Method and system for dynamic reconfiguration of balanced subnets and load recovery

Abstract

This invention provides a method and system for dynamic reconfiguration and load restoration of balanced subnets. It constructs a two-stage optimization model: the first stage determines mobile resource deployment and dynamic topology connections; the second stage determines equipment power output under uncertainty. After system modeling and defining multiple types of decision variables, an objective function is constructed to maximize the difference between the total weighted restored load and the total active power loss. Three types of constraints are established: topology, equipment operation, and system safety, and the schedulable load is linearized. To address the uncertainty of renewable energy output, Wasserstein fuzzy sets are introduced to construct bibru bar chance constraints. These constraints are transformed using conditional value at risk theory, and the model is then reconstructed using strong duality theory and the stochastic saddle point theorem, transforming it into a mixed integer convex optimization problem with second-order cone constraints. This invention can efficiently achieve dynamic networking and load restoration optimization of balanced subnets while ensuring system safety.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology, specifically to a method and system for dynamic reconfiguration and load restoration of a balanced subnet group, and more particularly to a method for dynamic reconfiguration and load restoration of a balanced subnet group based on data-driven distributed bar optimization. Background Technology

[0002] With the global energy transition, the penetration rate of renewable energy in distribution networks is constantly increasing, posing new challenges to the stable operation and post-disaster recovery capabilities of the power grid. Extreme events (such as natural disasters) may damage upstream substations or main lines of the distribution network, causing widespread power outages. Traditional feeder reconfiguration methods mainly focus on minimizing network losses under normal operating conditions, and often fail in extreme scenarios where the main grid loses power after a disaster.

[0003] Balanced subgrids, as a solution for integrating and locally controlling distributed energy resources, can enhance the resilience of the power grid. Interconnecting multiple balanced subgrids to form a network balanced subgrid, through coordinated operation and energy sharing, can more effectively maintain power supply to critical loads in post-disaster "islanding" scenarios. Existing post-disaster recovery research mainly focuses on balanced subgrid partitioning and resource scheduling based on deterministic predictions. However, the output of renewable energy sources such as wind and solar power exhibits significant stochasticity and volatility. Deterministic optimization models cannot effectively handle this uncertainty, potentially leading to overly optimistic and infeasible recovery plans, or overly conservative plans that waste recovery potential.

[0004] While robust optimization methods have been introduced to address uncertainty, they are typically based on a fixed set of uncertainties, and their decisions tend to address the "worst-case" scenario, potentially leading to overly conservative and inefficient solutions. In contrast, sub-Bruker optimization methods describe uncertainty by constructing a fuzzy set of probability distributions based on historical data, achieving a better balance between economy and robustness. However, effectively embedding sub-Bruker optimization, especially data-driven sub-Bruker chance constraints, into the complex mixed-integer nonlinear programming problem of dynamic formation of network balancing subnets, deployment and scheduling of mobile resources, and achieving efficient solutions, remains a challenge for current technology.

[0005] Patent document CN109617132B discloses a resource allocation and network reconfiguration optimization method to improve the resilience of a resilient distribution network. The method inputs distribution network structural parameters, load, and raw data on photovoltaic dispatch cycles. Upper-level optimization variables include: distributed power source access location and capacity, tie-line connection node location, population size, and initialization of particle swarm optimization parameters for the maximum iteration count. Lower-level optimization variables include: tie-line switch switching status, extreme disaster scenarios, population size, and initialization of iteration count parameters. Based on the upper-level resilient resource optimization configuration model, resilient resource optimization is performed to obtain the economically optimal and most resilient configuration result. Based on the upper-level optimization configuration result, the PSO algorithm is used to execute the lower-level network reconfiguration optimization model, optimizing the lower-level network reconfiguration tie-line switch switching status to obtain the reconfiguration result with the maximum resilience. The patent document proposes a method to improve the resilience of the distribution network by optimizing resource allocation and reconfiguring the network through two-layer optimization. However, it adopts a deterministic model, does not consider the randomness of renewable energy, and focuses on static planning and single reconfiguration. In response to the above shortcomings, this invention proposes a dynamic reconfiguration and recovery method based on data-driven bibliometric optimization. It handles uncertainty through Wasserstein chance constraints, establishes a two-stage optimization model to realize the temporal coordination of mobile resources and topology, and finally transforms it into a deterministic mixed integer programming solution.

[0006] Patent document CN121216444A discloses a power supply restoration method and related device for flexible interconnected distribution networks that considers the uncertainties of wind and solar power. This method fully considers the uncertainty model of wind and solar power and incorporates an energy storage-type intelligent soft switch E. The loss situation of SOP was analyzed, and the objective function, system power flow constraints, and E were constructed. Based on the constraints of SOP operation, system safety operation, and wind and solar power output, the objective function is solved, and the optimal power restoration topology E obtained from the solution is used for control. SOP (Start of Operation) is used to restore power supply to power-loss nodes in flexible interconnected distribution networks. However, the patent document proposes a two-stage control framework combining intraday scheduling and real-time control by constructing a voltage control model that coordinates photovoltaic active and reactive power, achieving a balance between the economy and reliability of distributed voltage regulation. In contrast, this invention focuses on constructing a data-driven sub-Bruker optimization-based dynamic reconfiguration and load restoration method for network balancing subnets in scenarios where extreme disasters cause main grid power outages. This invention describes the uncertainty of renewable energy output using Wasserstein fuzzy sets and uses CVaR theory to transform the sub-Bruker chance constraints into a deterministic optimization problem. Ultimately, it achieves coordinated optimization of mobile emergency resource deployment, dynamic network topology switching, and multi-period power scheduling, providing a robust and economical decision-making framework for the rapid and reliable restoration of critical loads in post-disaster distribution networks. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for dynamic reconfiguration and load recovery of balanced subnet groups.

[0008] A method for dynamic reconfiguration and load restoration of a balanced subnet group according to the present invention includes the following steps: Step S1: Construct a two-stage optimization model, and use the two-stage optimization model to perform dynamic topology planning and load recovery optimization of the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Step S2: Based on the two-stage optimization model framework constructed in Step S1, complete the system modeling and the definition of multiple types of decision variables. The system modeling includes the modeling of nodes, lines and various energy equipment. Step S3: Combining the decision variables defined in Step S2 and the system modeling results, construct an objective function, which aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. Step S4: Based on the objective function constructed in Step S3, establish three types of key constraints and linearize the schedulable load. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Step S1, and also match the system modeling logic of Step S2. Step S5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second stage of Step S1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. Step S6: Integrate the objective function in Step S3, the three types of key constraints in Step S4, and the partial Brull chance constraints in Step S5 to form an initial optimization model containing partial Brull chance constraints. Transform the partial Brull chance constraints in the initial optimization model into a solvable form using conditional value at risk theory, and build a bridge between the constraints and the subsequent model solution process to achieve the solvability of the objective function in Step S3 under the constraints of Step S4 and Step S5. Step S7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob chance constraints formed and transformed in step S6 is reconstructed and transformed into a mixed integer convex optimization problem with second-order cone constraints, so as to solve the optimization model and satisfy the objective function requirements of step S3.

