A fault recovery method for AC / DC hybrid distribution networks based on network reconfiguration and chance constraints

Abstract

This invention discloses a fault recovery method for AC / DC hybrid distribution networks based on network reconfiguration and chance constraints, belonging to the field of AC / DC distribution network fault recovery. The invention includes the following steps: Step 1: Establishing a flexible interconnected distribution network reconfiguration model; Step 2: Solving the model constructed in Step 1 using a binary particle swarm optimization algorithm; Step 3: Constructing an interconnected distribution network fault recovery model considering chance constraints; Step 4: Modeling uncertainties in wind and solar power output; Step 5: Transforming and solving the chance constraint model; Step 6: Verifying the feasibility of the model through case studies. By establishing a flexible interconnected distribution network reconfiguration model and constructing an interconnected distribution network fault recovery model considering chance constraints, this invention can significantly shorten the computation time of the optimization process and significantly improve fault recovery efficiency while effectively ensuring the load recovery effect after a fault, which is of great significance for large-scale power grid security.

Description

Technical Field

[0001] This invention belongs to the field of AC / DC distribution network fault recovery, and relates to a flexible interconnected distribution network fault recovery method based on a combination of network reconfiguration and opportunity constraints. Background Technology

[0002] With the rapid development of DC power sources such as photovoltaics and DC loads such as charging piles, DC power distribution systems have been widely used. Compared with AC power distribution systems, DC power distribution systems have advantages such as high transmission power, low network loss, and flexible power control. AC / DC hybrid power distribution systems consist of interconnected DC and AC power distribution systems. By regulating the power of voltage source converters (VSCs), flexible power transfer can be achieved between AC and DC systems. This not only improves the distribution network's ability to absorb distributed power sources but also overcomes the radial constraint bottleneck of traditional AC distribution networks, providing a new solution for distribution network fault recovery. Furthermore, with the increasing number of DC loads, AC / DC hybrid power distribution networks are receiving increasing attention and will be an important form of future power distribution networks. To date, AC / DC hybrid power distribution networks have been extensively researched and applied.

[0003] Improving fault recovery capabilities and ensuring a continuous and reliable power supply to loads is of great significance to modern power distribution networks. Prolonged load interruptions can cause significant economic losses and disrupt social production and daily life. After a fault occurs, loads can be transferred between lines through network reconfiguration, and then the lost loads in the non-faulty areas can be restored by the upstream power grid. In addition, local resources such as distributed generation (DG) can be utilized for load restoration.

[0004] Because distributed generation (DG) in a distribution network is subject to uncertainties due to various factors, these uncertainties can cause significant fluctuations in line transmission power and voltage. During distribution network fault recovery, if deterministic constraints are still used, DG cannot fully utilize its capabilities, leading to a conservative recovery process. Therefore, considering uncertainties is particularly important in distribution network fault recovery. However, existing methods do not consider the impact of DG uncertainties on the fault recovery of AC / DC hybrid distribution networks. Summary of the Invention

[0005] The purpose of this invention is to propose a fault recovery model for AC / DC hybrid distribution networks with chance constraints. This model is reliable, reasonable, and practical. The model fully considers the impact of distribution network (DG) uncertainties on fault recovery, and its effectiveness is verified through numerical examples. It is applicable to the fault recovery problem of AC / DC hybrid distribution networks and has practical significance for solving the fault recovery problem of AC / DC hybrid distribution networks with uncertainties.

[0006] The objective of this invention is achieved as follows: a fault recovery method for AC / DC hybrid distribution networks based on network reconfiguration and chance constraints, comprising the following steps:

[0007] Step 1: Establish a flexible interconnected distribution network reconfiguration model;

[0008] Step 2: Solve the model constructed in Step 1 using the binary particle swarm optimization algorithm;

[0009] Step 3: Construct a fault recovery model for interconnected distribution networks that considers opportunity constraints;

[0010] Step 4: Model the uncertainties in wind and solar power output.

