker and the third equivalent phase may be connected to a third switching pole V of the circuit breaker to maintain a switching sequence of U-W-V. The second switching pole of the circuit breaker 126 may be closed after the first switching pole of the circuit breaker 126.

[0053] In an example, for the zigzag transformer with 30-degree phase shift lead to be energized from the grounded zigzag winding side, the residual fluxes of phase U and phase W may be averaged, i.e., the residual flux associated to the limb of winding W1 of phase U and the residual flux associated to th limb of winding W6 of phase W may be averaged to obtain the average residual flux value of the first equivalent phase ( UW). The averaged residual flux value may be referred to as the average residual flux value of the first equivalent phase (U and W). Consequently, the energization target for the first switching pole connected to phase U of the circuit breaker 126 is evaluated considering the aforesaid average residual flux value. The optimum target for closing the first switching pole U of the circuit breaker associated with the first equivalent phase UW may be when the source side flux for the first switching pole U equals the average residual flux value of the first equivalent phase UW. For the second equivalent phase (WV) and the third equivalent phase (VU) the delayed closing strategy may be applied. In one example the delayed closing strategy may be based on the principle of flux equalization, where, the residual flux values may be neglected. In one example, the second switching pole W connected to the second equivalent phase may be switched at a gap voltage peak followed by the third switching pole V connected to the third equivalent phase, at least 1 ms later, to maintain the U-W-V switching sequence. The target for closing the second switching pole W is considered when the resultant flux for phase W equals the source side flux neglecting the residual flux effect. In one example, the sequence for the closing of the first, second, and third switching pole of the circuit breaker may be in accordance with the switching sequence desired.

[0054] Fig. 4 illustrates a graph depicting controlled energization targets for zigzag transformer with 30-degree lagging phase shift, in accordance with an embodiment of the present subject matter. The method for controlled switching of the zigzag transformer 120 as discussed above is explained with reference to the graph depicted in Fig. 4. A zigzag transformer with a 30-degree phase shift (lagging) is considered. In this example, the three phases are considered to be U, V, and W, with a sequence of phase rotation as described below. However, other sequences for phase rotation are possible. Signal 402 depicts the source voltage of phase U, signal 404 depicts the source flux of phase U, signal 406 depicts the residual flux in phase U of the transformer, signal 408 depicts the residual flux in phase V of the transformer, and signal 410 depicts the average residual flux of phases U and V alternately referred to as the first equivalent phase. From Fig. 4, it may be observed that at time instants tl and t2, the average residual flux of the first equivalent phase is equal to the source flux of phase U, represented by point 412 and point 414. To minimize the resultant flux asymmetry in the successive operations, the point 412 with the rising slope of the voltage is considered as the switching target of the first switching pole connected to the first equivalent phase (UV) of the circuit breaker 126. Therefore, the time instant tl is considered as the energization target which is represent by 416. Further, at a time instant t3 and t4, the energization targets of phases W and V are considered. For a switching sequence U-W-V to be maintained, the second switching pole of the circuit breaker corresponds to phase W and the third switching pole of the circuit breaker corresponds to phase V. In one example, the time instant t3 may correspond to the first pre-determined time and the time instant t4 may correspond to the second pre- determined time as discussed above. The energization targets for closing the second switching pole at the time instant t3 and the third switching pole at the time instant t4 may be in accordance with a delayed closing strategy as discussed with reference to Fig. 5(a). In one example the first pre-determined time t3 and the second pre determined time t4 may be an absolute or a fraction of a half cycle or a full cycle duration. In one example, closing the second switching pole at the time instant t3 and the third switching pole at the time instant t4 at point 418 and point 420 respectively may be when a resultant flux of phase W equals the source flux of phase W and the resultant flux of phase V equals the source flux of phase V respectively or when the resultant flux values of phases W and V attains negligible asymmetry due to residual flux values in W and V phases. The value of t4 may be longer than the value of t3 to ensure a switching sequence of U-W-V.

