Energy storage site selection and sizing method considering distribution network fault recovery under extreme disasters

Abstract

The present invention relates to a method for energy storage site selection and sizing that takes into account distribution network fault recovery under extreme disasters. Its technical features are: using a consensus-based multi-objective particle swarm algorithm for global search optimization to obtain multiple non-dominated solutions close to Pareto optimality; using a shortest path method to search for the grid fault recovery area under extreme disasters based on the local depth optimization goal and screening out site selection schemes that can meet the power supply restoration goal; transforming the multi-objective energy storage site selection and sizing problem that considers economic benefits and fault recovery into a single-objective energy storage site selection and sizing optimization problem; using an interior point method to solve the distribution network energy storage device site selection and sizing optimization model, and obtaining a distribution network energy storage device site selection and sizing scheme that meets economic indicators and fault recovery indicators. The present invention is rationally designed and can quickly obtain the optimal solution that meets user preferences, meeting the load recovery requirements of the power grid in the event of a fault.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution network energy storage, and in particular to a method for energy storage site selection and sizing considering distribution network fault recovery under extreme disasters. Background Art

[0002] As one of the most crucial infrastructures in modern society, the power system maintains the normal operation and development of society. However, during "high-impact, low-probability" extreme natural disasters such as earthquakes, typhoons, and tsunamis, critical equipment and infrastructure within the distribution network are prone to multiple failures, making large-scale power outages unavoidable. Because power facilities within the distribution network are prone to damage, short circuits, and other failures during natural disasters, which can lead to widespread power outages, research is necessary to investigate emergency control methods for distribution networks during natural disasters in order to improve their power supply reliability.

[0003] Distributed energy storage devices have been introduced into distribution networks as a crucial regulatory tool. They will play a crucial role in this network, and the location and sizing of these devices are key challenges. Numerous studies have examined the location and sizing of these devices. For example, the energy storage system configuration and daily output optimization strategy for peak shaving and valley filling on the grid side take into account economic efficiency, combine energy storage cost with governance effect as a comprehensive evaluation standard for peak regulation, and provide an optimization model to solve the output optimization problem of peak shaving and valley filling; the distributed photovoltaic energy storage system optimization configuration for new energy consumption takes the net profit of the grid as the goal to achieve economic maximization, and establishes a distributed photovoltaic energy storage system optimization configuration model, which can not only solve the problem of distributed photovoltaic consumption, but also increase the profit of the grid; the user-side energy storage optimization configuration method based on the two-layer decision model analyzes the necessity of configuring energy storage, adopts the two-layer decision model to establish the objective function respectively, adopts the sparrow search algorithm to find the optimal solution, and configures the energy storage capacity; the configuration optimization method of the integrated photovoltaic storage and charging station improves the weed invasion algorithm, optimizes and improves the energy storage capacity optimization model, and adopts the particle swarm algorithm and the traversal algorithm to coordinate the configuration optimization of the photovoltaic energy storage system.

[0004] Most of the aforementioned distributed energy storage site selection and sizing models consider only economic benefits and costs, without considering the grid's reliability indicators for fault recovery under extreme disasters. In terms of solutions, due to the random search characteristics and convergence performance differences of intelligent optimization algorithms, the solution to the energy storage system site selection and sizing problem inevitably suffers from shortcomings such as high computational cost and unstable solution quality. Furthermore, from an engineering application perspective, decision makers' ultimate goal is not a complete Pareto solution set, but rather a Pareto optimal solution that meets the expectations of different objective functions. Therefore, the aforementioned methods are unlikely to meet the grid's load recovery requirements in the event of a fault. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and propose a method for energy storage site selection and sizing that takes into account distribution network fault recovery under extreme disasters. It can quickly obtain the optimal solution that meets user preferences and meets the load recovery requirements of the power grid in the event of a fault.

[0006] The present invention solves the technical problem by adopting the following technical solutions:

[0007] A method for selecting and sizing energy storage locations considering distribution network failure recovery under extreme disasters includes the following steps:

[0008] Step 1: Obtain the historical curve of renewable energy active output and load as input data;

[0009] Step 2: Using the installation location and capacity of the distribution network energy storage device as control variables, a distribution network energy storage device location and sizing optimization model is constructed for the distribution network energy storage location and sizing problem. The data from Step 1 is input into the model and a consensus-based multi-objective particle swarm algorithm is used for global search optimization to obtain multiple non-dominated solutions close to Pareto optimality.

[0010] Step 3: Set up a user decision list based on user preferences;

[0011] Step 4: According to the user decision list set in step 3, select the non-dominated solution that meets the user's preference in step 2. For the non-dominated solution that meets the user's preference, select the local depth optimization objective;

[0012] Step 5: Based on the local deep optimization goal selected in step 4, use the shortest path method to search for the power grid failure restoration area under extreme disasters and select a site selection plan that can meet the power supply restoration goal;

[0013] Step 6: Based on the restoration plan obtained in step 5, the multi-objective energy storage site selection and sizing problem considering economic benefits and fault recovery is transformed into a single-objective energy storage site selection and sizing optimization problem. The interior point method is used to solve the distribution network energy storage device site selection and sizing optimization model, and the control variable values ​​that meet the constraints are calculated. In this way, a distribution network energy storage device site selection and sizing plan that meets the economic indicators and fault recovery indicators is obtained.