[0011] Step 5: Transformation and solution of the chance constraint model;

[0012] Step 6: Verify the feasibility of the model through case study analysis;

[0013] The interconnected distribution network reconfiguration process in step 1, which uses flexible interconnection equipment as the core, is as follows:

[0014] (1) First, determine the set of DC-powered nodes. Establish the set of DC-powered nodes through breadth-first search, representing all possible connection relationships between the power supply node set and the VSC node set, i.e.:

[0015] (1)

[0016] In the formula: , These are the sets of power nodes and VSC nodes, respectively. for and The set of all possible connection paths between them; This is the set of DC-powered nodes, where each element refers to... All load nodes included in the path.

[0017] (2) Then determine the set of possible paths between the load node set and the DC power-available node set, based on the system load node set. Starting with the elements in, Using the elements in the table as endpoints, establish possible paths between any load node and a DC-powered node, i.e.:

[0018] (2)

[0019] (3) Finally, establish the network reconfiguration target. Since system operating losses are positively correlated with network impedance, the distribution network reconfiguration target, with flexible interconnection equipment as the core, is constructed based on the shortest path (minimum impedance) principle. Specifically, it can be expressed as:

[0020] (3)

[0021] In the formula: Let i be the impedance of the distribution line between nodes i and j. This represents the line impedance between the power supply node and the VSC node. The line impedance from the system load node to the DC-powered node. This is the set of system load nodes.

[0022] In the opportunity-constrained fault recovery model for interconnected distribution networks described in step 3, the objective is to minimize load reduction after a fault occurs, while ensuring reliable power supply to critical loads as much as possible. Therefore, the objective function of the fault recovery model can be expressed as:

[0023] (4)

[0024] In the formula: , These represent the total load and the load recovery amount carried by node i, respectively. This represents the total number of all nodes included in the distribution network. Let represent the load level weights for node i, with weight coefficients of 100, 10, and 1 for level I, II, and III loads, respectively. The constraints mainly include: AC / DC network power flow constraints; VSC steady-state operation constraints; transmission capacity constraints; voltage safety constraints; and opportunity constraints. The transmission capacity constraints primarily include those for AC / DC distribution lines and VSCs. The steady-state operation constraints of the VSC will be explained in detail with reference to the diagram.

[0025] 1) Power flow constraints in AC and DC networks:

[0026] (5)

[0027] (6)

[0028] (7)

[0029] (8)

[0030] (9)

[0031] (10)

[0032] In the formula: Equations (5), (6) and (8), (9) are the Dist-Flow power flow constraints of AC and DC networks, respectively, and Equations (7) and (10) are the standard second-order cone forms of the two. , The active and reactive power transmitted between nodes i and j in the AC distribution line are not specified. The active power transmitted by the DC distribution line between nodes i and j; , and These represent the active and reactive power injected into node j, respectively. , These are the squared terms of the voltage magnitude at node i; , These are the square terms of the current flowing through the AC / DC distribution lines between nodes i and j, respectively. , These are the resistance and reactance of the power distribution lines between nodes i and j, respectively. , These represent the total number of AC and DC nodes in the system.

[0033] The following formula is for chance constraints:

[0034] First, the power balance equations shown in equations (5) and (8) are relaxed into the following inequality constraint form:

[0035] (11)

[0036] (12)

[0037] Based on this, the inequality constraints shown in equations (11) and (12) are transformed into a probability constraint problem that satisfies a certain confidence level, namely:

[0038] (13)

[0039] (14)

[0040] In the formula: This represents the probability that event z is true. The confidence level of the inequality constraints shown in equations (11) and (12) is: .

[0041] (15)

[0042] (16)

[0043] Voltage constraint:

[0044] (17)

[0045] , These represent the active and reactive power transmitted by the AC distribution lines between nodes i and j, respectively. The active power transmitted by the DC distribution line between nodes i and j; , and Equations (15) and (16) are the upper limits of transmission capacity for AC and DC power distribution lines and VSC, respectively, and are the transmission capacity constraints.

[0046] Step 4 involves modeling uncertainties in wind and solar power output. Since the established flexible interconnected distribution network fault recovery model is a stochastic programming problem involving uncertainties in distributed photovoltaic and wind power output, this solution employs a probabilistic scenario-based stochastic optimization method. This method generates typical photovoltaic and wind power output states through uncertainty probability distributions, thereby transforming the original model into a stochastic optimization model described by uncertain states and their corresponding probabilities.

