Method and system for controlled switching on a compensated transmission line

Abstract

The present disclosure relates to a method (100) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line, cable, or hybrid line. The method comprises measuring (102) a gap-voltage or a per-phase reactor current of at least one de-energised phase during a dead-time interval to generate a measurement signal, estimating (104) resonant parameters of an equivalent electrical circuit of the transmission line based on the measurement signal, and calculating (106), for one or more poles separately, a circuit breaker closing instant during auto-reclosure by solving a boundary condition that ensures a resulting phase current exhibits a zero-crossing within a predefined time interval after electrical closing, and actuating (108) the circuit breaker at the calculated closing instant for one or more poles separately based on type of auto‑reclosure among single or multiple poles to perform the controlled switching operation.

Description

[0001] METHOD AND SYSTEM FOR CONTROLLED SWITCHING ON A COMPENSATED TRANSMISSION LINE TECHNICAL FIELD

[0002] The present disclosure relates to high-voltage power transmission and switching control systems. More specifically, the present disclosure relates to a method and system for controlled switching on a compensated transmission line as defined in the introductory parts of the independent claims.

[0003] BACKGROUND

[0004] In high-voltage transmission systems which may comprise of a transmission line and / or cable, reactive compensation is commonly utilized to enhance overall system performance by reducing voltage drops, improving power factor, and controlling reactive power flows. This practice is particularly prevalent in highly compensated transmission lines, which are generally characterized by compensation levels exceeding 50%. However, while reactive compensation provides operational benefits, it can also adversely impact current waveforms passing through circuit breakers. Under certain conditions, this may contribute to the occurrence of missing or delayed current zero crossings, which can present significant challenges during circuit interruption. In such cases, circuit breakers may be unable to de-energize the system properly, leading to severe arcing and potential maloperation of protective relays.

[0005] Upon reclosing a breaker following a dead time, the associated shunt reactor may respond to the sudden change in current by inducing a direct current (DC) offset. This DC component shifts the net alternating current (AC) waveform comprising both the line charging current and the reactor current away from the zero axis, thereby delaying the occurrence of a current zero. As illustrated in Figure 3, such delayed current zero crossings may persist for several hundred milliseconds following a closing event initiated at a gap-voltage zero-crossing. Although resonance between mutual capacitance and shunt reactance may also give rise to high-frequency components, these components typically exhibit high decay rates and symmetrical characteristics and, therefore, are not considered a primary cause of the delayed current zero phenomenon.Several mitigation strategies have been explored to address this issue. The use of preinsertion resistors is one such approach that is intended to suppress transients during the reclosing process. However, effective damping may require pre-insertion times longer than those supported by conventional breaker designs. Furthermore, once the main breaker contacts bypass the resistor, additional transients may be introduced, depending on the specific switching mechanism employed. The implementation of preinsertion resistors also incurs significant cost and complexity. Another potential approach involves reducing the degree of reactive compensation to below 50%, which may eliminate delayed current zero conditions. However, this may lead to elevated voltages at the remote end of the line, potentially resulting in system stability concerns. Controlled switching has also been proposed as a mitigation technique, wherein closing is synchronized to specific points on the voltage waveform. For example, closing at the peak of the gap voltage can ensure the presence of subsequent zero crossings. However, in highly compensated lines, this method may produce excessive switching overvoltage due to the line’s inherent capacitive characteristics. As such, while gap-voltage zerocrossing closing is suitable for low or uncompensated lines, it is not suitable for highly compensated lines.

[0006] Controlled switching and auto-reclosure of compensated transmission lines is a critical technology in various domains, including high-voltage transmission networks, extra-high-voltage (EHV) power systems, long-distance power transfer corridors, underground cable systems, and hybrid line-cable networks. Conventional devices primarily rely on predefined fixed reclosing delays, gap-voltage zero-crossing detection, or predetermined switching angles for circuit breaker operation. However, these devices often suffer from limitations, including lack of accurate prediction of post-close current behaviour, inability to account for residual oscillations, and failure to ensure an immediate current zero-crossing after switching.

[0007] Conventional devices often use fixed-time auto-reclosure strategies or zero-gap-voltage switching methods to restore transmission line operation following fault clearance. However, this method is effective only within a limited range of line compensation levels, network topologies, and operating conditions. Furthermore, in highly compensated transmission lines, particularly lines compensated by shunt reactors or combined shuntand series compensation, residual oscillations and reactor-induced DC offset components may result in a delayed current zero phenomenon, thereby adversely affecting breaker performance and system stability.

[0008] Existing solutions often fail to accurately determine an optimal closing instant that ensures a resulting phase current exhibits a zero-crossing within a predefined time interval after closing. Additionally, existing solutions lack the ability to dynamically update closing targets for remaining open phases during multi-pole auto-reclosing while considering mutual coupling effects between phases and switching overvoltage constraints.

[0009] Therefore, there is a need for identifying and applying an optimal closing instant on the gap voltage waveform that ensures current zero-crossings occur within a few nominal cycles following breaker closure, while simultaneously minimizing switching overvoltage. This challenge forms the basis for the present disclosure.

[0010] SUMMARY

[0011] It is an object of the present disclosure to mitigate, alleviate or eliminate one or more of the above-identified deficiencies and disadvantages in the prior art and solve at least the above-mentioned problem.

[0012] According to a first aspect there is provided a method for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line or cable or hybrid line consisting partly of line and partly of cable section, the method comprising measuring a gap-voltage or a per-phase reactor current for at least one de-energised phase before a dead time using at least one voltage measuring device to produce a measurement signal, estimating resonant parameters of an equivalent electrical circuit of the transmission line from the measurement signal, the equivalent electrical circuit comprising a shunt reactor inductance, a shunt reactor resistance calculated from steady-state current measurements of a reactor, and line-to-ground and mutual capacitances, calculating, for one or more poles separately, a circuit breaker closing instant during auto-reclosure after tripping, by solving a boundary condition that ensuresa resulting phase current exhibits a zero-crossing within a predefined time interval after electrical closing, and actuating the circuit breaker at the calculated closing instant for one or more poles separately based on type of auto-reclosure among single or multiple pole to perform the controlled switching operation.

[0013] An advantage of this aspect is that it enables accurate determination of an optimal circuit breaker closing instant that explicitly accounts for residual oscillations and reactor-induced DC offset components in the transmission line. By solving a boundary condition for ensuring a timely current zero-crossing, rather than relying solely on fixed reclosing delays or predefined switching angles, the system improves switching reliability, mitigates delayed current zero phenomena, allows for adaptive single-pole and multipole auto-reclosing operations, and reduces switching overvoltage and breaker stress. Unlike conventional controlled switching approaches that merely select predefined voltage phase angles, the present disclosure determines the closing instant by solving a physical boundary condition on the post-close current waveform, thereby transforming the switching problem into a predictive current-zero enforcement problem.

[0014] According to some embodiments, estimating comprises evaluating gap-voltage parameters of the gap-voltage waveform and determining a damped natural frequency and a damping factor.

[0015] According to some embodiments, estimating comprises at least one of a Prony fit, logarithmic-decrement estimation, FFT-based spectral analysis, Hilbert-transform envelope analysis, or Matrix Pencil method performed over gap-voltage waveform.

[0016] According to some embodiments, the equivalent electrical circuit is a simplified n-network in which a DC component of post-close current is modelled as dominated by the shunt reactor branch and a DC contribution of line-charging current is neglected above a compensation threshold.

