Energy storage locating and sizing method considering power distribution network fault recovery under extreme disasters

Abstract

The invention relates to an energy storage locating and sizing method considering power distribution network fault recovery under extreme disasters, and the method is technically characterized in that a plurality of non-dominated solutions close to Pareto optimum are obtained through the global search optimization of a multi-target particle swarm algorithm based on consensus; a shortest path method is used for searching a power grid fault recovery area under an extreme disaster, a site selection scheme capable of meeting a power supply recovery target is screened out from the power grid fault recovery area, and a multi-target energy storage site selection and sizing problem considering economic benefits and fault recovery is converted into a single-target energy storage site selection and sizing optimization problem. And solving the power distribution network energy storage device addressing and sizing optimization model by using an interior point method to obtain a power distribution network energy storage device addressing and sizing scheme meeting the requirements of an economic index and a fault recovery index. The method is reasonable in design, the optimal solution meeting user preferences can be quickly obtained, and the load recovery requirement when the power grid breaks down is met.

Description

Technical Field

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

[0002] As one of the most important infrastructure facilities in modern society, the power system maintains the normal operation and development of society. However, when "high-impact, low-probability" extreme natural disasters such as earthquakes, typhoons, and tsunamis occur, important equipment and infrastructure in the distribution network are prone to multi-point failures, and large-scale power outages are still difficult to avoid. When natural disasters occur, power facilities in the distribution network are prone to damage, short circuits, and other failures, which in turn cause large-scale power outages. Therefore, it is necessary to study the emergency control methods of distribution networks under natural disasters to improve the power supply reliability of distribution networks.

[0003] Distributed energy storage devices are introduced into the distribution network as an important means of regulation. Energy storage devices will play an important role in the distribution network. The location and scale of energy storage devices are the first issues to be solved. At present, a large number of scholars have conducted relevant research on the location and scale of energy storage 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 the economy, combine the energy storage cost and the governance effect as the comprehensive evaluation standard for peak regulation, and give 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 grid profit; 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 best, and configures the energy storage capacity; the configuration optimization method of the integrated photovoltaic storage and charging station configuration improves the weed invasion algorithm, optimizes and improves the energy storage capacity optimization model, and uses the particle swarm algorithm and the traversal algorithm to coordinate the configuration optimization of the photovoltaic energy storage system.

[0004] In the above-mentioned distributed energy storage site selection and sizing models, most of them only consider the economic benefit cost, but do not consider the reliability index of fault recovery of the power grid under extreme disasters. In terms of solution, due to the characteristics of random search and the difference in convergence performance of intelligent optimization algorithms, the solution of the site selection and sizing problem of energy storage systems inevitably has disadvantages such as high computational cost and unstable solution quality. Moreover, from the perspective of engineering application, the ultimate goal of decision makers is not a complete Pareto solution set, but to hope that the final Pareto optimal solution meets the expectations of different objective functions. The above methods are difficult to meet the load recovery requirements of the power grid when a fault occurs. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a method for energy storage site selection and sizing that takes into account distribution network fault recovery under extreme disasters, which can quickly obtain the optimal solution that meets user preferences and meets the load recovery requirements of the power grid when a fault occurs.

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

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

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

[0009] Step 2: Taking the installation location and installation capacity of the distribution network energy storage device as the control variables, an optimization model for the site selection and sizing of the distribution network energy storage device is constructed for the site selection and sizing of the distribution network energy storage device. The data of step 1 is input into the model and the global search optimization of the consensus-based multi-objective particle swarm algorithm is used to obtain multiple non-dominated solutions close to the 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, and select the local depth optimization target for the non-dominated solution that meets the user's preference;

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

[0013] Step 6: According to the recovery 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 distribution network energy storage device site selection and sizing optimization model is solved using the interior point method, and the control variable values ​​that meet the constraints are calculated, thereby obtaining a distribution network energy storage device site selection and sizing plan that meets the economic indicators and fault recovery indicators.