[0014] Furthermore, the distribution network energy storage device location and sizing optimization model takes minimizing the economic cost of the distribution network and maximizing power restoration in the event of a fault as the objective function:

[0015] Among them, the objective function of minimizing the economic cost of the distribution network is:

[0016]

[0017] Among them, C inv represents the installation cost of the energy storage device, Cm represents the operation and maintenance cost of energy storage, C O represents the cost of purchasing electricity from the upper power grid, γ represents the annual interest rate, C E,in is the unit price of the rated capacity of the energy storage device, C P,in is the unit price of the energy storage device rated power, The fixed installation cost of the energy storage device, E ES,i is the rated capacity of the energy storage device, P ES,N,i is the rated power of the energy storage device, u i is a binary variable associated with the energy storage device on node i. When i = 1, it means that the node is equipped with energy storage. N is the number of nodes.

[0018] The objective function for maximizing power restoration during a fault is:

[0019]

[0020] Among them, α i It is a binary variable. When the value is 1, it means that node i can use the energy storage device to restore power supply when a fault occurs. LDi Indicates the power that the node can recover after a failure occurs.

[0021] Furthermore, the constraints of the distribution network energy storage device site selection and sizing optimization model include parameterized power flow constraints, substation output power constraints, node voltage constraints, branch current constraints, energy storage device operation constraints, network operation constraints during fault recovery, and fault recovery network structure constraints.

[0022] Furthermore, the parameterized power flow constraint is:

[0023]

[0024] in, is the active power at the substation outlet at time t, is the active power discharged by the energy storage device at node i at time t, is the active power of the energy storage device at node i at time t, is the active load of node i at time t, is the reactive output of the photovoltaic unit at node i at time t, is the reactive power of the energy storage device at node i at time t, is the reactive load of node i at time t;

[0025] The power constraint at the substation outlet is:

[0026] P Gimin <P Gi,t <P Gimax

[0027] Q Gimin Gi,t Gimax

[0028] in, is the active power at the substation outlet at time t, is the reactive power at the substation outlet at time t, P Gimin 、P Gimax Represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax Respectively represent the minimum and maximum values ​​of reactive power provided by the substation;

[0029] The voltage constraint of the node is:

[0030] V i,min ≤V i,t ≤V i,max

[0031] Among them, V i,t represents the voltage amplitude of node i at time t, V i,min and V i,max are the upper and lower limits of the node voltage respectively; the branch current constraint is:

[0032] |I ij,t | ijmax

[0033] Among them, I ij,t is the current amplitude on the branch between nodes ij at time t, I ijmax is the maximum current amplitude that the branch between nodes ij can carry;

[0034] The energy storage device operation constraints are:

[0035] v i,ESS SOC min ≤SOC i,t ≤v i,ESS SOC max

[0036]

[0037] SOC i,0 =SOC i,24

[0038] Among them, SOC i,t , SOC i,t-1 are the capacity of the energy storage device at time t and time t-1, SOC min , SOC max Respectively represent the minimum and maximum capacity of the energy storage device, v i,ESS ​​​It is a binary variable. When the value is 1, it means that energy storage is installed at node i. are the charging power and discharging power of the energy storage device at node i at time t, respectively, C ,η D are the charging efficiency and discharging efficiency of the energy storage device, P Ci,max 、P Di,max are the maximum charging power and the maximum discharging power of the energy storage device at node i, respectively, and b i,t is a binary variable, and when its value is 1, it indicates that the energy storage is charging;

[0039] The network operation constraints during fault recovery are:

[0040]

[0041] Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i;

[0042] The fault recovery network structure constraints are:

[0043]

[0044] in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of nodes i and j. A value of 1 indicates recovery, and a value of 0 indicates non-recovery.

[0045] Furthermore, the global search optimization method based on the consensus multi-objective particle swarm algorithm in step 2 includes the following steps:

[0046] Step 2.1, set the number of particles, the maximum number of particles in the non-dominated solution library and the maximum number of iterations;

[0047] Step 2.2, initialize the position x of all particles i , the best position p of all particles at initialization best,i is x i , particle velocity v i is 0;

[0048] Step 2.3: For each particle position, calculate the corresponding fitness value according to each objective function, select the particle representing the non-dominated solution, and put it into the non-dominated solution library;

[0049] Step 2.4: Calculate the updated velocity and position based on the current position and velocity of each particle.

[0050]

[0051] in, is the position of the i-th particle after the k-th iteration, is the velocity of the i-th particle after the k-th iteration, g best,k is the best position of all particles after the kth iteration, p best,i,k is the optimal position of the i-th particle after the k-th iteration, round() is a function that discretizes the particle position; w is the inertia coefficient, r1 and r2 are random coefficients;

[0052] Step 2.5: Calculate the fitness values ​​of all particles after the update, select the particles representing the non-dominated solution, put them into the non-dominated solution library, update the non-dominated solution library, and filter out the particles representing the dominated solution;

[0053] Step 2.6: If the maximum number of iterations is reached, go to step 2.9; otherwise, go to step 2.7.

[0054] Step 2.7: If the number of particles in the non-dominated solution library reaches the maximum number, go to step 2.8; otherwise, go to step 2.4.

[0055] Step 2.8: Adaptive K-means clustering is used to cluster the particles in the non-dominated solution library, and the consensus state of the non-dominated solution is monitored and determined during the iteration process.

[0056] Step 2.9: Determine whether the particles have reached a consensus state. If they have reached a consensus state, go to step 2.10; otherwise, go to step 2.4.

[0057] Step 2.10: Output the particles in the non-dominated solution library that reaches consensus, including the non-dominated solution set close to Pareto optimality and the frontier close to Pareto.

