A flexible interconnection group planning method for distribution station areas for energy mutual assistance

Abstract

The present application discloses a method for planning flexible interconnection groups of distribution stations for energy mutual assistance, which relates to the technical field of distribution network planning. The method comprises: based on distribution network topology parameters, station loads and new energy output data, screening qualified station pairs to construct an initial interconnection set; constructing an initial two-stage opportunity constraint optimization model including planning and operation stages based on the set; in the planning stage, determining the interconnection strategy and the new energy absorption rate with the goal of minimizing investment cost and penalty cost; in the operation stage, verifying the feasibility of the strategy through random scenarios; performing polyhedron approximate linearization processing on the nonlinear constraints in the model, reconstructing the power flow model into a compact form, and using the sampling average approximation method to transform the probabilistic opportunity constraints into deterministic bilinear constraints to form a deterministic approximate model, and iteratively solving the problem through the column constraint generation decomposition algorithm to obtain the target interconnection group solution, thereby realizing efficient energy mutual assistance and load balancing between distribution stations.

Description

Technical Field

[0001] The present application relates to the technical field of distribution network planning, and in particular to a method for planning flexible interconnected groups of distribution station areas for energy mutual assistance. Background Art

[0002] With the diversification of household loads and the widespread integration of distributed energy resources on the low-voltage side of distribution networks, the reliability and economic efficiency of low-voltage distribution substations, as distribution units directly serving end users, have become increasingly important for both users and grid operators. This context places higher demands on the planning and optimization of distribution substations to adapt to energy structure transformation and meet users' diverse electricity needs.

[0003] Currently, a large body of research has been conducted on distribution network planning, particularly at the medium and high voltage (MV / HV) level, introducing uncertainty modeling and optimization methods. These studies primarily focus on improving the stability and economic efficiency of distribution networks in the face of uncertainty through the use of advanced mathematical models and algorithms. At the same time, traditional distribution network planning methods are also undergoing continuous improvement, aiming to reduce model conservatism and enhance risk mitigation capabilities. However, existing research and methods have exposed several issues when applied to the planning of low-voltage (LV) distribution substations. The continued growth in the scale of distributed energy resources (DGE) integration presents significant challenges in dynamic capacity expansion, power balancing, and operational reliability across distribution substations. The traditional model of isolated single-substation operation is no longer sufficient to efficiently accommodate DGE and flexibly adjust power. This is particularly true when addressing random fluctuations in power sources and loads, making it difficult to achieve inter-substation power coordination and load balancing. Furthermore, existing planning methods suffer from inefficient model solutions when dealing with the complexity and uncertainty of LV distribution substations, making them unable to quickly respond to and adapt to operational changes. Therefore, achieving efficient energy coordination and load balancing across distribution substations has become an urgent challenge. Summary of the Invention

[0004] The purpose of this application is to provide a flexible interconnection group planning method for distribution station areas for energy mutual assistance, aiming to solve the technical problem of how to achieve efficient energy mutual assistance and load balancing between distribution station areas.

[0005] To achieve the above-mentioned purpose, the present application proposes a method for planning flexible interconnection groups of distribution substations for energy mutual assistance, the method comprising: based on distribution network topology parameters, substation loads and new energy output data, screening substation pairs that meet preset load rate conditions or excess output conditions to construct an initial interconnection set; based on the initial interconnection set, constructing an initial two-stage opportunity constraint optimization model including a planning stage and an operation stage, the planning stage determines the interconnection strategy and the new energy consumption rate with the goal of minimizing investment cost and penalty cost, and the operation stage verifies the feasibility of the interconnection strategy based on random scenarios; performing polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage opportunity constraint optimization model, and reconstructing the flow model in the initial two-stage opportunity constraint optimization model into a compact form to obtain a target two-stage opportunity constraint optimization model; converting the probabilistic opportunity constraints in the target two-stage opportunity constraint optimization model into deterministic bilinear constraints through the sampling average approximation method to obtain a deterministic approximate model; iteratively solving the deterministic approximate model through a column constraint generation decomposition algorithm to obtain a target interconnection group solution.