[0009] Preferably, in step S2, the system modeling includes: a set of nodes, a set of lines, a set of mobile distributed generators, a set of mobile energy storage devices, a set of renewable energy units, and a set of time steps; The expression for the set of nodes is: , represents all bus nodes in the distribution network; The expression for the set of lines is: , indicating the feeder or tie line connecting the nodes; The expression for the set of mobile distributed generators is: This refers to mobile-deployable generators, including diesel generators and gas turbines; The expression for the set of mobile energy storage devices is: This indicates a mobile, deployable battery energy storage system; The expression for the set of renewable energy units is: This indicates the installed new energy power sources, including distributed photovoltaic and distributed wind turbines; The expression for the set of time steps is: , which represents the entire time range of the optimized scheduling.

[0010] Preferably, in step S3, the objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system, specifically expressed as:

[0011] Where T represents the set of time steps; N represents the set of nodes; Represents a node Weighting coefficients; Represents a node At any moment The actual active power supplied from the grid side; Represents a node With nodes The lines between; L represents the set of lines; Indicates the line The line impedance; Indicates the line The meritorious trend; Indicates the line The unproductive current; This represents the reference voltage.

[0012] Preferably, in step S4, the balanced subnet topology constraint specifically includes:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] in, A binary variable representing a node. At any moment Does it belong to the k-th balanced subnet? ; This is a binary variable representing the k-th mobile distributed generator. Whether connected to the node throughout the entire scheduling cycle superior; This is a binary variable representing the s-th mobile energy storage device. Whether connected to the node throughout the entire scheduling cycle superior; A binary variable representing a line. At any moment Assign to a balanced subnet ; A binary variable representing a line. At any moment The on / off state.

[0021] Preferably, in step S4, the equipment output and operational constraints are specifically as follows:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] in, A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; express Lower limit of output active power; Represents a node At any moment of Active power output; express Upper limit of output active power; express Lower limit of output reactive power; Represents a node At any moment of The reactive power output; express Upper limit of reactive power output; Represents a node The r Renewable energy units The lower limit of the active power output; Represents a node At any moment The r Renewable energy units The active power generated; Represents a node The r Renewable energy units The upper limit of active power output; Represents a node The r Renewable energy units The lower limit of reactive power output; Represents a node At any moment The r Renewable energy units The reactive power generated; Represents a node The r Renewable energy units The upper limit of reactive power output; Represents a node At any moment Energy storage charging power; express The upper limit of charging power; These are binary variables, representing respectively At any moment Whether to charge / discharge; Represents a node At any moment The energy storage discharge power; express The upper limit of discharge power; express At any moment Energy levels; express The charging efficiency; express The discharge efficiency; Indicates changes over time; express The lower limit of capacity; express Maximum capacity; Indicates when time t is T Energy levels; Indicates when t is 0 Energy level.

[0032] Preferably, in step S4, the system power flow and operational safety constraints specifically include:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] in, Represents all the sets of routes L and nodes. i Connected upstream nodes j , Indicates the line At any moment The meritorious trend; Indicates the line At any moment The meritorious trend; Represents a node At any moment Net active power generation; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Indicates the line At any moment The unproductive current; Indicates the line At any moment The unproductive current; Represents a node At any moment Net reactive power generation; Represents a node Inherent reactive load demand; Represents a node At any moment of Active power output; Represents a node i renewable energy units RES In time t Active power output; Represents a node At any moment Energy storage charging power; Represents a node At any moment The energy storage discharge power; Represents a node At any moment of Reactive power output; Represents a node i renewable energy units RES In time t The reactive power output; Represents a node At any moment The voltage amplitude; Indicates that node j at time... The voltage amplitude; and Indicates the line The line resistance and reactance; Indicates the reference voltage; This represents an auxiliary variable used to relax the DistFlow model, allowing the voltage equation to not hold when the line is disconnected; A binary variable representing a line. At any moment The on / off state; and They represent the lines respectively. Active transmission capacity and reactive transmission capacity; Indicates the lower limit of the node voltage amplitude; Indicates the upper limit of the node voltage amplitude; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; Represents a balanced subnet At any moment Its resilience; Represents a balanced subnet middle Total rated capacity; Represents a node At any moment Critical load requirements; This is a preset resilience index.

[0044] Preferably, in step S4, an equivalent linear constraint is also established, specifically:

[0045]

[0046]

[0047]

[0048]

[0049] in, Represents a node At any moment The actual active power supplied from the grid side; Represents a node At any moment The actual reactive power supplied from the grid side; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Represents a node At any moment The actual restored adjustable load active power meets the requirements. ; Represents a node Inherent reactive load demand; The parameter is a binary parameter, representing the node. Is the load dispatchable? If so, what is its minimum recovery power? .

[0050] Preferably, in step S5, the probability constraint of the split bar is specifically as follows:

[0051] in, Let be a probability function; Q represents the probability distribution under the worst-case scenario. This represents a Wasserstein fuzzy set constructed from historical data; Inf represents the probability of allowing a violation of the requirement; Inf represents the infimum; This indicates that the probability distribution Q belongs to a fuzzy set. D W , Indicates in fuzzy set D W The infimum of the probability distribution Q under the worst-case scenario; Represents a node i renewable energy units RES In time t Active power at any given time Represents a node i renewable energy units RES In time t The upper limit of active power at any given time.

[0052] Preferably, in step S5, the construction of the uncertain parameters and the fuzzy set specifically involves: Define random variables For random variables that contribute to renewable energy, the Wasserstein distance metric is used to measure the difference between the empirical distribution and the true distribution. based on A sample of historical data Construct a system with the empirical distribution Q0 as the center and a radius of [missing information]. All probability distributions within the Wasserstein sphere are treated as fuzzy sets. ;

[0053] in, This represents the Wasserstein distance between the probability distribution Q and the empirical distribution Q0; , representing a random variable support set, and To support the centralized parameters; , represents the Cartesian product of the sample space, and the domain of the integral; This represents a random sample from the empirical distribution Q0; Represents random variables and norm distance; This represents the joint probability measure with Q and Q0 as marginal distributions; Indicates support at All probability distributions; The number of samples; Represents random variables The i-th historical observation sample; Indicated by The Dirac measure centered on the center; Denotes the Cartesian product in the sample space Above, to and Distance with respect to joint probability measure Perform integration to calculate the expected handling cost; Conditional Value at Risk (CVaR) is introduced as a risk measurement tool, and equivalent transformations are performed using CVaR for a given decision variable. and random variables The original DRCC can be equivalently transformed into a constraint on the worst-case CVaR, specifically:

[0054] in, and For decision variables The affine functions represent the coefficient vector and the right-hand bound function, respectively; sup is the supremum function. Indicates in fuzzy set D W The supremum of the probability distribution Q under the worst-case scenario; Indicates the confidence level as The value at risk of CVaR under conditions; Indicates in random variables Under the premise of following the probability distribution Q, The probability of occurrence; Q- This represents the conditional value of risk of the random loss variable within parentheses, given that the random variable follows a probability distribution Q and the confidence level is ε. Based on the definition of CVaR, and grounded in strong duality theory and the stochastic saddle point theorem, the worst-case CVaR constraints are further equivalently transformed into a set of finite-dimensional convex constraints, specifically:

[0055]

[0056]

[0057]

[0058]

[0059] in, Indicates when The expected value when it follows the distribution Q; For newly introduced auxiliary variables, It is the dual norm.

