Energy storage station siting and sizing method for improving operation flexibility of power distribution network in multiple scenarios

Abstract

The present application relates to the method for selecting and sizing energy storage power station to improve the operation flexibility of distribution network in multiple scenarios, and belongs to the technical field of distribution network, which comprises the following steps: inputting the basic data of city distribution network; proposing the evaluation index of city distribution network operation flexibility; constructing the planning layer model with the minimum city distribution network comprehensive cost as the objective function; constructing the operation layer model with the minimum city distribution network comprehensive operation flexibility deficiency rate as the optimization objective; establishing the double-layer planning model and solving it by using the improved NSGA-III algorithm. The present application breaks the boundary between the conventional flexibility and reliability of city distribution network, defines the city distribution network comprehensive operation flexibility deficiency rate, and solves the proposed multi-objective double-layer optimization model by using the Levy flight and Lorenze domination to improve the NSGA-III algorithm, and the calculation result is helpful for the subsequent planning and operation design of city distribution network.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network technology, specifically relating to a method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of power distribution networks in multiple scenarios. Background Technology

[0002] As the penetration rate of distributed energy in distribution networks continues to increase, its volatility, intermittency, and randomness cause frequent fluctuations in the net load of the distribution network. This leads to distribution equipment operating at low load levels for extended periods, resulting in significant grid investment. Furthermore, the asynchrony between distributed power output and load can easily cause load shedding, wind and solar power curtailment, and localized operational safety issues, thus reducing the flexibility of the distribution network. It can be said that the distribution network is undergoing a comprehensive and profound transformation and development, and flexibility will be a crucial factor to consider in future distribution network planning and operation. Energy storage devices are considered a highly efficient and stable flexible resource, capable of storing energy when the grid has surplus power and generating energy when the grid is insufficient. Their flexible adjustment of power magnitude and flow direction further enhances the temporal and spatial flexibility of energy utilization. Optimizing the configuration of energy storage in the distribution network and comprehensively considering its flexibility can alleviate peak load demand, optimize distribution network flow, and effectively address the asynchrony between distributed power output and load. This contributes to the safe, stable, and efficient operation of the distribution network, improves its flexibility, and thus delays the construction of power sources and the grid.

[0003] Generally, the optimal configuration of energy storage power stations in distribution networks often requires a two-level programming problem that comprehensively considers both the configuration scheme and the operating curve. The configuration scheme and operating curve are continuously updated and optimized iteratively to obtain the optimal energy storage configuration scheme. Many scholars both domestically and internationally have conducted extensive research on the optimal configuration of energy storage power stations. The literature "Grid Inertial Response-Based Probabilistic Determination of Energy Storage System Capacity Under High Solar Penetration" considers the system's inertial response and calculates the energy storage configuration capacity based on a probabilistic method; the literature "Long-term energy storage capacity optimization in energy buffer system" introduces an energy buffer system to account for the volatility of wind power and optimizes the energy storage capacity with the economic benefits of wind farms as the objective; the literature "Optimal placement of energy storage in the grid" uses a semi-definite relaxation method to solve the optimal energy storage configuration problem, thereby optimizing the configuration point of the energy storage system. However, the above literature only considers the capacity or site selection optimization of energy storage power stations and cannot achieve joint optimization of both. The paper "Optimized planning of distribution network with photovoltaic system, battery storage, and DSTATCOM" establishes a joint optimization configuration model for photovoltaic and energy storage, maximizing both economic and ecological benefits while achieving optimal voltage distribution, and solves the problem based on the NSGA-II algorithm. The paper "Economic Optimization Configuration Method of Distributed Energy Storage to Improve Distribution Network Voltage Quality" considers the peak-shaving and valley-filling effects of energy storage, proposing a two-layer optimization model coupling energy storage configuration schemes and operating curves. However, the above papers do not consider other flexible resources existing in the distribution network. The paper "Multi-objective Optimization Configuration Method of Distribution Network Energy Storage with Renewable Energy Generation" uses voltage quality and distribution network investment and operating costs as optimization objectives, comprehensively considering the impact of various flexible resources such as controllable distributed power sources, energy storage, and reactive power equipment, and constructs a two-layer multi-objective optimization energy storage configuration model. However, this study lacks depth in its research on the uncertainty of flexibility requirements, simply treating it as a deterministic model. In terms of existing literature, most studies either only analyze the power output of generating units without specifically analyzing grid flexibility from the perspective of source-grid-load-storage coordination, or only consider the configuration of energy storage devices with fixed capacity or location of energy storage power stations, ignoring the joint optimization of their scale and location. Furthermore, planning methods that consider grid-side flexibility enhancement measures still need further research.

