Reinforcement recovery method and terminal for power distribution system based on disaster uncertainty

Abstract

The application discloses a kind of based on disaster uncertainty of power distribution system's reinforcement recovery method and terminal, first, based on the destruction intensity of disaster to power distribution system element is modeled;Second, for the uncertainty of disaster evolution law and element failure probability, the fuzzy set generation method based on moment measure and minimum transmission cost measure is combined, the fuzzy set of element failure probability is constructed, and then a pre-disaster reinforcement and post-disaster recovery collaborative distribution robust optimization model of power distribution system is proposed;Then, using column constraint generation algorithm, the above-mentioned distributed robust optimization model is solved in a distributed manner, to improve the calculation efficiency of the model.In this way, the reinforcement and recovery coordination problem of the existing power distribution system facing disasters can be solved, and efficient reinforcement and rapid recovery of the power system can be ensured.

Description

Technical Field

[0001] This invention relates to the technical field of power system operation, and in particular to an enhanced recovery method and terminal for power distribution systems based on disaster uncertainty. Background Technology

[0002] In recent years, low-probability, high-loss extreme natural disasters have seriously affected the safe and stable operation of the power system and have attracted widespread attention from the whole society. Therefore, improving early warning and defense capabilities has become an important issue that the power system urgently needs to address.

[0003] However, with the large-scale grid connection of new energy sources, the "double high" problem of high proportion of renewable energy and high proportion of power electronic devices will make the power system more vulnerable to extreme events, further reducing its operational reliability. Under the attack of extreme natural disasters, it will be more prone to cascading failures and complete blackouts. Therefore, it is necessary to carry out targeted and efficient reinforcement of the power system before extreme natural disasters occur, and to implement network reconstruction and repair measures after the disaster to ensure rapid recovery of the power system. This is of great significance for the power system to effectively cope with extreme natural disasters.

[0004] Meanwhile, due to the randomness of the occurrence and evolution of typhoons, the changes in their location and intensity of damage can have a strong impact on the pre-disaster reinforcement and post-disaster recovery of power systems. The problem of effectively incorporating them into the synergistic optimization method for power system reinforcement and recovery has not been well solved. Moreover, when factors such as climate, environment, and human activities change drastically, the number of typhoon variations and feasible scenarios will increase dramatically, and the computational efficiency will decrease exponentially, making it impossible to provide real-time reinforcement and recovery strategies for power systems when facing extreme natural disasters. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method and terminal for strengthening and restoring power distribution systems based on disaster uncertainty, which can solve the problem of coordination between strengthening and restoring existing power distribution systems in the face of disasters, and ensure efficient strengthening and rapid restoration of power systems.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] An enhanced recovery method for power distribution systems based on disaster uncertainty includes the following steps:

[0008] Based on the severity of the disaster, the failure probability of components in the power distribution system is modeled;

[0009] To address the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set of component failure probabilities is constructed by combining moment metric and minimum transmission cost metric. Based on the fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established.

[0010] By performing distributed solution on the sub-Bruker optimization model using column constraints, pre-disaster reinforcement and post-disaster recovery schemes are obtained.

[0011] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0012] An enhanced recovery terminal for a power distribution system based on disaster uncertainty includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the following steps:

[0013] Based on the severity of the disaster, the failure probability of components in the power distribution system is modeled;

[0014] To address the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set of component failure probabilities is constructed by combining moment metric and minimum transmission cost metric. Based on the fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established.

[0015] By performing distributed solution on the sub-Bruker optimization model using column constraints, pre-disaster reinforcement and post-disaster recovery schemes are obtained.

[0016] The beneficial effects of this invention are as follows: First, it models the destructive intensity of disasters on power distribution system components; second, addressing the uncertainties in disaster evolution patterns and component failure probabilities, it employs a fuzzy set generation method combining moment metrics and minimum transmission cost metrics to construct fuzzy sets of component failure probabilities, thereby proposing a collaborative sub-Bruker optimization model for pre-disaster reinforcement and post-disaster recovery of the power distribution system; then, it utilizes a column constraint generation algorithm to perform distributed solution of the aforementioned sub-Bruker optimization model, improving the model's computational efficiency. In this way, it can solve the existing problem of coordinated reinforcement and recovery of power distribution systems in the face of disasters, ensuring efficient reinforcement and rapid recovery of the power system. Attached Figure Description

[0017] Figure 1 This is a flowchart of an enhanced recovery method for a power distribution system based on disaster uncertainty, according to an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of an enhanced recovery terminal for a power distribution system based on disaster uncertainty, according to an embodiment of the present invention.

[0019] Figure 3This is a schematic diagram of the wind field of a typhoon model according to an embodiment of the present invention;

[0020] Figure 4 This is a flowchart of the column constraint generation algorithm according to an embodiment of the present invention;

[0021] Figure 5 This is a topology diagram of the test system according to an embodiment of the present invention;

[0022] Figure 6 This illustrates the load recovery scenarios under different examples in this invention.

[0023] Label Explanation:

[0024] 1. Enhanced recovery terminal for power distribution systems based on disaster uncertainty; 2. Memory; 3. Processor. Detailed Implementation

[0025] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0026] Please refer to Figure 1 This invention provides an enhanced recovery method for power distribution systems based on disaster uncertainty, comprising the following steps:

[0027] Based on the severity of the disaster, the failure probability of components in the power distribution system is modeled;

[0028] To address the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set of component failure probabilities is constructed by combining moment metric and minimum transmission cost metric. Based on the fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established.

