A method for improving the resilience of a power distribution network with energy storage type flexible soft switch in a fault state

Abstract

The application discloses a kind of fault state containing energy storage type flexible soft switch's distribution network toughness promotion method, belong to electric power system and its automation field, including: extracting the time series data and fault information of distributed power supply and load;Integrated optimization model of fusion fault isolation, multi-stage dynamic maintenance, network reconfiguration and energy storage type flexible soft switch cooperation is constructed, with the minimum whole process power loss, branch and device loss as target, and the multiple constraints of time balance, device operation, maintenance resources and decoupling flow are considered, wherein the energy storage type flexible soft switch realizes cross-period energy time shift through embedded energy storage system;Rolling solution is carried out using mixed integer second-order cone programming algorithm, and island division, maintenance sequence and device operation strategy are optimized synchronously in each stage.The application can realize global collaboration and space-time energy management in multi-stage recovery process, and significantly improve the power supply recovery capability and toughness of distribution network under extreme fault.

Description

Technical Field

[0001] This invention belongs to the field of power system and automation technology, and particularly relates to a method for improving the resilience of distribution networks with energy storage-type flexible soft switches under fault conditions. Background Technology

[0002] With the increasing frequency of low-probability, high-impact events such as extreme weather, distribution network faults exhibit complex characteristics including multi-point concurrency, cross-regional propagation, and cascading evolution. This significantly increases the difficulty of fault isolation and recovery, easily leading to large-scale power outages and substantial economic losses. Distribution networks directly face end users, and their resilience directly determines the continuous power supply capacity of critical loads and the system recovery efficiency under extreme events. Currently, research on distribution network fault recovery mainly focuses on establishing a relatively reliable fault recovery system through network reconfiguration, active islanding using local resources such as distributed generation (DG) and energy storage systems (ESS), and the assistance of flexible interconnection devices. The main advantages of these existing technologies are: constructing autonomous islanded microgrid units based on controllable DG and other local resources effectively overcomes the topology optimization bottleneck in traditional distribution network reconfiguration, significantly improving power supply recovery speed; simultaneously, in cascading fault scenarios caused by extreme disasters, the islanded areas can operate decoupled, achieving effective fault isolation and autonomous recovery. In addition, as a flexible interconnection device, the soft open point (SOP) can switch to voltage-frequency control mode on the fault side and maintain PQ control mode on the non-fault side, quickly providing voltage support and reactive power compensation. It can also achieve dynamic power mutual assistance between feeders through power regulation, thereby improving load recovery rate, suppressing voltage over-limit caused by DG fluctuations, and preventing fault propagation by utilizing its DC-side fault current blocking characteristics.

[0003] However, existing technologies still have significant shortcomings: On the one hand, existing studies often assume that DG output and load demand are fixed values, or only optimize for a single moment of islanded operation, failing to fully consider the temporal fluctuation characteristics of DG and load. This leads to power quality degradation during multi-stage fault repair due to intermittent power output and load fluctuations, limiting the continuous improvement of power restoration levels. On the other hand, although existing studies have explored the application of SOPs in multi-stage fault repair strategies, they mainly remain at the level of "flexible interconnection," failing to fully explore the potential of energy storage-type flexible soft open points (ESOPs) for cross-time period energy shifting and multi-port power synergy. Furthermore, existing methods often consider multi-stage repair sequence, network reconfiguration, islanding, and ESOP operation separately, lacking a collaborative optimization model that incorporates these aspects into a unified decision-making framework. This results in insufficient coordination between various recovery stages, making it difficult to achieve the globally optimal improvement of distribution network resilience under extreme fault scenarios. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method for enhancing the resilience of distribution networks with energy storage-type flexible soft switches under fault conditions, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, the present invention provides a method for improving the resilience of a distribution network with energy storage-type flexible soft switches under fault conditions, comprising:

[0006] S1. Extract the output curves and access location information of distributed power sources, load demand curves, line fault information, distribution network topology and operation data of energy storage flexible soft switches of multi-regional distribution networks under extreme events.

[0007] S2. Based on the data obtained in step S1, establish an integrated resilience enhancement model that integrates fault isolation, multi-stage maintenance, network reconfiguration, and energy storage flexible soft switching. The integrated resilience enhancement model takes the weighted minimum of the power loss load, branch loss, and energy storage flexible soft switching loss during the entire maintenance process as the objective function. The constraints include islanded radial structure and connectivity constraints, time-series balance constraints between distributed power sources and loads, energy storage flexible soft switching operation constraints including the state of charge and charging / discharging efficiency of the embedded energy storage system, maintenance resource constraints, and power flow constraints.

[0008] S3. The integrated resilience enhancement model is solved by a mixed integer second-order cone programming algorithm. In each maintenance stage, the islanding strategy, line switch status, energy storage flexible soft switch charging and discharging and power support strategy are optimized simultaneously to output the global optimization scheme with the minimum power loss load.