[0017] Accordingto some embodiments, calculating comprises modellingthe phase current as a sum of a steady-state AC component and a shunt-reactor DC component with an envelope-crossing factor, and solving a boundary condition such that a minimum of the composite current at or immediately after closing is non-negative.According to some embodiments, calculating comprises iteratively solving a nonlinear equation by a Newton-Raphson procedure initialised at a peak of a sinusoidal lobe within the beat-minimum region.

[0018] Accordingto some embodiments, the Newton-Raphson procedure is bounded by at least one of: a maximum iteration count, a derivative magnitude clamp, and a fallback bracketing or bisection upon non-convergence.

[0019] According to some embodiments, the envelope-crossing factor is adaptively tuned to compensate neglected series and mutual inductive contributions to a DC offset.

[0020] Accordingto some embodiments, the method further comprises a commissioning mode in which is identified from at least one controlled close by minimising an error between measured post-close current extrema and model-predicted extrema, and an operational mode usingthe identified.

[0021] According to some embodiments, predicting a switching overvoltage for the calculated closing instant and enforcing an overvoltage constraint by at least one of: adjusting the closing instant, deferringto a subsequent beat-minimum window, or abortingthe closing command.

[0022] According to some embodiments, calculating comprises selecting a closing instant that satisfies both the zero-crossing boundary condition and a switching overvoltage threshold.

[0023] According to some embodiments, the method is performed individually for each phase in a three-phase power system and for auto-reclosing onto a de-energised line exhibiting residual oscillations.

[0024] Accordingto some embodiments, the method is applied to a switching device such as a circuit breakerto perform a single-pole auto-reclose on a transmission line compensated by at least 50%, and the closing instant is determined as an inception angle relative to a gap-voltage sinusoidal lobe.

[0025] Accordingto some embodiments, the inception angle is at or above a boundary angle at which a first current zero-crossing occurs immediately after closing for a given initial shunt-reactor current and k.According to some embodiments, the method is applied to a two-pole auto-reclose comprising predicting the closure of a first pole at a future target instant, recomputing, for the remaining open phase, at least one of a gap-voltage and an initial shunt-reactor current using a coupled-phase subnetwork including mutual capacitances, based on the predicted closure of the first pole at the future target instant, and determining an updated closing instant for the remaining phase.

[0026] According to some embodiments, the method is applied to a three-pole auto-reclose comprising selecting a closing order for phases, predicting the sequential closure of preceding phases at their respective future target instants, recomputing closing targets for each remaining open phase using the coupled-phase subnetwork and updated initial conditions based on the predicted sequential closure of the preceding phases at their respective future target instants, and commanding closures according to updated targets.

[0027] Accordingto some embodiments, selectingthe closing order comprises choosinga next phase that minimises a cumulative deviation between updated closing targets and independently determined targets for remaining phases.

[0028] According to some embodiments, compensating pole discrepancy by adding a timing offset to an electrical closing instant to obtain a breaker command time and executing computations within a latency budget sufficient to meet the predefined time interval. According to some embodiments, logging gap-voltage waveforms, estimated parameters, and commanded instants with event markers for post-event verification. According to some embodiments, noise-robust windowing of the measurement signals and outlier rejection prior to parameter estimation.

[0029] According to a second aspect there is provided for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line or cable or hybrid line consisting partly of line and partly of cable section. The system comprises at least one voltage or current measuring device configured to measure a per-phase current of a shunt reactor and a per-phase gap-voltage on a line side of a circuit breaker, a parameter estimator configured to estimate resonant parameters of an equivalent electrical circuitcomprising a shunt reactor branch and line-to-ground and mutual capacitances, a target generator configured to calculate a circuit breaker closing instant by solving a boundary condition for a post-close zero-crossing using an iterative solver initialised at a beat-minimum lobe peak and an adaptive factor k, a mutual-coupling updater configured, for multi-pole auto-reclosing, to recompute closing targets for remaining open phases after each closure using the coupled-phase subnetwork, an overvoltage predictor configured to enforce a switching overvoltage constraint, and an actuator interface configured to actuate the circuit breaker at the calculated closing instant with pole discrepancy compensation.

[0030] The boundary condition corresponds to enforcing that a minimum value of the composite current waveform at or immediately after the closing instant is non-negative.

[0031] Accordingto some embodiments, the system is implemented in a protection and control device for high-voltage applications, configured to operate with timing accuracy sufficient to ensure a current zero-crossing within the predefined time interval after closing.

[0032] According to some embodiments, a computer program comprising program code to cause a processor to carry out the method steps.

[0033] Effects and features of the second aspect are to a large extent analogous to those described above in connection with the first aspect.

[0034] The present disclosure will become apparent from the detailed description given below. The detailed description and specific examples disclose preferred embodiments of the present disclosure by way of illustration only. Those skilled in the art understand from guidance in the detailed description that changes and modifications may be made within the scope of the present disclosure.

[0035] BRIEF DESCRIPTIONS OF THE DRAWINGS

[0036] The above objects, as well as additional objects, features and advantages of the present disclosure, will be more fully appreciated by reference to the following illustrative andnon-limiting detailed description of example embodiments of the present disclosure, when taken in conjunction with the accompanying drawings.

[0037] Figure 1 illustrates a method (100) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line, according to an embodiment of the present disclosure.

[0038] Figure 2 illustrates a system (200) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line, according to an embodiment of the present disclosure.

[0039] Figure 3 illustrates an exemplary waveform (300) depicting a delayed current zero phenomenon during auto-reclosure of a compensated transmission line, according to the prior art.

[0040] Figure 4 illustrates a three-phase equivalent n-network model (400) of a compensated transmission line including a shunt reactor and line capacitances, according to an embodiment of the present disclosure.

[0041] Figure 5 illustrates a simplified equivalent electrical circuit (500) for decomposition of post-close current into a steady-state AC component and a reactor-dominated DC component, accordingto an embodiment of the present disclosure.

[0042] Figure 6 illustrates an exemplary gap-voltage waveform (600) of a de-energised phase during a dead-time interval prior to reclosing, accordingto an embodiment of the present disclosure.

[0043] Figure 7 illustrates an exemplary current waveform (700) showing absence of an immediate zero-crossing following an uncontrolled switching operation, according to an embodiment of the present disclosure.

[0044] Figure 8 illustrates an exemplary voltage waveform (800) corresponding to a selected switching instant during controlled switching, according to an embodiment of the present disclosure.Figure 9 illustrates an exemplary post-close current waveform (900) showing zerocrossing behaviour achieved by controlled switching at an optimized closing instant, accordingto an embodiment of the present disclosure.

[0045] Figure 10 illustrates an equivalent circuit representation (1000) for two-pole autoreclosing (2PAR) analysis including mutual coupling effects, according to an embodiment of the present disclosure.

[0046] Figure 11 illustrates an exemplary phase-voltage waveform (1100) showing variation in phase conditions following closure of a first pole, according to an embodiment of the present disclosure.

[0047] Figure 12 illustrates an equivalent circuit (1200) representation for three-pole autoreclosing including mutual coupling effects between phases, according to an embodiment of the present disclosure.

[0048] Figure 13 illustrates an exemplary waveform (1300) showing updated phase conditions after closure of a first pole during multi-pole auto-reclosing, accordingto an embodiment of the present disclosure.

[0049] Figure 14 illustrates an equivalent circuit (1400) representation for three-pole sequential auto-reclosing with iterative updating of closing targets for remaining phases, according to an embodiment of the present disclosure.

[0050] Figure 15 illustrates an exemplary multi-phase waveform (1500) representation associated with sequential controlled switching and updated closing targets, according to an embodiment of the present disclosure.