[0058] Furthermore, the method of clustering particles in the non-dominated solution library using adaptive K-means clustering in step 2.8 includes the following steps:

[0059] Step 2.8.1. Set the upper and lower limits of the number of clusters and set a threshold θ for each class. max ;

[0060] Step 2.8.2: Randomly select K data points from the data set as the initial center points of the cluster;

[0061] Step 2.8.3: Cluster the dataset using the K-means clustering algorithm based on the initial cluster centers obtained in step 2.8.2.

[0062] Step 2.8.4: Based on the clustering results of step 2.8.3, for each class, calculate the θ index to evaluate the similarity between the class center and the members:

[0063]

[0064] Among them, c is the cluster center, x i is the i-th data in the class, n k is the number of data in the class;

[0065] Step 2.8.5. Compare the θ index of each class. If θ≤θ max , then the clustering result is acceptable, go to step 2.8.7; otherwise, the result is not acceptable, go to step 2.8.6;

[0066] Step 2.8.6: For the indicator θ>θ max The class is split into 2 classes using the K-means clustering algorithm. For each subclass of the new split, the θ index is continued to be calculated. If θ≤θ max , the clustering result is acceptable, go to step 2.8.7; otherwise, the result is not acceptable, repeat step 2.8.6;

[0067] Step 2.8.7: Output the clustering results.

[0068] Furthermore, the specific implementation method of step 3 is: after obtaining a non-dominated solution set close to Pareto optimality through global target search optimization, directly set the objective function value for each objective function through the decision list:

[0069]

[0070] Among them, f k (u,x) is the kth objective function, n is the number of objective functions, The upper limit of the objective function, The lower limit of the objective function, wl k A specific objective function value.

[0071] Furthermore, the specific implementation method of selecting the local deep optimization target in step 4 is: after the location, rated capacity and rated power of the energy storage device are obtained based on the preliminary calculation, the objective function f2 fault recovery load is selected as the local deep optimization target, and the objective function f2 fault recovery load is converted into a constraint condition.

[0072] Furthermore, the method for searching the recovery area in step 5 includes the following steps:

[0073] Step 5.1: Input initial data;

[0074] Step 5.2: When a fault occurs, prioritize using energy storage to power important loads. Use the Dijkstra algorithm to find the energy storage device and its path with the shortest distance to the important loads. Set the calculated important load nodes, energy storage nodes, and their paths as the recovery area.

[0075] Step 5.3: Update the restored area network information and determine a possible new restoration node based on the network structure. The new restoration node must have only one connection line to the original restoration area to ensure the radial topology of the restoration area network.

[0076] Step 5.4: Determine a new recovery area based on the new recovery nodes obtained in step 5.3. Consider the network operation constraints during the failure and the network structure constraints for failure recovery. Calculate the power flow in the new recovery area to determine whether the recovery plan is feasible. If convergence is achieved, the plan is feasible.

[0077] Step 5.5: If all possible new recovery plans have been calculated, proceed to the next step; if not, return to step 5.3 to continue calculating possible recovery plans.

[0078] Step 5.6: Select the recovery plan that meets the recovery goal from the multiple recovery plans calculated in step 5.4.

[0079] Furthermore, the network operation constraints during the failure are:

[0080]

[0081] Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i;

[0082] The fault recovery network structure constraints are:

[0083]

[0084] in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of nodes i and j. A value of 1 indicates recovery, and a value of 0 indicates non-recovery.

[0085] The advantages and positive effects of the present invention are:

[0086] 1. The present invention uses user preference information as a guide, combining the global search capability of the multi-objective particle swarm algorithm and the local rapid optimization capability of the interior point method to solve the siting and sizing problem of the energy storage system. It can quickly obtain the optimal solution that meets user preferences and meets the load recovery requirements of the power grid in the event of a fault.

[0087] 2. The present invention fully considers the recovery of distribution network failures under extreme disasters to select the location and capacity of energy storage. In the global optimization search, the adaptive K-means clustering algorithm is used to improve the multi-objective particle swarm algorithm, which can quickly obtain multiple non-dominated solutions close to the Pareto optimality. Compared with the traditional method of terminating the iterative process by setting the maximum number of iterations in advance, it has the characteristics of fast speed and guaranteed globality. The user decision list is introduced, and the solution process based on user preferences is more in line with actual engineering needs. A good initial point is provided by the global optimization search, which allows the interior point method to be solved quickly. The present invention combines the globality of the intelligent algorithm and the speed of the local algorithm, with short calculation time and better results, and user preferences are taken into account in the solution process. At the same time, the present invention takes into account the economic cost of the distribution network and the recovery of the power grid failure under extreme disasters. The calculated configuration scheme of the energy storage device can meet the load recovery requirements of the power grid in the event of a failure under the lowest economic conditions.