[0047] To analyze the output power of photovoltaic and wind turbines and The uncertainty will and The system is divided into M and Y states, and any state m (m=1,2,…,M) has upper and lower power limits. and For any state y (y=1,2,…,Y), there exist upper and lower power limits. , Then in the probability density function , The weighted average output power of photovoltaic and wind turbines within each state limit under defined limit constraints. , They can be represented as:

[0048] (18)

[0049] (19)

[0050] Furthermore, the probability that any states m and y are true. , It can be derived from its probability density function , The probability distribution function obtained by integrating from the lower bound to the upper bound , This means, that is:

[0051] (20)

[0052] (twenty one)

[0053] In summary, by utilizing the average output power of photovoltaic and wind turbines under the aforementioned different states and their corresponding probabilities, a method is generated. ( Given a combination of uncertain states, the general steps to determine this combination are three:

[0054] Construct average output power scenario sets for photovoltaic and wind turbines respectively. , ,Right now:

[0055] (twenty two)

[0056] The average output power of photovoltaic and wind turbines is paired and grouped using the Cartesian product of the two sets shown in equation (22):

[0057] (twenty three)

[0058] Calculate the probability corresponding to each combination of uncertain states:

[0059] (twenty four)

[0060] In step 5, the transformation and solution of the chance constraint model, this scheme uses the sample average approximation method to transform and solve the distribution network fault recovery model considering chance constraints. The principle is to use the sampling idea to represent random variables with samples, thereby transforming the stochastic optimization problem into a deterministic problem and solving it.

[0061] The unified form of opportunity constraints can be expressed as:

[0062] (25)

[0063] In the formula: Indicates the constraint conditions; x and These represent ordinary variables and random variables, respectively. This represents the confidence level of the inequality constraint.

[0064] Equation (25) can be approximated using the SAA method as follows:

[0065] (26)

[0066] (27)

[0067] In the formula: This is an indicator function that determines whether a constraint condition is true or false. It takes the value 1 when the constraint condition is true and 0 otherwise. It refers to a sample obtained through sampling.

[0068] Therefore, according to the SAA method, the chance constraints of the distribution network fault recovery model shown in equations (13) and (14) can be converted into:

[0069] (28)

[0070] (29)

[0071] (30)

[0072] (31)

[0073] Formula (28) - Formula (31): For indicator functions; It is a combination of uncertain states; , These represent the active and reactive power transmitted by the AC distribution lines between nodes i and j, respectively. , These represent the active power transmitted by the AC distribution lines between nodes i and k, respectively. The active power transmitted by the DC distribution line between nodes i and j; The active power transmitted by the DC distribution line between nodes j and k; , and These represent the active and reactive power injected into node j, respectively. , These are the square terms of the current flowing through the AC / DC distribution lines between nodes i and j, respectively. , These are the resistance and reactance of the power distribution lines between nodes i and j, respectively. , These represent the total number of AC and DC nodes in the system;

[0074] It should be noted that the indicator functions in the above four equations... It is still a non-convex function and cannot be solved directly. Therefore, binary variables are introduced. and The sum of the indicator functions is represented by the sum of the binary variables of all samples in different scenarios. The above process can be described by equations (32) to (35), that is:

[0075] (32)

[0076] (33)

[0077] (34)

[0078] (35)

[0079] In equations (32) and (33): Let K be the probability corresponding to each combination of uncertain states; K is a very large positive number that always guarantees that when... and When the value is 1, equations (32) and (33) are absolutely true; when... or When the value is 0, it indicates that the corresponding l-th sampling state is taken into account, meaning that the determined fault recovery scheme can guarantee the power balance and safe operation of the system under state l; when or When the value is 1, it means that state l is not taken into account, that is, the determined fault recovery plan cannot guarantee the power balance and safe operation of the system under state l.

[0080] After the above deterministic transformation of the chance constraint, the fault recovery model of the flexible interconnected distribution network considering the chance constraint proposed in this scheme has been transformed into a mixed integer second-order cone programming model, which can be solved efficiently by relying on Yamlip to call the commercial CPLEX solver.