[0006] In addition, to achieve the above-mentioned purpose, the present application also proposes a distribution substation flexible interconnection group planning device for energy mutual assistance, the device comprising: an initial set construction module for screening substation pairs that meet preset load rate conditions or excess output conditions based on distribution network topology parameters, substation loads and new energy output data, and constructing an initial interconnection set; a model construction module for constructing an initial two-stage opportunity constraint optimization model including a planning stage and an operation stage based on the initial interconnection set, the planning stage determines the interconnection strategy and the new energy absorption rate with the goal of minimizing investment cost and penalty cost, and the operation stage is based on random scenario verification. The feasibility of the interconnection strategy is verified; a linearization processing module is used to perform polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model, and reconstruct the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain a target two-stage chance-constrained optimization model; an equivalent conversion module is used to convert the probabilistic chance constraints in the target two-stage chance-constrained optimization model into deterministic bilinear constraints through a sampling average approximation method to obtain a deterministic approximate model; a solution module is used to iteratively solve the deterministic approximate model through a column constraint generation decomposition algorithm to obtain a target interconnection group solution.

[0007] In addition, to achieve the above-mentioned purpose, the present application also proposes a distribution substation area flexible interconnection group planning device for energy mutual assistance, the device including: a memory, a processor and a computer program stored on the memory and runnable on the processor, the computer program is configured to implement the steps of the distribution substation area flexible interconnection group planning method for energy mutual assistance as described above.

[0008] In addition, to achieve the above-mentioned purpose, the present application also proposes a storage medium, which is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by the processor, the steps of the flexible interconnection group planning method for distribution station areas for energy mutual assistance as described above are implemented.

[0009] One or more technical solutions proposed in this application have at least the following technical effects:

[0010] First, based on distribution network topology parameters, substation loads, and renewable energy output data, the planning system screens substation pairs that meet preset load rate or excess output conditions to construct an initial interconnection set. This step, by screening substation pairs that meet these conditions, preliminarily identifies substations that may require interconnection, effectively narrowing the optimization scope and improving the efficiency of subsequent optimization processes. Next, based on this initial interconnection set, an initial two-stage chance-constrained optimization model is constructed, encompassing both the planning and operation phases. The planning phase determines the interconnection strategy and renewable energy consumption rate with the goal of minimizing investment and penalty costs. The operation phase verifies the feasibility of the interconnection strategy based on stochastic scenarios. This step simultaneously considers the requirements of both the planning and operation phases, ensuring a balance between the economic and reliability aspects of the optimization solution. Then, the nonlinear constraints in the initial two-stage chance-constrained optimization model are linearized using polyhedral approximation, and the power flow model is reconstructed into a compact form, resulting in the target two-stage chance-constrained optimization model. This step improves solution efficiency by simplifying the model's complexity. Finally, the probabilistic chance constraints in the target two-stage chance-constrained optimization model are converted into deterministic bilinear constraints using the sampling average approximation method, resulting in a deterministic approximate model. This step enables the optimization model to be solved on a finite set of samples, significantly improving its solvability and computational efficiency. Finally, a column-constrained generation decomposition algorithm is used to iteratively solve the deterministic approximate model, resulting in the target interconnected cluster solution. This algorithm dynamically adds cut constraints to gradually approach the optimal solution, improving both efficiency and accuracy. The resulting target interconnected cluster solution achieves efficient energy conservation and load balancing between distribution stations. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0012] Figure 1 A flowchart of the first embodiment of the method for planning flexible interconnected groups of distribution substations for energy mutual assistance provided in this application;

[0013] Figure 2A schematic diagram of normalized wind power and photovoltaic output forecast curves and daily load variation curves provided for the first embodiment of the method for planning flexible interconnected groups of distribution stations for energy mutual assistance in this application;