[0029] By performing distributed solution on the sub-Bruker optimization model using column constraints, pre-disaster reinforcement and post-disaster recovery schemes are obtained.

[0030] As described above, the beneficial effects of this invention are as follows: First, it models the destructive intensity of disasters on power distribution system components; second, addressing the uncertainties in disaster evolution patterns and component failure probabilities, it employs a fuzzy set generation method combining moment metric and minimum transmission cost metric to construct a fuzzy set of component failure probabilities, thereby proposing a collaborative sub-Bruker optimization model for pre-disaster reinforcement and post-disaster recovery of the power distribution system; then, it utilizes a column constraint generation algorithm to perform distributed solution of the aforementioned sub-Bruker optimization model, improving the model's computational efficiency. In this way, it can solve the existing problem of coordinated reinforcement and recovery of power distribution systems in the face of disasters, ensuring efficient reinforcement and rapid recovery of the power system.

[0031] Furthermore, the modeling of the component failure probability of the power distribution system based on the destructive intensity of the disaster includes:

[0032] Establish a model for component failure probability:

[0033]

[0034]

[0035]

[0036] In the formula, T SS Indicates the duration of the fault. Let (i,j) represent the failure probability of line (i,j). Let m represent the failure probability of tower q in line (i,j). R and ξ R Let represent the median and log-standard deviation of a log-normal distribution, respectively. This represents the fault probability of line (i,j) and the operating state of the line at any given time after considering the cumulative effect over time.

[0037] As can be seen from the above description, establishing a component failure probability model can effectively support the coordinated strengthening and restoration of the subsequent power distribution system and provide solutions.

[0038] Furthermore, the sub-Blu-ray optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system, based on the fuzzy set, includes:

[0039]

[0040]

[0041]

[0042]

[0043] In the formula, Y and F represent fuzzy sets of line fault probabilities, Ξ har Indicates the set of alternative enhanced routes. This indicates the cost of strengthening the line. Indicates whether line (i,j) is reinforced, Ξ BS Represents a set of nodes. This represents the cost of the load depletion penalty for node i. This represents the load shedding rate of node i. This represents the active load at node i. This represents the reactive load at node i. P represents the generation cost of distributed power source g. g,t This represents the active power output of a distributed power source. and The energy storage cost represents the cost of generating electricity from energy storage i.

[0044] and These represent the maximum output and capacity of energy storage i, respectively. δ represents the operating cost of energy storage i. MS Represents a collection of energy storage facilities; This represents the active power output of energy storage m at time t; and Represent the active and reactive power flowing through line (i,j), respectively; n max This indicates the upper limit of the total reinforced lines in the power distribution system. ξ represents the set of all routes; ij,t ξ represents the repair status of the line. If line (i,j) is being repaired, then ξ... ij,t =1, if line (i,j) has been repaired or not, then ξ ij,t =0; fic ij,t Let fic be an auxiliary variable representing when the line is repaired. If line (i,j) is repaired at time t, then fic is the result. ij,t =1.

[0045] As described above, constructing a distributed robust optimization model can solve the problem of coordinated reinforcement and recovery of existing power distribution systems in the face of disasters.

[0046] Furthermore, by performing a distributed solution on the sub-Bruker optimization model through column constraints, the pre-disaster reinforcement and post-disaster recovery schemes are obtained, including:

[0047] The sub-Bruker model is decomposed into a main problem and multiple sub-problems. The main problem is a small-scale optimization problem model that is not affected by the number of scenarios.

[0048] Each scenario has a corresponding sub-problem, which is an optimization problem model under that scenario, and each scenario is independent of the others;

[0049] The solution to each iteration of the subproblem will be used to generate new constraints and added to the constraint set of the main problem, in order to eliminate infeasible solutions;

[0050] By iterating between the main problem and its sub-problems, the optimal pre-disaster reinforcement and post-disaster recovery solutions can be obtained.

[0051] As described above, the distributed algorithm based on column constraints decomposes the sub-Bruker optimization model, effectively improving the computational efficiency of model solving. It can be applied to power distribution systems facing extreme disasters, allowing engineers and dispatchers to make rapid decisions on pre-disaster reinforcement and post-disaster recovery of the power distribution system.

[0052] Furthermore, the construction of a fuzzy set of the component failure probability by combining the moment metric and the minimum transmission cost metric, addressing the uncertainty of the disaster evolution pattern and the component failure probability, includes:

[0053] A fuzzy set of the component failure probabilities is constructed by combining the moment metric and the minimum transmission cost metric:

[0054]

[0055] In the formula, E Y Let Y represent the expected value of the line fault probability distribution. The support set Ω is defined as follows:

[0056]

[0057] The minimum transmission cost metric is as follows:

[0058]

[0059] In the formula, x ij,t Indicates the operating status of the line. and Y and Yfault represent the upper limit of the line fault probability and the number of line fault samples, respectively; E Let Y(Ω) represent the line fault probability distribution obtained through fitting and the line fault probability distribution based on historical data statistics, respectively; Y(Ω) represents the probability distribution based on the support set Ω; θ represents the metric radius of the minimum transmission cost metric, which is Y and Y. E Geometric distance between; Π represents the distance based on x ij,t and The distribution function.