[0081] This invention presents a fault recovery method for AC / DC hybrid distribution networks based on network reconfiguration and opportunity constraints, applied to load fault recovery scenarios with uncertainty. It proposes a fault recovery strategy for flexible interconnected distribution networks considering network reconfiguration and opportunity constraints. First, a network reconfiguration method for interconnected distribution networks with flexible interconnection devices as the core is proposed, and the system topology is generated using the binary particle swarm optimization (BSO) algorithm. Then, considering the uncertainty of distributed generation (DG) output, an opportunity constraint model for load recovery in interconnected distribution networks is proposed, aiming to maximize graded load recovery, by constructing a set of uncertainty probability scenarios. The proposed model is then transformed and solved using the sample average approximation (SAA) method. Finally, a test case based on an interconnected IEEE 33-node distribution network verifies the effectiveness and superiority of the proposed fault recovery strategy. By establishing a flexible interconnected distribution network reconfiguration model and constructing an interconnected distribution network fault recovery model considering opportunity constraints, this invention can significantly shorten the computation time of the optimization process and significantly improve fault recovery efficiency while effectively ensuring the load recovery effect after a fault, which is of great significance for large-scale power grid security. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of flexible interconnected distribution network reconfiguration.

[0083] Figure 2This is a framework diagram of a fault recovery model for flexible interconnected distribution networks.

[0084] Figure 3 This is a flowchart of the binary PSO algorithm solution.

[0085] Figure 4 This is the equivalent circuit diagram of VSC.

[0086] Figure 5 This is a diagram of a multi-regional flexible interconnected power distribution network structure.

[0087] Figure 6 This is a diagram showing the active power load distribution of the nodes.

[0088] Figure 7 It is a state division of photovoltaic and wind power probability density and its corresponding probability diagram.

[0089] Figure 8 This is a diagram of VSC transmission power before and after reconstruction.

[0090] Figure 9 This is a diagram showing the load recovery results before and after the reconfiguration.

[0091] Figure 10 This is a graph showing the load recovery results of different reconstruction methods.

[0092] Figure 11 This is a diagram showing the load recovery results, taking into account both opportunity constraints and non-opportunity constraints.

[0093] Figure 12 These are the load recovery results under different confidence levels;

[0094] Figure 13 This is a graph showing the percentage of power balance violation scenarios at different confidence levels. Detailed Implementation

[0095] The preferred embodiments will now be described in detail with reference to the accompanying drawings.

[0096] Figure 1 This is a schematic diagram of flexible interconnected distribution network reconfiguration. Taking a three-terminal flexible interconnected distribution network as an example, after a fault occurs, the system forms several isolated regions (IRs), as explained below:

[0097] ① First, through network reconstruction centered on the VSC-based flexible DC interconnection link, and by switching power distribution lines and tie lines, as well as the flexible power regulation function of the flexible interconnection device, a power supply restoration area for multiple power sources to multiple load nodes is constructed, realizing power mutual assistance and load restoration between feeders or different power supply areas.

[0098] ② To ensure the economic efficiency of system operation, the above-mentioned reconfigured network aims to minimize the total impedance of the distribution lines and is solved using the Binary-PSO algorithm. Of course, for the islanded IR2 that cannot be connected to the VSC node, it can only rely on the DG within the island to supply power to the load. When the output of the DG is insufficient, the load must be abandoned.

[0099] Figure 2 This is a framework diagram of the fault recovery model for flexible interconnected distribution networks. The proposed fault recovery strategy for flexible interconnected distribution networks mainly includes two stages, which are explained in detail below.

[0100] ① Network reconstruction centered on flexible interconnect devices. According to... Figure 1 The power distribution network reconfiguration process shown is a network reconfiguration centered on flexible interconnection devices.

[0101] ② Load restoration considering the uncertainty of distributed photovoltaic and wind power output. This part proposes a load restoration model that undergoes a deterministic transformation using a stochastic optimization method based on uncertain scenarios, and then solves the model using a solver. The two stages work together to effectively ensure efficient power restoration to the load after a fault.

[0102] Figure 3 This is a flowchart of the binary PSO algorithm solution, which provides a detailed explanation of the algorithm flow for solving the network reconstruction model in step one.