[0014] Figure 3 A flowchart of the second embodiment of the method for planning flexible interconnected groups of distribution substations for energy mutual assistance provided in this application;

[0015] Figure 4 A schematic diagram of changes in total system cost under different violation probabilities provided in Example 2 of the method for planning flexible interconnected groups of distribution stations for energy mutual assistance in this application;

[0016] Figure 5 A schematic diagram showing the changes in infeasible scenarios, actual violation probabilities, and iterative convergence of the main and subproblems in the CCG algorithm provided in Example 2 of the method for planning flexible interconnected groups of distribution stations for energy mutual assistance in this application;

[0017] Figure 6 Schematic diagram of flexible interconnection planning results and substation grouping conditions provided in Example 2 of the method for planning flexible interconnection groups of distribution substations for energy mutual assistance of this application;

[0018] Figure 7 This is a schematic diagram of the module structure of a flexible interconnected group planning device for distribution station areas for energy mutual assistance according to an embodiment of the present application;

[0019] The purpose, features and advantages of this application will be further explained with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0020] It should be understood that the specific embodiments described herein are merely used to explain the technical solutions of the present application and are not intended to limit the present application.

[0021] In order to better understand the technical solution of the present application, a detailed description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0022] It should be noted that the execution subject of the embodiments of the present application may be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, mobile phone, etc., or an electronic device, planning system, computer system, etc. capable of implementing the above functions. The following uses the planning system as an example to illustrate this embodiment and the following embodiments.

[0023] Based on this, the embodiment of the present application provides a method for planning flexible interconnection groups of distribution stations for energy mutual assistance, referring to Figure 1 , Figure 1 This is a flow chart of the first embodiment of the method for planning flexible interconnected groups of distribution stations for energy mutual assistance in this application.

[0024] In this embodiment, the method for planning flexible interconnection groups of distribution substations for energy mutual assistance includes steps S10 to S50:

[0025] Step S10 , based on the distribution network topology parameters, substation loads, and renewable energy output data, screen substation pairs that meet preset load rate conditions or excess output conditions to construct an initial interconnection set.

[0026] It's important to note that distribution network topology parameters refer to various data describing the structure and connectivity of a distribution network. These include node information, line connectivity, and parameters such as line resistance and reactance. These parameters determine the connection method and electrical distance between distribution sub-areas and serve as the foundation for building a distribution sub-area interconnection model. For example, the node numbering, node connection sequence, and resistance and reactance values ​​of each line segment in an IEEE 33-node distribution network system are all considered distribution network topology parameters.

[0027] Substation load refers to the total load power of all electrical equipment within a distribution substation, typically expressed as active power and reactive power. It reflects the power demand of the distribution substation at a given moment. In this embodiment, substation load is determined by obtaining load power data from the distribution system. This is used to assess substation load conditions and determine whether there is overload risk, thereby providing a basis for substation interconnection decisions.

[0028] Renewable energy output data refers to the actual power generated by distributed renewable energy sources (such as wind power and photovoltaic power) connected to a distribution network at a specific moment, including both active and reactive power. This data reflects the generating capacity of these renewable energy devices and is an important basis for assessing the region's renewable energy absorption capacity and power balance. In this embodiment, renewable energy output data is used to determine whether a region has excess renewable energy output and, therefore, to determine whether to include it in an interconnected set.

[0029] Please refer to Figure 2 , Figure 2This diagram shows the normalized wind power and photovoltaic power output forecast curves and daily load variation curves for the first embodiment of the flexible interconnected cluster planning method for energy-efficient distribution substations in this application. The blue curve in the figure represents the daily load variation on the load demand side, the orange curve represents the daily output variation of photovoltaic power generation, and the green curve represents the daily output variation of wind power generation. It can be seen that the load curve exhibits two distinct peaks throughout the day, occurring at noon and dusk, respectively. This is due to the fact that these two periods are peak times for residential electricity consumption. Photovoltaic output reaches its peak during the day when solar radiation is strongest, while wind power output is relatively stable throughout the day, but exhibits some volatility due to changes in wind speed. The dotted lines in the figure represent the forecast error range. The actual output error range for photovoltaic and wind power is ±5% of the forecast curve, while the actual load power error range is set to ±10% of the forecast curve. These curves are used to simulate and analyze the power balance of renewable energy in the distribution network, helping to plan the system's operating strategy in the face of uncertainty, ensuring that the absorption rate of renewable energy is improved while meeting load demand and reducing wind and solar power curtailment.