[0060] This invention also provides a balanced subnet dynamic reconfiguration and load recovery system, comprising the following modules: Module M1: Constructs a two-stage optimization model, which is used to perform dynamic topology planning and load recovery optimization for the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Module M2: Based on the two-stage optimization model framework built by Module M1, it completes system modeling and defines multiple types of decision variables. The system modeling includes modeling of nodes, lines and various energy equipment. Module M3: Combining the decision variables defined in Module M2 and the system modeling results, construct an objective function. The objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. Module M4: Based on the objective function constructed in Module M3, three types of key constraints are established, and the schedulable load is linearized. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Module M1, and also match the system modeling logic of Module M2. Module M5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second phase of Module M1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. Module M6: Integrates the objective function in Module M3, the three types of key constraints in Module M4, and the fractional Brussels opportunity constraints in Module M5 to form an initial optimization model containing fractional Brussels opportunity constraints. Through conditional value at risk theory, the fractional Brussels opportunity constraints in this initial optimization model are transformed into a solvable form, and a bridge is built between the constraints and the subsequent model solution process to achieve the solvability of the objective function of Module M3 under the constraints of Module M4 and Module M5. Module M7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob bar chance constraints formed and transformed by Module M6 is reconstructed, transforming it into a mixed integer convex optimization problem with second-order cone constraints, so as to realize the solution of the optimization model and meet the objective function requirements of Module M3.

[0061] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention proposes a data-driven optimization method for dynamic reconfiguration and load recovery of network balancing subnets based on partial Bruker opportunity constraints. It characterizes the distribution uncertainty of renewable energy output by using fuzzy sets based on Wasserstein metric, and uses conditional value at risk theory to transform partial Bruker opportunity constraints into a solvable convex optimization form to construct a two-stage optimization model, thereby realizing the dynamic reconfiguration and load recovery of the balancing subnet group.

[0062] 2. This invention addresses the problem of post-disaster power distribution network recovery and resilience enhancement by constructing a data-driven sub-bar optimization method, establishing a dynamic equilibrium sub-network formation model, and providing a collaborative recovery decision-making framework that considers the uncertainty of renewable energy.

[0063] 3. This invention reveals the optimization mechanism for improving system resilience under uncertain environments by constructing an optimization objective function that includes weighted load recovery, line loss and resilience indices, and a partial Bruker chance constraint based on Wasserstein fuzzy sets and CVaR approximation.

[0064] 4. The dynamic balance subnet formation and distributed bar optimization model proposed in this invention can fully stimulate the recovery potential of mobile distributed power sources and energy storage, enhance the flexibility and reliability of system post-disaster recovery, and has good engineering application prospects. Attached Figure Description

[0065] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A schematic diagram of the IEEE 33-node system; Figure 2This is a schematic diagram showing the results of dynamic reconfiguration and load recovery of the network balancing subnet group within 24 hours. Figure 3 This is a schematic diagram illustrating the evolution of the system topology from t=11 to t=14. Figure 4 A flowchart illustrating the steps involved in balancing the dynamic reconfiguration and load recovery of subnet groups. Detailed Implementation

[0066] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0067] Example 1 This embodiment provides a method for dynamic reconfiguration and load recovery of a balanced subnet group, including the following steps: Step S1: Construct a two-stage optimization model, and use the two-stage optimization model to perform dynamic topology planning and load recovery optimization of the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Step S2: Based on the two-stage optimization model framework constructed in Step S1, complete the system modeling and the definition of multiple types of decision variables. The system modeling includes the modeling of nodes, lines and various energy equipment. In step S2, the system modeling includes: a set of nodes, a set of lines, a set of mobile distributed generators, a set of mobile energy storage devices, a set of renewable energy units, and a set of time steps; The expression for the set of nodes is: , represents all bus nodes in the distribution network; The expression for the set of lines is: , indicating the feeder or tie line connecting the nodes; The expression for the set of mobile distributed generators is: This refers to mobile-deployable generators, including diesel generators and gas turbines; The expression for the set of mobile energy storage devices is: This indicates a mobile, deployable battery energy storage system; The expression for the set of renewable energy units is: This indicates the installed new energy power sources, including distributed photovoltaic and distributed wind turbines; The expression for the set of time steps is: , which represents the entire time range of the optimized scheduling.

[0068] Step S3: Combining the decision variables defined in Step S2 and the system modeling results, construct an objective function, which aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. In step S3, the objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system, specifically expressed as follows:

[0069] Where T represents the set of time steps; N represents the set of nodes; Represents a node Weighting coefficients; Represents a node At any moment The actual active power supplied from the grid side; Represents a node With nodes The lines between; L represents the set of lines; Indicates the line The line impedance; Indicates the line The meritorious trend; Indicates the line The unproductive current; This represents the reference voltage.

[0070] Step S4: Based on the objective function constructed in Step S3, establish three types of key constraints and linearize the schedulable load. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Step S1, and also match the system modeling logic of Step S2. In step S4, the balanced subnet topology constraint specifically includes:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] in, A binary variable representing a node. At any moment Does it belong to a balanced subnet? ; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable representing a line. At any moment Assign to a balanced subnet ; A binary variable representing a line. At any moment The on / off state; In step S4, the equipment output and operational constraints are specifically as follows:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] in, A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; express Lower limit of output active power; Represents a node At any moment of Active power output; express Upper limit of output active power; express Lower limit of output reactive power; Represents a node At any moment of The reactive power output; express Upper limit of reactive power output; Represents a node The r Renewable energy units The lower limit of the active power output; Represents a node At any moment The r Renewable energy units The active power generated; Represents a node The r Renewable energy units The upper limit of active power output; Represents a node The r Renewable energy units The lower limit of reactive power output; Represents a node At any moment The r Renewable energy units The reactive power generated; Represents a node The r Renewable energy units The upper limit of reactive power output; Represents a node At any moment Energy storage charging power; express The upper limit of charging power; These are binary variables, representing respectively At any moment Whether to charge / discharge; Represents a node At any moment The energy storage discharge power; express The upper limit of discharge power; express At any moment Energy levels; express The charging efficiency; express The discharge efficiency; Indicates changes over time; express The lower limit of capacity; express Maximum capacity; Indicates when time t is T Energy levels; Indicates when t is 0 Energy levels; In step S4, the system power flow and operational safety constraints are specifically as follows:

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] in, Indicates the line At any moment The meritorious trend; Indicates the line At any moment The meritorious trend; Represents a node At any moment Net active power generation; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Indicates the line At any moment The unproductive current; Indicates the line At any moment The unproductive current; Represents a node At any moment Net reactive power generation; Represents a node Inherent reactive load demand; Represents a node At any moment of Active power output; Represents a node At any moment Energy storage charging power; Represents a node At any moment The energy storage discharge power; Represents a node At any moment of Reactive power output; Represents a node At any moment The voltage amplitude; Indicates that node j at time... The voltage amplitude; and Indicates the line The line impedance; Indicates the reference voltage; This represents an auxiliary variable used to relax the DistFlow model, allowing the voltage equation to not hold when the line is disconnected; A binary variable representing a line. At any moment The on / off state; and They represent the lines respectively. Active transmission capacity and reactive transmission capacity; Indicates the lower limit of the node voltage amplitude; Indicates the upper limit of the node voltage amplitude; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; Represents a balanced subnet At any moment Its resilience; Represents a balanced subnet middle Total rated capacity; Represents a node At any moment Critical load requirements; Preset resilience index; In step S4, equivalent linear constraints are also established, specifically as follows:

[0100]

[0101]

[0102]

[0103]

[0104] in, Represents a node At any moment The actual active power supplied from the grid side; Represents a node At any moment The actual reactive power supplied from the grid side; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Represents a node At any moment The actual restored adjustable load active power meets the requirements. ; Represents a node Inherent reactive load demand; The parameter is a binary parameter, representing the node. Is the load dispatchable? If so, what is its minimum recovery power? .