[0088] 3. The present invention is rationally designed and proposes a consensus-based multi-objective particle swarm evolution method. It analyzes the maturity of the population through a clustering algorithm and implements local fine-tuning in combination with a local optimization algorithm, effectively shortening the time consumption of the evolution process and thus improving computational efficiency. Combining the globality of the intelligent optimization algorithm with the rapid convergence of the local method, the invention incorporates user preferences by setting a user decision list during the solution process, thereby realizing the rapid calculation of one or more Pareto optimal solutions that meet the user preferences. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 Schematic diagram of the adaptive K-means clustering of the present invention;

[0090] Figure 2 A 24-hour load forecast curve diagram provided by an embodiment of the present invention;

[0091] Figure 3 A 24-hour wind turbine active power output curve diagram provided in an embodiment of the present invention;

[0092] Figure 4 A 54-node structure diagram and a schematic diagram of the energy storage alternative location provided in an embodiment of the present invention;

[0093] Figure 5 This is a result diagram of global search optimization based on consensus particle swarm algorithm given in an embodiment of the present invention;

[0094] Figure 6A schematic diagram of an area where power supply can be restored through an energy storage device when a generator stops supplying power due to an extreme fault according to an embodiment of the present invention;

[0095] Figure 7 This is a schematic diagram of an area where power supply can be restored through an energy storage device when a generator stops supplying power due to an extreme fault in an embodiment of the present invention. DETAILED DESCRIPTION

[0096] The present invention is further described below in conjunction with the accompanying drawings.

[0097] The design concept of the present invention is as follows: when constructing the optimization model for the site selection and sizing of energy storage devices in the distribution network, the present invention fully considers the economic cost and the system's fault recovery capability in the event of extreme disasters. In the first stage, global search optimization is adopted, and a consensus-based multi-objective particle swarm algorithm is used to output multiple non-dominated solutions close to Pareto optimality, set a user decision preference list, and select a preliminary configuration plan for the site selection and capacity of the distribution network energy storage that meets the user's preferences based on the decision list; in the second stage, from the preliminary site selection plan selected in the previous stage, a local deep optimization target is selected for the set of non-dominated solutions that meet the user's preferences. First, the recovery area is searched based on the user's recovery preference under extreme disasters, and then the user's preference for economic cost is considered, and the optimal capacity configuration plan is solved using the interior point method.

[0098] Based on the above design concept, the present invention proposes a method for energy storage site selection and sizing considering distribution network fault recovery under extreme disasters, including the following steps:

[0099] Step 1: Obtain the historical curves of renewable energy active output and load as input data.

[0100] Step 2: Using the installation location and installation capacity of the distribution network energy storage device as the control variables, a mathematical model is constructed for the distribution network energy storage site selection and sizing problem. The data from step 1 is input and a global search optimization is performed using a consensus-based multi-objective particle swarm algorithm to obtain multiple non-dominated solutions close to Pareto optimality.

[0101] In this step, a distribution network energy storage device location and sizing optimization model is constructed with the objective function of minimizing the economic cost of the distribution network and maximizing the restoration of power supply during a fault. The economic cost is:

[0102]

[0103] Among them, C inv represents the installation cost of the energy storage device, C m represents the operation and maintenance cost of energy storage, C O represents the cost of purchasing electricity from the upper power grid, γ represents the annual interest rate, C E,in is the unit price of the rated capacity of the energy storage device, C P,inis the unit price of the energy storage device rated power, The fixed installation cost of the energy storage device, E ES,i is the rated capacity of the energy storage device, P ES,N,i is the rated power of the energy storage device, u i is a binary variable associated with the energy storage device on node i. When i = 1, it means that the node is equipped with energy storage. N is the number of nodes.

[0104] The recovery goals are:

[0105]

[0106] Among them, α i It is a binary variable. When the value is 1, it means that node i can use the energy storage device to restore power supply when a fault occurs. LDi Indicates the power that the node can recover after a failure occurs.

[0107] The constraints of the distribution network energy storage device location and sizing optimization model include parameterized power flow constraints, substation output power constraints, node voltage constraints, branch current constraints, energy storage device operation constraints, network operation constraints during fault recovery, and fault recovery network structure constraints.

[0108] Parametric power flow constraints:

[0109]

[0110] in, is the active power at the substation outlet at time t, is the active power discharged by the energy storage device at node i at time t, is the active power of the energy storage device at node i at time t, is the active load of node i at time t, is the reactive output of the photovoltaic unit at node i at time t, is the reactive power of the energy storage device at node i at time t, is the reactive load of node i at time t;

[0111] Power constraints at substation outlet:

[0112] P Gimin <P Gi,t <P Gimax

[0113] Q Gimin Gi,t Gimax

[0114] in, is the active power at the substation outlet at time t, ​​is the reactive power at the substation outlet at time t, Q Gimin 、P Gimax Represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax Respectively represent the minimum and maximum values ​​of reactive power provided by the substation;

[0115] Voltage constraints of nodes:

[0116] V i,min ≤V i,t ≤V i,max

[0117] Among them, V i,t represents the voltage amplitude of node i at time t, V i,min and V i,max are the upper and lower limits of the node voltage respectively; branch current constraints:

[0118] |I ij,t | ijmax

[0119] Among them, I ij,t is the current amplitude on the branch between nodes ij at time t, I ijmax is the maximum current amplitude that the branch between nodes ij can carry;

[0120] Energy storage device operation constraints:

[0121] v i,ESS SOC min ≤SOC i,t ≤v i,ESS SOC max

[0122]

[0123] SOC i,0 =SOC i,24

[0124] Among them, SOC i,t , SOC i,t-1 are the capacity of the energy storage device at time t and time t-1, SOC min , SOC max Respectively represent the minimum and maximum capacity of the energy storage device, v i,ESS It is a binary variable. When the value is 1, it means that energy storage is installed at node i. are the charging power and discharging power of the energy storage device at node i at time t, respectively, C ,η D are the charging efficiency and discharging efficiency of the energy storage device, P Ci,max 、P Di,max ​are the maximum charging power and the maximum discharging power of the energy storage device at node i, respectively, and b i,t It is a binary variable, and when its value is 1, it means that the energy storage is charging.