[0030] The preset load rate condition refers to the load rate threshold set when planning the interconnection of distribution substations for screening the substations that need to be interconnected; in this embodiment, when the load rate of the distribution transformer in the substation exceeds 80%, the substation is considered to need to be interconnected with other substations to achieve power mutual assistance and avoid overload operation. The excess output condition means that when the power generation power of the distributed renewable energy connected to the substation exceeds the load demand of the substation itself, the substation is considered to have excess output; in this embodiment, this condition is used to screen out substations that can perform power mutual assistance with other substations to achieve effective consumption of new energy and energy balance between substations. Substation pair refers to a combination of two distribution substations that meet certain conditions (such as excessively high load rate or excess output) and are considered for interconnection in the planning of distribution substation interconnection.

[0031] The initial interconnection set refers to the set of substation pairs selected based on the preset load rate and excess output conditions in the initial stage of distribution substation interconnection planning. This set includes all substation pairs that may need to be interconnected and is the input basis for the subsequent two-stage opportunity-constrained substation interconnection planning model. The initial interconnection set L is expressed as follows:

[0032]

[0033] in, represents the pth station pair in the set L; and : Represent the identifiers of the two interconnected substations in the p-th substation pair; in each interconnected substation pair in the set, at least one substation meets one of the following conditions: ① The substation distribution transformer load rate exceeds 80%; ② The substation has excess wind and solar power output.

[0034] As an example, the step of screening substation pairs that meet preset load rate conditions or excess output conditions based on distribution network topology parameters, substation loads and renewable energy output data, and constructing an initial interconnected set includes: obtaining distribution network topology parameters, substation loads and renewable energy output data, the distribution network topology parameters include distribution network node connection relationships and line impedance parameters, and the substation loads include substation load power; calculating the distribution transformer load rate of each substation based on the substation load power, and identifying the first type of substation whose distribution transformer load rate exceeds the preset load rate threshold; identifying the second type of substation whose wind and solar output exceeds the preset rated capacity based on the renewable energy output data; screening target substation pairs containing at least one of the first type of substation or the second type of substation within the entire distribution network node range based on the distribution network node connection relationship; calculating the effective electrical distance of the target substation pairs based on the line impedance parameters; eliminating the substation pairs to be eliminated in the target substation pairs to generate an initial interconnected set, and the effective electrical distance of the substation pairs to be eliminated is greater than the preset distance threshold.

[0035] The node connection relationship of a distribution network refers to the connection sequence and topology between nodes in the distribution network. It reflects the electrical connection paths between nodes, clarifies the physical connection between distribution substations, and serves as the foundation for building a distribution substation interconnection model. Line impedance parameters refer to the resistance and reactance of lines in a distribution network, describing their electrical characteristics. In this embodiment, they are used to calculate the effective electrical distance between target substation pairs, thereby assessing the engineering feasibility and economic viability of substation interconnection. Substation load power refers to the total power demand of all electrical devices in a distribution substation at a given moment, typically including active power and reactive power. In this embodiment, it is part of the process of acquiring distribution network operating data and is used to calculate the distribution transformer load factor of the substation. The distribution transformer load factor is the ratio of the actual load power of a transformer in a distribution substation to its rated capacity, measuring the transformer load level. The preset load factor threshold is the upper limit of the load factor set when planning distribution substation interconnection to determine whether a substation is overloaded. In this embodiment, this threshold is set to 80%. When the distribution transformer load factor of a substation exceeds this value, the substation is considered to require interconnection with other substations to achieve power sharing.