[0105] Step S5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second stage of Step S1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. In step S5, the specific Bruker chance constraint is as follows:

[0106] in, Let be a probability function; Q represents the probability distribution under the worst-case scenario. This represents a Wasserstein fuzzy set constructed from historical data; This indicates the probability that a violation of the requirement is permitted. In step S5, the construction of the uncertain parameters and the fuzzy set is specifically as follows: Define random variables For random variables that contribute to renewable energy, the Wasserstein distance metric is used to measure the difference between the empirical distribution and the true distribution. based on A sample of historical data Construct a system with the empirical distribution Q0 as the center and a radius of [missing information]. All probability distributions within the Wasserstein sphere are treated as fuzzy sets. ;

[0107] in, Represents the Wasserstein distance; , representing a random variable The support set; Indicates support at All probability distributions; The number of samples; Indicated by The Dirac measure centered on the centered .

[0108] Step S6: Integrate the objective function in Step S3, the three types of key constraints in Step S4, and the partial Bruker chance constraints in Step S5 to form an initial optimization model containing partial Bruker chance constraints. Transform the partial Bruker chance constraints in the initial optimization model into a solvable form using conditional value at risk theory, and build a bridge between the constraints and the subsequent model solution process to achieve the solvability of the objective function in Step S3 under the constraints of Step S4 and Step S5.

[0109] Step S7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob chance constraints formed and transformed in step S6 is reconstructed and transformed into a mixed integer convex optimization problem with second-order cone constraints, so as to solve the optimization model and satisfy the objective function requirements of step S3.

[0110] Conditional Value at Risk (CVaR) is introduced as a risk measurement tool, and equivalent transformations are performed using CVaR for a given decision variable. and random variables The original DRCC can be equivalently transformed into a constraint on the worst-case CVaR, specifically:

[0111] in, and Distribution represents the distribution with respect to decision variables affine functions; Based on the definition of CVaR, and grounded in strong duality theory and the stochastic saddle point theorem, the worst-case CVaR constraints are further equivalently transformed into a set of finite-dimensional convex constraints, specifically:

[0112]

[0113]

[0114]

[0115]

[0116] in, For newly introduced auxiliary variables, It is the dual norm.

[0117] The present invention also provides a balanced subnet dynamic reconfiguration and load recovery system, which can be implemented by executing the process steps of the balanced subnet dynamic reconfiguration and load recovery method. That is, those skilled in the art can understand the balanced subnet dynamic reconfiguration and load recovery method as a preferred embodiment of the balanced subnet dynamic reconfiguration and load recovery system.

[0118] Example 2 This embodiment provides a balanced subnet dynamic reconfiguration and load recovery system, including the following modules: Module M1: Constructs a two-stage optimization model, which is used to perform dynamic topology planning and load recovery optimization for the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Module M2: Based on the two-stage optimization model framework built by Module M1, it completes system modeling and defines multiple types of decision variables. The system modeling includes modeling of nodes, lines and various energy equipment. In module M2, the system modeling includes: a set of nodes, a set of lines, a set of mobile distributed generators, a set of mobile energy storage devices, a set of renewable energy units, and a set of time steps; The expression for the set of nodes is: , represents all bus nodes in the distribution network; The expression for the set of lines is: , indicating the feeder or tie line connecting the nodes; The expression for the set of mobile distributed generators is: This refers to mobile-deployable generators, including diesel generators and gas turbines; The expression for the set of mobile energy storage devices is: This indicates a mobile, deployable battery energy storage system; The expression for the set of renewable energy units is: This indicates the installed new energy power sources, including distributed photovoltaic and distributed wind turbines; The expression for the set of time steps is: , which represents the entire time range of the optimized scheduling.

[0119] Module M3: Combining the decision variables defined in Module M2 and the system modeling results, construct an objective function. The objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. In module M3, the objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system, specifically expressed as follows:

[0120] Where T represents the set of time steps; N represents the set of nodes; Represents a node Weighting coefficients; Represents a node At any moment The actual active power supplied from the grid side; Represents a node With nodes The lines between; L represents the set of lines; Indicates the line The line impedance; Indicates the line The meritorious trend; Indicates the line The unproductive current; This represents the reference voltage.

[0121] Module M4: Based on the objective function constructed in Module M3, three types of key constraints are established, and the schedulable load is linearized. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Module M1, and also match the system modeling logic of Module M2. In module M4, the balanced subnet topology constraints are specifically as follows:

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] in, A binary variable representing a node. At any moment Does it belong to a balanced subnet? ; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable representing a line. At any moment Assign to a balanced subnet ; A binary variable representing a line. At any moment The on / off state; In module M4, the specific equipment output and operational constraints are as follows:

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] in, A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; express Lower limit of output active power; Represents a node At any moment of Active power output; express Upper limit of output active power; express Lower limit of output reactive power; Represents a node At any moment of The reactive power output; express Upper limit of reactive power output; Represents a node The r Renewable energy units The lower limit of the active power output; Represents a node At any moment The r Renewable energy units The active power generated; Represents a node The r Renewable energy units The upper limit of active power output; Represents a node The r Renewable energy units The lower limit of reactive power output; Represents a node At any moment The r Renewable energy units The reactive power generated; Represents a node The r Renewable energy units The upper limit of reactive power output; Represents a node At any moment Energy storage charging power; express The upper limit of charging power; These are binary variables, representing respectively At any moment Whether to charge / discharge; Represents a node At any moment The energy storage discharge power; express The upper limit of discharge power; express At any moment Energy levels; express The charging efficiency; express The discharge efficiency; Indicates changes over time; express The lower limit of capacity; express Maximum capacity; Indicates time t When T Energy levels; Indicates when t is 0 Energy levels; In module M4, the system power flow and operational safety constraints are specifically as follows:

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] in, Indicates the line At any moment The meritorious trend; Indicates the line At any moment The meritorious trend; Represents a node At any moment Net active power generation; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Indicates the line At any moment The unproductive current; Indicates the line At any moment The unproductive current; Represents a node At any moment Net reactive power generation; Represents a node Inherent reactive load demand; Represents a node At any moment of Active power output; Represents a node At any moment Energy storage charging power; Represents a node At any moment The energy storage discharge power; Represents a node At any moment of Reactive power output; Represents a node At any moment The voltage amplitude; Indicates that node j at time... The voltage amplitude; and Indicates the line The line impedance; Indicates the reference voltage; This represents an auxiliary variable used to relax the DistFlow model, allowing the voltage equation to not hold when the line is disconnected; A binary variable representing a line. At any moment The on / off state; and They represent the lines respectively. Active transmission capacity and reactive transmission capacity; Indicates the lower limit of the node voltage amplitude; Indicates the upper limit of the node voltage amplitude; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; Represents a balanced subnet At any moment Its resilience; Represents a balanced subnet middle Total rated capacity; Represents a node At any moment Critical load requirements; Preset resilience index; In module M4, equivalent linear constraints are also established, specifically as follows:

[0151]

[0152]

[0153]

[0154]

[0155] in, Represents a node At any moment The actual active power supplied from the grid side; Represents a node At any moment The actual reactive power supplied from the grid side; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Represents a node At any moment The actual restored adjustable load active power meets the requirements. ; Represents a node Inherent reactive load demand; The parameter is a binary parameter, representing the node. Is the load dispatchable? If so, what is its minimum recovery power? .