[0004] Therefore, at this stage, it is necessary to design a site selection and capacity determination method for energy storage power stations to improve the operational flexibility of the distribution network in multiple scenarios in order to solve the above problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of distribution networks in multiple scenarios, in order to solve the technical problems existing in the prior art. In terms of existing literature, most studies either only analyze the unit output without specifically analyzing the grid flexibility from the perspective of source-grid-load-storage coordination, or only consider the configuration of energy storage devices with fixed capacity or location, ignoring the joint optimization of their scale and site selection. Furthermore, planning methods that consider grid-side flexibility improvement measures still need further research.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of distribution networks in multiple scenarios includes the following steps: S1. Input basic data for the urban power distribution network; S2. Propose evaluation indicators for the operational flexibility of urban power distribution networks; S3. Construct a planning layer model with the objective function of minimizing the comprehensive cost of the urban power distribution network; S4. Construct an operation layer model with the optimization objective of minimizing the rate of insufficient comprehensive operational flexibility of urban power distribution networks; S5. Based on the research foundations of S3 and S4, a bi-level programming model is established and solved using the improved NSGA-III algorithm.

[0007] Furthermore, the basic data for the urban power distribution network in step S1 includes: inputting the urban power distribution network topology, line parameters, typical wind and solar power output curves, typical daily load curves, energy storage selection, and other relevant basic data for power distribution network planning and operation calculations.

[0008] Furthermore, step S2 is detailed as follows: Considering the flexibility of routine adjustments to the overall distribution network while also taking into account the reliability of the urban distribution network during operation, the comprehensive operational flexibility insufficiency rate of the urban distribution network is defined, and its mathematical expression is as follows: (1) (2) (3) (4) In the formula: Defined as the rate of insufficient overall operational flexibility of urban power distribution networks; This indicates the rate of insufficient flexibility in the urban power distribution network; The unavailability rate of power supply in urban power distribution networks refers to the percentage of abnormal power consumption time by users in urban power distribution networks. , Defined as the rate of insufficient flexibility in adjusting urban power distribution network rates (both upward and downward). This indicates the weighting coefficient for increasing the rate of insufficient operational flexibility; This indicates the proportion of insufficient flexibility and power supply unavailability in the urban power distribution network.

[0009] Furthermore, step S3 is as follows: The operation layer takes minimizing the overall cost of the urban power distribution network as its objective function, and uses the location and parameter configuration of the ESS as decision variables, as shown in the following formula: (5) In the formula: The total annual investment cost of ESS; Costs related to network losses in urban power distribution networks; The cost of purchasing electricity from the higher-level power grid for the city's power distribution network. The cost incurred in utilizing resources from the source, network, and load sides; This is a penalty imposed on urban power distribution networks due to insufficient flexibility. , , , , These are the weighting coefficients for each cost, and their sum is 1; (1) Annual comprehensive investment cost of energy storage device (6) In the formula: N ess For the number of ESS; For the first j The coefficient for converting the present value of an ESS to its annual value; r The discount rate; This is the investment cost per unit power of the ESS; This is the investment cost per unit capacity of ESS; It is the first j One ESS power parameter; It is the first j One ESS capacity parameter; (2) Urban power distribution network loss cost C loss (7) In the formula: Represents a multi-scenario set, Represents the set of 24 hours in a day. The electricity price sold on the distribution network at time t in scenario s. This refers to the active power loss generated by the distribution network lines in the corresponding scenario. (3) Cost of purchasing electricity from the upstream power grid for urban distribution networks C BUY (8) In the formula: The price at which the power distribution system purchases electricity from the next higher level power grid at time t in scenario s. For the first s Number of days in each scenario The amount of electricity purchased by the distribution network from the upper-level power grid at time t in scenario s; (4) Cost of calling source network load resources Including source-side ESS operating costs Grid-side distribution network reconfiguration costs and load-side demand response costs ; (9) In the formula: , , These represent the unit operating cost, reconfiguration cost, and demand response cost of the ESS, respectively. Representative scenarios s time t Distribution network nodes j The charging and discharging power of the ESS; N b Represents the number of switches in the distribution network; Representative scenarios s time t Distribution network switch i The on / off state is a 0-1 variable; For the scene s time t The power reduction due to demand response; (5) Penalties for insufficient flexibility of urban power distribution networks (10) (11) (12) In the formula: Represents the number of days in a year. , This represents the penalty imposed on the distribution network due to insufficient vertical and horizontal flexibility; , These represent the rates of insufficient operational flexibility in urban power distribution networks when adjustments are made upwards and downwards, respectively.P s This represents the probability of each scenario occurring; , This indicates the flexibility required for the city's power distribution network to move both downwards and upwards; , This indicates the flexible upward and downward power that can be provided through distribution network reconfiguration. , This indicates the flexible upward and downward power that can be provided through ESS; , This indicates the upward and downward flexible power that can be provided through demand response; , This represents the total downward and total upward flexible power required in the corresponding scenario. The planning layer model satisfies the following constraints: (13) In the formula: P r Pess,max、 E rPess,max represent the values ​​at node j The maximum power and maximum capacity that the ESS can be installed at.