[0036] The first type of substation refers to a distribution substation where the load rate of the distribution transformer exceeds the preset load rate threshold. Wind and solar output refers to the actual power generation of distributed new energy equipment such as wind power and photovoltaics connected to the distribution substation at a certain moment. It is part of the new energy output data and is used to evaluate the new energy absorption capacity and power balance of the substation. The preset rated capacity refers to the designed maximum power generation capacity of the distributed new energy equipment. It is the standard for judging whether the new energy equipment has excess output. When the actual output exceeds this value, the substation is considered to have excess output. The second type of substation refers to a distribution substation where the wind and solar output exceeds the preset rated capacity. This type of substation has the potential to be interconnected with other substations due to the excess output of new energy to achieve effective absorption of new energy. The full node range of the distribution network refers to the collection of all nodes in the distribution network, covering the entire topology of the distribution network, ensuring that substation pairs that meet the conditions are found throughout the entire network.

[0037] The target substation pair refers to a substation pair that contains at least one first-class substation or second-class substation, which is selected based on the connection relationship of the distribution network nodes within the entire node range of the distribution network. These substation pairs are the basis for constructing the initial interconnection set, aiming to identify substation combinations that may need to be interconnected to optimize load distribution or new energy consumption. The screening of the target substation pairs takes into account the electrical connection relationship between substations to ensure that the selected substation pairs have the feasibility of electrical interconnection and potential mutual benefits.

[0038] The effective electrical distance refers to the electrical distance between target cell pairs, calculated based on line impedance parameters. It reflects the electrical characteristics and engineering feasibility of the interconnection between the cells and is used to assess the suitability of the target cell pairs for interconnection. The preset distance threshold refers to the maximum electrical distance set when screening the initial interconnection set to determine whether a cell pair is suitable for interconnection. In this embodiment, this threshold is set to 1 km. Cell pairs to be eliminated are those that, when screening the initial interconnection set, are deemed unsuitable for interconnection because their effective electrical distance exceeds the preset distance threshold.

[0039] First, the planning system collects detailed data on the distribution network, including topological parameters (node ​​connection relationships and line impedance parameters), the load power of each substation, and the output data of connected new energy equipment. These data are the basis for building the initial interconnection set and are used to fully understand the operating status of the distribution network and potential interconnection needs. Secondly, the system uses the substation load power to calculate the distribution transformer load rate of each substation, and identifies substations with load rates exceeding the preset threshold as first-class substations. These substations may face overload risks and need to be alleviated through interconnection. At the same time, based on the new energy output data, the system identifies substations whose wind and solar output exceeds the preset rated capacity as second-class substations. These substations have the potential to output excess energy to other substations.

[0040] Then, the planning system selects target pairs of substations that contain at least one first-class substation or second-class substation based on the node connection relationship within the entire distribution network node range. This is to ensure that the interconnected substation pairs can effectively solve overload problems or achieve effective absorption of new energy. After that, the system uses the line impedance parameters to calculate the effective electrical distance of these target substation pairs and evaluate the engineering feasibility and economic efficiency of the interconnection. Finally, the planning system eliminates substation pairs whose effective electrical distance is greater than the preset distance threshold, because excessive electrical distance may result in excessively high interconnection costs or technical infeasibility. After this series of screening and calculations, an initial interconnection set is generated, providing an optimized basis for the subsequent flexible interconnection planning of distribution substations, ensuring that the interconnection solution is both economical and efficient.

[0041] Step S20: Based on the initial interconnection set, an initial two-stage chance-constrained optimization model is constructed, which includes a planning stage and an operation stage. The planning stage determines the interconnection strategy and the new energy consumption rate with the goal of minimizing investment cost and penalty cost. The operation stage verifies the feasibility of the interconnection strategy based on random scenarios.