[0103] ① Each particle is encoded using binary variables 0-1, where 1 represents a closed switch and 0 represents an open switch; the particle length is the total number of switches in the network, and the number of particle groups is the number of loops in the network; the initial state of the particles is that all switches in the network are closed. The particle update rules are as follows: , These represent the individual and global optimal positions, respectively. and Let be the velocity and position of the i-th particle at the s-th iteration, respectively;

[0104] (34)

[0105] (35)

[0106] ②The specific steps of solving the binary PSO (Particle Swarm Optimization) algorithm are as follows:

[0107] Step 1: Initialize the power distribution network parameters and particles.

[0108] Step 2: Verify whether the network exhibits a radial pattern and whether there are isolated islands using the parameters input in Step 1. If isolated islands exist or the network is not radial, return to Step 1; otherwise, proceed to the next step.

[0109] Step 3: Calculate and sort the particle swarm fitness to obtain individual and global optimal values.

[0110] Step 4: Update the position and velocity of the particles, and calculate the fitness value of the new particles.

[0111] Step 5: Compare the fitness of the new and old particles, and calculate the position of the particles with poor fitness.

[0112] Step 6: Update the individual and global optimal values ​​of the particle history.

[0113] Step 7: Determine whether the iterative convergence condition is met. If it is met, output the final network reconstruction result; otherwise, return to Step 1.

[0114] Figure 4 This is the equivalent circuit diagram of VSC, and the details are as follows:

[0115] ①For example Figure 4 The diagram shows the equivalent circuit of VSC. and The active and reactive power input to the VSC are respectively converted from AC side. This refers to the active power output from the DC side of the VSC. This refers to the equivalent reactive power within the VSC. and These are the AC and DC sides of VSC, respectively; This refers to the internal voltage of the VSC. , and These represent the current, resistance, and reactance of the equivalent branch of VSC, respectively.

[0116] ②The steady-state operating constraints of VSC are:

[0117] (36)

[0118] (37)

[0119] In the formula: for The squared term. Furthermore, assuming VSC uses SPWM modulation, the intermediate variable in Equation 37, namely the DC voltage utilization rate of VSC, is taken as... The modulation ratio of VSC is taken .

[0120] Figure 5 This is a diagram of a multi-regional flexible interconnected distribution network structure, detailed below;

[0121] To verify the effectiveness and superiority of the fault recovery strategy for flexible interconnected distribution networks considering network reconfiguration and chance constraints proposed in this embodiment, three AC / DC hybrid distribution network examples were established, consisting of three standard IEEE 33-node distribution networks interconnected via VSC. Figure 5 It showcases its grid structure, photovoltaic and wind power connection points, and the location of fault lines.

[0122] Figure 6 This is a diagram showing the active power load distribution of the nodes, explained in detail below.

[0123] ① The reference voltage of the simulation system is 12.66kV; the upper and lower limits of the system's allowable operating voltage are 1.05pu and 0.95pu, respectively.

[0124] ② The original data samples were filtered using Empirical Mode Decomposition (EMD). The graph shows the active load and corresponding importance of each node in each IEEE 33-node system. The reactive load is directly proportional to the active load according to the standard example parameters.

[0125] Figure 7 This document presents the probability density state classification of photovoltaic (PV) and wind power and their corresponding probability diagrams. Due to the small geographical area covered by the distribution network, it is assumed that the PV and wind power outputs connected to each node in the system exhibit consistent fluctuation states. The probability density curves of PV and load power are obtained using the proposed probability scenario generation method. The following formula yields 50 representative PV and wind power scenarios, which are then applied to solve a fault recovery model for a flexible interconnected distribution network considering chance constraints. The specific results of the probability density state classification of PV and wind power and their corresponding scenario probabilities are as follows: Figure 7 As shown.

[0126] (38)

[0127] (39)

[0128] (40)

[0129] Equation (38) constructs the average output power scenario sets for photovoltaic and wind turbines respectively. and Equation (39) is a formula for pairing and grouping the average output power of photovoltaic and wind turbines using the Cartesian product of the two sets shown in Equation (38). and Let be the weighted average of the output power of photovoltaic and wind turbine in each state limit, respectively. Equation (40) calculates the probability corresponding to each uncertain state combination.