[0060] As described above, the fuzzy set generation method based on the combination of moment metric and minimum transmission cost metric can accurately construct the fuzzy set of component failure probability by combining the uncertainty of disaster occurrence with the component failure model.

[0061] Please refer to Figure 2 Another embodiment of the present invention provides an enhanced recovery terminal for a power distribution system based on disaster uncertainty, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the following steps:

[0062] Based on the severity of the disaster, the failure probability of components in the power distribution system is modeled;

[0063] To address the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set of component failure probabilities is constructed by combining moment metric and minimum transmission cost metric. Based on the fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established.

[0064] By performing distributed solution on the sub-Bruker optimization model using column constraints, pre-disaster reinforcement and post-disaster recovery schemes are obtained.

[0065] As described above, the beneficial effects of this invention are as follows: First, it models the destructive intensity of disasters on power distribution system components; second, addressing the uncertainties in disaster evolution patterns and component failure probabilities, it employs a fuzzy set generation method combining moment metric and minimum transmission cost metric to construct a fuzzy set of component failure probabilities, thereby proposing a collaborative sub-Bruker optimization model for pre-disaster reinforcement and post-disaster recovery of the power distribution system; then, it utilizes a column constraint generation algorithm to perform distributed solution of the aforementioned sub-Bruker optimization model, improving the model's computational efficiency. In this way, it can solve the existing problem of coordinated reinforcement and recovery of power distribution systems in the face of disasters, ensuring efficient reinforcement and rapid recovery of the power system.

[0066] Furthermore, the modeling of the component failure probability of the power distribution system based on the destructive intensity of the disaster includes:

[0067] Establish a model for component failure probability:

[0068]

[0069]

[0070]

[0071] In the formula, T SS Indicates the duration of the fault. Let (i,j) represent the failure probability of line (i,j). Let m represent the failure probability of tower q in line (i,j). R and ξ R Let represent the median and log-standard deviation of a log-normal distribution, respectively. This represents the fault probability of line (i,j) and the operating state of the line at any given time after considering the cumulative effect over time.

[0072] As can be seen from the above description, establishing a component failure probability model can effectively support the coordinated strengthening and restoration of the subsequent power distribution system and provide solutions.

[0073] Furthermore, the sub-Blu-ray optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system, based on the fuzzy set, includes:

[0074]

[0075]

[0076]

[0077]

[0078] In the formula, Y and F represent fuzzy sets of line fault probabilities, Ξ har Indicates the set of alternative enhanced routes. This indicates the cost of strengthening the line. Indicates whether line (i,j) is reinforced, Ξ BS Represents a set of nodes. This represents the cost of the load depletion penalty for node i. This represents the load shedding rate of node i. This represents the active load at node i. This represents the reactive load at node i. Pg represents the generation cost of distributed power source g. ,t This represents the active power output of a distributed power source. and The energy storage cost represents the cost of generating electricity from energy storage i.

[0079] and These represent the maximum output and capacity of energy storage i, respectively. δ represents the operating cost of energy storage i. MS Represents a collection of energy storage facilities; This represents the active power output of energy storage m at time t; and Represent the active and reactive power flowing through line (i,j), respectively; n max This indicates the upper limit of the total reinforced lines in the power distribution system. ξ represents the set of all routes; ij,t ξ represents the repair status of the line. If line (i,j) is being repaired, then ξ... ij,t =1, if line (i,j) has been repaired or not, then ξ ij,t =0; fic ij,t Let fic be an auxiliary variable representing when the line is repaired. If line (i,j) is repaired at time t, then fic is the result. ij,t =1.

[0080] As described above, constructing a distributed robust optimization model can solve the problem of coordinated reinforcement and recovery of existing power distribution systems in the face of disasters.

[0081] Furthermore, by performing a distributed solution on the sub-Bruker optimization model through column constraints, the pre-disaster reinforcement and post-disaster recovery schemes are obtained, including:

[0082] The sub-Bruker model is decomposed into a main problem and multiple sub-problems. The main problem is a small-scale optimization problem model that is not affected by the number of scenarios.

[0083] Each scenario has a corresponding sub-problem, which is an optimization problem model under that scenario, and each scenario is independent of the others;

[0084] The solution to each iteration of the subproblem will be used to generate new constraints and added to the constraint set of the main problem, in order to eliminate infeasible solutions;

[0085] By iterating between the main problem and its sub-problems, the optimal pre-disaster reinforcement and post-disaster recovery solutions can be obtained.

[0086] As described above, the distributed algorithm based on column constraints decomposes the sub-Bruker optimization model, effectively improving the computational efficiency of model solving. It can be applied to power distribution systems facing extreme disasters, allowing engineers and dispatchers to make rapid decisions on pre-disaster reinforcement and post-disaster recovery of the power distribution system.