[0042] It should be noted that the planning phase refers to the phase in which the optimal interconnection strategy and renewable energy absorption rate are determined based on predicted load power and distributed renewable energy output data, with the goal of minimizing the system's overall investment cost and penalty costs. The operation phase refers to the phase in which the feasibility of the interconnection strategy determined in the planning phase is verified and revised based on actual operational scenarios. The initial two-stage chance-constrained optimization model is a mathematical model for planning flexible interconnection clusters within distribution substations, consisting of a planning phase and an operation phase. By introducing chance constraints, the model allows certain constraints to be violated within a certain probability range, thereby achieving a balance between optimization accuracy and computational cost, improving the model's adaptability and solution efficiency. Investment cost refers to the capital expenditure associated with interconnection line construction and equipment installation in the planning of flexible interconnection clusters within distribution substations. It includes the annualized investment cost of interconnection lines and equipment purchase costs. During the planning phase, investment cost is part of the optimization objective, aiming to reduce the overall system investment burden and ensure the economic feasibility of the planned solution through rational interconnection strategy planning.

[0043] Penalty costs refer to the additional costs incurred due to violations of certain operational constraints (such as distribution transformer overload, abandonment of new energy, etc.) in the planning of flexible interconnection clusters of distribution substations, including penalty costs for wind and solar power abandonment and distribution transformer overload penalty costs. Penalty costs reflect the risks and uneconomical nature of system operation and are part of the optimization goal. They aim to reduce the risks and additional costs of system operation by optimizing interconnection strategies and new energy absorption rates. Interconnection strategy refers to the decision-making plan for determining which substations to interconnect and how to interconnect in the planning of flexible interconnection clusters of distribution substations, including the deployment location of interconnection lines, interconnection priority, etc. The optimization goal of the interconnection strategy is to achieve power mutual assistance and load balancing between substations while meeting the system operation constraints, thereby improving the reliability and economy of the system.

[0044] The renewable energy absorption rate refers to the ratio of the actual renewable energy consumption to the maximum available capacity of renewable energy equipment within the flexible interconnection clusters of distribution substations, reflecting the system's effective utilization of renewable energy. During the planning phase, the renewable energy absorption rate is part of the optimization objective, aiming to improve renewable energy absorption, reduce wind and solar power curtailment, and enhance the system's energy efficiency through rationally planned interconnection strategies. Random scenarios refer to multiple possible operating conditions generated through random sampling during the operational phase, based on the uncertainty of distributed renewable energy output and load power. These scenarios reflect the uncertainty in system operation and are used to verify the feasibility and reliability of interconnection strategies under different operating conditions.

[0045] As can be understood, the planning system first uses data from the initial interconnection set to construct an initial two-stage, chance-constrained optimization model, encompassing both the planning and operation phases. During the planning phase, the system uses mathematical optimization methods to calculate the optimal interconnection strategy and renewable energy absorption rate, minimizing investment and penalty costs. The goal of this phase is to identify a cost-effective interconnection solution at the planning level to achieve effective renewable energy absorption and overall system economics. Secondly, during the operation phase, the system verifies the feasibility of the interconnection strategy determined during the planning phase in actual operation using stochastic scenarios. The system simulates various possible operational scenarios to test the interconnection strategy's performance under different conditions, ensuring its effective operation in the face of uncertainty, thereby improving system reliability and adaptability. This phase aims to verify the feasibility and robustness of the interconnection strategy determined during the planning phase in actual operation. Finally, through these two optimization and verification phases, the planning system generates an economical and reliable interconnection plan, providing decision support for flexible interconnection of distribution substations. This ensures power balancing and load balancing between substations while meeting system operational constraints, while also improving renewable energy absorption.

[0046] Step S30 , performing polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model, and reconstructing the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain a target two-stage chance-constrained optimization model.