[0009] Preferably, in step S2, the objective function is specifically a weighted sum of the following three items: the total power loss load, which is obtained by summing the product of the load at each node in each stage and the degree of load not being restored; the total branch active power loss, which is calculated by the admittance, voltage amplitude and phase angle difference of each branch in each stage; and the total energy storage flexible soft switch active power loss, which is obtained by summing the active power loss at each port in each stage.

[0010] Preferably, in step S2, the island radial structure and connectivity constraints are achieved by combining the "L-1" method with virtual power flow, specifically including: ensuring that the number of closed branches in each island is equal to the number of nodes in the island minus one, and ensuring topological connectivity between any nodes in the island through virtual network constraints.

[0011] Preferably, in step S2, the timing balance constraint between the distributed power source and the load ensures that at each moment during each maintenance phase, the output of all distributed power sources in each isolated island and the recovery load demand of all nodes in that island maintain a real-time power balance.

[0012] Preferably, in step S2, the operating constraints of the energy storage flexible soft switch include: the transmission power constraints of each port of the energy storage flexible soft switch, the state of charge constraints of the embedded energy storage system, the charging and discharging power constraints, and the charging and discharging efficiency constraints.

[0013] Preferably, the energy storage type flexible soft switch operation constraints enable the voltage source converters at each port to operate autonomously, realizing energy transfer across time periods.

[0014] Preferably, in step S2, the maintenance resource constraint is that the number of faulty lines repaired in each maintenance stage does not exceed a preset upper limit.

[0015] Preferably, in step S2, the power flow constraints include node voltage magnitude constraints, branch current magnitude constraints, and branch power balance constraints, and the Big M method is used to decouple the reconstructed network so that the constraints still hold when the branch switches are open.

[0016] Preferably, in step S3, the process of solving the problem using a mixed-integer second-order cone programming algorithm includes:

[0017] The integrated resilience enhancement model is transformed into a solvable form of second-order cone programming.

[0018] The optimization solution is performed in stages using a rolling time window approach. In each iteration, the state of the island boundary switch, the order of lines to be inspected, the power of the energy storage flexible soft switch port, and the state of charge of the embedded energy storage system are decided simultaneously.

[0019] Preferably, in step S3, the global optimization scheme specifically includes: the optimal islanding result, the optimal line maintenance sequence for each maintenance stage, and the optimal port power allocation and embedded energy storage system charging and discharging strategy for the energy storage flexible soft switch at each stage.

[0020] Compared with the prior art, the present invention has the following advantages and technical effects:

[0021] This invention achieves global collaborative optimization of multi-stage dynamic maintenance and flexible resources through a technical solution that integrates fault isolation, multi-stage dynamic maintenance, network reconfiguration, and energy storage flexible soft switch coordination. This significantly improves overall recovery efficiency and power supply reliability under extreme fault conditions. By incorporating maintenance sequence, network topology adjustment, and energy storage flexible soft switch (ESOP) operation strategies into a unified decision-making framework and performing rolling optimization, this invention overcomes the shortcomings of existing technologies where fragmented processes make it difficult to achieve global optimization. It ensures dynamic coordination of all controllable resources within limited maintenance resources and time, thereby maximizing load recovery throughout the fault process and achieving overall optimization of the power supply restoration process.

[0022] This invention, through the "operational constraints of the energy storage-type flexible soft switch including the state of charge and charge / discharge efficiency of the embedded energy storage system" and the collaborative optimization characteristics of the integrated model, fully leverages the cross-period energy shifting and multi-terminal power mutual assistance capabilities of the energy storage-type flexible soft switch, achieving spatiotemporal coordinated energy management and effectively addressing long-term, multi-stage faults. This invention clarifies the role of the ESOP embedded energy storage system (ESS), enabling its voltage source converter (VSC) to acquire autonomous power regulation capabilities, breaking through the rigid constraint that the total active power between ports of the traditional flexible soft switch (SOP) must be instantaneously balanced. This allows the system to implement a "storage first, release later" strategy on a time scale based on the temporal fluctuations of distributed generation (DG) output and load demand, transferring surplus energy to power shortage periods. This solves the problem that existing technologies' SOPs can only perform instantaneous spatial power mutual assistance and cannot cope with long-term power gaps, greatly enhancing the continuous power supply capability of the distribution network under continuous faults.

[0023] This invention ensures the continuous and stable operation of active islanding during multi-stage maintenance processes by employing "time-sequence balance constraints between distributed generation (DG) output and load demand curves" and the rolling optimization characteristics of the integrated model, thereby improving the reliability and continuity of power restoration. In its islanding partitioning and operation model, this invention explicitly introduces the time-sequence characteristics of DG output and load demand, and ensures real-time power balance of the islanding during each maintenance stage through time-sequence balance constraints. This overcomes the shortcomings of existing technologies that often use static or single-moment power balance models, failing to guarantee the continuous and stable operation of islanding during dynamic maintenance processes. This allows the partitioned islanding to adaptively follow source-load fluctuations, reliably maintaining long-term power supply to critical loads.

