AC / DC power distribution network reliability evaluation method and device based on Monte Carlo and improved grey wolf optimization

Abstract

The invention discloses an AC / DC power distribution network reliability evaluation method and device based on Monte Carlo and improved grey wolf optimization, and relates to the technical field of power distribution networks, and the method comprises the steps: carrying out the sampling of an in-operation element of an AC / DC power distribution network, and generating one-time fault-free operation time and repair time; selecting an in-operation element with a minimum one-time fault-free operation time value as a fault element, propelling a Monte Carlo simulation clock, determining a topology after fault isolation of the fault element according to the fault mode consequence analysis table, and determining the fault isolation of the fault element based on the source load equipment parameters of the AC / DC power distribution network and the topology after fault isolation. Outputting a target fault recovery scheme through an improved grey wolf optimization algorithm, determining a reliability evaluation index based on the target fault recovery scheme, and advancing a Monte Carlo simulation clock according to the recovery time of a fault element; and if the Monte Carlo simulation clock reaches the target evaluation time window, outputting a reliability evaluation index. Based on the above scheme, the balance of the reliability evaluation of the AC / DC hybrid power distribution network between precision and efficiency is effectively realized.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and in particular to a method and apparatus for reliability assessment of AC / DC power distribution networks based on Monte Carlo and improved gray wolf optimization. Background Technology

[0002] As a crucial component of the distribution network, the reliability assessment of AC / DC hybrid distribution networks is a core technical aspect of ensuring the safe and stable operation of the power system. Currently, distribution network reliability assessment mainly employs analytical methods and Monte Carlo simulation methods. Analytical methods rely on rigorous mathematical models and network simplification assumptions, offering high computational efficiency. However, they struggle to accurately characterize multiple uncertainties, such as system operating constraints, the fluctuating characteristics of distributed generation sources, and post-fault reconfiguration strategies. Their modeling accuracy is particularly insufficient when dealing with large-scale AC / DC hybrid systems. In contrast, sequential Monte Carlo simulation, a method within Monte Carlo simulation, considers the temporal nature of system operation, enabling more accurate simulation of the temporal evolution of random fault events and system operating states. However, its computational complexity is high, especially in solving the high-dimensional discrete combinatorial optimization problem of fault recovery, where search efficiency is low. Therefore, a balanced approach between accuracy and efficiency is urgently needed, highlighting the urgent need for an accurate and efficient reliability assessment method for AC / DC distribution networks. Summary of the Invention

[0003] This invention provides a method and apparatus for reliability assessment of AC / DC distribution networks based on Monte Carlo and improved gray wolf optimization, which solves the technical problem that existing AC / DC hybrid distribution network reliability assessment methods are difficult to balance in terms of accuracy and efficiency.

[0004] The first aspect of this invention provides a reliability assessment method for AC / DC distribution networks based on Monte Carlo and improved gray wolf optimization, comprising:

[0005] Initialize the Monte Carlo simulation clock and target evaluation time window, and obtain the source and load equipment parameters of the AC / DC distribution network;

[0006] The in-operation components of the AC / DC distribution network are sampled to generate a fault-free operation time and a repair time. The in-operation component with the minimum fault-free operation time is selected as the faulty component, and the Monte Carlo analog clock is advanced based on the minimum fault-free operation time.

[0007] The fault isolation topology of the faulty component is determined according to the preset fault mode consequence analysis table;

[0008] Based on the source and load device parameters and the topology after fault isolation, a target fault recovery scheme is output through an improved gray wolf optimization algorithm. The improved gray wolf optimization algorithm introduces an improved Tent chaotic mapping for the initialization of the continuous intermediate state positions of operable switches, topology feasibility repair after binarization of the continuous intermediate state positions of operable switches, and a position update strategy based on Lévy flight and adaptive disturbance mechanism.

[0009] Based on the target fault recovery scheme, reliability assessment indicators are determined, and the Monte Carlo analog clock is advanced according to the repair time of the faulty component.

[0010] If the Monte Carlo simulation clock reaches the target evaluation time window, then the reliability evaluation index is output.

[0011] Furthermore, the step of outputting a target fault recovery scheme based on the source-load device parameters and the topology after fault isolation, using an improved Grey Wolf optimization algorithm, includes:

[0012] Set the basic solution parameters for the algorithm;

[0013] Taking the fault recovery scheme as the individual gray wolf, the gray wolf population is initialized based on the initialization of the continuous intermediate state positions of the operable switch by the improved Tent chaotic mapping and the topological feasibility repair of the binarized continuous intermediate state positions of the operable switch, and the current iteration number is initialized.

[0014] For each individual gray wolf in the gray wolf population, the fitness value with constraint-based violation penalty is calculated using source load device parameters and topology after fault isolation.

[0015] The fitness values ​​are compared to determine the three best gray wolf individuals. After updating the position of the gray wolf individuals based on the Lévy flight and adaptive perturbation mechanism, the topological feasibility repair is performed after binarizing the continuous intermediate position of the operable switch. The new fitness values ​​are calculated and greedily retained to determine the updated gray wolf population and update the current iteration number.

[0016] Determine whether the iteration stopping condition is met based on the current iteration count and the minimum fitness value;

[0017] If the iteration stopping condition is not met, the process jumps to the step of comparing each fitness value to determine the three best gray wolf individuals until the iteration stopping condition is met. Then, the gray wolf individual with the smallest fitness value is output as the target fault recovery scheme.

[0018] Furthermore, it also includes:

[0019] If the Monte Carlo simulation clock does not reach the target evaluation time window, the fault-free operation time of the faulty component is updated, and the process jumps to the step of selecting the operating component with the minimum fault-free operation time as the faulty component, until the Monte Carlo simulation clock reaches the target evaluation time window, and then the reliability evaluation index is output.

[0020] Furthermore, the process of initializing the operable switch continuous intermediate state positions of the Tent chaotic map is improved, including:

[0021]

[0022] In the formula, Indicates the first Chaotic variables in a sub-chaotic mapping Indicates the first Chaotic variables in a sub-chaotic mapping Indicates the first Perturbation of sub-chaotic mapping Indicates operable switch Chaotic variables, Indicates operable switch The position of the continuous intermediate state in the 0th iteration;

[0023] The process of binarizing the continuous intermediate positions of an operable switch includes:

[0024]

[0025] In the formula, Indicates operable switch The probability value, This represents an exponential function with the natural constant as its base. Indicates the binarization threshold. Indicates steepness. Indicates operable switch The continuous intermediate state positions, Indicates operable switch The open and closed states, Indicates an indicator function, Indicates that it conforms to the interval Uniform distribution on Indicates a Random numbers that are uniformly distributed across an interval.

[0026] Furthermore, the position update strategy based on Lévy flight and adaptive perturbation mechanism includes:

[0027]

[0028] In the formula, Indicates the first The three priorities guiding this iteration This indicates the position of the individual gray wolf calculated from the first guiding direction. This indicates the position of the individual gray wolf calculated from the second guiding direction. This indicates the position of the individual gray wolf calculated from the third guiding direction. Indicates the operable switch at the first The position vector of consecutive intermediate states in each iteration. Indicates the scale of the disturbance. This indicates the step size of Lévy's flight. A scalar representing the position movement control coefficient. This indicates the location of an individual gray wolf.

[0029] Furthermore, the fitness determination process of the gray wolf optimization algorithm is improved, including:

[0030]

[0031] In the formula, This refers to an individual gray wolf. Indicates the fitness value. This represents the normalized function for unrestored load. This represents the network loss normalization function. This represents a function that normalizes the number of switching operations. This represents the weights of the unrecovered load normalization function. The weights represent the network loss normalization function. The weights of the normalization function representing the number of switching operations; Indicates the first Measurement of penalties for breach of constraints Indicates the first The penalty factor for each constraint condition. This represents the constraint index.