[0014] Furthermore, the distribution network energy storage device location and capacity optimization model takes minimizing the economic cost of the distribution network and maximizing the restoration of power supply during 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, and N is the number of nodes;

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

[0019]

[0020] Among them, α i 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 amount of 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 flow constraints, substation output power constraints, node voltage constraints, branch current constraints, energy storage device operation constraints, fault recovery network operation constraints 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 charged by the energy storage device at node i at time t, is the active load of node i at time t, is the reactive power 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 Respectively represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax They represent the minimum and maximum values ​​of reactive power provided by the substation respectively;

[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 ​​​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 being charged;

[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-on status of the line between node i and node j at time t. When the value is 1, it means power-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.

[0045] Furthermore, the global search optimization method based on 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 For 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, based on the current position and velocity of each particle, calculate the updated velocity and position;

[0050]

[0051] in, is the position of the ith particle after the kth iteration, is the velocity of the ith particle after the kth 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 ith particle after the kth iteration, round() is a function that discretizes the particle position; w is the inertia coefficient, r1, 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, cluster the particles in the non-dominated solution library using adaptive K-means clustering, and monitor and determine the consensus state of the non-dominated solution 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 have reached 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 in the data set as the initial center points of the cluster;

[0061] 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;

[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 formula 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 , it indicates that the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not accepted, go to step 2.8.6;

[0066] Step 2.8.6: For the index θ>θ max The class is split into two classes using the K-means clustering algorithm. For each new subclass, the θ index is calculated. If θ≤θ max , it indicates that the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not accepted, 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 objective search optimization, directly set the objective function value for each objective function through a 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, give priority to using energy storage to supply power to important loads. Use the Dijkstra algorithm to find the energy storage device with the shortest distance from the important load and its path, and 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 the possible new restoration node according to 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;

[0076] Step 5.4: Determine a new recovery area based on the new recovery node obtained in step 5.3, consider the network operation constraints at the time of 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, and if convergence occurs, it means that 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 a solution that meets the recovery goal from among the multiple recovery solutions 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-on status of the line between node i and node j at time t. When the value is 1, it means power-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.

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

[0086] 1. The present invention uses user preference information as a guide, combines the global search capability of the multi-objective particle swarm algorithm and the local fast optimization capability of the interior point method to solve the site selection and sizing problem of the energy storage system, and can quickly obtain the optimal solution that meets the user's preferences and meets the load recovery requirements of the power grid when a fault occurs.

[0087] 2. The present invention fully considers the failure recovery of the distribution network 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. By providing a good initial point through global optimization search, the interior point method can be solved quickly. The present invention combines the globality of intelligent algorithms and the rapidity of local algorithms, 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 failure recovery of the power grid 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 reasonably 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, which effectively shortens the time consumption of the evolution process and improves the computational efficiency. It combines the globality of the intelligent optimization algorithm with the rapid convergence of the local method, and adds 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 user preferences. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a schematic diagram of the adaptive K-means clustering of the present invention;

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

[0091] Figure 3 A 24-hour wind turbine active 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 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 in detail below with reference to the accompanying drawings.

[0097] The design concept of the present invention is: when constructing the optimization model for the site selection and capacity determination of energy storage devices in the distribution network, the present invention fully considers the economic cost and the system's fault recovery capability when encountering 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, in the preliminary site selection plan selected in the previous stage, a local deep optimization target is selected for the non-dominated solution set that meets the user's preferences. First, the recovery area is searched according to 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 selecting and sizing energy storage sites considering distribution network fault recovery under extreme disasters, including the following steps:

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

[0100] Step 2: Taking 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 of step 1 is input and the global search optimization of the consensus-based multi-objective particle swarm algorithm is used to obtain multiple non-dominated solutions close to Pareto optimality.

[0101] In this step, a distribution network energy storage device location and capacity optimization model is constructed to minimize the economic cost of the distribution network and maximize the restoration of power supply during failure as the objective function: 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, and N is the number of nodes;

[0104] The recovery goals are:

[0105]

[0106] Among them, α i 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 amount of power that the node can recover after a failure occurs.

[0107] The constraints of the optimization model for the location and capacity of energy storage devices in the distribution network include parameterized power flow constraints, power constraints of substation output, voltage constraints of nodes, 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 charged by the energy storage device at node i at time t, is the active load of node i at time t, is the reactive power 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 Respectively represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax They represent the minimum and maximum values ​​of reactive power provided by the substation respectively;

[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 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 its value is 1, which means that the energy storage is being charged.