[0024] This invention constructs a complete, collaborative, and efficiently solvable comprehensive constraint model, improving the engineering practicality and decision-making accuracy of fault recovery strategies. This addresses the shortcomings of existing technologies where incomplete or inaccurate model constraints lead to weak practicality or the inability to obtain feasible solutions for recovery strategies. It ensures that the proposed strategy can quickly and accurately calculate the optimal recovery scheme while satisfying all actual operational safety constraints. Attached Figure Description

[0025] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0026] Figure 1 This is a schematic diagram of the four-port ESOP topology according to an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the modified IEEE 33 and IEEE 69 node topology according to an embodiment of the present invention;

[0028] Figure 3 This is a schematic diagram of the power supply recovery rate and cumulative power supply recovery rate in the first three stages of a fault according to an embodiment of the present invention, wherein (a) is the first stage, (b) is the second stage, (c) is the third stage, and (d) is a cumulative schematic diagram of the first three stages;

[0029] Figure 4 This represents the cumulative loss of each branch during the fault phase in this embodiment of the invention.

[0030] Figure 5 This is the network topology without any devices installed in the first stage of this embodiment of the invention;

[0031] Figure 6 This is the network topology for installing a 4-port SOP in the first stage of this embodiment of the invention;

[0032] Figure 7 This is the network topology for installing a 4-port ESOP in the first stage of this embodiment of the invention;

[0033] Figure 8 This is a flowchart of a method for improving the resilience of a distribution network with an energy storage-type flexible switch under fault conditions, according to an embodiment of the present invention. Detailed Implementation

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0036] Example 1

[0037] like Figure 8 As shown in the figure, this embodiment provides a method for improving the resilience of a distribution network with energy storage-type flexible soft switches under fault conditions, including:

[0038] S1. Extract the output curves and access location information of distributed power sources, load demand curves, line fault information, distribution network topology and operation data of energy storage flexible soft switches of multi-regional distribution networks under extreme events.

[0039] S2. Based on the data obtained in step S1, establish an integrated resilience enhancement model that integrates fault isolation, multi-stage maintenance, network reconfiguration, and energy storage flexible soft switching. The integrated resilience enhancement model takes the weighted minimum of the power loss load, branch loss, and energy storage flexible soft switching loss during the entire maintenance process as the objective function. The constraints include islanded radial structure and connectivity constraints, time-series balance constraints between distributed power sources and loads, energy storage flexible soft switching operation constraints including the state of charge and charging / discharging efficiency of the embedded energy storage system, maintenance resource constraints, and power flow constraints.

[0040] Specifically, based on the complete data obtained in step S1, an integrated resilience enhancement model of "fault isolation - multi-stage maintenance - network reconfiguration - ESOP collaboration" is established. The core of this model is to construct a mathematical optimization problem with the objective function of minimizing the power loss load, branch loss, and ESOP loss throughout the maintenance process. The objective function specifically includes the following three items: power loss load (power load × (1 - power recovery rate)), branch active power loss, and ESOP operation loss (ESOP active power transmission × loss coefficient). In terms of constraint setting, five types of constraints are mainly considered: 1) island radial structure and connectivity constraints, implemented through the "L-1" method and virtual power flow; 2) DG / load timing balance constraints to ensure real-time power balance within the island; 3) ESOP operation constraints, including port power, battery SOC upper and lower limits, and charging and discharging efficiency; 4) Maintenance resource constraints, with an upper limit on the number of lines repaired in each stage; 5) Power flow constraints, including node voltage and branch current safe operation constraints, and the Big M method is used to decouple the reconfigured network to ensure that the island part meets the power flow constraints.

[0041] Further, in step S2, the objective function is specifically a weighted sum of the following three items: the total power loss load, which is obtained by summing the product of the load at each node in each stage and the degree of load not being restored; the total branch active power loss, which is calculated by the admittance, voltage amplitude and phase angle difference of each branch in each stage; and the total energy storage flexible soft switch active power loss, which is obtained by summing the active power loss at each port in each stage.

[0042] Specifically, the objective function described in step S2, which uses the weighted minimum of "total power loss load + branch loss + ESOP loss", is characterized as follows:

[0043] (1)

[0044] (2)

[0045] (3)

[0046] (4)

[0047] In the formula: , Stages Time Node The degree of load recovery and the amount of load, A value of 0 indicates a complete power outage. A value of 1 indicates that power has been fully restored; For the stage Time Node With the next node Branch admittance between; , In the stage The time is the voltage amplitude at both ends of the branch; In the stage The voltages at both ends of the branch point intersect and differ at any given moment; Indicates the number of maintenance stages. This represents the collection of all ports in the SOP. Indicates ESOP port In the stage Active power loss at all times.