[0032] Furthermore, the unrestored load normalization function includes:

[0033]

[0034] In the formula, This indicates that the load normalization value has not been restored. Indicates load node , Represents the set of load nodes. Indicates load node Importance weight, Indicates load node Rated active power, Indicates load node The charged state;

[0035] Network loss normalization functions include:

[0036]

[0037] In the formula, This represents the normalized value of network loss. Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the set of AC branches. Indicates the resistance of the AC branch. Indicates the AC branch current. Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the collection of DC branches. Indicates the DC branch resistance. Indicates the DC branch current. Indicates the power converter index. This represents a collection of power converters. Indicates the first Active power on the AC side of the power converter Indicates the first The active power on the DC side of the power converter. Indicates equivalent loss. This represents the normalized reference power for network loss.

[0038] The normalization function for the number of switching operations includes:

[0039]

[0040] In the formula, This represents the normalized value of the number of switch operations. Indicates the index of operation steps. This indicates the total number of operation steps. Indicates the index of operable switches. Represents the set of operable switches. Indicates the first The switch can be operated during the operation steps. The open and closed states, Indicates the first The switch can be operated during the operation steps. The open and closed states, This indicates the maximum number of operation steps allowed in the operation.

[0041] Furthermore, the constraints include: AC power flow and limit constraint metrics, DC power flow and limit constraints, voltage source converter coupling-capacity-ramp constraints, topology connectivity and radiation constraints, islanded power balance constraints, power flow-switch linkage constraints, operational feasibility and response budget constraints, load and distributed power output and ramping constraints, and load accessibility constraints.

[0042] Furthermore, the AC-side power flow and limit constraints include:

[0043]

[0044]

[0045]

[0046] In the formula, Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the set of AC branches. Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node , Indicates load node and load nodes The branch roads formed Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node The generated active power Indicates load node Required active power Indicates load node The charged state, Indicates the power converter index. Indicates load node The connected power converter assembly Indicates the first Active power on the AC side of the power converter Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node The generated reactive power Indicates load node Required reactive power Indicates the first The reactive power on the AC side of the power converter. Indicates load node voltage, Indicates load node voltage, Indicates the resistance of the AC branch. Indicates the AC branch reactance. Indicates load node The lower limit of voltage amplitude, Indicates load node The upper limit of voltage amplitude, This indicates the apparent power limit of the AC branch. Indicates the operational status of the AC branch;

[0047] DC power flow and limit constraints include:

[0048]

[0049]

[0050] In the formula, Indicates load node voltage, Indicates load node voltage, Indicates the DC branch resistance. Indicates the DC branch current. Indicates load node and load nodes The active power of the DC branch is composed of Indicates load node The lower limit of DC voltage. Indicates load node The upper limit of DC voltage, Indicates the upper limit of the DC branch current. Indicates the status of the DC branch being in operation;

[0051] Voltage source converter coupling-capacity-ramp constraints include:

[0052]

[0053]

[0054]

[0055]

[0056] In the formula, Indicates the first The active power on the DC side of the power converter. Indicates the first The efficiency of the AC-to-DC conversion of the power converter. Indicates the first Active power on the AC side of the power converter Indicates the first The reactive power on the AC side of the power converter. Indicates the first The power converter is currently at its maximum apparent power limit. Indicates the first DC side current of the power converter Indicates the first The upper limit of DC-side current of the power converter. Indicates the first The lower limit of reactive power on the DC side of the power converter. Indicates the first The upper limit of reactive power on the DC side of the power converter. Indicates the first The power converter is at the moment AC-side active power, Indicates the first The power converter is at the moment AC-side active power, Indicates the first The upper limit of the rate of change of active power of the power converter. Indicates the first The power converter is at the moment AC-side reactive power, Indicates the first The power converter is at the moment AC-side reactive power, Indicates the first The upper limit of the rate of change of reactive power of the power converter.

[0057] Topological connectivity and radiation constraints include:

[0058]

[0059]

[0060] In the formula, Represents the set of power supply nodes in an AC power grid. Represents the set of source nodes in an AC power grid. Represents any AC loop in an AC power grid;

[0061] Island power balance constraints include:

[0062]

[0063]

[0064] In the formula, Indicates the power supply index. Indicates a certain isolated island. This indicates that power is available within the isolated island. Indicates the first The active power of a generator. Represents the set of load nodes within an island. Indicates the first The reactive power of a power source Indicates load node The charged state;

[0065] Power flow-switching linkage constraints include:

[0066]

[0067]

[0068] In the formula, Indicates the upper limit of active power of the AC branch. Indicates the upper limit of reactive power in the AC branch. Indicates the upper limit of the DC branch current;

[0069] Operational feasibility and response budget constraints include:

[0070]

[0071]

[0072] In the formula, Indicates the index of operation steps. This indicates the total number of operation steps. Indicates the index of operable switches. Represents the set of operable switches. Indicates the first The switch can be operated during the operation steps. The open and closed states, Indicates the first The switch can be operated during the operation steps. The open and closed states, This indicates the maximum number of operation steps allowed in the operation. This represents the maximum number of operations that can be executed in parallel within each operation step. Indicates operable switch Response weights Indicates operable switch In the Step-by-step operation steps and the first An indicator function for when the open and closed states of the operation steps are the same or different. Indicates operable switch The upper limit of the response value;

[0073] Load and distributed power output and ramping constraints include:

[0074]

[0075] In the formula, Indicates the first The lower limit of active power of a generator. Indicates the first The power supply at the moment active power, Indicates the first The upper limit of active power of a generator. Indicates the first The lower limit of reactive power of a power source. Indicates the first The power supply at the moment reactive power, Indicates the first The upper limit of reactive power of a power source. Indicates the first The upper limit of the rate of change of active power of a power source. Indicates the first The upper limit of the rate of change of reactive power of a power source;

[0076] Load reachability constraints include:

[0077]

[0078] In the formula, Indicates the connection of load nodes With any set of candidate paths for a power source, Indicates a DC or AC branch. Indicates the status of DC or AC branch connection. This represents the set of load nodes.

[0079] The second aspect of the present invention provides an AC / DC distribution network reliability assessment device based on Monte Carlo and improved gray wolf optimization, comprising: a parameter determination module, used to initialize the Monte Carlo simulation clock and the target assessment time window, and to obtain the source and load equipment parameters of the AC / DC distribution network;

[0080] The fault component determination module is used to sample the operating components of the AC / DC distribution network to generate a fault-free operation time and repair time, select the operating component with the minimum fault-free operation time as the fault component, and advance the Monte Carlo analog clock based on the minimum fault-free operation time.

[0081] The topology determination module is used to determine the topology after fault isolation of the faulty component based on a preset fault mode consequence analysis table.

[0082] The fault recovery scheme determination module is used to output a target fault recovery scheme based on the source load device parameters and the topology after fault isolation by using an improved gray wolf optimization algorithm. The improved gray wolf optimization algorithm introduces the initialization of the continuous intermediate state position of the operable switch by the improved Tent chaotic mapping, the topology feasibility repair after binarization of the continuous intermediate state position of the operable switch, and the position update strategy based on the Lévy flight and adaptive disturbance mechanism.

[0083] The indicator statistics module is used to determine reliability evaluation indicators based on the target fault recovery scheme and advance the Monte Carlo analog clock according to the repair time of the faulty component.

[0084] The indicator output module is used to output a reliability assessment indicator if the Monte Carlo simulation clock reaches the target evaluation time window.