[0051] DETAILED DESCRIPTION

[0052] The present disclosure will now be described with reference to the accompanying drawings, which illustrate preferred example embodiments of the present disclosure. However, it should be understood that the present disclosure is not limited to these embodiments, and modifications and variations may be made within the scope of the present disclosure as will be appreciated by those skilled in the art.Hence, it is to be understood that the herein disclosed present disclosure is not limited to the particular component parts of the device described or steps of the methods described since such device and method may vary. It is also to be understood that the terminology used herein is for purpose of describing particular embodiments only and is not intended to be limiting. It should be noted that, as used in the specification and the appended claim, the articles "a", "an", "the", and "said" are intended to mean that there are one or more of the elements unless the context explicitly dictates otherwise. Thus, for example, reference to "a unit" or "the unit" may include several devices, and the like. Furthermore, the words "comprising", "including", "containing" and similar wordings does not exclude other elements or steps.

[0053] The present disclosure relates to high-voltage transmission systems, which may comprise a transmission line and / or cable. It involves modelling the transmission line using a simplified equivalent n network. The model focuses primarily on shunt reactor characteristics and the line’s capacitive components, while neglecting series and mutual inductances that contribute minimally to the DC component.

[0054] Figure 1 illustrates a method (100) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line, cable, or hybrid line according to an embodiment of the present disclosure.

[0055] As shown in Figure 1, the method (100) includes a sequence of interconnected steps includingmeasuring(102), estimating (104), calculating(106), and actuating (108), which collectively enable adaptive and controlled auto-reclosure of one or more poles of a circuit breaker following a tripping event. The illustrated sequence is configured to ensure that a resulting phase current exhibits a zero-crossing within a predefined time interval after electrical closing, thereby reducing delayed current zero phenomena, switching stress, and transient overvoltages.

[0056] In particular, at step S102, the method includes measuring (102) a gap-voltage or a perphase reactor current for at least one de-energised phase before a dead-time interval using at least one voltage measuring device to produce a measurement signal.

[0057] In an embodiment, following tripping of a circuit breaker due to a transient fault, the affected phase remains de-energised for a predetermined dead-time before auto-reclosure is attempted. During this interval, residual oscillatory voltage and current components may persist due to the interaction of line capacitances and shunt compensation elements such as shunt reactors. Accordingly, the voltage measuring device may be configured as a voltage transformer, capacitive voltage transformer, current transformer, sensor interface, or equivalent measurement arrangement adapted to acquire the electrical condition of the de-energised phase. The measurement signal generated in this step may represent the instantaneous gap-voltage across the breaker contacts, residual oscillation waveform characteristics, reactor current magnitude, and associated phase information. This real-time acquisition of residual electrical conditions provides an important technical basis for the subsequent adaptive determination of an optimized reclosing instant.

[0058] Upon measurement, the method proceeds to step S104, which includes estimating (104) resonant parameters of an equivalent electrical circuit of the transmission line from the measurement signal. In this step, the acquired waveform is processed to derive parameters of an equivalent electrical circuit representing the compensated transmission line under de-energised conditions.

[0059] In an embodiment, signal preprocessing may include filtering, windowing, and outlier rejection to improve estimation robustness and reduce the influence of measurement noise.

[0060] In an embodiment, the equivalent electrical circuit may comprise a shunt reactor inductance, a shunt reactor resistance calculated from steady-state current measurements of the reactor, and line-to-ground and mutual capacitances. The estimation may further include determination of resonant parameters such as damped natural frequency, damping factor, residual oscillation amplitude, initial reactor current, and instantaneous phase angle. In certain embodiments, the estimation may be carried out using signal processing techniques including Prony fitting, logarithmic decrement estimation, FFT-based spectral analysis, Hilbert-transform envelope extraction, or Matrix Pencil methods. By dynamically estimating the electrical state of the transmission line immediately prior to reclosing, the method provides a significant improvement over conventional fixed-delay switching schemes that do not account for real-time resonant behaviour.Thereafter, at step S106, the method includes calculating (106), for one or more poles separately, a circuit breaker closing instant during auto-reclosure after tripping, by solving a boundary condition that ensures a resulting phase current exhibits a zerocrossing within a predefined time interval after electrical closing. This step forms a principal inventive aspect of the present disclosure. More specifically, the post-close current is modelled as a composite waveform including a steady-state AC current component and a shunt-reactor-dominated DC offset component arising from residual stored energy. Based on the estimated parameters from step S104, a boundary condition is solved to determine an optimized closing instant at which the composite current waveform is expected to cross zero substantially immediately after breaker closure or within the predefined permissible interval.

[0061] In an embodiment, the calculation may be performed separately for each pole in singlepole, two-pole, or multi-pole auto-reclosure operations. Further, the calculation may include iterative numerical solving, such as a Newton-Raphson based procedure, to determine an electrical closing angle that minimizes the delayed current zero effect. The step may further account for mutual coupling between phases, switching overvoltage constraints, and breakertimingdiscrepancies. This adaptive determination of the closing instant distinguishes the invention from conventional switching approaches based solely on predefined delays or zero gap-voltage criteria.

[0062] Subsequently, at step S108, the method includes actuating (108) the circuit breaker at the calculated closing instant for one or more poles separately based on the type of auto-reclosure among single-pole or multiple-pole auto-reclosure to perform the controlled switching operation. In this step, the calculated electrical closing instant is translated into a breaker command time by compensatingfor mechanical breaker operating delay, control device latency, and pole discrepancy. A command signal is then issued to the circuit breaker such that the actual electrical contact closing occurs substantially at the optimized instant determined in step S106. In single-pole embodiments, the command may be applied only to the fault-cleared phase, whereas in multi-pole embodiments separate target instants may be generated and executed for multiple poles in a coordinated sequence. As a result, the controlled switching operation significantlyimproves reclosing performance and reduces stress on the switching device and associated transmission system components.

[0063] The method (100) facilitates a real-time adaptive controlled switching operation, enabling optimized circuit breaker reclosing based on dynamically estimated resonant parameters and residual oscillation conditions in real time. Therefore, the method (100) ensures that a resulting phase current exhibits a zero-crossing within a predefined time interval after electrical closing, without requiring fixed reclosing delays, predefined switching angles, or static switching assumptions.

[0064] In alternative embodiments, certain steps (S102-S108) may be performed in parallel or in a different order. For instance, parameter estimation at step (S104) may be continuously updated during the dead-time interval while preliminary closing instant calculations at step (S106) are iteratively refined in parallel based on successive measurement samples obtained in step (S102). Such variations are within the scope of the present disclosure.

[0065] Figure 2 illustrates a system (200) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line according to an embodiment of the present disclosure.

[0066] As shown, the system (200) is configured to implement the method described with reference to Figure 1 and comprises a plurality of functionally interconnected components including a transmission line (202), a voltage or current measuring device (204), a circuit breaker (206), a parameter estimator (208) associated with an equivalent electrical circuit (210), a target generator (212), a mutual coupling updater (214), an overvoltage predictor (216), an actuator interface (218), and a control device (220). These components collectively cooperate to determine and execute an optimized circuit breaker closing instant that ensures a timely current zero-crossing after reclosing.

[0067] In an embodiment, the transmission line (202) may comprise a shunt compensated transmission line, a shunt-cum-series compensated transmission line, a cable, or a hybrid line consisting partly of overhead line sections and partly of cable sections. The transmission line (202) may be part of a high-voltage or extra-high-voltage powertransmission network and may include shunt reactors, line capacitances, and mutual coupling between phases. During a fault trip and subsequent dead-time interval, the transmission line (202) may exhibit residual oscillatory voltage and current conditions which are utilized by the system for adaptive reclosing control.