[0048] Furthermore, in step S2, the island radial structure and connectivity constraints are implemented by combining the "L-1" method with virtual power flow, specifically including: ensuring that the number of closed branches in each island is equal to the number of nodes in the island minus one, and ensuring topological connectivity between any nodes in the island through virtual network constraints.

[0049] Furthermore, in step S2, the timing balance constraint between the distributed power source and the load ensures that at every moment during each maintenance phase, the output of all distributed power sources in each isolated island and the recovery load demand of all nodes in that island maintain a real-time power balance.

[0050] Furthermore, in step S2, the operational constraints of the energy storage flexible soft switch include: transmission power constraints at each port of the energy storage flexible soft switch, state of charge constraints of the embedded energy storage system, charging and discharging power constraints, and charging and discharging efficiency constraints.

[0051] The energy storage-type flexible soft switch operation constraints enable the voltage source converters at each port to operate autonomously, achieving energy transfer across time periods.

[0052] Furthermore, in step S2, the maintenance resource constraint is that the number of faulty lines repaired in each maintenance stage does not exceed a preset upper limit.

[0053] Furthermore, in step S2, the power flow constraints include node voltage magnitude constraints, branch current magnitude constraints, and branch power balance constraints. The Big M method is used to decouple the reconstructed network so that the constraints still hold when the branch switches are open.

[0054] Specifically, the various constraints described in step S2 are characterized as follows:

[0055] (1) Radial constraint;

[0056] To ensure the island maintains its radial topology after operation, both connectivity and radial logic must be satisfied: First, all nodes within the island must be topologically connected, meaning any two nodes can be reached from each other via at least one closed-loop path. Second, the number of closed-loop paths must equal the number of nodes minus one to prevent loops. This ensures that at least one branch in every potential loop in the network is disconnected. This approach is simply called the "L-1" constraint, where L is the total number of branches in the loop, and 1 represents the minimum number of disconnections. The corresponding mathematical expression is as follows: The model's constraints are as follows:

[0057] (5)

[0058] In the formula: Indicates a branch During the maintenance phase The on / off state at any given time. This indicates a closed branch, and vice versa; Indicates an isolated island The number of branches distributed internally, This indicates the number of isolated islands.

[0059] (2) Island partitioning constraints;

[0060] 1) Active islands must operate independently of the main distribution network. In the event of a fault in the main distribution network, they must ensure that the fault disturbance does not propagate to the island, and rely on local resources and energy storage to regulate power supply and maintain local power demand and operational stability.

[0061] 2) The available capacity of distributed power sources and energy storage on the island must be prioritized to meet the needs of critical loads; if the capacity is insufficient, secondary loads should be cut off according to the predetermined priority to ensure continuous power supply to critical loads.

[0062] (6)

[0063] In the formula: , Representation phase The island of time All DG outputs and the load of nodes within the island;

[0064] 3) The constraints of power flow, voltage, and current within the island must be within the allowable range to ensure reasonable power distribution and stable system operation.

[0065] (3) Fault repair strategies and constraints;

[0066] In the event of a natural disaster or a sudden large-scale line outage, the distribution network must be restored in stages according to the strategy of "isolation first, repair later," systematically restoring each faulty line in sequence, and accurately identifying the optimal maintenance sequence during the fault's duration. At the onset of a fault, damaged branches should be immediately disconnected and the open / closed status of intact lines locked. Simultaneously, islanding and network reconfiguration should be implemented to restore power to the maximum extent possible while ensuring system stability. During the maintenance period, the number of lines restored in each stage should not exceed h, and the repair sequence should be continuously optimized to achieve precise allocation of limited maintenance resources and continuous load restoration. The constraints of the maintenance strategy are as follows:

[0067] (7)

[0068] (8)

[0069] (9)

[0070] In the formula: This is a set of vectors composed of the start and end nodes of all faulty lines; This indicates that during the first stage of all fault repairs, all faulty branches are in the open state. Indicates the number of maintenance stages; This indicates the time required for a single maintenance operation, i.e., the time required for each stage.

[0071] (4) ESOP constraint;

[0072] The VSC in the ESOP can synchronously absorb or inject active power to the DC terminal, indicating that the VSC exhibits semi-autonomous characteristics and offers more flexible operation and control. The port constraints of the SOP are as follows:

[0073] (10)

[0074] (11)

[0075] (12)

[0076] In the formula: , SOP ports In the stage Active and reactive power transmission at any given moment This represents the collection of all ports in the SOP; Indicates SOP port In the stage Active power loss at all times, This is the loss coefficient.