[0085] As can be seen from the above technical solutions, the present invention has the following advantages:

[0086] The above-mentioned solution of the present invention provides a reliability assessment method for AC / DC distribution networks based on Monte Carlo and improved Grey Wolf optimization, including: initializing the Monte Carlo simulation clock and the target assessment time window, and obtaining the source and load equipment parameters of the AC / DC distribution network; sampling the operating components of the AC / DC distribution network to generate a fault-free operation time and a repair time, selecting the operating component with the minimum fault-free operation time as the faulty component, and advancing the Monte Carlo simulation clock based on the minimum fault-free operation time; determining the topology after fault isolation of the faulty component according to a preset fault mode consequence analysis table; outputting a target fault recovery scheme through the improved Grey Wolf optimization algorithm based on the source and load equipment parameters and the topology after fault isolation, wherein the improved Grey Wolf optimization algorithm introduces the initialization of the continuous intermediate state positions of operable switches by improved Tent chaotic mapping, the topology feasibility repair after binarization of the continuous intermediate state positions of operable switches, and a position update strategy based on Lévy flight and adaptive disturbance mechanism; determining the reliability assessment index based on the target fault recovery scheme, and advancing the Monte Carlo simulation clock according to the repair time of the faulty component; if the Monte Carlo simulation clock reaches the target assessment time window, then outputting the reliability assessment index. Based on the above scheme, by improving the Grey Wolf optimization algorithm to avoid premature convergence and initialization bias, the global search capability and convergence stability of the algorithm in solving high-dimensional discrete combinatorial optimization problems are significantly improved. By deeply combining sequential Monte Carlo simulation with the improved Grey Wolf optimization algorithm, an event-driven and collaborative computing evaluation framework is constructed, which effectively achieves a balance between accuracy and efficiency in the reliability evaluation of AC / DC hybrid distribution networks. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0088] Figure 1 This is a flowchart illustrating the steps of an AC / DC distribution network reliability assessment method based on Monte Carlo and improved gray wolf optimization, as provided in Embodiment 1 of the present invention.

[0089] Figure 2 This is a flowchart illustrating the improved gray wolf optimization algorithm provided in Embodiment 1 of the present invention;

[0090] Figure 3 This is a structural block diagram of an AC / DC distribution network reliability assessment device based on Monte Carlo and improved gray wolf optimization, provided in Embodiment 2 of the present invention. Detailed Implementation

[0091] This invention provides a method and apparatus for reliability assessment of AC / DC distribution networks based on Monte Carlo and improved gray wolf optimization, which addresses the technical problem that existing AC / DC hybrid distribution network reliability assessment methods struggle to balance accuracy and efficiency.

[0092] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0093] Please see Figure 1 The present invention provides a reliability assessment method for AC / DC distribution networks based on Monte Carlo and improved gray wolf optimization, comprising:

[0094] Step 101: Initialize the Monte Carlo simulation clock and target evaluation time window, and obtain the source and load equipment parameters of the AC / DC distribution network.

[0095] The Monte Carlo simulation clock refers to the virtual clock used in Monte Carlo simulations to record the simulation process and drive the timeline forward; its value can be understood as the "current moment" of the simulation.

[0096] The target assessment time window refers to the simulation time period range set for the reliability assessment.

[0097] Source and load equipment parameters refer to parameters that describe the operating attributes of AC / DC distribution networks. These parameters can be obtained based on simulation needs, and this embodiment does not impose any limitations. For example, they may include source and load sequences and equipment parameters. Exemplarily, the source and load sequence (source and load time series model) includes, but is not limited to, hourly resolution load / reactive power curves and DG (distributed generation) output curves, completing time axis alignment, missing data filling, and anomaly truncation. Exemplarily, equipment parameters include, but are not limited to: ① AC / DC network topology parameters, such as AC / DC buses, lines / cables, transformers, tie switches and their connection relationships, branch impedance / resistance, rated current / capacity, upper and lower limits of bus voltage, and protection settings; ② Component reliability parameters, such as failure rates and repair rates of lines, transformers, VSCs, circuit breakers, etc.; ③ VSC (power converter) capabilities and execution constraints, such as the rated capacity / current limit of each VSC, the default available control set (…). / / , Indicates active power. Indicates reactive power. Indicates the DC side voltage. Indicates AC voltage. This indicates voltage phase angle, current limiting, speed limiting, etc.

[0098] It should be noted that, in order to align with the event process of the distribution network, this embodiment uses an event-driven analog clock based on sequential Monte Carlo simulation, and initializes and sets the Monte Carlo simulation clock. With the target evaluation window And prepare the source load device parameters.

[0099] Understandably, an hourly index T can be extracted with equal probability from the discrete hourly axis throughout the year, and the load, wind power, and photovoltaic output values ​​for that hour can be directly read from the curve library of last year's T. In this way, the mapping of "time → source load level" can be completed in one go. After reading, the basic operating scenario of this simulation is locked, providing a consistent source load background for subsequent fault injection and topology changes.

[0100] Step 102: Sample the operating components of the AC / DC distribution network to generate a fault-free operation time and repair time, select the operating component with the minimum fault-free operation time as the fault component, and advance the Monte Carlo analog clock based on the minimum fault-free operation time.

[0101] In-operation components refer to components currently in operation in the AC / DC distribution network, which can act as fault triggers. Time To Failure (TTF) refers to the duration of continuous operation of a component. Recovery Time (FFR) refers to the time required for operation to return to normal after a component fails. Faulty component refers to a component that has failed.

[0102] It should be noted that for any sampled operating component (e.g., AC / DC lines, transformers, VSCs, and circuit breakers), a first-time fault-free operating time (TTF) and repair time (TTR) are generated based on its failure rate and repair rate. Specifically:

[0103] The TTF of a component can be calculated using an exponential distribution:

[0104]

[0105] In the formula, Indicator element One trouble-free operation time, Indicator element failure rate, Indicates that it conforms to the interval Uniform distribution on Represents a uniformly random number between 0 and 1;

[0106] Similarly, the TTR of this component can be calculated using an exponential distribution:

[0107]

[0108] In the formula, Indicator element Repair time, Indicates the component repair rate. Indicates that it conforms to the interval Uniform distribution on Represents a uniformly random number between 0 and 1;

[0109] The minimum value among all TTFs is determined as the next fault arrival time, and the Monte Carlo analog clock is advanced to that moment. Identify the component that triggered the fault and record the trigger component key and the time of the event.

[0110] Step 103: Determine the fault isolation topology of the faulty component based on the preset fault mode consequence analysis table.

[0111] A Failure Mode and Effects Analysis (FMEA) table refers to a table that, based on the source and load equipment parameters of an AC / DC distribution network, pre-analyzes the possible failure modes, required failure isolation strategies, and the resulting topology for each component of the AC / DC distribution network. For example, the FMEA table pre-generates entries for each component according to the rule of "failure → protection isolation → post-topology," including but not limited to recording "failure mode, failure isolation time, repair time, impact (e.g., failure impact, isolation impact), post-failure topology, and affected load set." Given the hybrid AC / DC characteristics, the FMEA table after adding a VSC (Vehicle Switched Controller) must include a VSC failure outage entry. When the power converter fails or is disconnected by protection, based on the post-failure topology and power transfer accessibility, the table clearly records the isolated network structure and affected load set to support subsequent recovery optimization and reliability index statistics.

[0112] Post-fault isolation topology refers to the distribution network topology formed after performing a sequence of isolation actions on faulty components.

[0113] It should be noted that by querying the FMEA table using the triggered faulty component as the key, isolation parameters such as isolation time and isolation action sequence (e.g., disconnecting the faulty component, segmenting / closing tie switches, freezing unavailable equipment status, etc.) are obtained. These isolation parameters are then applied to the current AC / DC distribution network to perform the isolation operation, resulting in the topology after fault isolation. Understandably, by parsing the topology after fault isolation, information such as islanding formation and equipment connection relationships can be obtained, providing a data foundation including target sets and initial boundaries for subsequent power flow verification, load shedding, and recovery optimization.

[0114] Step 104: Based on the source and load device parameters and the topology after fault isolation, output the target fault recovery scheme through the improved Grey Wolf optimization algorithm.

[0115] The target fault recovery scheme refers to the scheme of restoring power supply by controlling the opening and closing of operable switches to adjust their opening and closing states based on the topology after fault isolation.

[0116] It should be noted that this embodiment improves the Grey Wolf optimization algorithm to form an improved Grey Wolf optimization algorithm, and then determines the target fault recovery scheme based on the improved Grey Wolf optimization algorithm.

[0117] In one specific embodiment of this example, step 104 includes the following sub-steps:

[0118] S1. Set the basic solution parameters of the algorithm;

[0119] S2. Taking the fault recovery scheme as the individual gray wolf, initialize the gray wolf population and the current iteration number based on the initialization of the continuous intermediate state positions of the operable switch by the improved Tent chaotic mapping and the topological feasibility repair of the binarized continuous intermediate state positions of the operable switch.

[0120] S3. For each individual gray wolf in the gray wolf population, calculate the fitness value with constraint-based penalty terms using source load device parameters and topology after fault isolation.