[0087] Furthermore, the construction of a fuzzy set of the component failure probability by combining the moment metric and the minimum transmission cost metric, addressing the uncertainty of the disaster evolution pattern and the component failure probability, includes:

[0088] A fuzzy set of the component failure probabilities is constructed by combining the moment metric and the minimum transmission cost metric:

[0089]

[0090] In the formula, E Y Let Y represent the expected value of the line fault probability distribution. The support set Ω is defined as follows:

[0091]

[0092] The minimum transmission cost metric is as follows:

[0093]

[0094] In the formula, x ij,t Indicates the operating status of the line. and Y and Yfault represent the upper limit of the line fault probability and the number of line fault samples, respectively; E Let Y(Ω) represent the line fault probability distribution obtained through fitting and the line fault probability distribution based on historical data statistics, respectively; Y(Ω) represents the probability distribution based on the support set Ω; θ represents the metric radius of the minimum transmission cost metric, which is Y and Y. E Geometric distance between; Π represents the distance based on x ij,t and The distribution function.

[0095] As described above, the fuzzy set generation method based on the combination of moment metric and minimum transmission cost metric can accurately construct the fuzzy set of component failure probability by combining the uncertainty of disaster occurrence with the component failure model.

[0096] The enhanced recovery method and terminal for power distribution systems based on disaster uncertainty described above are applicable to solving the problem of coordinated enhancement and recovery of existing power distribution systems in the face of disasters, ensuring efficient enhancement and rapid recovery of the power system. The following detailed implementation methods illustrate this:

[0097] Example 1

[0098] Please refer to Figure 1 An enhanced recovery method for power distribution systems based on disaster uncertainty includes the following steps:

[0099] S1. Model the component failure probability of the power distribution system based on the intensity of the disaster.

[0100] Specifically, a model for the probability of component failure is established:

[0101]

[0102]

[0103]

[0104] In the formula, T SS Indicates the duration of the fault. Let (i,j) represent the failure probability of line (i,j). Let m represent the failure probability of tower q in line (i,j). R and ξ R Let represent the median and log-standard deviation of a log-normal distribution, respectively. This represents the fault probability of line (i,j) and the operating state of the line at any given time after considering the cumulative effect over time.

[0105] S2. Addressing the uncertainties in the disaster evolution pattern and the component failure probability, a fuzzy set of the component failure probability is constructed by combining the moment metric and the minimum transmission cost metric. Based on this fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established. In this embodiment, the minimum transmission cost metric is the Wasserstein metric.

[0106] First, a fuzzy set of the component failure probabilities is constructed by combining the moment metric and the minimum transmission cost metric:

[0107]

[0108] In the formula, E Y Let Y represent the expected value of the line fault probability distribution. The support set Ω is defined as follows:

[0109]

[0110] The minimum transmission cost metric is as follows:

[0111]

[0112] In the formula, x ij,t Indicates the operating status of the line. and Y and Yfault represent the upper limit of the line fault probability and the number of line fault samples, respectively; E Let Y(Ω) represent the line fault probability distribution obtained through fitting and the line fault probability distribution based on historical data statistics, respectively; Y(Ω) represents the probability distribution based on the support set Ω; θ represents the metric radius of the minimum transmission cost metric, which is Y and Y. E Geometric distance between; Π represents the distance based on x ij,t and The distribution function.

[0113] Secondly, based on the fuzzy set, the sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system includes:

[0114]

[0115]

[0116]

[0117]

[0118] In the formula, Y and F represent fuzzy sets of line fault probabilities, Ξ har Indicates the set of alternative enhanced routes. This indicates the cost of strengthening the line. Indicates whether line (i,j) is reinforced, Ξ BS Represents a set of nodes. This represents the cost of the load depletion penalty for node i. This represents the load shedding rate of node i. This represents the active load at node i. This represents the reactive load at node i. P represents the generation cost of distributed power source g. g,t This represents the active power output of a distributed power source. and The energy storage cost represents the cost of generating electricity from energy storage i.

[0119] and These represent the maximum output and capacity of energy storage i, respectively. δ represents the operating cost of energy storage i. MS Represents a collection of energy storage facilities; This represents the active power output of energy storage m at time t; and Represent the active and reactive power flowing through line (i,j), respectively; n max This indicates the upper limit of the total reinforced lines in the power distribution system. ξ represents the set of all routes; ij,t ξ represents the repair status of the line. If line (i,j) is being repaired, then ξ... ij,t =1, if line (i,j) has been repaired or not, then ξ ij,t =0; fic ij,t Let fic be an auxiliary variable representing when the line is repaired. If line (i,j) is repaired at time t, then fic is the result. ij,t =1.

[0120] S3. The distributed solution of the sub-Bruker optimization model is obtained by using column constraints to obtain pre-disaster reinforcement and post-disaster recovery schemes.

[0121] Specifically, the sub-Bruk model is decomposed into a main problem and multiple sub-problems. The main problem is a small-scale optimization problem model that is not affected by the number of scenarios.

[0122] Each scenario has a corresponding sub-problem, which is an optimization problem model under that scenario, and each scenario is independent of the others;

[0123] The solution to each iteration of the subproblem will be used to generate new constraints and added to the constraint set of the main problem, in order to eliminate infeasible solutions;

[0124] By iterating between the main problem and its sub-problems, the optimal pre-disaster reinforcement and post-disaster recovery solutions can be obtained.