[0156] Module M5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second phase of Module M1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. In module M5, the specific Bruker chance constraint is as follows:

[0157] in, Let be a probability function; Q represents the probability distribution under the worst-case scenario. This represents a Wasserstein fuzzy set constructed from historical data; This indicates the probability that a violation of the requirement is permitted. In module M5, the construction of the uncertain parameters and fuzzy sets is specifically as follows: definition For random variables that contribute to renewable energy, the Wasserstein distance metric is used to measure the difference between the empirical distribution and the true distribution. based on A sample of historical data Construct a system with the empirical distribution Q0 as the center and a radius of [missing information]. All probability distributions within the Wasserstein sphere are treated as fuzzy sets. ;

[0158] in, Represents the Wasserstein distance; , representing a random variable The support set; Indicates support at All probability distributions; The number of samples; Indicated by The Dirac measure centered on the centered .

[0159] Module M6 integrates the objective function in Module M3, the three types of key constraints in Module M4, and the fractional Brussels opportunity constraints in Module M5 to form an initial optimization model containing fractional Brussels opportunity constraints. Through conditional value at risk theory, the fractional Brussels opportunity constraints in this initial optimization model are transformed into a solvable form, building a bridge between the constraints and the subsequent model solution process, so as to realize the solvability of the objective function of Module M3 under the constraints of Module M4 and Module M5.

[0160] Module M7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob bar chance constraints formed and transformed by Module M6 is reconstructed, transforming it into a mixed integer convex optimization problem with second-order cone constraints, so as to realize the solution of the optimization model and meet the objective function requirements of Module M3.

[0161] Conditional Value at Risk (CVaR) is introduced as a risk measurement tool, and equivalent transformations are performed using CVaR for a given decision variable. and random variables The original DRCC can be equivalently transformed into a constraint on the worst-case CVaR, specifically:

[0162] in, and Distribution represents the distribution with respect to decision variables affine functions; Based on the definition of CVaR, and grounded in strong duality theory and the stochastic saddle point theorem, the worst-case CVaR constraints are further equivalently transformed into a set of finite-dimensional convex constraints, specifically:

[0163]

[0164]

[0165]

[0166]

[0167] in, For newly introduced auxiliary variables, It is the dual norm.

[0168] Example 3 Those skilled in the art can understand this embodiment as a more specific description of Embodiment 1.

[0169] This embodiment provides a method for dynamic reconfiguration and load recovery of balanced subnet groups based on data-driven distributed bar optimization.

[0170] This embodiment relates to the field of electrical engineering, specifically to an optimization decision-making method that utilizes mobile emergency resources to dynamically construct a balanced subgrid group after extreme events in order to maximize the recovery of critical loads. In particular, it relates to a partial blue bar chance constraint modeling and solution technique that considers the uncertainty of renewable energy output.

[0171] The technical solution of this embodiment is a dynamic reconfiguration and load recovery method for balanced subnets based on data-driven partial Bruker chance constraints. Its core lies in constructing a two-stage optimization model: the first stage determines the placement of mobile resources and the dynamic topology connections of the network; the second stage, under a given uncertainty description, determines the power of generators, energy storage, and dispatchable loads within each balanced subnet. The distribution uncertainty of renewable energy output is characterized by fuzzy sets based on Wasserstein metrics, and the conditional value-at-risk theory is used to transform the partial Bruker chance constraints into a solvable convex optimization form.

[0172] The specific implementation is as follows: A. System modeling and definition of decision variables.

[0173] The system modeling includes the following physical and logical components, and corresponding mathematical sets are defined: Node set: , represents all bus nodes in the distribution network.

[0174] Route Collection: , indicates the feeder or tie line connecting the node.

[0175] Mobile Distributed Generator (DG) Collection: This refers to mobile-deployable diesel generators, gas turbines, etc.

[0176] Mobile energy storage (ES) device collection: This indicates a mobile, deployable battery energy storage system.

[0177] Collection of Renewable Energy Units (RES): This indicates that distributed photovoltaic, wind turbines and other new energy power sources have been installed.

[0178] Time step set: , which represents the entire time range of the optimized scheduling.

[0179] Key parameters and weights: Load parameters: per node It has a fixed active power load requirement. and reactive load demand .

[0180] Load weight: per node Assign a weight coefficient This is used to prioritize critical workloads.

[0181] Scheduled load identifier: binary parameter Represents a node Is the load dispatchable? If so, what is its minimum recovery power? .

[0182] Equipment technical parameters: including the upper and lower limits of DG output. , , , ; Upper limit of ES charging and discharging power , and capacity upper and lower limits , and charge / discharge efficiency , Line impedance , Node voltage upper and lower limits , and reference voltage .

[0183] The optimization problem being modeled includes the following continuous and binary decision variables: Load recovery variables: These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node At any moment The actual restored adjustable load active power meets the requirements. ; , Represents a node At any moment The actual active and reactive power supplied from the grid side is used for linearization.

[0184] Topology and device deployment variables: A binary variable representing a node. At any moment Does it belong to a balanced subnet? ; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; A binary variable representing a line. At any moment Assign to a balanced subnet ; A binary variable representing a line. At any moment The on / off state.

[0185] Equipment output and state variables: and Representing nodes respectively At any moment of Active and reactive power output; and Representing nodes respectively At any moment of The active and reactive power generated are the key uncertainties to be optimized. and Representing nodes respectively At any moment Energy storage charging / discharging power; These are binary variables, representing respectively At any moment Whether to charge / discharge; express At any moment Energy levels; and Representing nodes respectively At any moment Net power generation.

[0186] Power grid operating variables: and They represent the lines respectively. At any moment The trend of meritorious and ineffective actions; Represents a node At any moment The voltage amplitude; As an auxiliary variable used to relax the DistFlow model, it allows the voltage equation to not hold when the line is disconnected.

[0187] B. Optimize the objective function.

[0188] The model aims to maximize the total weighted recovery load of all nodes within the scheduling period, as shown in Equation (1). After improvement, in order to handle schedulable load and take into account the line network loss based on the DistFlow model, the objective function is expanded to Equation (2), that is, to maximize the difference between the total weighted recovery load and the total active power loss of the system.

[0189] (1) (2) In equation (2), the first term The weight represents the total load for weighted recovery. The higher the value, the higher the recovery priority for that load; the second item It is based on the linearized DistFlow model to approximate the total active power loss of the line, and introduces it as a penalty term into the objective function, which can optimize the network operation economy while restoring the load.

[0190] C. Three types of key constraints.