[0047] It should be noted that nonlinear constraints refer to mathematical expressions containing nonlinear terms, such as product terms and square terms, within the optimization model. In this embodiment, nonlinear constraints primarily occur in components such as VSC transmission power constraints and safety constraints. These constraints describe nonlinear relationships in system operation, such as the relationship between VSC transmission power and substation load. Nonlinear constraints complicate model solution, necessitating linearization to simplify the solution process.

[0048] Polyhedral approximate linearization involves constructing a polyhedron (a geometric solid formed by multiple planes) to approximate the feasible domain of nonlinear constraints, thereby converting them into a set of linear constraints. By constructing a compact polyhedral approximation envelope, complex nonlinear relationships are simplified into a linear form, making the optimization model easier to solve while maintaining the physical meaning of the original model and the basic properties of the constraints.

[0049] A power flow model is a mathematical model that describes the power flow and voltage distribution in a distribution network. In this embodiment, the power flow model includes linear power flow equations for the distribution network, such as node power balance equations and line power transmission equations. It serves as the basis for evaluating the distribution network's operating status and making optimization decisions, reflecting the physical characteristics of the distribution network under given operating conditions.

[0050] Compact form refers to simplifying a complex mathematical model or set of equations into a simpler and easier to handle form. In this embodiment, reconstructing the power flow model into a compact form means converting the linear power flow equation of the distribution network into a simpler matrix form for use in the optimization model.

[0051] The target two-stage chance-constrained optimization model refers to the final optimization model obtained after linearizing the initial two-stage chance-constrained optimization model and reconstructing the power flow model. It is simplified and optimized, easier to solve, and at the same time maintains the main characteristics and optimization objectives of the original model.

[0052] As an example, the nonlinear constraints include voltage source converter transmission power constraints and distribution transformer load rate constraints, and the power flow model includes distribution network active power flow equations, reactive power flow equations and voltage amplitude equations; the steps of performing polyhedron approximation linearization processing on the nonlinear constraints in the initial two-stage chance constraint optimization model and reconstructing the power flow model in the initial two-stage chance constraint optimization model into a compact form to obtain the target two-stage chance constraint optimization model include: using the polyhedron envelope method to linearize the voltage source converter transmission power constraints and the distribution transformer load rate constraints to generate linearized constraint conditions; constructing an impedance matrix based on the line impedance parameters in the distribution network topology parameters; reconstructing the distribution network active power flow equations, the reactive power flow equations and the voltage amplitude equations into node power-voltage matrix relationships according to the impedance matrix; integrating the linearized constraints with the node power-voltage matrix relationship to replace the nonlinear constraints and power flow equations in the initial two-stage chance constraint optimization model to obtain the target two-stage chance constraint optimization model.

[0053] The voltage source converter (VSC) transmission power constraint limits the active and reactive power transmitted by the VSC at a given moment to within its rated capacity. In this embodiment, this constraint ensures that the VSC will not be damaged during operation due to power exceeding the design range. The VSC transmission power constraint formula is as follows:

[0054]

[0055] in, and They represent the active power and reactive power of the VSC in the grid i at time t respectively; Indicates the rated capacity of the VSC.

[0056] The distribution transformer load factor constraint is a constraint that limits the transformer load factor in the distribution area to a preset threshold (such as 80%). It is used to prevent transformer overload and ensure the safety and reliability of the distribution area.

[0057] The active power flow equation for a distribution network is a mathematical equation that describes the flow of active power at each node in the network. It reflects the active power balance between sources and loads in the network and serves as the basis for evaluating the network's operating status and making optimization decisions. In this embodiment, the active power flow equation is used to calculate the active power injection and outflow at each node, ensuring system power balance.

[0058] The reactive power flow equation is a mathematical equation that describes the flow of reactive power at each node in a distribution network. It reflects the distribution of reactive power within the network and is crucial for maintaining system voltage stability and improving power quality. In this embodiment, the reactive power flow equation is used to calculate the reactive power injection and outflow at each node, ensuring reactive power balance in the system.