[0125] Example 2

[0126] The difference between this embodiment and Embodiment 1 is that it provides a specific application scenario based on typhoon disasters, as follows:

[0127] 1. Component failure probability modeling based on typhoon damage intensity:

[0128] (1) Typhoon damage intensity model

[0129] The destructive intensity of a typhoon on components in a power distribution system depends primarily on the wind speed and central pressure difference at the component location. The difference between the atmospheric pressure in the undisturbed outer environment and the atmospheric pressure at the typhoon's center is defined as the typhoon's central pressure difference. For tropical cyclones in the Northwest Pacific, the outer atmospheric pressure is generally taken as 1010.0 hPa, and my country also uses 1010.0 hPa as the typhoon's central pressure difference. The typhoon's central pressure difference generally falls within the range of 0-135 hPa and can be characterized using a log-normal distribution, with the probability density function as follows:

[0130]

[0131] Where μ and σ 2 These are the parameters to be estimated in a log-normal distribution.

[0132] The wind speed of a typhoon (i.e., the speed at which the typhoon's eye moves) can be calculated using data points from two consecutive frames in the optimal typhoon path dataset. The wind speed can be obtained by dividing the spherical distance from the typhoon's center by the time interval between the two frames. Typhoon speeds generally range from 2 km / h to 65 km / h and are typically represented by a log-normal distribution, with the following probability density function:

[0133]

[0134] Where μ and σ 2 V is the parameter to be estimated in a log-normal distribution. T This represents the speed at which the typhoon's center moves.

[0135] Based on the central pressure difference of a typhoon and its wind speed equation, a typhoon wind field and filling model can be constructed, and then the wind speed value at the typhoon research point can be determined using empirical formulas. Ignoring friction, maximizing the gradient wind speed can be expressed as:

[0136]

[0137] Where f represents the Coriolis force coefficient of Earth's rotation, f = 2ωsinψ, ω represents the angular velocity rate of Earth's rotation, and Ψ represents latitude; K is an empirical coefficient, generally taken as 6.72; R max The radius of maximum wind speed is expressed in km; ΔP represents the pressure difference at the typhoon center, expressed in hPa.

[0138] The average maximum wind speed of a typhoon usually occurs within the radius R of the maximum wind speed. max At location R, the radius of maximum wind speed max The statistical fitting relationship between the pressure difference ΔP at the typhoon center and the typhoon center can be expressed as:

[0139] R max =1.119×10 3 ×ΔP -0.805 ;

[0140] The average maximum wind speed can be expressed as the maximum gradient wind speed and the center movement speed V. T Superposition:

[0141] V Rmax =0.865V gx +0.5V T ;

[0142] The distribution of the horizontal wind field of a typhoon varies depending on the region. The maximum wind speed V at a distance r from the typhoon center within the typhoon wind field is... r It can be represented as:

[0143]

[0144] Where x is a parameter related to the radial intensity attenuation of the typhoon, and its value ranges from 0.5 to 0.7. r This represents the average wind speed at a distance r between the straight line OM and the typhoon center O. The straight line OM is a straight line at 115° clockwise with respect to the typhoon's direction of movement. (See reference for details.) Figure 3 .

[0145] After a typhoon makes landfall on the coast, its central pressure difference gradually decreases, causing the typhoon's intensity to weaken until it dissipates. The typhoon's direction of movement remains unchanged near the coast and after landfall. Before landfall, the central pressure of the typhoon near the coast remains essentially constant. The decrease in the central pressure difference is related to the time the typhoon travels after landfall and the angle between the typhoon's direction of movement and the coastline. In other words, the central pressure difference decreases after landfall according to the following formula:

[0146]

[0147] Where t represents the time the typhoon travels after making landfall, in hours; ΔP(t) is the central pressure difference at the moment the typhoon makes landfall; and ΔP0 is the central pressure difference at sea before the typhoon makes landfall. This is the angle between the typhoon's direction of movement and the coastline at the time of landfall.

[0148] (2) Failure probability model of power distribution system components based on typhoon wind speed

[0149] A power distribution system consists of multiple towers. When any one of the supporting towers is damaged, the transmission line will enter a fault state. Therefore, the fault probability of any transmission line (i,j) can be expressed as:

[0150]

[0151] Among them, T SS Duration of the fault Let V be the fault probability of line (i,j). r,t Let be the maximum wind speed value within the typhoon wind field at time t, at a distance r from the typhoon center. Let the failure probability of tower q in line (i,j) be represented by the log-normal cumulative probability distribution function of typhoon wind speed as shown below:

[0152]

[0153] Where, m R and ξ R represents the median and log-standard deviation of a log-normal distribution.