[0010] Furthermore, step S4 is detailed as follows: The lower-level model sets the optimization objective as minimizing the rate of insufficient flexibility in the overall operation of the urban power distribution network. (14) The meanings of the variables in the formula have been explained in S2; The runtime model satisfies the following constraints: (1) Current constraints (15) In the formula: P i , Q i Indicates input node i Active and reactive power in the data; Represents a node i and nodes j The difference in voltage phase angle; , This represents the admittance parameters of each line in the distribution network topology; (2) Constraints on Energy Storage Operation (16) (17) (18) (19) In the formula: Represents the state of charge of the ESS. , Limit the upper limit of the fluctuation range of the ESS state of charge; , η represents the charging or discharging power of the ESS; η represents the charging and discharging efficiency of the ESS. (3) Distribution network reconfiguration constraints In reality, the number of times each line in a power distribution network can be switched is limited; at the same time, the operational structure of a restructured urban power distribution network is constrained to exhibit a radial pattern. (20) (twenty one) In the formula: This represents the i-th node in the distribution network at time t in scenario s. i The number of times the switches on the line were activated; This represents the maximum number of times the corresponding switch is allowed to open and close within a year. This refers to the topology of the urban power distribution network at time t in scenario s. It is the set of all radial network topologies of the urban power distribution network.

[0011] Furthermore, step S5 is detailed as follows: In the two-layer planning model, the upper planning layer configures the location and rated parameters of the energy storage power station with the goal of minimizing the overall cost of the urban power distribution network; the lower operation layer sets the insufficiency rate of the urban power distribution network operation as the objective function, and makes full use of the flexibility resources of the source-grid-load three sides to simulate the optimal operation strategy; the planning layer sends the site selection and capacity determination information of the urban power distribution network energy storage power station to the operation layer, and the operation layer uploads the optimal operation scheme to the planning layer; with the continuous iterative optimization of the operation layer and the planning layer, the site selection and capacity determination scheme of the energy storage power station that improves the operation flexibility of the urban power distribution network under multiple scenarios is finally solved.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: One of the beneficial effects of this scheme is that it breaks down the boundary between the conventional flexibility and reliability of urban power distribution networks. It integrates the flexibility of the distribution network's conventional adjustments while also considering the reliability of the urban power distribution network during operation, defining a comprehensive operational flexibility insufficiency rate for the urban power distribution network. It improves the NSGA-III algorithm using Levy flight and Lorenze domination, and solves the proposed multi-objective bi-level optimization model based on this. On the one hand, updating the offspring population based on Levy flight and merging it with the offspring population generated through crossover and mutation enhances the algorithm's local and global search performance, better ensuring population diversity. On the other hand, modifying all objective functions using Lorenze domination and then sorting these new objective function values ​​using non-dominated methods improves the convergence and uniformity of the solution set to some extent. Compared to the traditional NSGA-II algorithm, its computational efficiency, accuracy, and convergence are all significantly improved. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the process provided by the present invention.

[0014] Figure 2 A two-layer model framework diagram for energy storage planning and operation to improve the operational flexibility of urban power distribution networks.

[0015] Figure 3 Flowchart of the improved NSGA-III algorithm combining Levy flight and Lorenze domination.

[0016] Figure 4 Flowchart for solving a multi-objective, two-layer optimization model. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0018] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0019] like Figure 1 As shown, a method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of urban power distribution networks in multiple scenarios includes the following steps: S1. Input basic data of urban power distribution network, specifically: input the urban power distribution network topology, line parameters, wind and solar power output curves for typical scenarios, typical daily load curves, energy storage selection and other relevant basic data for power distribution network planning and operation calculations.