[0068] Operatively coupled to the transmission line (202) is the voltage or current measuring device (204).

[0069] In an embodiment, the measuring device (204) is configured to measure a per-phase current of a shunt reactor and a per-phase gap-voltage on a line side of the circuit breaker (206). The measuring device (204) may include one or more voltage transformers, capacitive voltage transformers, current transformers, digital sensors, merging units, or equivalent sensing interfaces. The measured electrical quantities are converted into a measurement signal, as shown in Figure 2, which is transmitted to the control device (220) for subsequent signal processing and decision making. The real-time acquisition of residual oscillatory conditions forms an important technical basis of the invention and contributes to the adaptive nature of the controlled switching operation.

[0070] The circuit breaker (206) is electrically connected to the transmission line (202) and is configured to selectively isolate and reconnect one or more phases of the transmission line duringtripping and auto-reclosure operations.

[0071] In an embodiment, the circuit breaker (206) may be a single-pole or multi-pole breaker arrangement suitable for high-voltage applications. The breaker (206) receives a command signal from the control device (220) through the actuator interface (218) and performs physical pole closing substantially at the optimized instant determined by the system.

[0072] The control device (220) constitutes the central processing and control architecture of the system (200). In an embodiment, the control device (220) may be implemented as a protection relay, intelligent electronic device (IED), digital controller, microprocessorbased switching controller, or an integrated protection and control unit. The control device (220) functionally incorporates the parameter estimator (208), target generator (212), mutual coupling updater (214), overvoltage predictor (216), and actuator interface(218) as shown in Figure 2. This integrated architecture enables real-time signal processing, model estimation, optimization, and actuation.

[0073] Within the control device (220), the parameter estimator (208) is configured to receive the measurement signal from the measuring device (204) and estimate resonant parameters of the transmission system. In particular, the parameter estimator (208) operates with reference to the equivalent electrical circuit (210), which models the electrical behaviour of the compensated transmission line. The equivalent electrical circuit (210) may comprise a shunt reactor branch, line-to-ground capacitances, mutual capacitances, and associated resistive components. Based on the acquired measurement signal, the parameter estimator (208) determines parameters such as resonant frequency, damping factor, initial current conditions, and residual oscillation magnitude. This dynamic estimation of system state represents a significant inventive feature over conventional static reclosing scheme.

[0074] The equivalent electrical circuit (210) serves as the mathematical and physical representation of the actual network condition at the time of reclosing.

[0075] In an embodiment, the equivalent electrical circuit (210) may be implemented as a simplified n-network or a multi-phase coupled network model. The use of this adaptive equivalent model enables the system to explicitly account for residual oscillations and reactor-dominated DC offset effects when determining the reclosing instant.

[0076] The output of the parameter estimator (208) is supplied to the target generator (212). The target generator (212) is configured to calculate a circuit breaker closing instant by solving a boundary condition for a post-close zero-crossing. In particular, the target generator (212) may employ an iterative solver initialized at a beat-minimum lobe peak together with an adaptive factor k, as illustrated in the claims and specification. In an embodiment, the target generator (212) determines the electrical angle or time instant at which the resulting phase current is expected to cross zero substantially immediately after breaker closure. This calculation forms the inventive core of the present disclosure, as it directly addresses delayed current zero phenomena in compensated lines.

[0077] For multi-pole auto-reclosure embodiments, the system further comprises the mutual coupling updater (214). The mutual coupling updater (214) is configured to recomputeclosing targets for remaining open phases after closure of one pole by taking into account mutual capacitive and inductive coupling effects between phases. As shown in Figure 2, the mutual coupling updater (214) may provide feedback to the target generator (212) so that the closing target for the next pole is dynamically updated. This recursive updating mechanism significantly improves the technical performance of sequential multi-pole reclosing and represents an additional inventive aspect of the disclosed system.

[0078] Downstream of the mutual coupling updater (214), the overvoltage predictor (216) is configured to predict switching overvoltage associated with the calculated closing instant.

[0079] In an embodiment, the overvoltage predictor (216) evaluates whether the proposed reclosing instant satisfies a predefined overvoltage threshold. Where necessary, the predicted overvoltage constraint may be used to modify the target generated by the target generator (212), thereby improving system safety and equipment protection.

[0080] The switching overvoltage may be estimated using known transient simulation or analytical methods based on the equivalent circuit parameters and switching instant. The actuator interface (218) is configured to convert the optimized electrical closing instant into a physical breaker command signal. In particular, the actuator interface (218) may compensate for breaker mechanical operating delay, pole discrepancy, and control latency so that the actual electrical closing event occurs substantially at the calculated target instant. The command signal is then transmitted to the circuit breaker (206) to execute the controlled switching operation.

[0081] All of the aforementioned components are communicatively coupled via one or more signal communication buses, control interfaces, or data communication links, and are managed under the supervisory control and processing architecture of the control device (220).

[0082] Accordingly, the system (200) facilitates an adaptive model-based controlled switching architecture, enabling real-time determination and execution of an optimized reclosing instant based on measured residual oscillations and dynamically estimated network parameters. Therefore, the system (200) ensures that the resulting post-close phasecurrent exhibits a zero-crossing within a predefined time interval after electrical closing, without requiring fixed-time reclosing delays or predetermined switching angles.

[0083] In some embodiments, the system (200) may be utilized in a variety of applications, including, but not limited to, high-voltage and extra-high-voltage power transmission networks, long-distance overhead transmission corridors, underground cable systems, hybrid line-cable networks, and controlled auto-reclosure systems for compensated transmission lines employing single-pole or multi-pole switching schemes.

[0084] Therefore, the system (200) ensures improved switching reliability, reduced switching overvoltage, and mitigation of delayed current zero phenomena, without requiring static switching assumptions, fixed dead-time settings, or conventional zero-gap-voltage-based reclosing strategies.

[0085] In alternative embodiments, one or more components may be implemented as software modules, hardware logic blocks, firmware routines, or distributed functional units across multiple control devices. For instance, the parameter estimator (208) and target generator (212) may be implemented in parallel processing architecture for reduced computational latency. Such variations are within the scope of the present disclosure.

[0086] Figure 3 illustrates an exemplary waveform (300) depicting a delayed current zero phenomenon during auto-reclosure of a compensated transmission line, according to the prior art.

[0087] As shown in Figure 3, the waveform (300) represents a phase current response plotted with respect to time during a conventional auto-reclosure operation following a tripping event. The horizontal axis corresponds to time, and the vertical axis corresponds to current. In particular, the waveform (300) shows that following reclosing at approximately 0.5 seconds, the resulting current exhibits a prolonged oscillatory transient instead of achieving an immediate zero-crossing. As indicated, the oscillatory current persists for an extended interval of approximately 700 ms before settling toward a steady-state condition.Such delayed current zero behaviour is commonly observed in conventionally switched shunt-compensated transmission lines due to the interaction between line capacitances and shunt reactor branches, which introduces a significant DC offset component in the post-close current waveform. This phenomenon may adversely affect breaker performance, dielectric recovery, and switching reliability, particularly in high-voltage and extra-high-voltage transmission systems. Accordingly, Figures illustrates a technical limitation associated with conventional fixed-delay or non-adaptive auto-reclosure schemes.

[0088] Figure 4 illustrates an equivalent electrical circuit model (400) of a three-phase shunt compensated or shunt-cum-series compensated transmission line according to an embodiment of the present disclosure.