[0130] Figure 8 and Figure 9These are the VSC transmission power diagrams before and after reconfiguration, and the load recovery results diagrams before and after reconfiguration. Figure 4 Under the fault conditions shown, fault recovery models are used to perform fault recovery on interconnected distribution networks considering network reconfiguration or not. It should be noted that the photovoltaic and wind power outputs in the two comparative schemes used in this embodiment are determined values ​​obtained by weighting the scenario with its corresponding probability, without considering the chance constraints of uncertainty. The network reconfiguration results of the proposed method in this embodiment are shown in the table below. The transmission power of the VSC and the recovery results of various loads in the system under the two schemes are shown in the table below. Figure 8 and Figure 9 As shown.

[0131] Branch road category Operating branch Faulty branch (disconnected) 0-1、37-38、44-45、90-91 Reconstructing and cutting off branches 3-4、6-7、9-10、19-20、20-21、39-40、40-41、57-58、74-75、75-76 Reconstructing closed branches 7-20，8-14、11-21、17-32、24-28、39-52、40-46、43-53、49-64、56-60、72-78、75-85、81-96、88-92

[0132] refer to Figure 10 To verify the superiority of the network reconfiguration method proposed in this embodiment compared with existing reconfiguration methods, and to compare the load restoration effect of common fault recovery strategies that aim to minimize network loss, minimize voltage deviation, minimize a combination of network loss and voltage deviation, and maximize load restoration, the statistical results of load restoration computation time under each reconfiguration scheme are shown in the table below:

[0133] Reconstruction Goals Calculation time / s Minimize network loss 33834 Minimize voltage deviation 50833 Minimize network loss + voltage deviation 48366 Maximize load recovery 32424 Method of this embodiment 235

[0134] Depend on Figure 10 It can be seen that the different reconfiguration schemes mentioned above have no significant impact on the load restoration effect, and the total load restoration capacity deviation of each scheme is within 1.59%. Furthermore, the computation time statistics shown in the table above indicate that under the network reconfiguration strategy proposed in this embodiment, which uses flexible interconnected devices as the core, the total computation time for load restoration is significantly reduced, with a maximum reduction of 99.54%. This is because the method proposed in this embodiment only constructs the network reconfiguration centered on flexible DC devices based on network impedance relationships, without involving the optimization of the distribution network operating status. This significantly reduces the dimension of the optimization solution space and the computational complexity. In summary, the above analysis demonstrates that the method proposed in this embodiment can significantly shorten the computation time of the optimization process and significantly improve fault restoration efficiency while effectively ensuring the load restoration effect after a fault.

[0135] Figure 11 This is a load recovery result diagram considering both opportunity constraints and non-opportunity constraints. Details are as follows:

[0136] Considering the uncertainties in photovoltaic and wind power output, a chance constraint is used to characterize and transform the uncertainty in the proposed fault recovery model. Based on 50 typical wind and solar power scenarios generated in the above results figure, the initial confidence level is set to 100%, meaning that the uncertainty state fully satisfies the system operation constraints. The chance constraint model is then solved, yielding load recovery results at 100% confidence. Compared to the deterministic model results, considering the uncertainties in photovoltaic and wind power output, the total load survival of the system after the fault is reduced, from 8.57+j4.86MW in the deterministic model to 7.81+j4.37MW, a decrease of approximately 11%. This is because, under the 100% confidence condition considering wind and solar power uncertainties, the load recovery decision needs to ensure that the system can operate safely and reliably in any scenario, avoiding possible extreme fluctuations in wind and solar power output. It cannot achieve optimal decision-making for any scenario, and the resulting load recovery scheme has a certain degree of conservatism.