[0077] In ESOP, there is a strong coupling between ESS and SOP. However, ESS also enables each VSC to largely operate autonomously, overcoming the constraint that the total transmission power between ports is zero. The power and capacity constraints of ESOP ports are as follows:

[0078] (13)

[0079] (14)

[0080] (15)

[0081] In the formula: , For the active power transmission and loss of the ESOP port, among which A value greater than 0 indicates that the VSC injects active power into the node, while a value less than 0 indicates that the VSC absorbs active power from the node. , Indicates the next moment and stage of ESS Battery level at any given moment; This represents the total capacity of the ESS.

[0082] The operating constraints of the ESS are as follows, where the charge / discharge efficiency reflects the actual conversion efficiency after deducting power losses during the charge / discharge process.

[0083] (16)

[0084] (17)

[0085] (18)

[0086] In the formula: , These represent the charging and discharging states of the ESS, respectively, and are variables ranging from 0 to 1; , These are the ESS single-charge power and discharge power, respectively; Regarding the state of charge (SOC) of the ESS, this embodiment achieves consistency between the initial and final SOCs of the ESS through a power purchase and sale method. , This refers to the minimum remaining battery level and the full charge level of the ESS. , These are the maximum single-charge power and maximum discharge power of ESS, respectively.

[0087] (19)

[0088] when hour, (20)

[0089] when hour, (twenty one)

[0090] In the formula: This indicates that the total power output from the ESOP to the port node is less than 0, and the ESS is in a charging state. This indicates that the total power output from the E-SOP to the port node is greater than 0, and the ESS is in a discharging state; , These are the ESS charging efficiency and discharging efficiency, respectively.

[0091] (5) Current constraints;

[0092] Power flow constraints ensure the safe and stable operation of a distribution network during fault recovery. During recovery, voltage and current must be kept within permissible ranges to prevent equipment overload and voltage collapse. System power flow constraints include active and reactive power balance in branches, node voltage amplitude limits, and branch current amplitude limits.

[0093] Voltage and current constraints:

[0094] (twenty two)

[0095] (twenty three)

[0096] In the formula: , These represent the maximum and minimum values ​​of the voltage amplitude, respectively. , These represent the maximum and minimum values ​​of the current amplitude, respectively.

[0097] System power flow constraints:

[0098] (twenty four)

[0099] (25)

[0100] (26)

[0101] (27)

[0102] (28)

[0103] (29)

[0104] In the formula: , Branch roads In the stage The active and reactive power transmitted at all times. , Branch roads In the stage The active and reactive power transmitted at all times; , Branch roads Resistance and reactance; , Stages Injecting nodes at all times The active and reactive power, in this embodiment mainly refers to the output of DG and the injection of ESOP; branch road In the stage The current amplitude at a given moment; , Stages Time Node and nodes The voltage amplitude; For the stage Time Node Active power injection at DG; , Stages Time Node The active and reactive power of the load; For the stage Time Node The recovery coefficient of the load.

[0105] This ensures the correctness of constraints when branch switches are closed and opened, avoiding unreasonable power flow distribution. The above power flow model only applies to static system operation, and the constraints... This constraint is not applicable to the network structure after distribution network fault reconfiguration because it only satisfies the corresponding lines in the operating state, but cannot constrain branches in a faulted or disconnected state after reconfiguration. Therefore, this embodiment uses the Big M method constraint to decouple the reconfigured network. The decoupled constraints are as follows:

[0106] (30)

[0107] (31)

[0108] (32)

[0109] (33)

[0110] (34)

[0111] (35)

[0112] For the transformed constraints and When the controllable switch of the branch is closed, the two constraints are equivalent to the constraints before decoupling; when the controllable switch of the branch is open, the two constraints after decoupling are transformed into constraints. As long as M is large enough, the magnetic constraint will not be limited by the branch switch state, thus achieving constraint decoupling.

[0113] Since this model is designed for island division during the fault repair phase, and considering the situation where multiple DGs are integrated within an island, this embodiment uses virtual network constraints to implement constraints on active islands, automatically identify the number of island regions, and realize the integration of multiple DGs. This mainly includes island connectivity, power flow constraints, and the balance between the power supply of DGs within the island and the load demand.

[0114] (36)

[0115] (37)

[0116] During the recovery phase, according to the regulations for the safe operation of distribution networks, only load nodes equipped with distributed generation (DG) and sufficient energy storage capacity can serve as starting power sources in emergencies. Therefore, during topology transformation after a fault, only substation nodes and some DG can serve as power sources for the fault recovery segmentation area, and multiple power sources may exist within a segmentation area. Indicates the number of maintenance stages Number of rows and DGs A virtual flow source matrix of columns, Indicates the number of nodes in the distribution network Number of operation and maintenance phases A virtual branch flow in a column. The radial constraint of an island in a virtual network can be unified with and realized with the connectivity constraint. The virtual network satisfies the following constraints:

[0117] (38)

[0118] (39)

[0119] (40)

[0120] (41)

[0121] in, This indicates the node connected to the DG, serving as a backup node for startup power; M is set to 100. branch road During the maintenance phase The on / off state at any given time. A branch is closed if it is open, otherwise it is closed. branch road The size of the virtual branch flow, branch road The size of the virtual branch flow, This represents the size of a virtual flow source in the virtual flow source matrix.