[0020] S2. Propose evaluation indicators for the operational flexibility of urban power distribution networks, specifically: Considering the flexibility of routine adjustments to the overall distribution network while also taking into account the reliability of the urban distribution network during operation, the comprehensive operational flexibility insufficiency rate of the urban distribution network is defined, and its mathematical expression is as follows: (1) (2) (3) (4) In the formula: Defined as the rate of insufficient overall operational flexibility of urban power distribution networks; This indicates the rate of insufficient flexibility in the urban power distribution network; The unavailability rate of urban power distribution network refers to the percentage of abnormal power consumption time of users in the urban power distribution network; , Defined as the rate of insufficient flexibility in adjusting urban power distribution network rates (both upward and downward). This indicates the weighting coefficient for increasing the rate of insufficient operational flexibility; This indicates the proportion of insufficient flexibility and power supply unavailability in the urban power distribution network.

[0021] S3. Construct a planning layer model with the objective function of minimizing the overall cost of the urban power distribution network, specifically as follows: The operation layer takes minimizing the overall cost of the urban power distribution network as its objective function, and uses the location and parameter configuration (capacity, power) of the ESS as decision variables, as shown in the following formula: (5) In the formula: The total annual investment cost of ESS; Costs related to network losses in urban power distribution networks; The cost of purchasing electricity from the higher-level power grid for the city's power distribution network. The cost incurred in utilizing resources from the source, network, and load sides; This is a penalty imposed on urban power distribution networks due to insufficient flexibility. , , , , These are the weighting coefficients for each cost, and their sum is 1.

[0022] (1) Annual comprehensive investment cost of energy storage device (6) In the formula: N ess For the number of ESS; For the first j The coefficient for converting the present value of an ESS to its annual value; r The discount rate; This is the investment cost per unit power of the ESS; This is the investment cost per unit capacity of ESS; It is the first j One ESS power parameter; It is the first j Each ESS capacity parameter.

[0023] (2) Urban power distribution network loss cost C loss (7) In the formula: Represents a multi-scenario set, Represents the set of 24 hours in a day. The electricity price sold on the distribution network at time t in scenario s. This refers to the active power loss generated by the distribution network lines in the corresponding scenario.

[0024] (3) Cost of purchasing electricity from the upstream power grid for urban distribution networks C BUY (8) In the formula: The price at which the power distribution system purchases electricity from the next higher level power grid at time t in scenario s. For the first s Number of days in each scenario This refers to the amount of electricity purchased by the distribution network from the next higher level power grid at time t in scenario s.

[0025] (4) Cost of calling source network load resources Including source-side ESS operating costs Grid-side distribution network reconfiguration costs and load-side demand response costs .

[0026] (9) In the formula: , , These represent the unit operating cost, reconfiguration cost, and demand response cost of the ESS, respectively. Representative scenarios s time t Distribution network nodes j The charging and discharging power of the ESS; N b Represents the number of switches in the distribution network; Representative scenarios s time t Distribution network switch i The on / off state is a 0-1 variable; For the scene s time t The power reduction due to demand response.

[0027] (5) Penalties for insufficient flexibility of urban power distribution networks (10) (11) (12) In the formula: Represents the number of days in a year. , This represents the penalty imposed on the distribution network due to insufficient vertical and horizontal flexibility; , These represent the rates of insufficient operational flexibility in urban power distribution networks when adjustments are made upwards and downwards, respectively. P s This represents the probability of each scenario occurring; , This indicates the flexibility required for the city's power distribution network to move both downwards and upwards; , This indicates the flexible upward and downward power that can be provided through distribution network reconfiguration. , This indicates the flexible upward and downward power that can be provided through ESS; , This indicates the upward and downward flexible power that can be provided through demand response; , This indicates the total downward and total upward flexible power required in the corresponding scenario.

[0028] The planning layer model satisfies the following constraints: (13) In the formula: P r Pess,max、 E rPess,max represent the values ​​at node j The maximum power and maximum capacity that the ESS can be installed at.

[0029] S4. Construct an operation layer model with the optimization objective of minimizing the insufficient rate of comprehensive operational flexibility of the urban power distribution network, specifically as follows: The lower-level model sets the optimization objective as minimizing the rate of insufficient flexibility in the overall operation of the urban power distribution network. (14) The meanings of the variables in the formula have been explained in S2.

[0030] The runtime model satisfies the following constraints: (1) Current constraints (15) In the formula: P i , Q i Indicates input node i Active and reactive power in the data; Represents a node i and nodes j The difference in voltage phase angle; , This represents the admittance parameters of each line in the distribution network topology.