[0191] To ensure the feasibility and security of the system design, this invention establishes the following multiple constraints: Balanced subnet topology constraints: These constraints ensure that the network can be reasonably divided into multiple electrically independent balanced subnets after a disaster, and each balanced subnet must have one and only one DG as the main power source. Equation (3) ensures that each node must belong to one and only one balanced subnet at any given time; Equations (4) and (5) stipulate that each DG and ES must be connected to one and only one node; Equations (6)-(10) use binary variables to associate the line switch status, balanced subnet affiliation, and node affiliation, ensuring that power lines are only connected between nodes connected to the same balanced subnet, i.e., Equation (6) indicates that if a node connect Then the node must belong to the node at all times. The formed balanced subnet Equations (7)-(9) indicate that a line belongs to a balanced subnet. Equation (10) states that if the nodes at both ends of the line belong to the balanced subnet, then the line must be disconnected.

[0192] (3) (4) (5) (6) (7) (8) (9) (10) Equipment Output and Operational Constraints: These constraints are used to simulate the physical operational limitations of various power sources and energy storage systems. Equations (11) and (12) contain the upper and lower limits of active / reactive power output of the DG; Equations (13) and (14) represent the upper and lower limits of renewable energy output constraints, where the upper limit is... The uncertainty will be handled by subsequent pluripotent rod opportunity constraints; Equations (15) and (16) are the charging / discharging power limits of energy storage, and Equation (17) is the charging and discharging mutual exclusion constraint, indicating that the same energy storage device cannot be charged and discharged at the same time; Equations (18)-(20) specify the energy storage state equation and boundary constraints, where Equation (20) indicates that at the end of the scheduling cycle, the energy storage should be restored to the initial state to ensure sustainable operation.

[0193] (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) System power flow and operational safety constraints: The distribution network adopts a linearized DistFlow power flow model to ensure computational efficiency, where equations (21)-(24) and (25)-(26) describe power balance and voltage relationship, respectively; equations (27)-(28) and (29)-(30) constrain line transmission power capacity and node voltage amplitude, respectively; to enhance system resilience, the resilience index constraint shown in equation (31) is introduced, requiring that the available capacity of distributed power sources in each balanced subnetwork must be higher than the total critical load they bear by a certain proportion. R .

[0194] (twenty one) (twenty two) (twenty three) (twenty four) (25) (26) (27) (28) (29) (30) (31) In the formula, and They represent the lines respectively. The active and reactive transmission capacity, and These are the upper and lower limits of the node voltage amplitude. Represents a balanced subnet At any moment The resilience, Represents a balanced subnet middle Total rated capacity, Represents a node At any moment Critical load requirements, This is a preset resilience index.

[0195] In addition, to avoid in the objective function and The nonlinearity caused by multiplication requires linearization of the schedulable load by introducing auxiliary variables. and Representing the actual power supply, the following equivalent linear constraints are established: (32)-(36) (32) (33) (34) (35) (36) D. Modeling the uncertainty of renewable energy and handling the random chance constraint of the split-blob model.

[0196] The key innovation of the model lies in handling the maximum available output of renewable energy. Uncertainty. Traditional robust constraints Under uncertainty, excessive conservatism may lead to significant economic losses. Therefore, this invention introduces the Distributed Broken Bar Chance Constraint (DRCC), as shown in equation (37): (37) In the formula, Let Q be a probability function, representing the worst-case probability distribution derived from a Wasserstein fuzzy set constructed from historical data. , This indicates the probability that a violation of the requirement is permitted.

[0197] This constraint requires that, under probability distribution Q, the probability that the actual output of renewable energy does not exceed its dispatch value is still not less than [a certain percentage]. Thus, with a quantifiable level of risk Ensure the robustness of decision-making.

[0198] E. Construction of Uncertain Parameters and Fuzzy Sets.

[0199] The mixed-integer programming model containing DRCC established by the above steps is difficult to solve directly. This invention constructs a data-driven Wasserstein fuzzy set: definition For the random variable contributing to renewable energy, the Wasserstein distance metric is used to measure the difference between the empirical and true distributions. Equations (38)-(40) are based on... A sample of historical data Construct a system with the empirical distribution Q0 as the center and a radius of [missing information]. All probability distributions within the Wasserstein sphere are treated as fuzzy sets. This fuzzy set does not presuppose the specific form of the distribution, but relies solely on the data, thus combining data-driven nature with statistical rigor.

[0200]

[0201] In the formula, Represents the Wasserstein distance. Represents random variables support set, Indicates support at All probability distributions, For the sample size, Indicated by The Dirac measure centered on the centered .

[0202] F. DRCC transformation based on CVaR.

[0203] Conditional Value at Risk (CVaR) is introduced as a risk measurement tool, and equivalent transformations are performed using CVaR. For a given decision variable... and random variables In equation (41), the original DRCC can be equivalently transformed into the constraint on worst-case CVaR in equation (42).

[0204]

[0205] In the formula, and Distribution represents the distribution with respect to decision variables affine functions.

[0206] G. Model reconstruction and solution.

[0207] According to the definition of CVaR in equation (43), based on strong duality theory and stochastic saddle point theorem, the worst-case CVaR constraint is further equivalently transformed into a series of finite-dimensional convex constraint sets, as shown in equations (44)-(47).

[0208] (43) (44) (45) (46) (47) In the formula, For newly introduced auxiliary variables, It is the dual norm.

[0209] Ultimately, the complex partial boolean chance-constrained programming problem is reconstructed into a mixed integer convex optimization problem with second-order cone constraints in equation (47): (48) This embodiment aims to address the problem of unreliable or overly conservative recovery decisions caused by the uncertainty of renewable energy output during the post-disaster power distribution network recovery process. It proposes a data-driven sub-Browser optimization framework to achieve the following objectives: a. Unlike traditional deterministic programming or static robust optimization methods, this method constructs a fuzzy set-driven partial robust chance constraint model based on Wasserstein metric data to handle the stochasticity of renewable energy with a quantifiable risk confidence level, achieving an optimal balance between the economy and robustness of recovery decisions.

[0210] b. Design a dynamic reconfiguration mechanism for the network balance subnet under the post-disaster "island" mode. By jointly optimizing the placement of mobile distributed power sources and energy storage, the timing of network topology switching, and multi-period power scheduling, the optimal spatiotemporal matching of recovery resources and load demand can be achieved.

[0211] c. Establish a refined model that includes line loss and resilience indicators to maximize the weighted load recovery while reducing network loss and ensuring that each balanced subnet has sufficient reserve capacity, thereby improving the practical operability of the recovery plan and the long-term support capability of the system.

[0212] d. Provides a framework for transforming and solving random chance constraints based on conditional risk value theory, which reconstructs complex stochastic optimization problems into deterministic mixed-integer programming problems that can be efficiently processed by commercial solvers, combining theoretical rigor with engineering practicality.

[0213] Example 4 like Figure 1 As shown, the IEEE 33-node distribution system is selected as the case study. It is assumed that after an extreme disaster, the system is completely disconnected from the upstream power grid and enters an islanded operation state. Within 24 hours after the disaster, dynamic reconfiguration and resource coordination are needed to maximize load recovery.

[0214] In this system, three photovoltaic devices with different parameters are connected to nodes 3, 24, and 28 respectively; the loads of nodes 10, 18, and 22 are set as secondary important loads, and the loads of nodes 14, 25, and 32 are set as tertiary important loads; at the same time, the loads of nodes 15, 20, 23, and 31 are set as dispatchable loads. The photovoltaic devices, energy storage devices, mobile distributed generators, and related network parameters connected to the system are shown in Table 1.