[0125] Network operation constraints during failure 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-on status of the line between node i and node j at time t. When the value is 1, it means power-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.

[0131] In this step, the method of obtaining multiple non-dominated solutions close to Pareto optimality based on global search optimization of consensus multi-objective particle swarm algorithm includes 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 For 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 speed and position based on the current position and speed of each particle:

[0136]

[0137] in, is the position of the ith particle after the kth iteration, is the velocity of the ith particle after the kth iteration, g best,k is the best position of all particles after the kth iteration, p best,i,k is the best position of the ith particle after the kth iteration, and round() is a function that discretizes the particle position. The particle velocity update consists of three parts: the inertia of the particle itself, the direction of the particle's own best position, and the direction of the group's best position. w is the inertia coefficient, which should be taken as a larger value in the initial iteration stage to ensure that the particle has a better global search ability. As the iteration proceeds, the coefficient should be appropriately reduced to ensure the efficiency of the iteration. r1, 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 particles in the non-dominated solution library, and the consensus state of the non-dominated solution during the iteration process is monitored and determined. 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, use the K-means clustering algorithm to cluster the data set.

[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 formula 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 , then the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not accepted, go to step 2.8.6.

[0149] Step 2.8.6: For the index θ>θ max The class is split into two classes using the K-means clustering algorithm. For each new subclass, the θ index is calculated. If θ≤θ max , then the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not acceptable, 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 have reached consensus, including the non-dominated solution set close to Pareto optimality and the frontier close to Pareto.

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

[0154] In actual engineering, the ultimate goal of the user is generally not to obtain a complete Pareto non-dominated solution set, but a non-dominated solution set that satisfies 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 the Pareto optimality, a specific upper limit value (acceptable worst case) is directly set for each objective function through the decision list, or a preference interval is set, or even a specific objective function value is set:

[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 that meets the user's preference in step 2, and at the same time, for the non-dominated solution that meets the user's preference, select the local depth optimization target.

[0160] After the location, rated capacity and rated power of the energy storage device are obtained based on preliminary calculations, 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 deep optimization target selected in step 4, use the shortest path method to search for the power grid fault recovery area under extreme disasters and select the site selection plan that can meet the power supply restoration target.

[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 with the shortest distance from the important load and its path, 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 according to 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 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 failure:

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

[0173] Restore the 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 region, V res,i,min 、V res,i,max Respectively represent its lower and upper limits;

[0176] Restoring regional energy storage power constraints:

[0177] P essres,D,i ≤P res,i,max

[0178] Where 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 the i-node.

[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 a solution that meets the recovery goal from among the multiple recovery solutions calculated in step 5.4.

[0181] Step 6: According to the recovery plan obtained by searching the fault recovery area 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 obtain the distribution network energy storage device that meets the economic and technical indicators.

[0182] The problem of optimizing the location and capacity of energy storage 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] Select one objective function for deep optimization, and convert the remaining objective functions into constraints and add them 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 restoration area search result in step 5, the restoration target and restoration plan 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 given distribution network structure contains 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 rated capacity unit price of the energy storage device is 600 yuan / kWh, and the rated power unit price is 400 yuan / kW. There are 12 alternative energy storage installation addresses, 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 to 8:00, 0.6648 yuan / kWh from 8:00 to 16:00, and 0.1090 yuan / kWh from 16:00 to 24:00.

[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 given. It can be seen that all non-dominated solutions have been listed. In step 3 and step 4, the recovery plan of the load user demand is selected. Among them, Table 1 shows the configuration of the energy storage device of the optimal solution after the first-stage global search optimization. The total annual economic cost is 35.77 million yuan. 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. Computation results of consensus-based multi-objective particle swarm

[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 obtained by the final calculation result, with a total annual economic cost of 33.66 million yuan. 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] It can be seen from the above data that the configuration scheme calculated by the method proposed in the present invention can reduce the annual economic cost and restore more loads during extreme power grid faults. Table 3 shows the comparison of the three situations.