[0031] (2) Constraints on Energy Storage Operation (16) (17) (18) (19) In the formula: Represents the state of charge of the ESS. , This limits the upper limit of the fluctuation range of the ESS state of charge; , η represents the charging or discharging power of the ESS; η represents the charging and discharging efficiency of the ESS.

[0032] (3) Distribution network reconfiguration constraints In real-world environments, the number of times each line in a power distribution network can operate is limited. Furthermore, the operational structure of a restructured urban power distribution network should ideally be constrained to exhibit a radial pattern.

[0033] (20) (twenty one) In the formula: This represents the i-th node in the distribution network at time t in scenario s. i The number of times the switches on the line were activated; This represents the maximum number of times the corresponding switch is allowed to open and close within a year. This refers to the topology of the urban power distribution network at time t in scenario s. It is the set of all radial network topologies of the urban power distribution network.

[0034] S5. Based on the research foundations of S3 and S4, a bi-level programming model is established and solved using an improved NSGA-III algorithm. Specifically: A two-layer planning and operation model for energy storage in urban distribution networks is presented to improve operational flexibility. The upper planning layer primarily configures the location and rated parameters of energy storage power stations to minimize the overall cost of the urban distribution network. The lower operation layer sets the urban distribution network's operational flexibility insufficiency rate as the objective function, fully utilizing the flexibility resources on the source, grid, and load sides to simulate the optimal operational strategy. The planning layer distributes the site selection and capacity determination information of urban distribution network energy storage power stations to the operation layer, while the operation layer uploads the optimal operational scheme back to the planning layer. Through continuous iterative optimization of the operation and planning layers, the final solution for energy storage power station site selection and capacity determination schemes to improve the operational flexibility of urban distribution networks under multiple scenarios is obtained. The model framework is shown in the appendix to the specification. Figure 2 As shown.

[0035] The optimal configuration problem of energy storage power stations, which considers improving the operational flexibility of the distribution network, constructed in steps S3 and S4, is a mixed-integer nonlinear optimization problem with multiple objectives, variables, and constraints. Based on this, the NSGA-III algorithm, improved by combining Levy flight and Lorenze dominance, is used to solve this model, finding a set of Pareto solutions for the optimal configuration of energy storage power stations oriented towards multiple objectives. This facilitates the grid company in making optimal decisions based on its objective preferences. Different energy storage configuration methods and operating curves will affect the actual operating technical indicators of the distribution network. For the nonlinear multi-objective optimization problem in the upper and lower layers of the proposed model, the Pareto solution set can usually be solved according to Pareto theory, and then decisions are made based on preferences within it. Among them, the NSGA-II algorithm based on genetic algorithm is widely used in multi-objective optimization problems in various fields due to its good global convergence and applicability, but it has the following problems: 1) The NSGA-II algorithm uses crowding sorting to select individuals entering the offspring population to ensure solution diversity. However, crowding sorting often performs poorly when facing multi-objective problems. 2) As the number of iterations of the NSGA-II algorithm increases, its lack of population diversity becomes more apparent, and it is easy to get trapped in local optima and fail to obtain the global optimum. 3) With more optimization objectives, it becomes difficult for Pareto dominance relationships to exist between solutions. Non-dominated solutions occupy a large proportion of the solution set of the NSGA-II algorithm, which limits the space for retaining new solutions in each generation of the population. As a result, the search speed of the algorithm slows down and greatly reduces the efficiency of the algorithm.

[0036] Therefore, the NSGA-III algorithm, which incorporates a reference point mechanism, is considered for solving the model. The upper-level solution determines the location and capacity of the energy storage power station. The site selection and capacity determination results are then input into the lower level for energy storage operation curve optimization. Finally, the calculation results are returned to the upper-level model, completing one algorithm iteration. The NSGA-III algorithm is largely the same as NSGA-II, except that in the last non-dominated level, it no longer uses congestion ranking to select solutions. Instead, it divides the solution space into grids based on the reference point in the standardized hyperplane solution space of the optimization objective to determine the degree of congestion, thus selecting solutions with larger congestion distances to enter the population, ensuring solution diversity. The basic steps of the NSGA-III algorithm are as follows: (1) Initialize the population The energy storage capacity installed at each candidate energy storage point is used as an optimization variable. When the energy storage capacity is 0, it means that no energy storage is installed at that point. Therefore, each individual in the population can be considered as a unit of length... e + m The vector, e This indicates the number of candidate energy storage installation sites. m This represents the number of objective functions. Therefore, a random number of functions of size [value] can be generated. N parental population P 0.