[0125] Network operation constraints during fault recovery:

[0126]

[0127] Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i.

[0128] Failure recovery network structure constraints:

[0129]

[0130] in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of nodes i and j. A value of 1 indicates recovery, and a value of 0 indicates non-recovery.

[0131] In this step, the global search optimization based on the consensus multi-objective particle swarm algorithm is used to obtain multiple non-dominated solutions close to the Pareto optimality, including the following steps:

[0132] Step 2.1. Set the number of particles, the maximum number of particles in the non-dominated solution library, and the maximum number of iterations.

[0133] Step 2.2, initialize the position x of all particles i , the best position p of all particles at initialization best,i is x i , particle velocity v i is 0.

[0134] Step 2.3: For each particle position, calculate the corresponding fitness value according to each objective function, select the particle representing the non-dominated solution, and put it into the non-dominated solution library.

[0135] Step 2.4. Calculate the updated velocity and position based on the current position and velocity of each particle:

[0136]

[0137] in, is the position of the i-th particle after the k-th iteration, is the velocity of the i-th particle after the k-th iteration, g best,k is the best position of all particles after the kth iteration, p best,i,k is the optimal position of the i-th particle after the k-th iteration, and round() is a function that discretizes the particle's position. The particle's velocity update is composed of three components: the particle's own inertia, the direction of the particle's optimal position, and the direction of the optimal position of the group's particles. w is the inertia coefficient. It should be large in the initial iterations to ensure good global search capabilities. As iterations proceed, this coefficient should be reduced to ensure iteration efficiency. r1 and r2 are random coefficients.

[0138] Step 2.5: Calculate the fitness values ​​of all particles after the update, select the particles representing the non-dominated solution, put them into the non-dominated solution library, update the non-dominated solution library, and filter out the particles representing the dominated solution.

[0139] Step 2.6: If the maximum number of iterations is reached, go to step 2.9; otherwise, go to step 2.7.

[0140] Step 2.7: If the number of particles in the non-dominated solution library reaches the maximum number, go to step 2.8; otherwise, go to step 2.4.

[0141] Step 2.8: Adaptive K-means clustering is used to cluster the particles in the non-dominated solution library, and the consensus state of the non-dominated solution in the iteration process is monitored and judged. The specific method is as follows: Figure 1 As shown, the following steps are included:

[0142] Step 2.8.1. Set the upper and lower limits of the number of clusters and set a threshold θ for each class. max .

[0143] Step 2.8.2: Randomly select K data points in the data set as the initial center points of the cluster.

[0144] Step 2.8.3: Based on the initial cluster center points obtained in step 2.8.2, cluster the data set using the K-means clustering algorithm.

[0145] Step 2.8.4: Based on the clustering results of step 2.8.3, for each class, calculate the θ index to evaluate the similarity between the class center and the members:

[0146]

[0147] Among them, c is the cluster center, x i is the i-th data in the class, n k is the number of data in the class.

[0148] Step 2.8.5. Compare the θ index of each class. If θ≤θ max , the clustering result is acceptable, go to step 2.8.7; otherwise, the result is unacceptable, go to step 2.8.6.

[0149] Step 2.8.6: For the indicator θ>θ max The class is split into 2 classes using the K-means clustering algorithm. For each subclass of the new split, the θ index is continued to be calculated. If θ≤θ max , the clustering result is acceptable, go to step 2.8.7; otherwise, the result is unacceptable, repeat step 2.8.6.

[0150] Step 2.8.7: Output the clustering results.

[0151] Step 2.9: Determine whether the particles have reached a consensus state. If they have reached a consensus state, go to step 2.10; otherwise, go to step 2.4.

[0152] Step 2.10: Output the particles in the non-dominated solution library that reaches consensus, including the non-dominated solution set close to Pareto optimality and the frontier close to Pareto.

[0153] Step 3: Set up a user decision list based on user preferences.

[0154] In actual engineering, the user's ultimate goal is generally not to obtain a complete Pareto non-dominated solution set, but a non-dominated solution set that meets the expectations of different objective functions. Therefore, the solution process based on user preferences better meets the needs of actual engineering.

[0155] After the global target search optimization obtains a non-dominated solution set close to Pareto optimality, a decision list can be used to directly set a specific upper limit (acceptable worst case) for each objective function, or to set a preference interval, or even a specific objective function value:

[0156]

[0157] f k (u,x)=wl k k=1,2,…n

[0158] Among them, f k (u,x) is the kth objective function, n is the number of objective functions, The upper limit of the objective function, The lower limit of the objective function, wl k A specific objective function value.

[0159] Step 4: According to the user decision list set in step 3, select the non-dominated solution in step 2 that meets the user's preferences. At the same time, for the non-dominated solution that meets the user's preferences, select the local depth optimization objective.

[0160] After the location, rated capacity and rated power of the energy storage device are obtained based on the preliminary calculation, the objective function f2 to restore the load is selected as the local deep optimization target, and the economic cost of the objective function f1 is transformed into a constraint condition.

[0161] Step 5: Based on the local depth optimization goal selected in step 4, use the shortest path method to search for the power grid failure recovery area under extreme disasters and select the site selection plan that can meet the power supply restoration goal.

[0162] In this step, the method for searching the power grid fault recovery area includes the following steps:

[0163] Step 5.1: Input initial data.

[0164] Step 5.2: When a fault occurs, give priority to using energy storage to supply power to important loads. Use the Dijkstra algorithm to find the energy storage device and its path with the shortest distance to the important loads, and set the calculated important load nodes, energy storage nodes, and their paths as the recovery area.