[0137] Figure 12 and Figure 13 The graph shows the load recovery results at different confidence levels and the percentage of power balance violation scenarios at different confidence levels. Detailed explanations are as follows:

[0138] To further analyze the impact of the opportunity constraint model proposed in this embodiment on system load recovery and safe operation when different confidence levels are set, this embodiment provides statistical results of load recovery results and the proportion of system power balance violation scenarios when the opportunity constraint confidence levels are 100%, 90%, 80%, 70%, 60%, 50%, and 40%. Figure 12 As shown in the load recovery results at different confidence levels, the system's load recovery increases as the confidence level gradually decreases. From 100% to 40%, the total surviving load capacity increases from 8.9518 MVA to 9.9138 MVA, a 10.75% increase. However, as the confidence level decreases, the system's ability to cope with uncertainties also decreases, significantly increasing the risk that the fault recovery strategy considering opportunity constraints will not meet power balance requirements. The number of scenarios failing to meet power balance constraints increases from 0 violations at 100% confidence to 59.42% at 40% confidence. Figure 13 The percentage of power balance violation scenarios at different confidence levels indicates that the safe and reliable operation of the system is difficult to guarantee. Therefore, power grid operators should set confidence parameters based on the actual operational needs and risk preferences of the system to ensure that as many loads as possible are restored after a fault, while effectively balancing the system's operational safety and robustness in the face of strong random fluctuations in the output of distributed power sources.

[0139] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for fault restoration of an AC / DC hybrid power distribution network based on network reconfiguration and chance constraints, characterized in that, It comprises the following steps: Step 1: establishing a flexible interconnected distribution network framework reconstruction model, the specific process is as follows: (1) First, determine the DC power supply node set, establish the DC power supply node set through the breadth-first search, represent all possible connection relationships between the power supply node set and the VSC node set, that is: （1） wherein: , are a set of power supply nodes and VSC nodes respectively; is a set of all possible connection paths between and ; is a set of DC supplyable nodes, where an element refers to all load nodes contained in a path; is a set of all possible connection paths between (2) Then, the possible path set between the load node set and the DC power supply node set is determined, taking the elements in the system load node set as the starting point and the elements in the DC power supply node set as the end point, to establish the possible path between any load node and DC power supply node, that is: （2） (3) Finally, establish the network framework reconstruction target, since the system operation loss is positively correlated with the network impedance, therefore, according to the shortest path principle, build the distribution network framework reconstruction target taking the flexible interconnected device as the core, which can be specifically represented as: （3） wherein: Zij is the line impedance between nodes i, j, Zij is the line impedance between nodes i, j, Zij is the line impedance between nodes i, j, is the set of system load nodes; Step 2: solving the model constructed in step 1 based on the binary particle swarm algorithm; Step 3: constructing an interconnected distribution network fault recovery model considering opportunity constraints; The interconnected distribution network fault recovery model considering opportunity constraints in step 3 takes the minimum load reduction after fault occurrence as the target, and tries to ensure reliable power supply to important loads as much as possible, therefore, the objective function of the fault recovery model can be represented as: （4） In the formula: , respectively, the total amount of load and the amount of load recovery of node i; is the total number of all nodes included in the distribution network; is the grade weight of the load of node i, and the weight coefficients of primary, secondary and tertiary loads are respectively taken as 100, 10 and 1; the constraint conditions include: AC and DC network power flow constraints; VSC steady-state operation constraints; transmission capacity constraints; voltage safety constraints; opportunity constraints; specifically: 1) AC and DC network power flow constraints: （5） （6） （7） （8） （9） （10） wherein: Dist-Flow constraints of AC and DC networks are given by equations (5), (6) and (8), (9) respectively, and equations (7) and (10) are the standard second order cone forms of both, , Pij and Qij are the active and reactive power transmitted over the AC distribution line between nodes i and j; Pij and Qij are the active and reactive power transmitted over the AC distribution line between nodes i and j; , and Pj and Qj are the active and reactive power injected at node j; , and , and , Rij and Xij are the resistance and reactance of the distribution line between nodes i and j; , Nac and Ndc are the total number of AC and DC nodes included in the system respectively. The following formula is for the opportunity constraint: First, relax the power balance equations represented by formula (5) and formula (8) into the following inequality constraint form: （11） （12） On this basis, convert the inequality constraints represented by formula (11) and formula (12) into a probability constraint problem that meets a certain confidence level, that is: （13） （14） wherein: denotes the probability that event z is true; is the confidence level of the inequality constraints of equations (11) and (12) is ; （15） （16） Voltage constraint: （17） , are the active and reactive power transmitted by the AC distribution line between nodes i, j, respectively; is the active power transmitted by the DC distribution line between nodes i, j; , and are the upper limits of the transmission capacity of the AC and DC distribution lines and the VSC, respectively, and equations (15) and (16) are the transmission capacity constraints; Step 4: modeling the uncertainty of wind and light output, the specific process is as follows: The photovoltaic output power and the wind turbine output power are divided into M and Y states respectively, and for any state m, m = 1, 2, …, M, there exist upper and lower power limits and , for any state y, y = 1, 2, …, Y, there exist upper and lower power limits and , then the weighted average of the output power of the photovoltaic and the wind turbine within the state limits under the limit constraint determined by the probability density function , can be represented as: , ​ （18） （19） Further, the probability that any state m and y correspond , The probability density function , The probability distribution function , is given by the integral from the lower limit to the upper limit, i.e.: （20） （21） In summary, the photovoltaic and wind turbine output power means in different states and their corresponding probabilities are used to generate a combination of uncertainty states, wherein The combination has 3 steps: respectively constructing a set of average output power scenarios for photovoltaics and wind turbines , i.e. （22） Use the Cartesian product of the two sets represented by formula (22) to pair and group the average output power of photovoltaic and wind turbines: （23） Calculate the probability corresponding to each uncertain state combination: （24） Step 5: transformation and solution of the opportunity constraint model; Step 6: verify the feasibility of the model through example analysis.