[0154] Furthermore, the failure probability of line (i,j) should take into account the cumulative effect over time, meaning that if a line falls into a fault state at any given moment, it will remain in a fault state at all subsequent moments. Therefore, the operating state of the line at any given moment can be represented as follows:

[0155]

[0156] II. The coordinated sub-Blu-ray optimization model for pre-disaster reinforcement and post-disaster recovery of power distribution systems, taking into account the uncertainties of typhoons, can be expressed as follows:

[0157] (1) A method for generating fuzzy sets of line fault probabilities based on the combination of moment metric and Wasserstein metric

[0158] In the split-Bruker model, the fuzzy set considering both the moment metric and the Wasserstein metric can be represented by the following equation:

[0159]

[0160] The Wasserstein metric in the formula can be represented as follows:

[0161]

[0162] Among them, E Y Let Y be the expected value of the line fault probability distribution. The support set Ω can be defined as follows:

[0163]

[0164] Where, x ij,t This refers to the operating status of the line. This is the upper limit of the probability of line failure, i.e., the maximum value. These are line fault samples, i.e., the line operating status in historical data statistics, which can be obtained through statistical calculations of historical data on power distribution systems affected by typhoons; Y and Y ELet Y represent the line fault probability distribution obtained through fitting and the line fault probability distribution obtained from historical data statistics, respectively, and let Y represent the line fault probability distribution obtained through fitting and the line fault probability distribution obtained from historical data statistics, respectively. E It is possible Calculated, p s For the sample The probability, For the sample The Dirac metric; Y(Ω) is the probability distribution based on the support set Ω; θ is the metric radius of the Wasserstein metric, denoted as Y and Y. E Geometric distance between them; Π is based on x ij,t and The distribution function.

[0165] (2) Coordinated sub-optimization model of pre-disaster reinforcement and post-disaster recovery of power distribution system

[0166] 1) Objective function

[0167] To comprehensively consider the reinforcement and load loss costs of the power distribution system during a typhoon, the objective function of the coordinated sub-optimal model for pre-disaster reinforcement and post-disaster recovery of the power distribution system should minimize the costs of line reinforcement, load loss, energy storage device configuration and operation, and unit dispatching, which can be specifically characterized as follows:

[0168]

[0169] in, To increase the cost of strengthening the line, The cost of penalty for node i losing load; and The energy storage cost is the energy storage cost that generates electricity for energy storage i. The generation cost of distributed power source g, It is the operating cost of energy storage. Let i be the load shedding rate. and For the maximum output and capacity of energy storage i, This indicates whether line (i,j) is strengthened. Let be the load at node i under normal conditions. Let Y be the active power output of energy storage i at time t, and let Y and F be fuzzy sets of line fault probabilities. har As an alternative enhanced route set, Ξ BS Let δ be the set of nodes. MS It is a collection of energy storage systems.

[0170] 2) Constraints

[0171] The constraints of the model are as follows:

[0172] 1. Power balance constraints

[0173] The active and reactive power balance constraints at each node of the power distribution system can be expressed as:

[0174]

[0175]

[0176] Among them, P g,t With Q g,t These represent the active and reactive power outputs of the distributed power source, respectively. Let i be the load shedding rate at node i. and Let i represent the active load and reactive load at node i, respectively. The active power output of energy storage m at time t and These represent the active and reactive power flowing through line (i,j), respectively, P. g and These represent the lower and upper limits of the active power output of the distributed power source g, respectively, and Q. g and These represent the lower and upper limits of the reactive power output of the distributed power source g, respectively.

[0177] 2. Power flow constraints of the line

[0178] Transmission lines in a power distribution system must meet line capacity constraints and ensure that voltage does not exceed limits. This can be expressed by the following equation:

[0179]

[0180] Among them, V i,t V j,t Let Dr be the voltage magnitude at nodes i and j. ij With Dx ij Let (i,j) be the resistance and reactance of the line. Let (i,j) be the capacity of line (i,j). and are the lower and upper limits of the voltage amplitude at node i, respectively, and M is a constant used for relaxation using the big M method.

[0181] 3. Enhanced line constraints

[0182] In a power distribution system, if a line is reinforced, it will not fail to operate in subsequent operation. Furthermore, due to the limited total reinforcement cost, there should be a limit to the total number of lines that can be reinforced. The relevant constraints on transmission line reinforcement can be described as follows:

[0183]

[0184] Where, n maxThe upper limit of the total reinforced lines of the power distribution system. This is the set of all routes.

[0185] 4. Energy storage configuration and operation constraints

[0186] To enhance the power distribution system's ability to cope with extreme events, a certain capacity of energy storage devices needs to be installed in the system before a typhoon strikes. Due to cost constraints, the installed capacity and output limits of energy storage should be limited. Similarly, after a typhoon, the output limits of energy storage should also be limited, as detailed below:

[0187]

[0188]

[0189] in, and These represent the maximum output capacity and maximum stored energy capacity that can be configured for energy storage before a typhoon strikes. For the output of energy storage device i at various times, Let represent the remaining stored energy of energy storage device i at each moment.

[0190] 5. Loss of load related constraints

[0191] The load failure rate of each node should be limited to a certain range, and under the system reinforcement strategy, the total system load failure should also be limited to a certain range, which can be specifically stated as follows:

[0192]

[0193] in, This is the upper limit of the load failure rate. This is the maximum loss of load. It is the set of all nodes.

[0194] 6. Network Repair and Reconstruction Constraints

[0195] After a typhoon, the system will recover from the load loss by repairing lines and reconstructing the network, as detailed below:

[0196]

[0197] Where ξ ij,t ξ represents the repair status of the line. If line (i,j) is being repaired, then ξ ij,t =1, if line (i,j) has been repaired or not, then ξ ij,t =0. fic ij,t As an auxiliary variable, it represents when the line is repaired. If line (i,j) is repaired at time t, then ficij,t =1 at other times, the variable is 0.