[0089] As shown, the equivalent circuit model (400) comprises three phase-to-ground source voltages, corresponding respectively to phases A, B, and C, together with associated circuit breakers disposed in the respective phase paths.

[0090] Each phase further comprises a shunt compensation branch including inductive components Lsha, Lshb, Ls / lcand corresponding resistive components Rsha, Rshband Rshc. The capacitive characteristics of the transmission line are represented by phase-to-ground capacitances Cga, Cgb, Cgc, together with inter-phase mutual capacitances Cmab, nbc’ and Cmac

[0091] The delayed current zero (DCZ) arises primarily due to the presence of a shunt compensating branch within the transmission line. Although series and mutual impedance components may contribute to a minor DC offset, their influence is negligible in comparison to that of the shunt reactor and may be disregarded for the purposes of this analysis. An equivalent circuit model of the transmission line, as illustrated in Figure 4, is employed to determine the time instant at which the DC offset current sufficiently offsets the AC waveform such that the net current crosses the zero axis immediately following the line-closing operation.Each phase gap voltage signal is analyzed to extract corresponding inductive and capacitive components of the transmission line.

[0092] In an embodiment, the shunt reactor resistance (RSh) is determined from steady-state operating measurements of the reactor. Specifically, during steady-state conditions prior to a switching event, the reactor current and corresponding phase voltage are measured, and the resistance component is calculated based on real power losses in the reactor branch. Alternatively, the resistance may be derived from equivalent impedance estimation using measured voltage and current phasors. This approach enables accurate parameterisation of the reactor model based on actual system conditions, thereby improving the accuracy of the equivalent circuit representation used for controlled switching analysis.

[0093] These derived parameters are subsequently utilized to construct an equivalent electrical representation of the transmission line suitable for switching analysis.

[0094] where, Va, Vb, and l^are phase-to-ground source voltage.

[0095] Lsha, shb’ Lshc> ^sha> ^shb and Rshc>areshunt compensation inductance and resistance values.

[0096] Cga, Cgb’ Cgc> Cmab> Cmbc’ and Cmacare capacitive components of the line derived from resonance frequency and damping.

[0097] In an embodiment, the equivalent circuit model (400) further serves as a mathematical basis for estimating the resonant frequency, damping factor, and initial current conditions associated with each phase during the dead-time interval preceding auto-reclosure. By representing the dominant inductive and capacitive energy storage elements of the compensated transmission line, the model enables accurate prediction of post-close transient behaviour and delayed zero-crossing conditions under varying compensation levels and network topologies.

[0098] Therefore, the equivalent circuit model (400) provides a technically robust analytical framework for determining an optimized switching instant, enabling accurate prediction of delayed current zero phenomena and facilitating adaptive controlled switching in shunt compensated and hybrid transmission line systemsFigure 5 illustrates a simplified equivalent electrical circuit (500) for decomposition of post-close current into a steady-state AC component and a reactor-dominated DC component, accordingto an embodiment of the present disclosure.

[0099] For single-pole auto-recloser (SPAR), the analysis is performed on an individual phase, represented by the single-phase equivalent circuit which is derived from the three-phase transmission line model.

[0100] In an embodiment, the simplified equivalent circuit (500) isolates the dominant currentproducing elements that govern the transient response immediately after breaker closure, thereby enabling analytical decomposition of the net current waveform into AC and DC constituents. This decomposition forms the technical basis for solving the boundary condition that ensures the first post-close current zero-crossing occurs within a predefined permissible time interval.

[0101] Additionally, the transmission line charging current exhibits a transient behavior, decaying within a few milliseconds subsequent to a switching event. Accordingly, the contribution of the transmission line charging current to the overall DC current is considered negligible and is therefore omitted.

[0102] In an embodiment, the above modelling simplification is applicable for transmission lines having a compensation level above a predefined threshold, for example greater than 50% shunt compensation. At such compensation levels, the DC component of the postclose current is predominantly governed by the shunt reactor response, while the contribution of the transmission line charging current to the DC component is negligible in comparison. This enables the equivalent electrical circuit to be simplified without materially affecting the accuracy of the current zero-crossing prediction.

[0103] Consequently, the DC current component analyzed herein is determined solely by the response of the shunt reactor to the switching operation, as described in the following section:

[0104] 4 / i=Ishtr+ lShSS= Ce-t / T+ , sin (a> * t + 0 + 0)

[0105]

[0106] J Rsh + (w*^s / i)2If initial condition of the reactor before closing is known to be Io, Then the value of constant C may be evaluated as,

[0107] sin(o) * t0+ 0 + * g to / T

[0108] And,

[0109] ^sh I A 'o- ,a^=sin(<D * t0+ 0 + 0) I * e &to^Tsin (a) * t +

[0110] jRsh + ((i>*Lsh)2 / Rsh

[0111]

[0112] 0 + 0)

[0113] Where, t0is initial time at which closing event takes place.

[0114] ris the time constant of the shunt reactor branch, given by T = LshI Rsh

[0115] 4> is the phase angle of the source voltage Vawith respect to a reference,

[0116] 0 is the impedance angle of the shunt reactor branch,

[0117] Where, Lshand Rshare shunt reactor inductance and resistance

[0118] Iois the initial current flowing through the reactor before closing

[0119] Cg, Cmare the line to ground and mutual capacitances of the line

[0120] IChargingSSis the steady state charging current

[0121] IChargingtris the transient response of the transmission line

[0122] Ishssis the steady state response of the shunt reactor

[0123] lshtris the transient response of the shunt reactor

[0124] Therefore, the equivalent electrical circuit (500) enables analytical determination of the critical reclosing instant, enabling real-time computation of an inception angle that mitigates missing current zero-crossings and improves breaker switching reliability in single-pole auto-reclosure operations.Figure 6 illustrates an exemplary gap-voltage waveform (600) of a de-energised phase during a dead-time interval prior to reclosing, according to an embodiment of the present disclosure.

[0125] A single pole of a transmission line, compensated to approximately 70% in a 400 kV, 100 MVA, 50 Hz system, was de-energized under a single-line-to-ground (SLG) fault condition. A reclosing operation was initiated after a time delay of approximately 0.853 seconds.

[0126] During the dead-time interval, the phase remains isolated by the circuit breaker while residual oscillatory voltage persists across the breaker contacts as a consequence of the interaction between the line capacitance and the shunt compensation branch.

[0127] As shown in Figure 6, the waveform (600) represents the gap voltage plotted with respect to time, wherein the horizontal axis corresponds to time in seconds, and the vertical axis corresponds to the instantaneous gap-voltage magnitude.

[0128] In an embodiment, the gap-voltage waveform shown in Figure 6 is utilized as the primary input signal for estimating resonant parameters of the equivalent transmission line model described with reference to Figures 4 and 5.

[0129] More specifically, the measured waveform may be analyzed to derive resonant frequency, damping factor, oscillation envelope, phase angle, instantaneous voltage polarity which are subsequently used for determining the optimal switching target. The beat-minimum region and zero-crossing positions of the waveform may further be used as preliminary references for determining candidate reclosing instants.

[0130] Accordingly, Figure 6 provides the measured electrical condition of the de-energised phase prior to switching and forms the basis for subsequent controlled switching analysis.Figure 7 illustrates an exemplary current waveform (700) showing absence of an immediate zero-crossing following an uncontrolled switching operation, according to an embodiment.