[0165] Step 5.3: Update the restored area network information and determine the possible new restoration node based on the network structure. The new restoration node has only one connection line with the original restoration area to ensure the radial topology of the restoration area network.

[0166] Step 5.4: Determine a new recovery area based on the new recovery node obtained in step 5.3. Consider the network operation constraints during the failure and the fault recovery network structure constraints. Calculate the power flow in the new recovery area to determine whether the recovery plan is feasible. If convergence occurs, it means that the plan is feasible.

[0167] Network operation constraints during failures:

[0168]

[0169] Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i;

[0170] Failure recovery network structure constraints:

[0171]

[0172] in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of node i and node j. A value of 1 indicates recovery and a value of 0 indicates non-recovery.

[0173] Restore regional node voltage constraints:

[0174] V res,i,min ≤V res,i,t ≤V res,i,max

[0175] V res,i,t Represents the voltage of node i in the recovery area, V res,i,min 、V res,i,max Represent its lower and upper limits respectively;

[0176] Restoring regional energy storage power constraints:

[0177] P essres,D,i ≤P res,i,max

[0178] Among them, P essres,D,i is the discharge power of energy storage at node i, P res,i,max is the maximum power of energy storage that can be installed on node i.

[0179] Step 5.5: If all possible new recovery plans have been calculated, proceed to the next step; if not, return to step 5.3 to continue calculating possible recovery plans.

[0180] Step 5.6: Select the recovery plan that meets the recovery goal from the multiple recovery plans calculated in step 5.4.

[0181] Step 6: Based on the recovery plan obtained from the fault recovery area search in step 5, the multi-objective optimization problem is converted into a single-objective energy storage site selection and sizing optimization problem. The model is solved using the interior point method to obtain the control variable values ​​that meet the constraints and the distribution network energy storage device that meets the economic and technical indicators.

[0182] The optimization problem of energy storage site selection and sizing in distribution networks can be expressed as a general multi-objective optimization problem:

[0183] miny=F(x)=[f1(x),f2(x),…,f m (x) T

[0184] stH(x)=0

[0185] G(x)=0

[0186] After selecting one objective function for deep optimization, the remaining objective functions are converted into constraints and added to the model:

[0187] minf i (x)

[0188] stf j (x)≤ε j j=1,2,…,m,j≠i

[0189] H(x)=0

[0190] G(x)=0

[0191] Among them, the objective function of deep optimization is economic cost. According to the search results of the restoration area in step 5, the restoration goals and restoration plans are converted into constraints and added to the model.

[0192] In order to further illustrate the effect of the present invention, according to the above method Figure 4 The power distribution network shown is tested in the example. Figure 4 The proposed distribution network structure consists of 54 nodes and 50 branches. Nodes 51, 52, 53, and 54 are generator nodes, and wind turbines 1, 2, 3, and 4 are connected at nodes 36, 1, 44, and 21, respectively. The energy storage device has a rated capacity price of 600 yuan / kWh and a rated power price of 400 yuan / kW. There are 12 potential energy storage installation locations, with node numbers 2, 4, 9, 12, 19, 28, 29, 30, 35, 38, 46, and 50. The electricity price is 0.3377 yuan / kWh from 0:00 AM to 8:00 AM, 0.6648 yuan / kWh from 8:00 AM to 4:00 PM, and 0.1090 yuan / kWh from 4:00 PM to midnight.

[0193] Figure 2 and Figure 3 The system load and distributed generator active output values ​​are given respectively. Without installing energy storage, the annual cost of the system is 37.58 million yuan.

[0194] After the global search optimization based on consensus multi-objective particle swarm algorithm in step 2, multiple non-dominated solutions close to Pareto optimality are obtained, such as Figure 5 All non-dominated solutions are listed. It can be seen that all non-dominated solutions are listed. In steps 3 and 4, the recovery plan for load user demand is selected. Table 1 shows the configuration of energy storage devices for the optimal solution after the first-stage global search optimization. The total annual economic cost is RMB 35.77 million. Figure 6 It shows the area where power supply can be restored through the energy storage device when the generator stops supplying power due to an extreme fault. The triangle is the restoration node, and the total restored load is 1424kw.

[0195] Table 1. Consensus-based multi-objective particle swarm computing results

[0196] node Rated active power (kW) Rated capacity (MWh) 9 842 6.43 30 682 5.63 38 794 6.44 35 850 7.11

[0197] In step 4, the energy storage installation location is determined, in step 5, the recovery plan under the fault state is determined, and in step 6, the minimum annual cost is calculated. Table 1 shows the energy storage device configuration plan with the total annual economic cost of RMB 33.66 million. Figure 7 It shows the area where power supply can be restored through the energy storage device when the generator stops supplying power due to an extreme fault. The triangle is the restoration node, and the total restored load is 1905kw.

[0198] Table 2 Calculation results of the method of the present invention

[0199] node Rated active power (kW) Rated capacity (MWh) 9 451 4.50 30 938 9.56 38 474 4.84 35 650 5.75

[0200] From the above data, it can be seen that the configuration scheme calculated by the method proposed in the present invention can reduce annual economic costs and restore more loads during extreme power grid faults. Table 3 shows the comparison of the three cases.

[0201] Table 3 Summary of technical cost and economic cost improvements

[0202]

[0203] Compared with the method without installing energy storage device and the method based on multi-objective consensus particle swarm, the method proposed in the present invention can effectively reduce the annual economic cost of the system and improve the power supply recovery of the system in case of fault.