[0198] A distributed bar optimization model for pre-disaster reinforcement and post-disaster recovery of power distribution systems, taking into account the uncertainties of typhoons, can be constructed by the objective function, constraints, and fuzzy sets.

[0199] III. Model Decomposition and Column Constraint Generation Solution Algorithm

[0200] (1) Vectorization representation and decomposition of complex models

[0201] The robust optimization model can be characterized as a two-stage robust optimization model. Using vectors and matrices, the original model can be represented as follows:

[0202]

[0203] stAx≤b

[0204] in:

[0205]

[0206] stGx+My+Nz≤h

[0207] The relevant fuzzy set can be represented as follows:

[0208]

[0209] Ω={z∈R I |Iz≤J}

[0210] Among them, the Wasserstein metric can be based on the N existing in the fuzzy set. s The scenario can be rewritten in the following form:

[0211]

[0212] Π(dz,dz E ) = p s Y s (dz)

[0213] Among them, Y s (dz) is when The conditional distribution at time. Based on the Wasserstein metric equation, the inner-layer maximization problem in the Bruker bar optimization model can be rewritten as follows:

[0214]

[0215] Subsequently, based on fuzzy sets, the two-stage maximization problem in the above equation can be rewritten in the following form with the help of auxiliary variables:

[0216]

[0217] st∫ z∈Ω Y s (dz)=1:ρ s

[0218]

[0219]

[0220] Reconstructing the above equation using the Slater condition, it can be further rewritten as a main problem and subproblems, with the equation for the main problem being:

[0221]

[0222] stAx≤b

[0223]

[0224]

[0225] The subproblem can be represented as: stG T ω=d.

[0226] Where ω is a vector consisting of all variables in the original problem.

[0227] (2) Column constraint generation algorithm

[0228] Based on the simplified vector form of the above-mentioned bilobal bar optimization model, the specific process of the column constraint generation algorithm is shown below, as illustrated in the flowchart. Figure 4 As shown:

[0229] Step 0: Set the initial line fault set Z = {z 0,s} and convergence criterion μ. Set the infimum LB of the iterations between the main problem and the subproblems to -∞, set the supremum UB to +∞, and set the number of iterations c = 1. Step 1: Solve the following main problem:

[0230]

[0231] stAx≤b

[0232]

[0233]

[0234]

[0235] (x) c ,ρ c,s,β c ,γ c ,ε c,s As the optimal solution to the main problem, φ MP The objective function value is to be solved as the main problem, and the lower bound is set as LB = φ. MP .

[0236] Step 2: Assume that the original problem has N fuzzy sets. s In different scenarios, based on the optimal solution obtained from solving the main problem, a distributed method is used to solve the N corresponding to the main problem. s There are s-th subproblems. The s-th subproblem can be expressed as follows:

[0237]

[0238] stIz≤J

[0239] G T ω=d

[0240] (z) c,s ,ω c,s As the optimal solution to the s-th subproblem, The objective function value under the optimal solution of this subproblem is used, and the supremum is updated to...

[0241] Step 3: Calculate (UB-LB) / LB and determine if the convergence criterion (UB-LB) / LB < μ is satisfied. If the convergence criterion is satisfied, output the calculation result and end the iteration loop; otherwise, update Z = Z∪{z T,c,s}, c = c + 1, and return to Step 1 to continue the loop.

[0242] IV. Case Analysis

[0243] To verify the above-mentioned distributed power system reinforcement and recovery collaborative sub-Browser optimization model that takes into account typhoon uncertainties, the following computing scenario is set up: a 33-node distributed power system in a real region of my country is used as the test case, including one substation and three distributed power sources, all with a power factor set to 0.9. The topology of the test system is shown below. Figure 5 As shown in Table 1, the installed capacity and parameters of the substation and each generator are listed below.

[0244] Table 1. Relevant data on substations and generators

[0245]

[0246] To verify the feasibility and advantages of the method proposed in this invention, this section sets up two cases for comparative analysis. Case 1 uses the proposed sub-Bruker optimization model for analysis and calculation, while Case 2 uses the traditional method for analysis. Table 2 shows the comparison of the enhancement cost of the entire system under the two different optimization strategies. In Case 1, the power system is strengthened by reinforcing lines and configuring energy storage when an early typhoon warning is issued. By adopting the method of this invention, the maximum output power of the energy storage configured in Case 1 is 15.6% lower than that of the energy storage in Case 2, and the total capacity is 22.8% lower. This makes the total enhancement cost of Case 1 8.6% lower than that of Case 2.

[0247] Table 2 Comparison of reinforcement cost results in the two cases

[0248]

[0249] Meanwhile, the load loss and recovery status of the power system after the typhoon are displayed in Figure 6 In the middle. For example Figure 6 As shown, when the typhoon first struck the power distribution system, the per-unit load loss in Case 1 was 5.72 pu, while in Case 2 it was 6.50 pu. The load loss in Case 1 was 12% lower than in Case 2. During the subsequent recovery process, Case 1 recovered the load faster and with a higher total recovery volume. Throughout the entire recovery process, Case 1's load recovery time was 100 minutes faster than Case 2's, and the total load recovery volume in Case 1 was 36.6% higher than that in Case 2. These enhancement and recovery effects demonstrate that the method proposed in this embodiment has certain advantages and feasibility.