[0122] S3. The integrated resilience enhancement model is solved by a mixed integer second-order cone programming algorithm. In each maintenance stage, the islanding strategy, line switch status, energy storage flexible soft switch charging and discharging and power support strategy are optimized simultaneously to output the global optimization scheme with the minimum power loss load.

[0123] Furthermore, in step S3, the process of solving the problem using the mixed-integer second-order cone programming algorithm includes:

[0124] The integrated resilience enhancement model is transformed into a solvable form of second-order cone programming.

[0125] The optimization solution is performed in stages using a rolling time window approach. In each iteration, the state of the island boundary switch, the order of lines to be inspected, the power of the energy storage flexible soft switch port, and the state of charge of the embedded energy storage system are decided simultaneously.

[0126] Furthermore, in step S3, the global optimization scheme specifically includes: the optimal islanding result, the optimal line maintenance sequence for each maintenance stage, and the optimal port power allocation and embedded energy storage system charging and discharging strategy for the energy storage flexible soft switch at each stage.

[0127] Specifically, the model solving stage in step S3 adopts the Mixed Integer Second-Order Cone Programming (MISOCP) algorithm, based on Matlab R2021a-YALMIP, and calls CPLEX for solving. The specific process is as follows: First, the integrated model of "island partitioning - network reconstruction - multi-stage maintenance - ESOP coordination" established in step S2 is transformed into a solvable form of second-order cone programming; then, it is optimized stage by stage in a rolling time window manner, and at each stage, the island boundary switch state, maintenance line sequence, ESOP port power and battery SOC are decided simultaneously; during the iteration process, the virtual power flow, radial pattern, power balance, ESOP operation and voltage safety constraints are verified in real time until all convergence conditions are met, and finally the globally optimal resilience improvement scheme with the minimum power loss loss is output.

[0128] Figure 1This is a four-port ESOP topology. By embedding the ESS (Electronic Power Supply) within the SOP's internal DC bus and DC / DC converter, a more flexible ESOP with better dispatch capabilities can be formed, as shown in the diagram below. Compared to the SOP, the ESOP can respond more flexibly and quickly to system operation in dealing with the volatility and randomness of high-penetration DG (Distributed Generation Gateway), ensuring power system stability while reducing potential risks caused by power fluctuations, exhibiting superior controllability. In distribution network fault environments, the ESOP demonstrates significant advantages in several aspects due to its unique structure and control strategy. Firstly, the ESOP, leveraging the fault current blocking characteristics of its internal DC bus, rapidly isolates the fault area instantly upon fault occurrence, effectively curbing the spread of fault current and significantly reducing the outage area. Simultaneously, the ESS can quickly inject active and reactive power into the lost-power area, optimizing power distribution and precisely adjusting voltage levels, effectively addressing voltage fluctuations caused by intermittent DG output and ensuring power quality in the distribution network. The ESOP also possesses islanding capability; when the connection between the distribution network and the main grid is interrupted, it can autonomously maintain power balance within the island, ensuring continuous and stable power supply to critical loads and enhancing the self-healing capability of the distribution network. On the other hand, ESOP, with its flexible interconnection characteristics, supports flexible switching of distribution network topologies, optimizes network layout, and enables multi-island collaborative operation, significantly improving the flexibility and adaptability of the distribution network. Its modular design allows it to flexibly adapt to different distribution network scenarios, significantly reducing device size and cost, and enhancing device integration and scalability.

[0129] Figure 2 This represents the modified IEEE 33 and IEEE 69 node topology. To verify the resilience improvement effect of the proposed strategy under complex fault scenarios, this embodiment constructs a distribution network platform with dual-system interconnection of IEEE 33 and IEEE 69 node systems, such as... Figure 2 As shown, based on the original voltage levels and load curves, time-varying DGs and loads are added: nodes 10, 16, 24, and 33 of the IEEE 33-node system; nodes 13, 19, 28, 36, 44, and 66 of the IEEE 69-node system; all node loads are time-varying curves. To increase the flexibility of network reconfiguration and islanding, tie switches are artificially added: 3 new tie switches (27-65, 35-50, and 46-52) are added to the IEEE 69 system; the original 5 tie switches are retained in the IEEE 33 system. The fault scenario settings follow the principle of "multi-point concurrency + cross-area propagation": the faulty lines are branches 6, 12, 18, 24, and 32 of the IEEE 33 system, and branches 23, 27, 38, 48, and 61 of the IEEE 69 system; the faults occur simultaneously to test the recovery capability of DG-ESOP coordination during the period of maximum power deficit.

[0130] To quantify the resilience contribution of ESOP in multi-stage failures, the experiment used "whether or not a flexible interconnect device is connected" as the first control variable and "number of ports" as the second control variable. The device connection scheme is shown in Table 1.