[0204] It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive. Therefore, the present invention includes but is not limited to the embodiments described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of the present invention also fall within the scope of protection of the present invention.

Claims

1. A method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters, characterized by: The following steps are involved: Step 1: Obtain the historical curve of renewable energy active output and load as input data; Step 2: Using the installation location and capacity of the distribution network energy storage device as control variables, a distribution network energy storage device location and sizing optimization model is constructed for the distribution network energy storage location and sizing problem. The data from Step 1 is input into the model and a consensus-based multi-objective particle swarm algorithm is used for global search optimization to obtain multiple non-dominated solutions close to Pareto optimality. Step 3: Set up a user decision list based on user preferences; Step 4: According to the user decision list set in step 3, select the non-dominated solution that meets the user's preference in step 2. For the non-dominated solution that meets the user's preference, select the local depth optimization objective; Step 5: Based on the local deep optimization goal selected in step 4, use the shortest path method to search for the power grid failure restoration area under extreme disasters and select a site selection plan that can meet the power supply restoration goal; In this step, when a fault occurs, priority is given to using energy storage to power important loads. The Dijkstra algorithm is used to find the energy storage device with the shortest distance from the important load and its path, and the calculated important load nodes, energy storage nodes and their paths are set as the recovery area. The network information of the restored area is updated and a possible new recovery node is determined based on the network structure. The new recovery node has only one connection line with the original recovery area to ensure the radial topology of the recovery area network. A new recovery area is determined based on the new recovery node. Considering the network operation constraints at the time of the fault and the fault recovery network structure constraints, the power flow of the new recovery area is calculated to determine whether the recovery plan is feasible. If convergence is achieved, it means that the plan is feasible. The fault recovery network structure constraints are: in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of node i and node j. A value of 1 indicates recovery and a value of 0 indicates non-recovery. Step 6: Based on the restoration plan obtained in Step 5, the multi-objective energy storage site selection and sizing problem, which considers both economic benefits and fault recovery, is transformed into a single-objective energy storage site selection and sizing optimization problem. The distribution network energy storage device site selection and sizing optimization model is solved using the interior point method to calculate the control variable values ​​that satisfy the constraints, thereby obtaining a distribution network energy storage device site selection and sizing plan that meets both economic and fault recovery requirements. The network operation constraints during the failure are: Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i.

2. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized by: The distribution network energy storage device location and sizing optimization model takes minimizing the economic cost of the distribution network and maximizing the restoration of power supply during faults as the objective function: Among them, the objective function of minimizing the economic cost of the distribution network is: Among them, C inv represents the installation cost of the energy storage device, C m represents the operation and maintenance cost of energy storage, C O represents the cost of purchasing electricity from the upper power grid, γ represents the annual interest rate, C E,in is the unit price of the rated capacity of the energy storage device, C P,in is the unit price of the energy storage device rated power, The fixed installation cost of the energy storage device, E ES,i is the rated capacity of the energy storage device, P ES,N,i is the rated power of the energy storage device, u i is a binary variable associated with the energy storage device on node i. When i = 1, it means that the node is equipped with energy storage. N is the number of nodes. The objective function for maximizing power restoration during a fault is: Among them, α i It is a binary variable. When the value is 1, it means that node i can use the energy storage device to restore power supply when a fault occurs. LDi Indicates the power that the node can recover after a failure occurs.

3. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 2 is characterized by: The constraints of the distribution network energy storage device site selection and sizing optimization model include parameterized power flow constraints, substation output power constraints, node voltage constraints, branch current constraints, energy storage device operation constraints, network operation constraints during fault recovery, and fault recovery network structure constraints.

4. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 3 is characterized by: The parameterized power flow constraint is: in, is the active power at the substation outlet at time t, is the active power discharged by the energy storage device at node i at time t, is the active power of the energy storage device charging at node i at time t, is the active load of node i at time t, is the reactive output of the photovoltaic unit at node i at time t, is the reactive power of the energy storage device at node i at time t, is the reactive load of node i at time t; The power constraint at the substation outlet is: P Gimin <P Gi,t <P Gimax Q Gimin <Q Gi,t <Q Gimax in, is the active power at the substation outlet at time t, is the reactive power at the substation outlet at time t, P Gimin 、P Gimax Represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax Respectively represent the minimum and maximum values ​​of reactive power provided by the substation; The voltage constraint of the node is: In i,min ≤V i,t ≤V i,max Among them, V i,t represents the voltage amplitude of node i at time t, V i,min and V i,max are the upper and lower limits of the node voltage respectively; The branch current constraint is: |I ij,t |<I ijmax Among them, I ij,t is the current amplitude on the branch between nodes ij at time t, I ijmax is the maximum current amplitude that the branch between nodes ij can carry; The energy storage device operation constraints are: v i,ESS SOC min ≤SOC i,t ≤v i,ESS SOC max SOCIETY i,0 =SOC i,24 Among them, SOC i,t , SOC i,t-1 are the capacity of the energy storage device at time t and time t-1, SOC min , SOC max Respectively represent the minimum and maximum capacity of the energy storage device, v i,ESS It is a binary variable. When the value is 1, it means that energy storage is installed at node i. are the charging power and discharging power of the energy storage device at node i at time t, respectively, C ,η D are the charging efficiency and discharging efficiency of the energy storage device, P Ci,max 、P Di,max are the maximum charging power and the maximum discharging power of the energy storage device at node i, respectively, and b i,t is a binary variable, and when its value is 1, it indicates that the energy storage is charging; The network operation constraints during fault recovery are: Among them, P essres,D,i is the active power discharged by the energy storage device at node i in the recovery state, P resL,i is the active load of node i in the recovery state, Q resE,i is the reactive power of the energy storage device at node i in the recovery state, Q resL,i is the reactive load of node i; The fault recovery network structure constraints are: in, is a binary variable representing the power status of the line between node i and node j at time t. When the value is 1, it means power is on. Indicates the recovery status of nodes i and j. A value of 1 indicates recovery, and a value of 0 indicates non-recovery.

5. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized by: The global search optimization method based on the consensus multi-objective particle swarm algorithm in step 2 includes the following steps: Step 2.1, set the number of particles, the maximum number of particles in the non-dominated solution library and the maximum number of iterations; Step 2.2, initialize the position x of all particles i , the best position p of all particles at initialization best,i is x i , particle velocity v i is 0; Step 2.3: For each particle position, calculate the corresponding fitness value according to each objective function, select the particle representing the non-dominated solution, and put it into the non-dominated solution library; Step 2.4: Calculate the updated velocity and position based on the current position and velocity of each particle. in, is the position of the i-th particle after the k-th iteration, is the velocity of the i-th particle after the k-th iteration, g best,k is the best position of all particles after the kth iteration, p best,i,k is the optimal position of the i-th particle after the k-th iteration, round() is a function that discretizes the particle position; w is the inertia coefficient, r1 and r2 are random coefficients; Step 2.5: Calculate the fitness values ​​of all particles after the update, select the particles representing the non-dominated solution, put them into the non-dominated solution library, update the non-dominated solution library, and filter out the particles representing the dominated solution; Step 2.6: If the maximum number of iterations is reached, go to step 2.9; otherwise, go to step 2.

7. Step 2.7: If the number of particles in the non-dominated solution library reaches the maximum number, go to step 2.8; otherwise, go to step 2.

4. Step 2.8: Adaptive K-means clustering is used to cluster the particles in the non-dominated solution library, and the consensus state of the non-dominated solution is monitored and determined during the iteration process. Step 2.9: Determine whether the particles have reached a consensus state. If they have reached a consensus state, go to step 2.10; otherwise, go to step 2.

4. Step 2.10: Output the particles in the non-dominated solution library that reaches consensus, including the non-dominated solution set close to Pareto optimality and the frontier close to Pareto.

6. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 5 is characterized by: The method of clustering particles in the non-dominated solution library using adaptive K-means clustering in step 2.8 includes the following steps: Step 2.8.

1. Set the upper and lower limits of the number of clusters and set a threshold θ for each class. max ; Step 2.8.2: Randomly select K data points from the data set as the initial center points of the cluster; Step 2.8.3: Cluster the dataset using the K-means clustering algorithm based on the initial cluster centers obtained in step 2.8.

2. Step 2.8.4: Based on the clustering results of step 2.8.3, for each class, calculate the θ index to evaluate the similarity between the class center and the members: Among them, c is the cluster center, x i is the i-th data in the class, n k is the number of data in the class; Step 2.8.

5. Compare the θ index of each class. If θ≤θ max , then the clustering result is acceptable, go to step 2.8.7; otherwise, the result is not acceptable, go to step 2.8.6; Step 2.8.6: For the indicator θ>θ max The class is split into 2 classes using the K-means clustering algorithm. For each subclass of the new split, the θ index is continued to be calculated. If θ≤θ max , the clustering result is acceptable, go to step 2.8.7; otherwise, the result is not acceptable, repeat step 2.8.6; Step 2.8.7: Output the clustering results.

7. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized by: The specific implementation method of step 3 is: after obtaining a non-dominated solution set close to Pareto optimality through global target search optimization, directly set the objective function value for each objective function through the decision list: f k (u,x)=wl k k=1,2,…n Among them, f k (u,x) is the kth objective function, n is the number of objective functions, The upper limit of the objective function, The lower limit of the objective function, wl k A specific objective function value.

8. The method for energy storage site selection and sizing considering distribution network failure recovery under extreme disasters according to claim 1 is characterized by: The specific implementation method of selecting the local deep optimization target in step 4 is: after the location, rated capacity and rated power of the energy storage device are obtained based on the preliminary calculation, the objective function f2 fault recovery load is selected as the local deep optimization target, and the objective function f2 fault recovery load is converted into a constraint condition.

9. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized by: The method for searching the recovery area in step 5 includes the following steps: Step 5.1: Input initial data; Step 5.2: When a fault occurs, prioritize using energy storage to power important loads. Use the Dijkstra algorithm to find the energy storage device and its path with the shortest distance to the important loads. Set the calculated important load nodes, energy storage nodes, and their paths as the recovery area. Step 5.3: Update the restored area network information and determine a possible new restoration node based on the network structure. The new restoration node must have only one connection line to the original restoration area to ensure the radial topology of the restoration area network. Step 5.4: Determine a new recovery area based on the new recovery nodes obtained in step 5.

3. Consider the network operation constraints during the failure and the network structure constraints for failure recovery. Calculate the power flow in the new recovery area to determine whether the recovery plan is feasible. If convergence is achieved, the plan is feasible. Step 5.5: If all possible new recovery plans have been calculated, proceed to the next step; if not, return to step 5.3 to continue calculating possible recovery plans. Step 5.6: Select the recovery plan that meets the recovery goal from the multiple recovery plans calculated in step 5.4.

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