[0250] Example 3

[0251] Please refer to Figure 2 The enhanced recovery terminal 1 for a power distribution system based on disaster uncertainty includes a memory 2, a processor 3, and a computer program stored in the memory 2 and executable on the processor 3. When the processor 3 executes the computer program, it implements the various steps of the enhanced recovery method for a power distribution system based on disaster uncertainty according to Embodiment 1 or 2.

[0252] In summary, the enhanced recovery method and terminal for distribution systems based on disaster uncertainty provided by this invention firstly models the destructive intensity of disasters on distribution system components; secondly, addressing the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set generation method combining moment and Wasserstein metrics is employed to construct fuzzy sets of component failure probabilities, thereby proposing a collaborative sub-Bruker optimization model for pre-disaster enhancement and post-disaster recovery of the distribution system; and thirdly, a column constraint generation algorithm is used to solve the aforementioned sub-Bruker optimization model in a distributed manner, improving the model's computational efficiency. In this way, the problem of coordinated enhancement and recovery of existing distribution systems in the face of disasters can be solved, ensuring efficient enhancement and rapid recovery of the power system.

[0253] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for enhanced recovery of power distribution systems based on disaster uncertainty, characterized in that, Including the following steps: Based on the severity of the disaster, the failure probability of components in the power distribution system is modeled; To address the uncertainty of disaster evolution patterns and component failure probabilities, a fuzzy set of component failure probabilities is constructed by combining moment metric and minimum transmission cost metric. Based on the fuzzy set, a sub-Bruker optimization model for the coordinated pre-disaster reinforcement and post-disaster recovery of the power distribution system is established. By performing distributed solution on the sub-Bruker optimization model through column constraints, pre-disaster reinforcement and post-disaster recovery schemes are obtained. The modeling of the component failure probability of the power distribution system based on the destructive intensity of the disaster includes: Establish a model for component failure probability: ； ； ； In the formula, T SS Indicates the duration of the fault. Indicates the line ( i , j The probability of failure. Indicates the line ( i , j Medium tower q The probability of failure, m R and ξ R Let represent the median and log-standard deviation of a log-normal distribution, respectively. Indicates the line ( i , j The failure probability of the line at any given time is considered after taking into account the cumulative effect over time. The sub-Blu-ray optimization model for coordinating pre-disaster enhancement and post-disaster recovery of the power distribution system based on the fuzzy set includes: ； ； ； ； In the formula, Y and F A fuzzy set representing the probability of line faults, Ξ har Indicates the set of alternative enhanced routes. This indicates the cost of strengthening the line. Indicates the line ( i , j Whether it is strengthened, Ξ BS Represents a set of nodes. Represents a node i The cost of load depletion penalty Represents a node i The load shedding rate, Represents a node i Active load at the location, Represents a node i reactive load at the location, Distributed power sources g The cost of electricity generation, This represents the active power output of a distributed power source. and They represent energy storage i The cost of power generation and the cost of energy storage; and They represent energy storage i Maximum output and capacity Indicates energy storage i Operating costs δ MS Represents a collection of energy storage facilities; express t Energy storage at all times m Those who have made meritorious contributions; and They represent the lines ( i , j The active and reactive power flowing through; n max This represents the total enhanced line limit of the power distribution system, and ΞCBR D represents the set of all lines; ξ ij,t Indicates the repair status of the line; if the line ( i , j (It is being repaired) ξ ij,t = 1, if the line ( i , j If it has been repaired or not, then ξ ij,t = 0; By performing a distributed solution to the sub-Bruker optimization model using column constraints, the pre-disaster reinforcement and post-disaster recovery schemes are obtained, including: The sub-Bruker model is decomposed into a main problem and multiple sub-problems. The main problem is a small-scale optimization problem model that is not affected by the number of scenarios. Each scenario has a corresponding sub-problem, which is an optimization problem model under that scenario, and each scenario is independent of the others; The solution to each iteration of the subproblem will be used to generate new constraints and added to the constraint set of the main problem, in order to eliminate infeasible solutions; The optimal pre-disaster reinforcement and post-disaster recovery plan is obtained through the mutual iteration between the main problem and sub-problems. The method for constructing a fuzzy set of component failure probabilities by combining moment metrics and minimum transmission cost metrics, addressing the uncertainty of disaster evolution patterns and component failure probabilities, includes: A fuzzy set of the component failure probabilities is constructed by combining the moment metric and the minimum transmission cost metric: ； In the formula, E Y Let Y represent the expected value of the line fault probability distribution. The support set Ω is defined as follows: ； The minimum transmission cost metric is as follows: ； In the formula, Indicates the operating status of the line. and Y and Yfault represent the upper limit of the line fault probability and the number of line fault samples, respectively; E These represent the line fault probability distribution obtained through fitting and the line fault probability distribution based on historical data statistics, respectively. Y (Ω) represents the probability distribution based on the support set Ω; θ The metric radius representing the minimum transmission cost metric is Y and Y'. E Geometric distance between; Π indicates based on and The distribution function.

2. An enhanced recovery terminal for a power distribution system based on disaster uncertainty, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps in the method as described in claim 1.

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