[0121] S4. Compare the fitness values ​​to determine the three-superior gray wolf individuals. After updating the position of the gray wolf individuals based on the Lévy flight and adaptive perturbation mechanism, perform topological feasibility repair after binarizing the continuous intermediate position of the operable switch, calculate the new fitness value for greedy retention, determine the updated gray wolf population, and update the current iteration number.

[0122] S5. Determine whether the iteration stopping condition is met based on the current iteration number and the minimum fitness value;

[0123] S6. When the iteration stopping condition is not met, jump to the step of comparing each fitness value to determine the three best gray wolf individuals until the iteration stopping condition is met, and output the gray wolf individual with the smallest fitness value as the target fault recovery scheme.

[0124] It should be noted that the traditional Grey Wolf Optimization (GWO) uses a combination of three optimal individuals as guidance and adaptive coefficients to simulate the "encirclement-hunt-attack" swarm hunting mechanism, with a linearly decreasing factor. Under the influence of [the algorithm], it automatically switches between global exploration and local development. In this embodiment, the improved Grey Wolf optimization algorithm has made several key improvements compared to the traditional Grey Wolf optimization algorithm, including the introduction of improved Tent chaotic mapping for the initialization of the continuous intermediate state positions of operable switches, topological feasibility repair after binarization of the continuous intermediate state positions of operable switches, and a position update strategy based on Lévy flight and adaptive perturbation mechanism; in specific implementation, such as Figure 2 As shown:

[0125] 1) Initialize and set the basic solution parameters of the algorithm, such as population size. Maximum number of iterations Binarization threshold Steepness Disturbance scale Penalty Factor wait;

[0126] 2) Generate the initial population location of gray wolves:

[0127] ① The initial distribution of the gray wolf population directly affects the subsequent convergence speed and whether it is premature. If a simple uniform random initialization is used, data points are prone to gaps / clustering in high-dimensional space, leading to uneven early search coverage. Therefore, this embodiment uses an improved Tent chaotic mapping. A sequence with good ergodicity and more uniform distribution is generated, and this sequence is mapped dimension-by-dimensionally to the continuous intermediate positions of individual gray wolves. The piecewise linearity of Tent makes it highly sensitive to initial values, and with the help of perturbation, periodic points can be avoided, thus preserving diversity and facilitating reproducibility. Based on this, the generation-mapping process corresponding to the operation switch of the improved Tent chaotic mapping for initializing the continuous intermediate positions can be described as follows:

[0128]

[0129] In the formula, Indicates the first Chaotic variables in a sub-chaotic mapping Indicates the first Chaotic variables in a sub-chaotic mapping Indicates the first Perturbation of sub-chaotic mapping Indicates operable switch Chaotic variables, Indicates operable switch The position of the continuous intermediate state in the 0th iteration;

[0130] ② To focus the solution on the executable operations of recovery / reconstruction, this embodiment only considers the opening / closing of operable switches as the optimization object; the continuous settings (VSC / DG / energy storage, etc.) are automatically obtained by a fixed control strategy during the evaluation stage. This has three advantages: a) the decision dimensions are significantly reduced and convergence is faster; b) each dimension corresponds to an actual achievable switch action, avoiding pseudo-states of partial opening or closing; c) it facilitates the direct generation of subsequent operation commands such as connections to be closed, loops to be opened, and operation sequences; therefore, the following purely binary decision vector is defined:

[0131]

[0132] In the formula, This refers to an individual gray wolf. Indicates the number of operable switches. Indicates the first The on / off state of an operable switch. Indicates transpose. Indicates operable switch (Opening and closing status of sections / connections / reclosing, etc.);

[0133] The Grey Wolf algorithm essentially updates positions in a continuous space. To adapt it to 0 / 1 decisions, this embodiment introduces a continuous intermediate position for each operable switch. First, iterate using GWO in a continuous space, then... The mapping is to the probability of taking 0 / 1. The logistic function transforms the distance from 0 / 1 into the probability of taking 1. In the early stages, using a random threshold can enhance diversity and help escape local conditions. In the later stages, increasing the threshold or steepness can improve the probability. This helps to make the solution more stable and closer to the definite 0 / 1; the mapping of the continuous intermediate state positions of the operable switch is as follows:

[0134]

[0135] In the formula, Indicates operable switch The probability value, This represents an exponential function with the natural constant as its base. This represents the binarization threshold (default 0.5, which can be increased generation by generation). Indicates steepness. Indicates operable switch The continuous intermediate state positions, Indicates operable switch The open and closed states, Indicates an indicator function, Indicates that it conforms to the interval Uniform distribution on Indicates a Uniformly distributed random numbers within an interval;

[0136] ③Topology feasibility repair (radiation / connectivity + switch linkage)

[0137] Direct binarization Violations of radiation / connectivity or inconsistencies with power flow-switch linkage (e.g., loop formation, power supply interruption, disconnected branches still carrying power) can lead to numerous infeasibility issues during the evaluation phase. To reduce penalty overhead and improve search efficiency, this embodiment introduces a minimal modification feasibility fix after each binarization. Only then does the fitness assessment begin; the specific process is recorded as follows: , To minimize the feasibility of topology modifications, for example: if a loop occurs, disconnect the loop with the lowest cost to ensure radial connectivity; if a disconnection occurs, prioritize closing critical connections to ensure reachability; and synchronize power flow-switching linkage (such as setting branch power to zero) to prevent disconnected branches from still carrying power. It can be understood that a "critical connection" can be defined as: if losing this line causes a significant power flow interruption, affecting the recovery of a large area of ​​load; if restoring this line can significantly improve system connectivity, recovery speed, and power flow; if this line is given a high recovery priority in the recovery strategy, and its restoration plays a crucial role in the recovery of other systems; if this line carries a large current or connects critical nodes in the system (such as major substations or core load areas); then it can be considered a critical connection.

[0138] Therefore, for the improved Tent chaotic map initialization, the first iteration can be obtained after binarization with minimal overhead. And initialize the current iteration count. ;

[0139] 3) Calculate the fitness value of all individual gray wolves.

[0140] To transform the multi-objective (prioritizing power restoration—reducing network losses—controlling operations) into a single-value driven indicator that can be used for swarm intelligence search, this embodiment constructs a fitness value with a constraint-based penalty for breach of contract:

[0141] ① Objectives: To reflect the scheduling preference of restoring power first, then reducing losses, and finally controlling operations, a normalized weighted sum of the three objectives is used, and weights are applied. Reflecting engineering preferences, including:

[0142] a) The recovery effectiveness is measured by the percentage of unrecovered load. The constructed normalization function for unrecovered load includes:

[0143]

[0144] In the formula, This indicates that the load normalization value has not been restored. Indicates load node , Represents the set of load nodes. Indicates load node Importance weight (power supply priority can be adjusted). Indicates load node Rated active power, Indicates load node The energized state (1 represents the load node) Energized, 0 indicates load node (Still without power); the smaller the normalized value of the unrestored load, the more weighted load is restored within a given time window, and the more critical users can be prioritized for power restoration.

[0145] b) While ensuring power restoration, the system network loss of integrated AC / DC operation should be considered. The conversion losses of AC and DC lines and converters should be combined and standardized to construct a network loss normalization function, including:

[0146]

[0147] In the formula, This represents the normalized value of network loss. Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the set of AC branches. Indicates the resistance of the AC branch. Indicates the AC branch current. Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the collection of DC branches. Indicates the DC branch resistance. Indicates the DC branch current. Indicates the power converter index. This represents a collection of power converters. Indicates the first Active power on the AC side of the power converter Indicates the first The active power on the DC side of the power converter. Indicates equivalent loss. This represents the normalized reference power for network loss (which can be either the system reference or the total active power of the load); the network loss normalization function ensures comparability between networks of different sizes and in different scenarios;

[0148] c) To suppress unnecessary operations, the number of switching operations is used as a third objective, and the number is counted step by step according to the recovery sequence. The normalization function for the number of switching operations includes:

[0149]

[0150] In the formula, This represents the normalized value of the number of switch operations. Indicates the index of operation steps. This indicates the total number of operation steps. Indicates the index of operable switches. Represents the set of operable switches. Indicates the first The switch can be operated during the operation steps. Open and closed states ( 1 indicates an operable switch. "On" indicates that the switch is operable (0). closure), Indicates the first The switch can be operated during the operation steps. The open and closed states, Indicates the maximum number of operation steps allowed in the operation;

[0151] ② Constraint violation penalties: A squared penalty is applied to violations of constraints such as voltage / current, radiation / connectivity, power balance, and operational budget. Specifically, the constraints include: AC power flow and limit constraint measurement, DC power flow and limit constraint, voltage source converter coupling-capacity-ramp constraint, topology connectivity and radiation constraint, islanded power balance constraint, power flow-switch linkage constraint, operational feasibility and response budget constraint, load and distributed power output and ramping constraint, and load accessibility constraint.