[0131] In an embodiment, when the circuit breaker is closed at the zero-crossing of the gap voltage, a persistent occurrence of prolonged missing or delayed current zero-crossing is observed. This phenomenon is caused primarily by the DC offset introduced by the shunt compensation branch, particularly the shunt reactor current response immediately after closure. Figure 7 presents a comparison between the current waveform derived from the equivalent circuit model and that obtained from a detailed Power Systems Computer Aided Design (PSCAD) simulation. In the PSCAD model, high-frequency oscillations are evident, attributable to resonant interactions among the series inductance, source inductance, and mutual capacitance of the transmission line. These high frequency effects are not accounted for in the simplified equivalent model. Accordingly, the equivalent model predominantly displays only a decaying DC response with only minimal deviation from the simulated result in the dominant transient region.

[0132] As illustrated, the waveform remains displaced from the zero axis for a substantial duration following closure, thereby preventing an immediate current zero-crossing. Inthisembodiment, theinitialshunt reactor currentwas Io=0.025 kA, and reclosingwas initiated after a dead-time of approximately 0.853 seconds following a single-line-to-ground fault on a 400 kV, 100 MVA, 50 Hz transmission line compensated to approximately 70%.

[0133] This delayed current zero condition may adversely affect breaker interruption performance, dielectric recovery, contact erosion, relay coordination, switching reliability particularly in highly compensated transmission lines.

[0134] Accordingly, Figure 7 demonstrates the principal technical problem addressed by the present disclosure.

[0135] Figure 8 illustrates an exemplary voltage waveform (800) corresponding to a selected switching instant during controlled switching, according to an embodiment of the present disclosure.In contrast to the uncontrolled zero-crossing closure illustrated in Figure 7, the embodiment shown in Figure 8 corresponds to a controlled reclosing operation performed at an inception angle of approximately 70 degrees.

[0136] In an embodiment, the initial current through the shunt reactor is denoted by Io, and an AC envelope crossing factor is defined as k.

[0137] - Sin(<D * t + 0 + 0) + ^charging l^sh2+ (0> * Lsh)2

[0138] k * -sin * t0+ 0 + 0) — Io* e &to^T\ J Rsh.2+ * ^sh)2J

[0139]

[0140] In an embodiment, the factor k may be adaptively updated based on measured deviations between predicted and observed current waveforms during operation, thereby improving model accuracy under varying system conditions.

[0141] The envelope-crossing factor k is determined through a commissioning mode and subsequently applied during an operational mode.

[0142] In the commissioning mode, one or more controlled switching operations are performed, and the resulting post-close current waveform is measured. The factor k is identified by minimizing an error between measured post-close current extrema and model-predicted extrema, thereby compensating for modelling simplifications including neglected series and mutual inductive effects.

[0143] In the operational mode, the identified value of k is used for real-time calculation of the closing instant without requiring repeated estimation, thereby reducing computational burden and enabling faster and more reliable switching decisions under varying system conditions.

[0144] The DC component of the charging current to the transmission line is minimal in magnitude relative to the DC component associated with the shunt branch.As shown, the selected switching instant is intentionally displaced from the zerocrossing position of the gap-voltage waveform and is located at a predetermined angular position relative to the sinusoidal lobe. This selected angle corresponds to the boundary condition at which the post-close current is expected to achieve a zero-crossing substantially immediately after closure.

[0145] In an embodiment, this switching instant is determined by solving the nonlinear boundary equation derived from the equivalent circuit model using an iterative numerical solver, preferably the Newton-Raphson method.

[0146] The iterative solution converges within a bounded number of iterations under practical operating conditions, thereby enabling real-time implementation within protection and control devices.

[0147] The switching instant shown in Figure 8 therefore represents the optimized inception angle for mitigatingthe delayed current zero phenomenon.

[0148] Figure 9 illustrates an exemplary post-close current waveform (900) demonstrating zerocrossing behaviour achieved by controlled switching at an optimized closing instant, accordingto an embodiment of the present disclosure.

[0149] The corresponding current waveform following the closing event is shown in Figure 9, where a current zero-crossing is detected immediately after reclosing. This condition represents a boundary case, reclosing at inception angles lower than this critical threshold results in the occurrence of missing zero-crossings.

[0150] As shown in Figure 9, the waveform (900) represents the phase current response following a controlled reclosing operation performed at a calculated inception angle derived from the equivalent circuit analysis described with reference to Figures 4 and 5. The horizontal axis corresponds to time, while the vertical axis represents current magnitude. In contrast to the delayed current zero behaviour illustrated in Figure 7, the waveform (900) exhibits a current zero-crossing substantially immediately after the closing instant, thereby satisfying the predefined boundary condition.In an embodiment, the controlled switching instant corresponds to an inception angle of approximately 70 degrees, selected based on the initial reactor current Io and an envelope-crossing factor k.

[0151] k is an envelope-crossing factor representing a scaling between the AC component and DC offset component of the post-close current. The resulting waveform demonstrates that the DC offset component introduced by the shunt reactor is effectively counterbalanced by the AC component of the current, such that the net current waveform intersects the zero axis within a minimal time interval following closure.

[0152] Therefore, Figure 9 validates the determination of a closing instant based on a boundary condition ensuring immediate or near-immediate current zero-crossing, thereby mitigating delayed current zero phenomena and improving breaker performance.

[0153] Figure 10 illustrates an equivalent circuit representation (1000) for two-pole autoreclosing (2PAR) analysis including mutual coupling effects, according to an embodiment of the present disclosure.

[0154] In this configuration, two phases are considered in a partially energized state, while the third phase remains open. The equivalent circuit (1200) includes phase voltages, shunt reactor branches, and mutual capacitances, enabling analysis of coupled-phase interactions.

[0155] In two-pole auto-reclosing (2PAR) operations, determining the optimal closing instant for each pole becomes more complex due to inter-phase electromagnetic interactions. Specifically, when a first pole is closed, the resulting electromagnetic coupling between phases causes a change in the gap voltage across the remaining open phases. This change in gap voltage alters the initial conditions of current flow in the associated shunt reactors, thereby modifying the calculated optimal closing instants for the subsequent phases. As a result of these interactions, the final pole to be closed often experiences the largest deviation from its independently determined optimal closing instant.

[0156] Consider the condition wherein two circuit breakers are de-energized as a result of a SLG fault occurring on phase A. Upon subsequent reclosing of circuit breaker CBaassociatedwith phase A, there is an abrupt alteration in the voltage at node A, causing it to instantaneously track the source voltage Va. The affected breaker is visually represented in blue in Figure 10. This sudden transition in voltage propagates throughout the electrical network, resulting in a corresponding variation in voltage at other nodal points, including point B.

[0157] Subsequently, a second breaker, depicted in Figure 10, is re-closed. The observed interdependence between phases arises due to the presence of mutual coupling elements, specifically designated as Cmab, Cmac, and Cmbc. These coupling elements illustrate that the transmission line is mutually coupled. The degree to which mutual coupling influences the system is directly proportional to its magnitude; greater mutual coupling yields more pronounced effects on the phases that have not yet been reenergized.

[0158] The initial voltages and derived electrical quantities of passive elements, as depicted in Figure 10, are utilized to compute the resultant changes in both voltage magnitude and phase angle across the system.

[0159] As shown, the equivalent circuit (1000) represents a condition in which one phase, for example phase A, is re-energized through circuit breaker CBa, while the remaining phases remain open. The circuit includes phase voltages Va, Vb, and Vc, shunt compensation branches, and mutual capacitive coupling elements Cmab, Cmac, and Cmbcinterconnectingthe phases.

[0160] In an embodiment, upon reclosing of circuit breaker CBa, the voltage at node A undergoes an abrupt transition and begins to follow the source voltage Va,. This sudden change propagates through the network via mutual coupling elements, thereby influencing the electrical conditions of the remaining open phases.