[0037] (2) Genetic recombination For the parent population P 0 undergoes uniform crossover (randomly selecting two individuals for crossover) and mutation to generate a sample of size . N offspring population Q 0. Merge the parent and offspring populations into a population of size 2N. R 0.

[0038] (3) Quick Non-Dominated Sort Calculate the number of dominated solutions in the population, sort the dominated solutions from smallest to largest, and assign all solutions to different non-dominated layers. F 1, F 2, …). Solutions in the non-dominated layer are retained in the next generation of the population from high to low, i.e., from… F Starting from level 1, retain each level in the set. S t middle.

[0039] Define the critical layer as a set S tThe number of solutions plus the number of solutions in this layer is greater than or equal to N The corresponding non-dominated layer, using F last To represent this. If the number of solutions after adding the critical layer is exactly equal to... N ,but P t+1 = S t + F last Otherwise, let P t+1 = S t At the same time, it is necessary to start from F last Selected from K = N - S t Each solution is added to P t+1 In the middle, make P t+1 The number of solutions is exactly equal to N .

[0040] (4) Solution filtering based on reference points ① Function normalization Since there are scale and unit differences between different objective functions, it is necessary to normalize each objective function in order to construct a standardized hyperplane solution space for the optimization objective.

[0041] First, we need to find the minimum value (i.e., the ideal point) of each objective function and construct the set of ideal points { zmin i}, and take it as the starting point of the axis where each objective function lies in the solution space. Therefore, it is necessary to traverse all solutions, and denote it as} zmin i For the first i The minimum value of each objective function, { zmin i That is, the set of ideal points.

[0042] Perform the first normalization operation on the objective function: (twenty two) In the formula: f i ( x ) indicates the first i One objective function, m The number of objective functions.

[0043] Next, we need to find the set of extreme points { zmax i}: (twenty three) (twenty four) In the formula: ω i Indicates the first i One dimension is 1, and the rest are 10. -6 of m A dimensional vector. Equation (24) represents zmax i It corresponds to different ω i lower envoy ASF Take the smallest value x .

[0044] The set of extreme points { zmax i The intercept obtained by the plane formed by the intersection of the plane and the axis of the solution space is denoted as . a i Then we can obtain the formula for the second step of the normalization operation of the objective function: (25) ② Construct a reference point vector and solve for the distance from each individual in the population to the nearest reference point phasor. First, generate reference points; the number of reference points is: (26) In the formula: h This indicates the number of parts into which the objective function is divided.

[0045] The formula for calculating the coordinates of the reference point is: (27) In the formula: s j Indicates the reference point is at j Coordinates on the axis.

[0046] After calculating the reference point, it is necessary to construct the reference point vector (i.e., the vector pointing from the origin to the reference point). Based on the distance formula from a point to a vector, the reference point vector closest to each solution and the distance between them are obtained, and this is recorded as the solution being associated with the reference point.

[0047] ③ Selecting offspring Solutions with sparser distributions are selected for inclusion by assessing their density in the optimization space. P t+1 In other words, the correlation is found based on the number of solutions associated with the reference point. S t The reference point with the fewest solutions in the middle. F last The solution closest to the reference point is selected and added. P t+1 Each time a solution is added, it needs to be removed from... F last Delete it and redo it. P t+1Update and sort the number of solutions associated with the reference point, and repeat the above steps until... P t+1 The size is exactly N .

[0048] (5) Regenerative and recombination Return to step (2) and re-apply. P t+1 Perform crossover, mutation, and recombination operations until the preset number of iterations is reached.

[0049] Meanwhile, to avoid the algorithm getting trapped in local optima, a Levy walk approach is proposed in the NSGA-III algorithm to update the offspring population, which is then merged with the offspring population generated through traditional crossover and mutation. This enhances the algorithm's local and global search performance, improving its computational accuracy, efficiency, and convergence. Levy walk, proposed by the French mathematician Paul Lévy, is a random walk model whose step size follows a heavy-tailed Levy distribution and is widely used in intelligent algorithm optimization. Generally, the Mantegna algorithm is used to simulate random Levy step sizes and expands the search space through a position update formula: (28) In the formula: ρ This is the step size coefficient. xt +1 i and xti Describe the solutions respectively x i No. t +1 generation and the t The position of the generation, Levy ( λ ) then means Levy A random search path that satisfies: (29) In the formula: λ Let represent the exponentiation. Since the above distribution is difficult to implement, the Mantegna algorithm is used to simulate the Levy distribution, and its step size can be expressed as: (30) In the formula: u Indicates step size, μ and v They are all direction vectors that satisfy a normal distribution, that is: (31) (32) Generally taken β =1.5.