[0215] Table 1 System Parameters

[0216] Simulation verification of the above system was conducted. The simulation results show that in each time period, the power distribution system is divided into three balanced subnets, and three mobile distributed generators are connected to the optimal locations, namely nodes 32, 10, and 25. Two mobile energy storage devices are arranged at nodes 24 and 5 to mitigate the fluctuations in renewable energy output.

[0217] The results of dynamic reconfiguration and load recovery of the balanced subnet group are as follows: Figure 2 As shown, to maximize the weighted load recovery, different nodes are dynamically allocated to different balancing subnets at different time periods. The results show that the system always prioritizes the recovery of critical loads. Even when renewable energy output fluctuates over time, reliable power supply to critical loads can still be guaranteed through reasonable control of energy storage devices and line switches.

[0218] The dynamic reconfiguration process of the system topology during the time period from t=11 to t=14 is as follows: Figure 3 As shown in the diagram, during time period 11, energy storage device 1 is charging and discharging during time period 12, working in conjunction with photovoltaic device 2 and distributed generator 3 to supply power to critical load 25. Simultaneously, photovoltaic device 1 supplies power to other loads and charges energy storage device 2 to store excess energy. During times 13 and 14, energy storage device 2 and energy storage device 1 discharge in different balanced subgrids to restore critical loads in their respective areas. These results demonstrate that introducing dynamic topology reconfiguration combined with coordinated energy storage control can effectively improve the efficiency of critical load restoration.

[0219] To verify the effectiveness of the proposed data-driven sub-branch optimization-based dynamic reconfiguration and load restoration method for balanced subnets, three load restoration modes were selected for comparative analysis.

[0220] Method 1: A dynamic reconfiguration model for balanced subnets based on distributed bar chance constraints (DRCC) allows network topology to change over time; Method 2: Static networked balanced subnet formation model based on DRCC, with network topology remaining unchanged; Method 3: A dynamic networked equilibrium subnet formation model based on robust optimization is used to handle the uncertainty of renewable energy output through traditional robust optimization methods.

[0221] The total weighted load recovery results under the three methods are shown in Table 2.

[0222] Table 2 Comparison of different load recovery methods

[0223] The results show that the network balancing subnet dynamic reconfiguration method based on data-driven sub-Bruker optimization proposed in this invention has advantages in load recovery performance, with its total weighted load recovery amount increasing by 1.76% and 3.29% compared to the static model and the traditional robust optimization model, respectively. This indicates that, compared to robust optimization methods that only consider the most unfavorable operating scenario, the sub-Bruker modeling approach adopted in this invention can further improve the recovery capability of the power distribution system after a disaster while taking into account both system security and operational flexibility. It also verifies that introducing a dynamic topology reconfiguration mechanism has a significant effect on improving system resilience and load recovery level.

[0224] This invention provides a method and system for dynamic reconfiguration and load restoration of balanced subnets. It constructs a two-stage optimization model: the first stage determines mobile resource deployment and dynamic topology connections; the second stage determines equipment power output under uncertainty. After system modeling and defining multiple types of decision variables, an objective function is constructed to maximize the difference between the total weighted restored load and the total active power loss. Three types of constraints are established: topology, equipment operation, and system safety, and the schedulable load is linearized. To address the uncertainty of renewable energy output, Wasserstein fuzzy sets are introduced to construct bibru bar chance constraints. These constraints are transformed using conditional value at risk theory, and the model is then reconstructed using strong duality theory and the stochastic saddle point theorem, transforming it into a mixed integer convex optimization problem with second-order cone constraints. This invention can efficiently achieve dynamic networking and load restoration optimization of balanced subnets while ensuring system safety.

[0225] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0226] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for dynamic reconfiguration and load recovery of a balanced subnet group, characterized in that, Includes the following steps: Step S1: Construct a two-stage optimization model, and use the two-stage optimization model to perform dynamic topology planning and load recovery optimization of the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Step S2: Based on the two-stage optimization model framework constructed in Step S1, complete the system modeling and the definition of multiple types of decision variables. The system modeling includes the modeling of nodes, lines and various energy equipment. Step S3: Combining the decision variables defined in Step S2 and the system modeling results, construct an objective function, which aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. Step S4: Based on the objective function constructed in Step S3, establish three types of key constraints and linearize the schedulable load. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Step S1, and also match the system modeling logic of Step S2. Step S5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second stage of Step S1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. Step S6: Integrate the objective function in Step S3, the three types of key constraints in Step S4, and the partial Brull chance constraints in Step S5 to form an initial optimization model containing partial Brull chance constraints. Transform the partial Brull chance constraints in the initial optimization model into a solvable form using conditional value at risk theory, and build a bridge between the constraints and the subsequent model solution process to achieve the solvability of the objective function in Step S3 under the constraints of Step S4 and Step S5. Step S7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob chance constraints formed and transformed in step S6 is reconstructed and transformed into a mixed integer convex optimization problem with second-order cone constraints, so as to solve the optimization model and satisfy the objective function requirements of step S3.

2. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S2, the system modeling includes: a set of nodes, a set of lines, a set of mobile distributed generators, a set of mobile energy storage devices, a set of renewable energy units, and a set of time steps; The expression for the set of nodes is: , represents all bus nodes in the distribution network; The expression for the set of lines is: , indicating the feeder or tie line connecting the nodes; The expression for the set of mobile distributed generators is: This refers to mobile-deployable generators, including diesel generators and gas turbines; The expression for the set of mobile energy storage devices is: This indicates a mobile, deployable battery energy storage system; The expression for the set of renewable energy units is: This indicates the installed new energy power sources, including distributed photovoltaic and distributed wind turbines; The expression for the set of time steps is: , which represents the entire time range for optimized scheduling.

3. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S3, the objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system, specifically expressed as follows: Where T represents the set of time steps; N represents the set of nodes; Represents a node Weighting coefficients; Represents a node At any moment The actual active power supplied from the grid side; Represents a node With nodes The lines between; L represents the set of lines; Indicates the line The line impedance; Indicates the line The meritorious trend; Indicates the line The unproductive current; This represents the reference voltage.

4. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S4, the balanced subnet topology constraint specifically includes: in, A binary variable representing a node. At any moment Does it belong to the k-th balanced subnet? ; This is a binary variable representing the k-th mobile distributed generator. Whether connected to the node throughout the entire scheduling cycle superior; This is a binary variable representing the s-th mobile energy storage device. Whether connected to the node throughout the entire scheduling cycle superior; A binary variable representing a line. At any moment Assign to a balanced subnet ; A binary variable representing a line. At any moment The on / off state.

5. The method for dynamic reconfiguration and load restoration of a balanced subnet group according to claim 1, characterized in that, In step S4, the equipment output and operational constraints are specifically as follows: in, A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; express Lower limit of output active power; Represents a node At any moment of Active power output; express Upper limit of output active power; express Lower limit of output reactive power; Represents a node At any moment of The reactive power output; express Upper limit of reactive power output; Represents a node The r Renewable energy units The lower limit of the active power output; Represents a node At any moment The r Renewable energy units The active power generated; Represents a node The r Renewable energy units The upper limit of active power output; Represents a node The r Renewable energy units The lower limit of reactive power output; Represents a node At any moment The r Renewable energy units The reactive power generated; Represents a node The r Renewable energy units The upper limit of reactive power output; Represents a node At any moment Energy storage charging power; express The upper limit of charging power; These are binary variables, representing respectively At any moment Is it charging / discharging? Represents a node At any moment The energy storage discharge power; express The upper limit of discharge power; express At any moment Energy levels; express The charging efficiency; express The discharge efficiency; Indicates changes over time; express The lower limit of capacity; express Maximum capacity; Indicates when time t is T Energy levels; Indicates when t is 0 Energy level.

6. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S4, the system power flow and operational safety constraints are specifically as follows: in, Represents all the sets of routes L and nodes. i Connected upstream nodes j , Indicates the line At any moment The meritorious trend; Indicates the line At any moment The meritorious trend; Represents a node At any moment Net active power generation; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Indicates the line At any moment The unproductive current; Indicates the line At any moment The unproductive current; Represents a node At any moment Net reactive power generation; Represents a node Inherent reactive load demand; Represents a node At any moment of Active power output; Represents a node i renewable energy units RES In time t Active power output; Represents a node At any moment Energy storage charging power; Represents a node At any moment The energy storage discharge power; Represents a node At any moment of Reactive power output; Represents a node i renewable energy units RES In time t The reactive power output; Represents a node At any moment The voltage amplitude; Indicates that node j at time... The voltage amplitude; and Indicates the line The line resistance and reactance; Indicates the reference voltage; This represents an auxiliary variable used to relax the DistFlow model, allowing the voltage equation to not hold when the line is disconnected; A binary variable representing a line. At any moment The on / off state; and They represent the lines respectively. Active transmission capacity and reactive transmission capacity; Indicates the lower limit of the node voltage amplitude; Indicates the upper limit of the node voltage amplitude; A binary variable, representing Whether connected to the node throughout the entire scheduling cycle superior; Represents a balanced subnet At any moment Its resilience; Represents a balanced subnet middle Total rated capacity; Represents a node At any moment Critical load requirements; This is a preset resilience index.

7. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S4, equivalent linear constraints are also established, specifically as follows: in, Represents a node At any moment The actual active power supplied from the grid side; Represents a node At any moment The actual reactive power supplied from the grid side; These are binary state variables, representing nodes. At any moment Has the load been restored? Represents a node Inherent active power load demand; Represents a node At any moment The actual restored adjustable load active power meets the requirements. ; Represents a node Inherent reactive load demand; The parameter is a binary parameter, representing the node. Is the load dispatchable? If so, what is its minimum recovery power? .

8. The method for dynamic reconfiguration and load recovery of balanced subnet groups according to claim 1, characterized in that, In step S5, the specific Bruker chance constraint is as follows: in, Let be a probability function; Q represents the probability distribution under the worst-case scenario. This represents a Wasserstein fuzzy set constructed from historical data; Inf represents the probability of allowing a violation of the requirement; Inf represents the infimum; This indicates that the probability distribution Q belongs to a fuzzy set. D W , Indicates in fuzzy set D W The infimum of the probability distribution Q under the worst-case scenario; Represents a node i renewable energy units RES In time t Active power at any given time Represents a node i renewable energy units RES In time t The upper limit of active power at any given time.

9. The method for dynamic reconfiguration and load recovery of a balanced subnet group according to claim 1, characterized in that, In step S5, the construction of the uncertain parameters and the fuzzy set is specifically as follows: Define random variables For random variables that contribute to renewable energy, the Wasserstein distance metric is used to measure the difference between the empirical and true distributions. based on A sample of historical data Construct a system with the empirical distribution Q0 as the center and a radius of [missing information]. All probability distributions within the Wasserstein sphere are treated as fuzzy sets. ; in, This represents the Wasserstein distance between the probability distribution Q and the empirical distribution Q0; , representing a random variable support set, and To support the centralized parameters; , represents the Cartesian product of the sample space, and the domain of the integral; This represents a random sample from the empirical distribution Q0; Represents random variables and norm distance; This represents the joint probability measure with Q and Q0 as marginal distributions; Indicates support at All probability distributions; The number of samples; Represents random variables The i-th historical observation sample; Indicates The Dirac measure centered on the center; Denotes the Cartesian product in the sample space Above, to and Distance with respect to joint probability measure Perform integration to calculate the expected handling cost; Conditional Value at Risk (CVaR) is introduced as a risk measurement tool, and equivalent transformations are performed using CVaR for a given decision variable. and random variables The original DRCC can be equivalently transformed into a constraint on the worst-case CVaR, specifically: in, and For decision variables The affine functions represent the coefficient vector and the right-hand bound function, respectively; sup is the supremum function. Indicates in fuzzy set D W The supremum of the probability distribution Q under the worst-case scenario; Indicates the confidence level as The value at risk of CVaR under conditions; Indicates in random variables Under the premise of following a probability distribution Q, The probability of occurrence; Q- This represents the conditional value of risk of the random loss variable within parentheses, given that the random variable follows a probability distribution Q and the confidence level is ε. Based on the definition of CVaR, and grounded in strong duality theory and the stochastic saddle point theorem, the worst-case CVaR constraints are further equivalently transformed into a set of finite-dimensional convex constraints, specifically: in, Indicates when The expected value when it follows the distribution Q; For newly introduced auxiliary variables, It is the dual norm.

10. A balanced subnet group dynamic reconfiguration and load recovery system, characterized in that, Includes the following modules: Module M1: Constructs a two-stage optimization model, which is used to perform dynamic topology planning and load recovery optimization for the balanced subnet group; wherein, the first stage determines the deployment location of mobile resources and the dynamic topology connection relationship of the network, and the second stage determines the power output of various devices in the balanced subnet under uncertainty description; Module M2: Based on the two-stage optimization model framework built by Module M1, it completes system modeling and defines multiple types of decision variables. The system modeling includes modeling of nodes, lines and various energy equipment. Module M3: Combining the decision variables defined in Module M2 and the system modeling results, construct an objective function. The objective function aims to maximize the difference between the total weighted recovery load and the total active power loss of the system. Module M4: Based on the objective function constructed in Module M3, three types of key constraints are established, and the schedulable load is linearized. The three types of key constraints are balanced subnet topology constraints, equipment output and operation constraints, and system power flow and operation safety constraints. The constraints match the topology planning and equipment output decision requirements of Module M1, and also match the system modeling logic of Module M2. Module M5: To address the uncertainty in the output distribution of renewable energy equipment involved in the second phase of Module M1, a fuzzy set based on Wasserstein metric and constructed from historical data is introduced to characterize the distribution uncertainty and establish a partial Bruker chance constraint. Module M6: Integrates the objective function in Module M3, the three types of key constraints in Module M4, and the fractional Brussels opportunity constraints in Module M5 to form an initial optimization model containing fractional Brussels opportunity constraints. Through conditional value at risk theory, the fractional Brussels opportunity constraints in this initial optimization model are transformed into a solvable form, and a bridge is built between the constraints and the subsequent model solution process to achieve the solvability of the objective function of Module M3 under the constraints of Module M4 and Module M5. Module M7: Based on strong duality theory and stochastic saddle point theorem, the optimization model with split-blob bar chance constraints formed and transformed by Module M6 is reconstructed, transforming it into a mixed integer convex optimization problem with second-order cone constraints, so as to realize the solution of the optimization model and meet the objective function requirements of Module M3.

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