[0131] Table 1

[0132]

[0133] The reason for selecting the above nodes is that they belong to the fault isolation boundary (nodes 18 and 19 of the IEEE33 system and nodes 24 and 54 of the IEEE69 system are all located downstream of the faulty line), which can maximize the power mutual assistance space of the flexible device.

[0134] Fault repair is divided into four stages: fault recovery stage, two fault repair stages, and network topology restoration stage. Details of the tasks and repairs during each stage are shown in Table 2.

[0135] Table 2

[0136]

[0137] Figure 3 The power restoration rate and cumulative power restoration rate are the power restoration rates for the three stages before the fault. Figure 3 Tables (a)-(c) respectively show the degree of node load power restoration for the three schemes in the first three stages: Scheme 1 (no device), Scheme 2 (4-port SOP), and Scheme 3 (4-port ESOP). A comparison shows that... Figure 3 In (a) at stage 1, SOP still maintains a 0% recovery rate at nodes 36 and 37 due to the rigid constraint that the algebraic sum of port power must be zero; while ESOP, thanks to the power adjustment of its internal ESS, makes the recovery rate at these two locations jump to 100% during the same period, and the recovery rates of other critical nodes are also improved. Figure 3 Further, in sections (b) and (c), it is shown that as the phases progressed, the ESOP continuously injected power into the power-loss area through multi-terminal DC buses, achieving power restoration in the power-loss area, while the SOP scheme still had some gaps up to phase 3. Therefore, the power restoration rate assessment results directly verify the amplification effect of ESOP on the resilience of the distribution network under extreme fault scenarios. Figure 3 As shown in (d) of the cumulative power restoration rate during the fault phase, Scheme 3 provides significantly better power support for the distribution network than Scheme 2 and Scheme 1 during all fault repair phases.

[0138] Figure 4 This represents the cumulative loss of each branch during the fault phase. Figure 4 The power curves for the entire process show that, in all fault repair phases (excluding phase 4), the access method of Scheme 3 provides significantly higher energy support for the IEEE-33 and IEEE-69 systems than Schemes 2 and 1. See... Figure 4 As shown, when converted to branch-level cumulative losses, the total branch loss caused by Scheme 3 is only 0.1552MW, which is 55.04% and 53.45% lower than Scheme 2 and Scheme 1, respectively, demonstrating a significant advantage. ESOP, with its fast power response capability and multi-port coordinated power regulation characteristics, and precise voltage level adjustment, effectively addresses the unnecessary losses caused by voltage fluctuations resulting from intermittent DG output, simultaneously improving power quality and operational economy.

[0139] Figure 5 This is the network topology for the first phase where no devices are installed.

[0140] Figure 6 The network topology for installing a 4-port SOP in the first phase.

[0141] Figure 7 The network topology for installing 4-port ESOPs in the first phase.

[0142] Figure 5 , Figure 6 and Figure 7 The different background colors visually illustrate the islanded topology after the initial reconstruction following the fault: Scheme 1 resulted in multiple micro-islands and a significant load loss of 2.5255 MW; Scheme 2, through flexible interconnection, compressed the islands into three, reducing the power loss to 1.9504 MW, but was still constrained by "real-time port power balance," and the terminal nodes 36 and 37 failed to regain power; Scheme 3 (4-port ESOP) utilized ESS cross-time period charging and discharging to further integrate the multiple islands into a single "large grid," drastically reducing the power loss to 1.9124 MW, and nodes 36 and 37 were instantly restored. Combined with... Figure 3 The results of the first phase of power restoration in Chengdu show that, compared with Schemes 1 and 2, after a fault event, the distribution network system, through the coordination of tie switches and DG (Distributed Generation) to implement network reconstruction and islanding, successfully ensured the restoration of power supply to the loads of the vast majority of nodes. However, limited by the scale of DG access and its generation capacity, and the lack of power supply capability of tie switches, the system still cannot fully meet the power demand of most loads. Therefore, relying solely on tie switches and the configuration mode of limited resources within the system is insufficient to achieve full load restoration in large-scale fault scenarios. SOP (Standardized Operational Program) connects adjacent feeders with flexible interconnection, realizing flexible conversion of spatial power and shifting the self-healing boundary from "node fault isolation" to "coordinated restoration between feeders," significantly improving the self-healing capability of the distribution system. Compared with Schemes 2 and 3, ESOP (Emergency Supported Operational Program) embeds the power time-shifting capability of ESS (Emergency Safe Supply) on this basis, using a "storage first, release later" strategy to move surplus power to the current gap, enhancing the power supply capacity of the distribution network to the power outage area, improving the refinement of islanded zone power supply, and alleviating the power supply pressure on DG.