[0050] Furthermore, the problem of too many non-dominated solutions due to the limited dominance space in the NSGA-II algorithm can be solved by adjusting the objective value of the solution to change the dominance relationship. Here, the NSGA-III algorithm is optimized based on Lorenz dominance. Lorenz dominance is used to modify all objective functions, and then these new objective function values ​​are sorted by non-dominated nature. This expands the dominance space of each solution and correspondingly improves the discriminability between different solutions. The Lorenz dominance formula can be expressed as follows: (33) In the formula: f 1( x ), f 2( x ),…, f i ( x ), f m ( x ) represent the 1st, 2nd, ..., i , m One objective function.

[0051] Therefore, the improved NSGA-III algorithm, combining Levy flight and Lorenze dominance, is as follows: Figure 3 As shown. Applying this to the proposed two-layer optimal configuration model for energy storage power stations, the solution process is as follows: Figure 4 As shown, the solution steps can be summarized as follows: Step 1: Input NSGA-III algorithm parameters, line and topology parameters, typical daily load and renewable energy output data.

[0052] Step 2 generates an initial population of energy storage power station configuration schemes that meet the constraints based on the initial conditions, and passes it to the lower-level model.

[0053] Step 3 generates an initial population of energy storage power station operation modes that meet the constraints, calculates the lower-level objective function values ​​for different operation modes, performs non-dominated sorting based on the objective function values, performs solution screening based on reference points, and then performs crossover, mutation, and recombination, repeating the operation until the iteration limit is reached.

[0054] Step 4 returns the optimal energy storage operation mode output by the lower-level model to the upper-level model, calculates the corresponding upper-level objective function value of the configuration scheme, performs non-dominated sorting based on the objective function value, performs solution screening based on the reference point, and then performs cross-mutation and recombination.

[0055] Step 5 repeats steps 3 and 4 until the iteration limit is reached. Finally, based on the upper-level objective function value, all configuration schemes are non-dominated and sorted, outputting the Pareto optimal solution set, i.e., the non-dominated layer. FAll solutions in 1.