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

[0202]

[0203] Compared with the method without installing energy storage device and based on multi-objective consensus particle swarm method, 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 failure.

[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 implementation manner. Any other implementation manners derived by those skilled in the art based on the technical solution 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 new energy active output and load as input data; Step 2: Taking the installation location and installation capacity of the distribution network energy storage device as the control variables, an optimization model for the site selection and sizing of the distribution network energy storage device is constructed for the site selection and sizing of the distribution network energy storage device. The data of step 1 is input into the model and the global search optimization of the consensus-based multi-objective particle swarm algorithm is used to obtain multiple non-dominated solutions close to the 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, and select the local depth optimization target for the non-dominated solution that meets the user's preference; Step 5: Based on the local deep optimization target selected in step 4, the shortest path method is used to search for the power grid fault recovery area under extreme disasters and select a site selection plan that can meet the power supply restoration target; Step 6: According to the recovery 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 distribution network energy storage device site selection and sizing optimization model is solved using the interior point method, and the control variable values ​​that meet the constraints are calculated, thereby obtaining a distribution network energy storage device site selection and sizing plan that meets the economic indicators and fault recovery indicators.

2. The method for selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized in that: The optimization model for the location and capacity of energy storage devices in the distribution network 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, and N is the number of nodes; The objective function for maximizing the restoration of power supply during a fault is: Among them, α i 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 amount of 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 in that: The constraints of the distribution network energy storage device location and capacity optimization model include parameterized power flow constraints, substation output power constraints, node voltage constraints, branch current constraints, energy storage device operation constraints, fault recovery network operation constraints 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 in that: 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 charged by the energy storage device at node i at time t, is the active load of node i at time t, is the reactive power 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 Gimm <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 Respectively represent the minimum and maximum active power provided by the substation, Q Gimin , Q Gimax They represent the minimum and maximum values ​​of reactive power provided by the substation respectively; 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 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 being charged; 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-on status of the line between node i and node j at time t. When the value is 1, it means power-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.

5. The method for selecting a location and determining the capacity of energy storage considering distribution network failure recovery under extreme disasters according to claim 1 is characterized in that: The global search optimization method based on consensus multi-objective particle swarm algorithm in step 2 comprises 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 For 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, based on the current position and velocity of each particle, calculate the updated velocity and position; in, is the position of the ith particle after the kth iteration, is the velocity of the ith particle after the kth 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 ith particle after the kth iteration, round() is a function that discretizes the particle position; w is the inertia coefficient, r1, 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, cluster the particles in the non-dominated solution library using adaptive K-means clustering, and monitor and determine the consensus state of the non-dominated solution 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 have reached 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 in that: 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 in the data set as the initial center points of the cluster; 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; 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 formula 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 , it indicates that the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not accepted, go to step 2.8.6; Step 2.8.6: For the index θ>θ max The class is split into two classes using the K-means clustering algorithm. For each new subclass, the θ index is calculated. If θ≤θ max , it indicates that the clustering result is acceptable, go to step 2.8.7, otherwise, the result is not accepted, 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 in that: The specific implementation method of step 3 is: after obtaining a non-dominated solution set close to Pareto optimality through global objective search optimization, directly set the objective function value for each objective function through the decision list: f k (u, x) = w l 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 selecting and sizing energy storage sites considering distribution network failure recovery under extreme disasters according to claim 1 is characterized in that: 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 in that: The method for searching the recovery area in step 5 comprises the following steps: Step 5.1, input initial data; 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 with the shortest distance from the important load and its path, and 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 the possible new restoration node according to 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; Step 5.4: Determine a new recovery area based on the new recovery node obtained in step 5.3, consider the network operation constraints at the time of 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, and if convergence occurs, it means that 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 a solution that meets the recovery goal from among the multiple recovery solutions calculated in step 5.

4.

10. The method for selecting a location and determining the capacity of energy storage considering distribution network failure recovery under extreme disasters according to claim 9 is characterized in that: 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; The fault recovery network structure constraints are: in, is a binary variable representing the power-on status of the line between node i and node j at time t. When the value is 1, it means power-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.

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