[0143] The beneficial effects of this embodiment:

[0144] This embodiment aims to minimize the weighted average of "total power outage loss, branch loss, and ESOP loss," while introducing virtual power flow and L-1 radial constraints to ensure accurate islanding and prevent circulating currents. The constraint system comprehensively considers DG / load timing balance, ESOP power-energy limits, maintenance resource limits, and voltage safety, enabling the resilience enhancement scheme to minimize power outage load while meeting all operational procedures. Through a rolling optimization framework of "fault isolation—multi-stage maintenance—network reconfiguration—ESOP coordination," islanding boundaries, switch operations, maintenance sequence, and ESOP charging / discharging / power support are incorporated into a unified decision-making process, avoiding fragmentation between different stages and achieving global optimization.

[0145] Validation in the improved IEEE33+IEEE69 interconnection system shows that power loss is reduced by 40.2% compared to the no-device solution, significantly improving resilience under extreme fault scenarios. This embodiment requires no additional hardware investment and can be implemented using only existing DG and tie switches. The calculation process can directly call the mature MISOCP solver, with clear steps, strong engineering feasibility, and suitability for rapid recovery from multi-point concurrent faults caused by extreme weather.

[0146] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for improving the resilience of a distribution network with energy storage-type flexible soft switches under fault conditions, characterized in that, Includes the following steps: S1. Extract the output curves and access location information of distributed power sources, load demand curves, line fault information, distribution network topology and operation data of energy storage flexible soft switches of multi-regional distribution networks under extreme events. S2. Based on the data obtained in step S1, establish an integrated resilience enhancement model that integrates fault isolation, multi-stage maintenance, network reconfiguration, and energy storage flexible soft switching. The integrated resilience enhancement model takes the weighted minimum of the power loss load, branch loss, and energy storage flexible soft switching loss during the entire maintenance process as the objective function. The constraints include islanded radial structure and connectivity constraints, time-series balance constraints between distributed power sources and loads, energy storage flexible soft switching operation constraints including the state of charge and charging / discharging efficiency of the embedded energy storage system, maintenance resource constraints, and power flow constraints. S3. The integrated resilience enhancement model is solved by a mixed integer second-order cone programming algorithm. In each maintenance stage, the islanding strategy, line switch status, energy storage flexible soft switch charging and discharging and power support strategy are optimized simultaneously to output the global optimization scheme with the minimum power loss load.

2. The method according to claim 1, characterized in that, In step S2, the objective function is specifically a weighted sum of the following three items: the total power loss load, which is obtained by summing the products of the load at each node in each stage and the degree of load not being restored; The active power loss of the entire branch is calculated from the admittance, voltage amplitude and phase angle difference of each branch at each stage; the active power loss of the energy storage type flexible soft switch is obtained by summing the active power loss of each port at each stage.

3. The method according to claim 1, characterized in that, In step S2, the island radial structure and connectivity constraints are achieved by combining the "L-1" method with virtual power flow. Specifically, this includes ensuring that the number of closed branches in each island is equal to the number of nodes in the island minus one, and ensuring topological connectivity between any nodes in the island through virtual network constraints.

4. The method according to claim 1 or 3, characterized in that, In step S2, the timing balance constraint between the distributed power source and the load ensures that at every moment during each maintenance phase, the output of all distributed power sources in each isolated island and the recovery load demand of all nodes in that island maintain a real-time power balance.

5. The method according to claim 1, characterized in that, In step S2, the operational constraints of the energy storage flexible soft switch include: the transmission power constraints of each port of the energy storage flexible soft switch, the state of charge constraints of the embedded energy storage system, the charging and discharging power constraints, and the charging and discharging efficiency constraints.

6. The method according to claim 5, characterized in that, The energy storage-type flexible soft switch operation constraints enable the voltage source converters at each port to operate autonomously, achieving energy transfer across time periods.

7. The method according to claim 1, characterized in that, In step S2, the maintenance resource constraint is that the number of faulty lines repaired in each maintenance stage does not exceed a preset upper limit.

8. The method according to claim 1, characterized in that, In step S2, the power flow constraints include node voltage magnitude constraints, branch current magnitude constraints, and branch power balance constraints. The Big M method is used to decouple the reconstructed network so that the constraints still hold when the branch switches are open.

9. The method according to claim 1, characterized in that, Step S3, the process of solving the problem using the mixed-integer second-order cone programming algorithm, includes: The integrated resilience enhancement model is transformed into a solvable form of second-order cone programming. The optimization solution is performed in stages using a rolling time window approach. In each iteration, the state of the island boundary switch, the order of lines to be inspected, the power of the energy storage flexible soft switch port, and the state of charge of the embedded energy storage system are decided simultaneously.

10. The method according to claim 1, characterized in that, In step S3, the global optimization scheme specifically includes: the optimal islanding result, the optimal line maintenance sequence for each maintenance stage, and the optimal port power allocation and embedded energy storage system charging and discharging strategy for the energy storage flexible soft switch at each stage.

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