[0055] Fig. 5(a) and 5(b) illustrates an example delayed closing strategy based on flux equalization and the corresponding inrush current pattern, in accordance with an embodiment of the present subject matter. Fig. 5(a) illustrates resultant flux and source flux values measured in per unit values of phases U, V, and W plotted against time measured in milliseconds. In this example, the three phases are considered to be U, V, and W, with a sequence of phase rotation as described below. However, other sequences for phase rotation are possible. Waveform 502 represents the source flux of phase U, waveform 504 represents the source flux of phase W and waveform 506 represents the source flux V. Waveforms 512, 514 and 516 represent the average residual flux in phases U, W, and V respectively. It may be observed from the graph, that the first switching pole of the circuit breaker is closed at an instant tl when the average residual flux in the first equivalent phase is equal to the source flux of phase U. The second switching pole of the circuit breaker and the third switching pole of the circuit breaker are closed at time instants t2 and t3 after flux equalization. In this example, the principle of flux equalization is considered for closing the second and the third switching pole of the circuit breaker. As it can be observed from the graph, the resultant flux values of phase W and phase V are different at the time instant tl . However, over a period of time, the resultant flux values of phase W and phase V become equal. The instant of time at when the source side flux of phase W and phase V equals the resultant flux value of phase W and phase V respectively, the second switching pole of the circuit breaker is closed. It may be observed that at t2 the resultant flux in phase W is equal to the resultant flux in phase V. The time period 520 of tl to t2 may be referred to as the time taken for flux equalization. In one example, the third switching pole of the circuit breaker may be closed at t3 after closing the second switching pole of the circuit breaker. The effect of optimized switching may be observed in Fig. 5(b). Fig. 5(b) illustrates the inrush current pattern in the zigzag transformer when energized, in accordance with an embodiment of the present subject matter. The graph illustrates inrush currents 522, 524, and 526 in phases U, V, and W.

[0056] The present subject matter thus provides an accurate phase wise controlled switching of a zigzag transformer by determining the energization targets based on the average residual flux value.

[0057] Fig. 6 illustrates a method for controlled switching of a zigzag transformer, in accordance with an embodiment of the present subject matter. The order in which method 600 is described is not intended to be construed as a limitation, and some of the described method blocks may be performed in a different order to implement the method 600 or an alternative method. Furthermore, the method 600 may be implemented in any suitable hardware, computer readable instructions, firmware, or combination thereof. For discussion, the method 600 is described with reference to the implementations illustrated in Fig. 1.

[0058] In the method 600, at block 602 an average residual flux value of a first equivalent phase of a transformer is obtained. Where, the first equivalent phase is associated with magnetically interdependent windings of two or more phases of the transformer. In one example, the transformer may be energized from a winding connected in a zig-zag configuration. In one example, the average residual flux value of the first equivalent phase of the transformer corresponds to an average of a residual flux in the magnetically interdependent windings. In one example, the magnetically interdependent windings of the transformer correspond to a series connection of a first winding of a first phase of the transformer and a second winding of a second phase of the transformer.

[0059] At block 604, the average residual flux value of the first equivalent phase is compared with a source flux of one phase of the two or more phases associated with the first equivalent phase. In one example, the average residual flux value of the first equivalent phase of the transformer corresponds to an average of a residual flux in the magnetically interdependent windings. In one example, the source flux is derived from a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase. In one example, the average residual flux value may be compared to any one of the three phase source voltages.

[0060] At block 606, a first switching pole of the circuit breaker is closed based on the comparison, where the first switching pole is associated with the first equivalent phase. In one example, the first switching pole of the circuit breaker is closed when the average residual flux value of the first equivalent phase is equal to the source flux. In one example, the first switching pole of the circuit breaker may be the switching pole associated with the first phase of the circuit breaker which may be connected to the first equivalent phase of the transformer. In one example, the first switching pole of the first equivalent phase of the circuit breaker is closed on a rising slope of a gap voltage or a source voltage of the one phase of the two or more phases associated with the first equivalent phase when the source flux is equal to the average residual flux value. Further, a second switching pole of the circuit breaker of a second equivalent phase is closed at a first pre-determined time after closing the first switching pole of the circuit breaker and a third switching pole of the circuit breaker of a third equivalent phase is closed at a second pre-determined time after closing the second switching pole of the circuit breaker. In one example, the first pre-determined time and the second determined time may be an absolute, a multiple, or a fraction, of a half or a full power cycle duration. The first pre determined time and the second pre-determined time may be based on a time taken for flux equalization, i.e., where the first pre-determined time and the second pre determined time is determined based on a time taken for a residual flux in the second equivalent phase of the transformer and the third equivalent phase of the transformer to reach a negligible value or a time taken for a resultant flux value of the second equivalent phase and the third equivalent phase to attain a negligible asymmetry. In one example, a primary winding may be a grounded zigzag transformer and a secondary winding of the transformer is grounded, ungrounded, or connected in a delta connection. The phase shift between the primary winding and the secondary winding of the transformer may be based on the switching sequence and the winding connection configurations. In one example, a first terminal and a second terminal of a first phase winding, a second phase winding and a third phase winding of the transformer are interconnected to achieve a phase shift between the windings to form equivalent phases.

[0061] The present subject matter thus provides a method to perform phase- wise controlled switching of zigzag transformers based on the residual flux values of the transformer, irrespective of their secondary winding configurations. [0062] Although the present subj ect matter has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiments, as well as alternate embodiments of the subject matter, will become apparent to persons skilled in the art upon reference to the description of the subject matter.