[0152] a) On the AC side, the DistFlow approximation is used for power balance and voltage calculation. The AC power flow and limit constraints are constructed as follows:

[0153]

[0154]

[0155]

[0156] In the formula, Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the set of AC branches. Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node , Indicates load node and load nodes The branch roads formed Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node The generated active power (including DG / voltage regulating equipment). Indicates load node Required active power Indicates load node The charged state, Indicates the power converter index. Indicates load node The connected power converter assembly Indicates the first Active power on the AC side of the power converter Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node The reactive power generated (including DG / voltage regulating equipment). Indicates load node Required reactive power Indicates the first The reactive power on the AC side of the power converter. Indicates load node voltage, Indicates load node voltage, Indicates the resistance of the AC branch. Indicates the AC branch reactance. Indicates load node The lower limit of voltage amplitude, Indicates load node The upper limit of voltage amplitude, This indicates the apparent power limit of the AC branch. Indicates the operational status of the AC branch;

[0157] b) The DC side is modeled as a resistive network, satisfying Ohm's law and voltage / current limits. The DC side power flow and limit constraints are constructed as follows:

[0158]

[0159]

[0160] In the formula, Indicates load node voltage, Indicates load node voltage, Indicates the DC branch resistance. Indicates the DC branch current. Indicates load node and load nodes The active power of the DC branch is composed of Indicates load node The lower limit of DC voltage. Indicates load node The upper limit of DC voltage, Indicates the upper limit of the DC branch current. Indicates the status of the DC branch being in operation;

[0161] c) The voltage source converter (VSC) connects to both AC and DC sides and is subject to capacity and efficiency coupling constraints. The coupling-capacity-ramp constraints of the voltage source converter include:

[0162]

[0163]

[0164]

[0165]

[0166] In the formula, Indicates the first The active power on the DC side of the power converter. Indicates the first The efficiency of the AC-to-DC conversion of the power converter. Indicates the first Active power on the AC side of the power converter Indicates the first The reactive power on the AC side of the power converter. Indicates the first The power converter is currently at its maximum apparent power limit. Indicates the first DC side current of the power converter Indicates the first The upper limit of DC-side current of the power converter. Indicates the first The lower limit of reactive power on the DC side of the power converter. Indicates the first The upper limit of reactive power on the DC side of the power converter. Indicates the first The power converter is at the moment AC-side active power, Indicates the first The power converter is at the moment AC-side active power, Indicates the first The upper limit of the rate of change of active power of the power converter. Indicates the first The power converter is at the moment AC-side reactive power, Indicates the first The power converter is at the moment AC-side reactive power, Indicates the first The upper limit of the rate of change of reactive power of the power converter.

[0167] d) The AC side requires a radiating structure, and the DC side requires connectivity with the option to set an upper limit for weak loops. Therefore, it can be represented using tree constraints and loop elimination. Constructing topological connectivity and radiating constraints includes:

[0168]

[0169]

[0170] In the formula, Indicates load node and load nodes The branch roads formed The set of AC branches is represented by the following representation: Indicates the operational status of the AC branch circuit. Represents the set of power supply nodes in an AC power grid. This represents the set of source nodes (such as generator nodes) in an AC power grid. This represents any AC loop in an AC power grid. A loop is a closed path consisting of a series of branches.

[0171] e) If the partitioning forms AC / DC islands, each island must satisfy a power balancing strategy. The power balancing constraints for each island include:

[0172]

[0173]

[0174] In the formula, Indicates the power supply index. Indicates a certain isolated island. This indicates that power is available within the isolated island. Indicates the first The active power of a generator. Represents the set of load nodes within an island. Indicates load node , Indicates load node Required active power Indicates the first The reactive power of a power source Indicates load node Required reactive power Indicates load node The charged state;

[0175] f) To avoid non-physical issues such as disconnected lines still carrying power, a linkage constraint between switch states and power flow is adopted. The power flow-switch linkage constraint includes:

[0176]

[0177]

[0178] In the formula, Indicates the upper limit of active power of the AC branch. Indicates the operational status of the AC branch circuit. Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates the upper limit of reactive power in the AC branch. Indicates the upper limit of the DC branch current. Indicates the status of the DC branch being in operation. Indicates the DC branch current;

[0179] g) Considering scheduling and on-site conditions, limit the number of operation steps, parallelism, and stress on critical equipment, and construct operational feasibility and response budget constraints, including:

[0180]

[0181]

[0182] In the formula, Indicates the index of operation steps. This indicates the total number of operation steps. Indicates the index of operable switches. Represents the set of operable switches. Indicates the first The switch can be operated during the operation steps. The open and closed states, Indicates the first The switch can be operated during the operation steps. The open and closed states, This indicates the maximum number of operation steps allowed in the operation. This represents the maximum number of operations that can be executed in parallel within each operation step. Indicates operable switch Response weights Indicates operable switch In the Step-by-step operation steps and the first An indicator function for when the open and closed states of the operation steps are the same or different (the function value is 1 when the states are different, and 0 otherwise). Indicates operable switch The upper limit of the response value;

[0183] h) For controllable power sources and energy storage, limit the output range and ramp rate to improve the feasibility of the solution. The constraints on load and distributed generation (DG / energy storage) output and ramp rate include:

[0184]

[0185] In the formula, Indicates the first The lower limit of active power of a generator. Indicates the first The power supply at the moment active power, Indicates the first The upper limit of active power of a generator. Indicates the first The lower limit of reactive power of a power source. Indicates the first The power supply at the moment reactive power, Indicates the first The upper limit of reactive power of a power source. Indicates the first The upper limit of the rate of change of active power of a power source. Indicates the first The upper limit of the rate of change of reactive power of a power source;

[0186] i) Loads determined to be restored must be connected to either source side on the AC / DC graph (cross-domain access via VSC is allowed), therefore, load reachability constraints are constructed as follows:

[0187]

[0188] In the formula, Indicates load node The charged state, Indicates the index of the candidate path composed of branches. Indicates the connection of load nodes With any set of candidate paths for a power source, Indicates a DC or AC branch. Indicates the status of DC or AC branch connection. Represents the set of load nodes;

[0189] 4) Fitness assessment: Given a specific fault recovery plan →Generate corresponding topology→Internally, quickly determine continuous quantities and power flow according to a preset fixed control strategy→Calculate target and default→Obtain fitness value:

[0190]

[0191] In the formula, This refers to an individual gray wolf. Indicates the fitness value. This represents the normalized function for unrestored load. This represents the network loss normalization function. This represents a function that normalizes the number of switching operations. This represents the weights of the unrecovered load normalization function. The weights represent the network loss normalization function. The weights of the normalization function representing the number of switching operations; Indicates the first Measurement of penalties for breach of constraints Indicates the first The penalty factor for each constraint (which can be adaptively adjusted according to the current feasibility rate, allowing the search to gradually transition from early lenient exploration to fine development of the feasible boundary). Indicates the constraint index;

[0192] Understandably, the three objectives are weighted and synthesized into a single optimization index, which serves as the fitness score for improving the Grey Wolf optimization algorithm, in order to implement the principle of restoring power first, then reducing losses, and finally controlling operations. Take the larger value (e.g., 0.8). The next best (e.g., 0.15) When the value is relatively small (e.g., 0.05), the weights of the three normalization functions decrease sequentially. Through the above normalization process, the differences in the dimensions and magnitudes of the three objectives are eliminated, which can significantly improve the convergence stability and result comparability of the improved Grey Wolf optimization algorithm under different network sizes and diverse scenarios. The fixed control strategy can be understood as, for a specific topology, pre-setting control rules for regulating continuous variables (such as VSC output and DG power) to avoid the randomness of the strategy and ensure the consistency of fitness evaluation results.