[0161] Therefore, Figure 10 establishes the basis for understanding inter-phase coupling effects, which are explicitly accounted for in the proposed method through dynamic updating of closing targets.Figure 11 illustrates an exemplary phase-voltage waveform (1100) showing variation in phase conditions following closure of a first pole, according to an embodiment of the present disclosure.

[0162] As shown, the waveform (1100) represents the gap voltage of a remaining open phase, such as phase B, following closure of phase A. Due to mutual coupling effects, the gap voltage waveform deviates from its independently estimated trajectory.

[0163] Figure 11 illustrates the impact of mutual coupling on the gap voltage at node B, attributable to its interaction with phase A. Notably, the anticipated voltage target for phase B was originally estimated at point Z in the absence of mutual coupling. However, under conditions incorporating the effects of said mutual coupling, the revised voltage estimation must instead be made at point Y.

[0164] This deviation highlights a the necessity of dynamically recomputing closing instants for remaining open phases during multi-pole auto-reclosing based on updated system conditions arisingfrom inter-phase coupling.

[0165] Figure 12 illustrates an equivalent circuit representation (1200) for three-pole autoreclosing including mutual coupling effects between phases, according to an embodiment of the present disclosure.

[0166] In an embodiment of a three-pole auto-reclose (3PAR) operation scenario, wherein all circuit breakers have been transitioned to a de-energized state in response to a detected fault condition. Prior to initiating the actual re-closer sequence, the system evaluates the potential impact of reclosing each individual pole on the remaining poles. This preclosure assessment ensures coordination and mitigates adverse interactions between the phases during the re-energization process.

[0167] Therefore, Figure 12 represents the recalculation of closing instants based on coupled-phase network behaviour.Figure 13 illustrates an exemplary waveform (1300) showing updated phase conditions after closure of a first pole during multi-pole auto-reclosing, according to an embodiment of the present disclosure.

[0168] In an embodiment, phase Ais assumed closed (as indicated), and the resulting electrical conditions of phases B and C are evaluated. The waveform (1300) reflects updated gap voltage conditions used to recompute closing targets.

[0169] In the first step of the method, phase A is considered to be in a closed state. This initial condition is utilized to evaluate the resulting voltage profile observed across the circuit breakers (CBs) correspondingto phases B and C (identified as shown in Figure 13). Based on this evaluation, the selection of the subsequent phase to be closed in the defined closing sequence is re-assessed. In the illustrative embodiment, phase B is identified as the next candidate for closure.

[0170] This iterative evaluation mechanism forms part of the adaptive reclosing strategy.

[0171] In an embodiment, the selection of phase B as the next phase for closure is made by evaluating the closing targets for all remaining open phases after the assumed closure of phase A and identifying the phase whose independently determined target deviates least from its updated target following the inter-phase coupling correction. This minimises cumulative timing deviation across the sequential reclosing operation.

[0172] Figure 14 illustrates an equivalent circuit representation (1400) for three-pole sequential auto-reclosing with iterative updating of closing targets for remaining phases, according to an embodiment of the present disclosure.

[0173] As shown, phases A and B are assumed closed, and the resulting impact on phase C is evaluated usingthe equivalent circuit (1400). The updated electrical conditions are used to determine a revised closing instant for the remaining phase.

[0174] In a subsequent step, phases A and B are assumed to be in the closed state in order to evaluate the resulting impact on the voltage appearing across the circuit breaker of phase C. Based on the voltage variation induced by the prior phase closures, the target closing instant for the next phase in the reclosing sequence phase C is re-evaluated to ensure optimal switching conditions.Figure 15 illustrates an exemplary multi-phase waveform (1500) representing sequential controlled switching and updated closing targets under mutual coupling conditions, accordingto an embodiment of the present disclosure.

[0175] As shown, phase A is closed at time instant W and phase B at time instant X, resulting in a modified gap voltage waveform for phase C. The original closing target at point Z is updated to point Y to reflect the altered system conditions.

[0176] In an embodiment, referring to Figure 15, phase A is closed at a first time instant, hereinafter referred to as point W, and phase B is closed at a subsequent time instant, hereinafter referred to as point X. The independently determined closing target for phase C, calculated without considering the effect of phase A and B closure, is identified as point Z. Following inter-phase coupling correction, the updated closing target for phase C is re-estimated at a revised time instant, hereinafter referred to as point Y.

[0177] Therefore, Figure 15 demonstrates the implementation wherein closing instants are dynamically adapted based on real-time system evolution.

[0178] In an embodiment, the following procedure corresponds to the method (100) described with reference to Figure 1 and the system (200) described with reference to Figure 2: determine a beat-minimum window on the gap voltage waveform for each de-energized phase, calculate the optimal reclosing instant at zero gap voltage, incorporating pole discrepancy, estimate line compensation to derive the resonant frequency and damping factor, construct the simplified equivalent circuit based on the resonance parameters. In the case of a single-pole auto-recloser (SPAR), where correction for missing current zero-crossings is required, an inception angle is calculated by solving the equivalent circuit representation of the transmission line. The calculated angle is subsequently combined with the initially determined optimal closing instant to obtain the adjusted switching target.

[0179] In the case of a two-pole or three-pole auto-recloser (2PAR or 3PAR), a reclosing sequence is first established for the circuit breaker poles, wherein each phase isassigned an order of reclosing based on system configuration and operational constraints.

[0180] For a two-pole auto-recloser (2PAR), the voltage magnitude and phase angle of the second phase are recalculated usingthe equivalent coupled-phase model, where in one of the poles is already considered to be closed while evaluating the targets for all the poles to be switched. The recalculated parameters, including the initial current across the shunt reactor and line capacitance are then used to determine the updated inception angle by referencing the equivalent circuit model.

[0181] For a three-pole auto-recloser (3PAR), the updated closing targets for the second and third phases are determined by iteratively applyingthe procedure described in above with reference to Figure 12. The inter-phase coupling effects are evaluated sequentially based on the predetermined closing order, using the equivalent network models.

[0182] In an example, the present disclosure is designed as a real-time adaptive controlled switching system for compensated transmission lines, configured to determine and execute an optimal circuit breaker closing instant based on dynamically estimated electrical parameters and residual oscillatory conditions.

[0183] The present disclosure is applicable to a wide range of high-voltage power transmission and switching control domains wherein precise and reliable auto-reclosure of transmission lines is required. These include extra-high-voltage (EHV) transmission networks, long-distance overhead transmission corridors, underground cable systems, hybrid line-cable networks, and compensated transmission systems employing shunt or shunt-cum-series compensation. In all such applications, the present disclosure facilitates adaptive determination of an optimal switching instant based on real-time system conditions without reliance on fixed reclosing delays or predefined switching angles, thereby improving switching reliability, system stability, and equipment protection.

[0184] The present disclosure is applicable to power system protection and control environments that require accurate switching instant determination based on dynamic system modelling and real-time measurement signals. Therefore, the present disclosure has several technical advantages including, but not limited to, mitigation of delayedcurrent zero phenomena, reduction of switching overvoltages, improved circuit breaker performance, and enhanced coordination of multi-pole auto-reclosing operations. Furthermore, the present disclosure enables dynamic updating of closing targets for remaining phases by accounting for mutual coupling effects and evolving network conditions.

[0185] The present disclosure enables precise and model-based controlled switching of compensated transmission lines under varying operating conditions. Unlike conventional methods that rely on fixed-time reclosing strategies or gap-voltage zerocrossing detection without integrated dynamic estimation and optimization mechanisms, the invention adaptively determines the closing instant by solving a boundary condition that ensures timely current zero-crossing. This results in improved switching accuracy, reduced electrical stress on switching devices, and enhanced overall performance and reliability of the power transmission system.