2. The method of claim 1, wherein the method is characterized in that: The process of step 2 for solving the model constructed in step 1 based on the binary particle swarm algorithm is as follows: Step one: initialize the distribution network parameters and particles; Step two: verify whether the network presents a radial shape and whether there is an island through the parameters input in step one, if there is an island or it is not a radial shape, then return to step one, otherwise proceed to the next step; Step three: calculate the fitness of the particle swarm and sort them to obtain the individual and global optimal values; Step four: update the position and speed of the particles and calculate the fitness value of the new particles; Step five: compare the fitness of the new and old particles, and calculate the position of the particles with poor fitness; Step six: update the individual optimal and global optimal values of the particles; Step seven: judge whether the iteration convergence condition is met, if yes, output the final network framework reconstruction result, otherwise return to step one. 3.The method of claim 1, wherein the method further comprises: The process of step 5 for transformation and solution of the opportunity constraint model is as follows: The unified form of the opportunity constraint can be represented as: （25） wherein: represents a constraint; x and represent a general variable and a random variable, respectively; represents a confidence level of inequality constraint; Approximate formula (25) to formula (26) by SAA: （26） （27） In the formula: is an indicator function for judging whether the constraint condition is established or not, taking 1 when the constraint condition is established, and 0 otherwise; is a certain sample obtained by sampling; According to the SAA method, convert the opportunity constraints of the distribution network fault recovery model represented by formula (13) and formula (14) to formula (27) and formula (28) respectively: （28） （29） （30） （31） Formula (28) - Formula (31): For indicator functions; It is a combination of uncertain states; , These represent the active and reactive power transmitted by the AC distribution lines between nodes i and j, respectively. , These represent the active power transmitted by the AC distribution lines between nodes i and k, respectively. The active power transmitted by the DC distribution line between nodes i and j; The active power transmitted by the DC distribution line between nodes j and k; , and These represent the active and reactive power injected into node j, respectively. , These are the square terms of the current flowing through the AC / DC distribution lines between nodes i and j, respectively. , These are the resistance and reactance of the power distribution lines between nodes i and j, respectively. , These represent the total number of AC and DC nodes in the system; The indicator function in the four equations of equation (28) - equation (31) above is still a non-convex function and cannot be solved directly, so binary variables and are introduced, and the sum of the indicator functions is expressed as the sum of the binary variables of all samples in different scenarios, and the above process is described by equation (32) - equation (35), that is: （32） (33) （34） （35） In formula (32) and formula (33) : is the probability corresponding to each uncertain state combination; K is a very large positive number, which can always guarantee that when and formula (32) and formula (33) are absolutely correct when 1 is taken; when or 0 is taken, it means that the corresponding lth sampling state is counted, that is, the determined fault recovery scheme can guarantee the power balance and safe operation of the system under state l; when or 1 is taken, it means that state l is not counted, that is, the determined fault recovery scheme cannot guarantee the power balance and safe operation of the system under state l.

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