[0193] 5) Update the location of the gray wolves

[0194] ① To achieve a dynamic balance between global exploration followed by local development in swarm search, the Grey Wolf algorithm introduces two sets of control coefficients, namely position movement control coefficients. Position control coefficient and the decaying scalar that decreases with the number of iterations ,in, The position movement control coefficient decreases linearly from 2 to 0, becoming a scalar. In the early stages, the size is larger, facilitating long-distance jumps to escape local situations; in the later stages, the size is smaller, facilitating encirclement and convergence. The random numbers are uniformly distributed, and random perturbation is used to prevent the group from moving uniformly in the same direction. Its mathematical expression is as follows:

[0195]

[0196] ② After giving the control coefficients, it is necessary to define the individual's relative position and orientation to the prey in order to generate an approach / passing encirclement movement; for this purpose, first use The prey's location is randomly scaled to obtain a jittered perceived location, and the distance required for the gray wolf to capture the prey is calculated based on this. Then use By applying a drag to this distance, a position update is completed; thus, the stride length adaptively scales with the distance between the individual and the prey: a larger distance results in a larger stride, which is beneficial for exploration, while a smaller distance results in a smaller stride, which is beneficial for detailed exploration; in the solution of this invention, This represents the individual position of the gray wolf, which corresponds to the continuous intermediate state position of the operable switch. After updating, it will fall back to the actual switch state through binarization and feasibility repair. The calculation formula is:

[0197]

[0198] In the formula, Indicates the location of an individual gray wolf. Indicates the location of the prey (approximated by elites);

[0199] ③ Aggregation guidance of three-excellent individuals

[0200] A single elite solution may deviate from the global optimum due to chance. To improve stability and reduce the probability of getting trapped in local minima, a contemporary triple-elite gray wolf individual is adopted. Joint guidance: Calculate three candidate positions based on the three optimizations. Then, taking its center of gravity as a new reference point, the effect of doing so is: in the early stages ( The probability is relatively high. Indicates the first The positional movement control coefficient of each individual gray wolf can generate divergent exploration outside the center of gravity; in the later stages ( Then, it contracts and approximates within the region enclosed by the three optimizations, achieving robust convergence. Its expression is as follows:

[0201]

[0202] In the formula, Indicates the location of the three superior gray wolves. This indicates the position of the individual gray wolf calculated from the first guiding direction. This indicates the position of the individual gray wolf calculated from the second guiding direction. This indicates the position of the individual gray wolf calculated from the third guiding direction. Indicates the first The three priorities guiding this iteration This represents the positional movement control coefficients for the 1st, 2nd, and 3rd individual gray wolves. This represents the position control coefficients of the 1st, 2nd, and 3rd individual gray wolves;

[0203] ④Lévy flight disturbance

[0204] Standard GWO is prone to problems such as excessively small step size and getting stuck in local optima in the later stages. To enhance the ability to occasionally jump far, this embodiment includes a step size adjustment during the exploration phase. The larger step size (as opposed to a larger step size) is the Lévy heavy-tailed step size used for position updates. Most of these steps are very small, while a few are extremely large. This approach maintains fine-grained convergence without compromising the convergence, while increasing the probability of escaping local bottlenecks by traversing disadvantageous basins with a small probability. In implementation, Mantegna sampling is used, with parameters... The thickness of the tail is determined by the following formula: In engineering, a value of 1.5 is often used to balance stability and long jump.

[0205]

[0206] In the formula, This indicates the step size of Lévy's flight. Represents the Lévy distribution. The exponential parameter of the Lévy distribution is represented. Represents a normally distributed variable (implemented using the Mantegna method);

[0207] ⑤ Segmented update based on three optimizations (with Lévy perturbation)

[0208] Position updates follow the approach of three-optimal aggregation: first, find the three-optimal guiding center of gravity. As the convergence base point. Then according to Size segmentation processing: when During the exploration phase, Lévy perturbations are added near the center of gravity; the perturbations are adaptively scaled according to the distance between the individual and the third best (larger distance → larger step size, smaller distance → smaller step size), and a coefficient is used to... Gradual decay across generations ensures a smooth transition from bold exploration to robust approximation; when During the development phase, the centroid is directly taken, emphasizing shrinking the enclosing area and improving convergence speed. The update rules are as follows:

[0209]

[0210] In the formula, Indicates the first The three priorities guiding this iteration This indicates the position of the individual gray wolf calculated from the first guiding direction. This indicates the position of the individual gray wolf calculated from the second guiding direction. This indicates the position of the individual gray wolf calculated from the third guiding direction. Indicates the operable switch at the first The position vector of consecutive intermediate states in each iteration. The perturbation scale (e.g., 0.01, which may decrease algebraically or be proportional to) Proportional Adaptation) This indicates the step size of Lévy's flight. A scalar representing the position movement control coefficient. Indicates the location of an individual gray wolf;

[0211] The aforementioned binarization and topology feasibility repair process will be executed immediately after the update;

[0212] 6) Greedy Retention

[0213] To ensure that the intergenerational optimum is monotonically non-inferior and to suppress backsliding caused by random perturbations, this embodiment employs greedy retention (survival of the fittest): replacement only occurs when the penalized fitness of the new solution is not higher than that of the current solution; if they are equal, the new solution can be either selected or preferentially retained to maintain diversity. Used in conjunction with binarization and repair, greedy retention ensures stable convergence while avoiding significant fitness degradation due to accidental large-step perturbations. The criteria are as follows:

[0214]

[0215] In the formula, Indicates the first The gray wolf individual in the next iteration. Indicates the first The gray wolf individual in the next iteration. This represents the fitness value calculated after updating the individual gray wolf's position. Indicates the first The fitness value of the gray wolf individual in the next iteration;

[0216] 7) Iteration stops

[0217] After each population update, update the current iteration count. Iteration stopping conditions include the current iteration count reaching the maximum iteration count or the population's minimum fitness value converging (improvement below a threshold). When the iteration stopping condition is met, output the gray wolf individual with the minimum fitness value. (Connections that should be closed, loops that should be broken, and operation sequences when necessary) are used as the target fault recovery scheme; when the iteration stopping condition is not met, the step of updating the gray wolf position is executed until the iteration stopping condition is met, and the gray wolf individual with the minimum fitness value is output as the target fault recovery scheme.

[0218] Step 105: Determine reliability assessment indicators based on the target fault recovery plan, and advance the Monte Carlo analog clock according to the repair time of the faulty component.

[0219] It should be noted that after determining the target fault recovery plan and implementing the repair, the reliability assessment metrics are updated, the repair time (TTR) of the faulty component is determined, and the clock is advanced. .

[0220] Step 106: If the Monte Carlo simulation clock reaches the target evaluation time window, output the reliability evaluation index.

[0221] It also includes: if the Monte Carlo simulation clock has not reached the target evaluation time window, update the fault-free operation time of the faulty component, and jump to the step of selecting the operating component with the minimum fault-free operation time as the faulty component, until the Monte Carlo simulation clock reaches the target evaluation time window, and then output the reliability evaluation index.

[0222] It should be noted that, if Then, the reliability assessment index is summarized and output. If the Monte Carlo simulation clock does not reach the target assessment time window, since no new fault is triggered during the repair, a new TTF is extracted for the component after the repair is completed. Other operating components continue to retain their respective remaining TTF, and the faulty component of the next fault event is selected until the simulation reaches the target assessment time window.

[0223] In one specific embodiment of this example, the reliability assessment metrics include in-sample load-side statistical assessment metrics and cross-sample system-level statistical assessment metrics. In-sample load-side statistical assessment metrics include the number of power outages at load nodes, the duration of power outages at load nodes, sample-level energy not supplied (ENS), and sample-level expected power not supplied (ENS). The system-level statistical evaluation indicators across samples include the system-level expected energy outages (EENS), system-level expected power outages (EPNS), system average outage frequency index (SAIFI), system average outage duration index (SAIDI), user average outage duration index (CAIDI), average power availability rate (ASAI), and subset (feeder / area / user group) indicators.