[0186] The present disclosure comprises several aspects and embodiments. Every feature described with respect to one of the aspects and embodiments is also disclosed herein with respect to the other aspects and embodiments, even if the respective feature is not explicitly mentioned in this context.

[0187] Therefore, the present disclosure provides a method and system for determining an optimal switching instant for circuit breaker reclosing operations applicable to singlepole, two-pole, and three-pole auto-reclosers based on dynamically estimated equivalent electrical parameters of the transmission line. The present disclosure ensures that the resulting current waveform crosses the zero axis within a predefined time interval following reclosing, thereby enabling reliable current interruption, reducing switching stress, and improving overall system stability and operational reliability.

[0188] Unlike conventional switching approaches that rely on fixed time delays, predefined switching angles, or gap-voltage zero-crossing detection, the present disclosure determines the switching instant by explicitly solving a physical boundary condition on the post-close current waveform, thereby ensuring the occurrence of a current zerocrossing within a predefined time interval. This approach inherently accounts for reactor-induced DC offset and residual oscillatory behaviour, and is further extended to multi-pole auto-reclosing through dynamic updating of switching targets based on inter-phase coupling effects, thereby providing a unified and adaptive controlled switching framework

Claims

Claims:

1. A method (100) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line or cable or hybrid line consisting partly of line and partly of cable section, the method comprising:measuring (102) a gap-voltage or a per-phase reactor current for at least one de-energised phase before a dead time using at least one voltage measuring device to produce a measurement signal;estimating (104) resonant parameters of an equivalent electrical circuit of the transmission line from the measurement signal, the equivalent electrical circuit comprising a shunt reactor inductance, a shunt reactor resistance calculated from steady-state current measurements of a reactor, and line-to-ground and mutual capacitances;calculating (106), for one or more poles separately, a circuit breaker closing instant during auto-reclosure after tripping, by solving a boundary condition that ensures a resulting phase current exhibits a zero-crossing within a predefined time interval after electrical closing; andactuating (108) the circuit breaker at the calculated closing instant for one or more poles separately based on type of auto-reclosure among single or multiple pole to perform the controlled switching operation.

2. The method of claim 1, wherein estimating (104) comprises evaluating gapvoltage parameters of the gap-voltage waveform and determining a damped natural frequency and a damping factor.

3. The method of any of claims 1 -2, wherein the estimating (104) comprises at least one of a Prony fit, logarithmic-decrement estimation, FFT-based spectral analysis, Hilbert-transform envelope analysis, or Matrix Pencil method performed over gap-voltage waveform.

4. The method of claim 1, wherein the equivalent electrical circuit is a simplified n-network in which a DC component of post-close current is modelled as dominated by34the shunt reactor branch and a DC contribution of line-charging current is neglected above a compensation threshold.

5. The method of any of claims 1-4, wherein calculating (106) comprises modelling the phase current as a sum of a steady-state AC component and a shunt-reactor DC component with an envelope-crossing factor k, and solving a boundary condition such that a minimum of the composite current at or immediately after closing is non-negative.

6. The method of claim 5, wherein calculating (106) comprises iteratively solving a nonlinear equation by a Newton-Raphson procedure initialised at a peak of a sinusoidal lobe within the beat-minimum region.

7. The method of claim 6, wherein the Newton-Raphson procedure is bounded by at least one of: a maximum iteration count, a derivative magnitude clamp, and a fallback bracketing or bisection upon non-convergence.

8. The method of any of claims 5-7, wherein the envelope-crossing factor k is adaptively tuned to compensate neglected series and mutual inductive contributions to a DC offset.

9. The method of claim 8, further comprising a commissioning mode in which k is identified from at least one controlled close by minimising an error between measured post-close current extrema and model-predicted extrema, and an operational mode usingthe identified k.

10. The method of any of claims 1-9, further comprising predicting a switching overvoltage for the calculated closing instant and enforcing an overvoltage constraint by at least one of: adjusting the closing instant, deferring to a subsequent beat-minimum window, or abortingthe closing command.

11. The method of claim 10, wherein calculating comprises selecting a closing instant that satisfies both the zero-crossing boundary condition and a switching overvoltage threshold.

12. The method of any of claims 1-11 is performed individually for each phase in a three-phase power system and for auto-reclosing onto a de-energised line exhibiting residual oscillations.

13. The method of any of claims 1-12, wherein the method (100) is applied to a switching device such as a circuit breaker to perform a single-pole auto-reclose on a transmission line compensated by at least 50%, and the closing instant is determined as an inception angle relative to a gap-voltage sinusoidal lobe.

14. The method of claim 13, wherein the inception angle is at or above a boundary angle at which a first current zero-crossing occurs immediately after closing for a given initial shunt-reactor current and k.

15. The method of any of claims 1-14, wherein the method (100) is applied to a two-pole auto-reclose comprising:predicting the closure of a first pole at a future target instant;recomputing, for the remaining open phase, at least one of a gap-voltage and an initial shunt-reactor current using a coupled-phase subnetwork including mutual capacitances, based on the predicted closure of the first pole at the future target instant; anddetermining an updated closing instant for the remaining phase.

16. The method of any of claims 1-15, wherein the method is applied to a three-pole auto-reclose comprising:selecting a closing order for phases;predicting the sequential closure of preceding phases at their respective future target instants;recomputing closing targets for each remaining open phase using the coupled-phase subnetwork and updated initial conditions based on the predicted sequential closure of the preceding phases at their respective future target instants; and commanding closures accordingto updated targets.

17. The method of claim 16, wherein selecting the closing order comprises choosing a next phase that minimises a cumulative deviation between updated closing targets and independently determined targets for remaining phases.

18. The method of any of claims 1-17, further comprising compensating pole discrepancy by adding a timing offset to an electrical closing instant to obtain a breaker command time, and executing computations within a latency budget sufficient to meet the predefined time interval.

19. The method of any of claims 1-18, further comprising logging gap-voltage waveforms, estimated parameters, and commanded instants with event markers for post-event verification.

20. The method of any of claims 1-19, further comprising noise-robust windowing of the measurement signals and outlier rejection prior to parameter estimation.

21. A system (200) for controlled switching on a shunt compensated or shunt-cum-series compensated transmission line or cable or hybrid line (202) consisting partly of line and partly of cable section, the system comprising:at least one voltage or current measuring device (204) configured to measure a per-phase current of a shunt reactor and a per-phase gap-voltage on a line side of a circuit breaker (206);a parameter estimator (208) configured to estimate resonant parameters of an equivalent electrical circuit (210) comprising a shunt reactor branch and line-to-ground and mutual capacitances;a target generator (212) configured to calculate a circuit breaker closing instant by solving a boundary condition for a post-close zero-crossing using an iterative solver initialised at a beat-minimum lobe peak and an adaptive factor;a mutual-coupling updater (214) configured, for multi-pole auto-reclosing, to recompute closing targets for remaining open phases after each closure using the coupled-phase subnetwork;an overvoltage predictor (216) configured to enforce a switching overvoltage constraint; andan actuator interface (218) configured to actuate the circuit breaker (206) at the calculated closing instant with pole discrepancy compensation.

22. The system of claim 21 , implemented in a protection and control device (220) for high-voltage applications, configured to operate with timingaccuracy sufficientto ensure a current zero-crossing within the predefined time interval after closing.

23. A computer program comprising program code to cause a processor to carry out the method of any of claims 1 to 20.38

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