[0056] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of distribution networks in multiple scenarios, characterized in that, Includes the following steps: S1. Input basic data for the urban power distribution network; S2. Propose evaluation indicators for the operational flexibility of urban power distribution networks; S3. Construct a planning layer model with the objective function of minimizing the comprehensive cost of the urban power distribution network; S4. Construct an operation layer model with the optimization objective of minimizing the rate of insufficient comprehensive operational flexibility of urban power distribution networks; S5. Based on the research foundation of S3 and S4, a bi-level programming model is established and solved using an improved NSGA-III algorithm that combines Levy flight and Lorenze dominance. The basic data for the urban power distribution network in step S1 includes: inputting the urban power distribution network topology, line parameters, wind and solar power output curves for typical scenarios, typical daily load curves, energy storage selection, and other relevant basic data for power distribution network planning and operation calculations; Step S2 is as follows: Considering the flexibility of routine adjustments to the overall distribution network while also taking into account the reliability of the urban distribution network during operation, the comprehensive operational flexibility insufficiency rate of the urban distribution network is defined, and its mathematical expression is as follows: （1） （2） （3） （4） In the formula: Defined as the rate of insufficient overall operational flexibility of urban power distribution networks; This indicates the rate of insufficient flexibility in the urban power distribution network; The unavailability rate of urban power distribution network refers to the percentage of abnormal power consumption time of users in the urban power distribution network; , Defined as the rate of insufficient flexibility in adjusting urban power distribution network rates (both upward and downward). This indicates the weighting coefficient for increasing the rate of insufficient operational flexibility; This indicates the proportion of insufficient flexibility and power supply unavailability in the urban power distribution network. Step S3 is as follows: The operation layer takes minimizing the overall cost of the urban power distribution network as its objective function, and uses the location and parameter configuration of the ESS as decision variables, as shown in the following formula: （5） In the formula: The total annual investment cost of ESS; Costs related to network losses in urban power distribution networks; The cost of purchasing electricity from the higher-level power grid for the city's power distribution network. The cost incurred in utilizing resources from the source, network, and load sides; This is a penalty imposed on urban power distribution networks due to insufficient flexibility. , , , , These are the weighting coefficients for each cost, and their sum is 1; (1) Annual comprehensive investment cost of energy storage device （6） In the formula: N ess For the number of ESS; For the first j The coefficient for converting the present value of an ESS to its annual value; r The discount rate; This is the investment cost per unit power of the ESS; This is the investment cost per unit capacity of ESS; It is the first j One ESS power parameter; It is the first j One ESS capacity parameter; (2) Urban power distribution network loss cost C loss （7） In the formula: Represents a multi-scenario set, Represents the set of 24 hours in a day. The electricity price sold on the distribution network at time t in scenario s. This refers to the active power loss generated by the distribution network lines in the corresponding scenario. (3) Cost of purchasing electricity from the upstream power grid for urban distribution networks C BUY （8） In the formula: The price at which the power distribution system purchases electricity from the next higher level power grid at time t in scenario s. For the first s Number of days in each scenario The amount of electricity purchased by the distribution network from the upper-level power grid at time t in scenario s; (4) Cost of calling source network load resources Including source-side ESS operating costs Grid-side distribution network reconfiguration costs and load-side demand response costs ; （9） In the formula: , , These represent the unit operating cost, reconfiguration cost, and demand response cost of the ESS, respectively. Representative scenarios s time t Distribution network nodes j The charging and discharging power of the ESS; N b Represents the number of switches in the distribution network; Representative scenarios s time t Distribution network switch i The on / off state is a 0-1 variable; For the scene s time t The power reduction due to demand response; (5) Penalties for insufficient flexibility of urban power distribution networks （10） （11） （12） In the formula: Represents the number of days in a year. , This represents the penalty imposed on the distribution network due to insufficient vertical and horizontal flexibility; , These represent the rates of insufficient operational flexibility in urban power distribution networks when adjustments are made upwards and downwards, respectively. P s This represents the probability of each scenario occurring; , This indicates the flexibility required for the city's power distribution network to move both downwards and upwards; , This indicates the flexible upward and downward power that can be provided through distribution network reconfiguration. , This indicates the flexible upward and downward power that can be provided through ESS; , This indicates the upward and downward flexible power that can be provided through demand response; , This represents the total downward and total upward flexible power required in the corresponding scenario. The planning layer model satisfies the following constraints: （13） In the formula: They represent the nodes respectively j The maximum power and maximum capacity that the ESS can be installed at.

2. The method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of distribution networks in multiple scenarios according to claim 1, characterized in that, Step S4 is as follows: The lower-level model sets the optimization objective as minimizing the rate of insufficient flexibility in the overall operation of the urban power distribution network. （14） The runtime model satisfies the following constraints: (1) Current constraints （15） In the formula: P i , Q i Indicates input node i Active and reactive power in the data; Represents a node i and nodes j The difference in voltage phase angle; , This represents the admittance parameters of each line in the distribution network topology; (2) Constraints on Energy Storage Operation （16） （17） （18） （19） In the formula: Represents the state of charge of the ESS. , Limit the upper limit of the fluctuation range of the ESS state of charge; , η represents the charging or discharging power of the ESS; η represents the charging and discharging efficiency of the ESS. (3) Distribution network reconfiguration constraints In reality, the number of times each line in a power distribution network can be switched is limited; at the same time, the operational structure of a restructured urban power distribution network is constrained to exhibit a radial pattern. （20） （21） In the formula: This represents the i-th node in the distribution network at time t in scenario s. i The number of times the switches on the line were activated; This represents the maximum number of times the corresponding switch is allowed to open and close within a year. This refers to the topology of the urban power distribution network at time t in scenario s. It is the set of all radial network topologies of the urban power distribution network.

3. The method for site selection and capacity determination of energy storage power stations to improve the operational flexibility of distribution networks in multiple scenarios according to claim 2, characterized in that, Step S5 is as follows: In the two-layer planning model, the upper planning layer configures the location and rated parameters of the energy storage power station with the goal of minimizing the overall cost of the urban power distribution network; the lower operation layer sets the insufficiency rate of the urban power distribution network operation as the objective function, and makes full use of the flexibility resources of the source-grid-load three sides to simulate the optimal operation strategy. The planning layer distributes the site selection and capacity determination information of urban power distribution network energy storage power stations to the operation layer, and the operation layer uploads the most flexible operation plan to the planning layer. With the continuous iteration and optimization of the operation layer and the planning layer, the site selection and capacity determination scheme of energy storage power stations that improves the operational flexibility of urban power distribution network under multiple scenarios is finally solved.

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