[0224] Specifically, the number of power outages at load nodes includes:

[0225]

[0226] In the formula, Indicates the index of fault event samples. Indicates the index of operation steps. This indicates the total number of operation steps. Indicates the first After the operation steps are completed, the load node Power-on determination (1 = charged, 0 = de-energized). Indicates an indicator function, Indicates load node The set of all power outage sections;

[0227] Specifically, the power outage duration at load nodes includes:

[0228]

[0229] In the formula, Indicates load node The duration of the power outage, Indicates the first The timestamp of the power outage. Indicates the first The timestamp of the next power restoration;

[0230] Specifically, sample-level unpowered energy ,include:

[0231]

[0232] In the formula, Indicates the load nodes within the power outage section The required power or the average demand over a given period;

[0233] Specifically, sample-level expected unsupplied power ,include:

[0234]

[0235] In the formula, Indicates the length of the evaluation window for the fault event sample;

[0236] Specifically, corresponding to the "priority power restoration" goal mentioned earlier, the recovery rate within the sample is given; the sample-level recovery rate is also provided. ,include:

[0237]

[0238] In the formula, Indicates load node Importance weighting is represented by the following: The load node at the final moment of the fault event sample Power-on determination;

[0239] Specifically, the weighted expectation of the sample size, and the system-level expectation of unpowered energy. and system-level expected unpowered power ,include:

[0240]

[0241]

[0242] In the formula, Indicates the sample weights of fault events (when weighted equally) ), This represents the total number of fault event samples. ;

[0243] Specifically, the system average outage frequency index (SAIFI), the system average outage duration index (SAIDI), the user average outage duration index (CAIDI), and the average power availability index (ASAI) include:

[0244]

[0245] In the formula, This represents a small constant that avoids a denominator of zero;

[0246] Specifically, it allows for refined assessment of specific feeders, areas, or key user groups, enabling the selection of arbitrary subsets from the load set. Statistical analysis is performed. The formula for calculating its subset index is as follows, including:

[0247]

[0248] In the formula, Indicates the first Duration of each power outage.

[0249] In this embodiment of the invention, by improving the Grey Wolf optimization algorithm to avoid premature convergence and initialization bias, the global search capability and convergence stability of the algorithm in solving high-dimensional discrete combinatorial optimization problems are significantly improved. By deeply combining sequential Monte Carlo simulation with the improved Grey Wolf optimization algorithm, an event-driven and collaborative computing evaluation framework is constructed, which effectively achieves a balance between accuracy and efficiency in the reliability evaluation of AC / DC hybrid distribution networks.

[0250] Please see Figure 3 Embodiment 2 of the present invention provides an AC / DC distribution network reliability assessment device based on Monte Carlo and improved gray wolf optimization, comprising:

[0251] The parameter determination module 301 is used to initialize the Monte Carlo simulation clock and the target evaluation time window, and to obtain the source and load equipment parameters of the AC / DC distribution network.

[0252] The fault component determination module 302 is used to sample the operating components of the AC / DC distribution network to generate a fault-free operation time and repair time, select the operating component with the minimum fault-free operation time as the fault component, and advance the Monte Carlo analog clock based on the minimum fault-free operation time.

[0253] The topology determination module 303 is used to determine the topology after fault isolation of the faulty component based on a preset fault mode consequence analysis table.

[0254] The fault recovery scheme determination module 304 is used to output the target fault recovery scheme based on the source load device parameters and the topology after fault isolation by using the improved gray wolf optimization algorithm. The improved gray wolf optimization algorithm introduces the initialization of the continuous intermediate state position of the operable switch by the improved Tent chaotic mapping, the topology feasibility repair after binarization of the continuous intermediate state position of the operable switch, and the position update strategy based on the Lévy flight and adaptive disturbance mechanism.

[0255] The indicator statistics module 305 is used to determine reliability assessment indicators based on the target fault recovery plan and advance the Monte Carlo analog clock according to the repair time of the faulty component.

[0256] The indicator output module 306 is used to output a reliability assessment indicator if the Monte Carlo simulation clock reaches the target evaluation time window.

[0257] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for example, the division of units is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms. The modules described as separate components may or may not be physically separate; the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of this embodiment. Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0258] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization, characterized in that, The method comprises the following steps: initializing a Monte Carlo simulation clock and a target evaluation time window, and obtaining source and load equipment parameters of an AC / DC distribution network; sampling a running element of the AC / DC distribution network to generate a first fault-free operation time and a repair time, selecting a running element with a minimum first fault-free operation time as a fault element, and advancing the Monte Carlo simulation clock based on the minimum first fault-free operation time; determining a topology after fault isolation of the fault element according to a preset fault mode consequence analysis table; outputting a target fault recovery scheme by an improved grey wolf optimization algorithm based on the source and load equipment parameters and the topology after fault isolation, wherein the improved grey wolf optimization algorithm introduces an improved Tent chaotic mapping operable switch continuous intermediate state position initialization, a topology feasibility repair after binaryzation of the operable switch continuous intermediate state position, and a position updating strategy based on Lévy flight and an adaptive disturbance mechanism; determining a reliability evaluation index based on the target fault recovery scheme, and advancing the Monte Carlo simulation clock according to the repair time of the fault element; if the Monte Carlo simulation clock reaches the target evaluation time window, outputting the reliability evaluation index.

2. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 1, characterized in that, The step of outputting the target fault recovery scheme by the improved grey wolf optimization algorithm based on the source and load equipment parameters and the topology after fault isolation comprises the following steps: setting basic solving parameters of the algorithm; initializing a grey wolf population based on the improved Tent chaotic mapping operable switch continuous intermediate state position initialization and the topology feasibility repair after binaryzation of the operable switch continuous intermediate state position, and initializing a current iteration number with the fault recovery scheme as a grey wolf individual; calculating a fitness value with a constraint condition violation penalty term for each grey wolf individual in the grey wolf population based on the source and load equipment parameters and the topology after fault isolation; determining three optimal grey wolf individuals by comparing the fitness values, updating the position of the grey wolf individual according to the three optimal grey wolf individuals through the position updating strategy based on Lévy flight and the adaptive disturbance mechanism, performing the topology feasibility repair after binaryzation of the operable switch continuous intermediate state position, calculating a new fitness value for greedy reservation, determining an updated grey wolf population, and updating the current iteration number; judging whether an iteration stop condition is met based on the current iteration number and a minimum fitness value; when the iteration stop condition is not met, jumping to the step of determining the three optimal grey wolf individuals by comparing the fitness values, and when the iteration stop condition is met, outputting a grey wolf individual with the minimum fitness value as the target fault recovery scheme. 3.The method of claim 1, wherein, The method further comprises the following steps: if the Monte Carlo simulation clock does not reach the target evaluation time window, updating a first fault-free operation time of the fault element, and jumping to the step of selecting a running element with a minimum first fault-free operation time as a fault element until the Monte Carlo simulation clock reaches the target evaluation time window, and then outputting the reliability evaluation index.

4. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 1 or 2, characterized in that, The process of the improved Tent chaotic mapping operable switch continuous intermediate state position initialization comprises the following steps: wherein represents a chaotic variable of the th chaotic map, represents a chaotic variable of the th chaotic map, represents a perturbation of the th chaotic map, represents a chaotic variable of the operable switch, represents a chaotic variable of the in the continuation of the intermediate state position at the 0th iteration; The process of binaryzation of the operable switch continuous intermediate state position comprises the following steps: In the formula, Indicates operable switch The probability value, This represents an exponential function with the natural constant as its base. Indicates the binarization threshold. Indicates steepness. Indicates operable switch The continuous intermediate state positions, Indicates operable switch The open and closed states, Indicates an indicator function, Indicates that it conforms to the interval Uniform distribution on Indicates a Random numbers that are uniformly distributed across an interval.

5. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 1 or 2, characterized in that, The position updating strategy based on Lévy flight and the adaptive disturbance mechanism comprises the following steps: wherein, denotes the third iteration of the three-optimal guiding barycenter, denotes the first guiding direction calculated gray wolf individual position, denotes the second guiding direction calculated gray wolf individual position, denotes the third guiding direction calculated gray wolf individual position, denotes the third guiding direction calculated gray wolf individual position, denotes the operable switch in the first denotes the continuous intermediate state position vector in the first denotes the perturbation scale, denotes the moving step length of Lévy flight, denotes the scalar of position movement control coefficient, denotes the gray wolf individual position.

6. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 1 or 2, characterized in that, The process of determining the fitness of the improved grey wolf optimization algorithm comprises the following steps: wherein, represents a gray wolf individual, represents a fitness value, represents a non-recovered load normalization function, represents a network loss normalization function, represents a switch operation number normalization function, represents a weight of the non-recovered load normalization function, represents a weight of the network loss normalization function, represents a weight of the switch operation number normalization function; represents a th constraint condition violation penalty metric, represents a th penalty factor of the constraint condition, represents a constraint condition index.

7. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 6, characterized in that, The non-restored load normalization function comprises: In the formula, represents the non-recovered load normalized value, represents the load node , represents the load node set, represents the load node importance weight, represents the load node rated active power, represents the load node charging state; The network loss normalization function comprises: wherein, denotes the normalized value of network loss, denotes the load node , denotes the load node , denotes the load node and the load node constitute a branch, denotes the set of AC branches, denotes the AC branch resistance, denotes the AC branch current, denotes the load node , denotes the load node , denotes the load node and the load node constitute a branch, denotes the set of DC branches, denotes the DC branch resistance, denotes the DC branch current, denotes the power converter index, denotes the set of power converters, denotes the AC-side active power of the th power converter, denotes the DC-side active power of the th power converter, denotes the equivalent loss, denotes the normalized reference power of network loss; The switch operation number normalization function comprises: In the formula, denotes a normalized value of the number of switching operations, denotes an operation step index, denotes the total number of operation steps, denotes an index of an operable switch, denotes a set of operable switches, denotes the on / off state of the operable switch at the operation step, denotes the on / off state of the operable switch at the operation step, denotes the on / off state of the operable switch at the operation step, denotes the maximum number of operation steps allowed in the operation.

8. The method for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization according to claim 2, characterized in that, The constraint conditions comprise: AC side power flow and limit constraint metrics, DC side power flow and limit constraints, voltage source converter coupling-capacity-slope constraints, topology connectivity and radial constraints, islanded power balance constraints, power flow-switch coordination constraints, operation feasibility and response budget constraints, load and distributed generation output and ramp constraints, and load reachability constraints.

9. The method of claim 8, wherein, The AC side power flow and limit constraint comprises: In the formula, Indicates load node , Indicates load node , Indicates load node and load nodes The branch roads formed Represents the set of AC branches. Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node , Indicates load node and load nodes The branch roads formed Indicates load node and load nodes The active power of the AC branch circuit. Indicates load node The generated active power Indicates load node Required active power Indicates load node The charged state, Indicates the power converter index. Indicates load node The connected power converter assembly Indicates the first Active power on the AC side of the power converter Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node and load nodes The reactive power of the AC branch circuit is Indicates load node The generated reactive power Indicates load node Required reactive power Indicates the first The reactive power on the AC side of the power converter. Indicates load node voltage, Indicates load node voltage, Indicates the resistance of the AC branch. Indicates the AC branch reactance. Indicates load node The lower limit of voltage amplitude, voltage amplitude upper limit of the load node voltage amplitude upper limit of the load node AC branch apparent power upper limit AC branch injection state The DC side power flow and limit constraint comprises: wherein V represents the voltage of the load node , V represents the voltage of the load node , R represents the DC branch resistance, I represents the DC branch current, P represents the active power of the DC branch consisting of the load node and the load node , Vmin represents the lower limit of the DC voltage of the load node , Vmax represents the upper limit of the DC voltage of the load node , Imax represents the upper limit of the DC branch current, S represents the DC branch state; The voltage source converter coupling-capacity-slope constraint comprises: In the formula, represents the first DC side active power of the station power converter, represents the first efficiency of the station power converter from AC side to DC side, represents the first AC side active power of the station power converter, represents the first AC side reactive power of the station power converter, represents the first total apparent power upper limit of the station power converter, represents the first DC side current of the station power converter, represents the first DC side current upper limit of the station power converter, represents the first DC side reactive power lower limit of the station power converter, represents the first DC side reactive power upper limit of the station power converter, represents the first AC side active power of the station power converter at time , represents the first AC side active power of the station power converter at time , represents the first active power change rate upper limit of the station power converter, represents the first AC side reactive power of the station power converter at time , represents the first AC side reactive power of the station power converter at time , represents the first reactive power change rate upper limit of the station power converter; The topology connectivity and radial constraint comprises: wherein denotes a set of supply nodes in the AC power grid, denotes a set of source nodes in the AC power grid, denotes an arbitrary AC loop in the AC power grid; The islanded power balance constraint comprises: In the formula, Indicates the power supply index. Indicates a certain isolated island. This indicates that power is available within the isolated island. Indicates the first The active power of a generator. Represents the set of load nodes within an island. Indicates the first The reactive power of a power source Indicates load node The charged state; The power flow-switch coordination constraint comprises: In the formula, denotes the upper limit of the active power of the AC branch, denotes the upper limit of the reactive power of the AC branch, denotes the upper limit of the DC branch current; The operation feasibility and response budget constraint comprises: In the formula, represents the operation step index, represents the total number of operation steps, represents the operable switch index, represents the set of operable switches, represents the on-off state of the operable switch at the first operation step, represents the on-off state of the operable switch at the second operation step, represents the on-off state of the operable switch at the third operation step, represents the maximum number of operation steps allowed in the operation, represents the maximum number of operations performed in parallel in each operation step, represents the response weight of the operable switch , represents the response value of the operable switch , represents the indication function of the on-off state of the operable switch at the first operation step and the second operation step being the same or different, represents the upper limit of the response value of the operable switch . The load and distributed generation output and ramp constraint comprises: In the formula, Indicates the first The lower limit of active power of a generator. Indicates the first The power supply at the moment active power, Indicates the first The upper limit of active power of a generator. Indicates the first The lower limit of reactive power of a power source. Indicates the first The power supply at the moment reactive power, Indicates the first The upper limit of reactive power of a power source. Indicates the first The upper limit of the rate of change of active power of a power source. Indicates the first The upper limit of the rate of change of reactive power of a power source; The load reachability constraint comprises: wherein represents a connection load node a candidate path set of any generation source, represents a DC or AC branch, represents a DC or AC branch investment state, represents a load node set.

10. A device for reliability evaluation of AC / DC distribution network based on Monte Carlo and improved grey wolf optimization, characterized in that, Comprise: A parameter determination module is configured to initialize a Monte Carlo simulation clock and a target evaluation time window, and to obtain source and load device parameters of an AC / DC power distribution network; A fault element determination module is configured to sample operating elements of the AC / DC power distribution network to generate primary fault-free operation time and repair time, to select an operating element with a minimum primary fault-free operation time as a fault element, and to advance the Monte Carlo simulation clock based on the minimum primary fault-free operation time; A topology determination module is configured to determine a topology after fault isolation of the fault element according to a preset fault mode consequence analysis table; A fault recovery scheme determination module is configured to output a target fault recovery scheme by using an improved grey wolf optimization algorithm based on the source and load device parameters and the topology after fault isolation, wherein the improved grey wolf optimization algorithm introduces an improved Tent chaotic mapping operable switch continuous intermediate state position initialization, a topology feasibility repair after binaryzation of the operable switch continuous intermediate state position, and a position update strategy based on Lévy flight and an adaptive disturbance mechanism; An index statistics module is configured to determine reliability evaluation indexes based on the target fault recovery scheme, and to advance the Monte Carlo simulation clock according to the repair time of the fault element; An index output module is configured to output the reliability evaluation indexes if the Monte Carlo simulation clock reaches the target evaluation time window.

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