[0059] The voltage amplitude equation refers to a mathematical equation that describes the voltage amplitude of each node in the distribution network. It reflects the voltage level of each node in the distribution network and is an important indicator for evaluating the system voltage stability and power quality. In this embodiment, the voltage amplitude equation is used to calculate the voltage value of each node to ensure that the system operates within a safe voltage range. The linearization constraint condition refers to the constraint condition obtained by approximating the nonlinear constraint to a linear form through methods such as the polyhedron envelope method. The impedance matrix refers to a matrix constructed based on the line impedance parameters in the distribution network topology parameters, which is used to describe the electrical connection relationship between each node in the distribution network. The node power-voltage matrix relationship refers to the relationship in matrix form obtained by reconstructing the active power flow equation, reactive power flow equation and voltage amplitude equation of the distribution network through the impedance matrix. This relationship is used to simplify the expression of the power flow model, making the optimization model more compact and easier to solve.

[0060] First, the planning system linearizes and approximates the voltage source converter transmission power constraints and distribution transformer load factor constraints using the polyhedron envelope method. Specifically, the system approximates the feasible domain of these nonlinear constraints with a polyhedron. By defining the boundaries of the polyhedron, the complex nonlinear relationship is converted into a set of linear inequality constraints, thereby generating linearized constraint conditions. The purpose of this process is to simplify nonlinear constraints that are difficult to solve directly into a linear form so that they can be solved using linear programming methods later. The linearized constraint condition formula is as follows:

[0061] ; ;

[0062] in, represents the power flowing through the voltage source converter (VSC) in the distribution station i during time period t, and They represent the active power and reactive power of the VSC in the grid i at time t, Indicates the rated capacity of the voltage source converter; Represents the power vector of node i in time period t, including active power and reactive power ; represents the maximum load rate allowed for node i; represents the rated capacity of the transformer at node i; represents the maximum power vector of node i at time period t, including the maximum active power and maximum reactive power ;ε represents a small positive number, which is used to ensure the feasibility of the constraint and allow a certain violation probability; and denote the coefficient matrix and constant term vector defining the boundary of the polyhedron, respectively.

[0063] Secondly, the system constructs an impedance matrix based on the line impedance parameters in the distribution network topology parameters. The specific operation is that the system extracts the resistance and reactance values ​​of each line and organizes these parameters into a matrix form, where the elements of the matrix represent the electrical connection relationship between each node. The purpose of constructing the impedance matrix is ​​to convert the power flow equation of the distribution network from a decentralized node equation form to a matrix form, which is convenient for subsequent matrix operations and model simplification. Then, the system reconstructs the active power flow equation, reactive power flow equation and voltage amplitude equation of the distribution network into a node power-voltage matrix relationship based on the impedance matrix. The specific approach is to use the impedance matrix to express the relationship between the power injection and voltage amplitude of each node in a matrix form, and simplify the power flow equation into a compact form through matrix operations. The purpose of this is to further simplify the power flow model and make it easier to use in the optimization model. The compact form formula is as follows:

[0064] ; ;

[0065] in, 、 、 、 、 Represents all nodes i at time t 、 、 、 、 vector, and Respectively by and Calculated, and is a diagonal matrix containing the resistance and reactance of all distribution network lines; P t A represents the node active power injection vector at time step t; -T represents the inverse transposed matrix of the node-branch correlation matrix, which is used to convert branch power into node power; represents the branch active power flow vector at time step t; represents the node reactive power injection vector at time step t; represents the branch reactive power flow vector at time step t; represents the node voltage magnitude vector at time step t; Represents the resistance matrix of the distribution network; Represents the reactance matrix of the distribution network; V0 represents the voltage amplitude of the reference node (usually the root node); Represents an N-dimensional vector whose elements are all 1.

[0066] Finally, the system integrates the linearized constraints with the node power-voltage matrix relationship, replacing the nonlinear constraints and power flow equations in the initial two-stage chance-constrained optimization model. Specifically, the linearized constraints and the compact power flow model are substituted into the initial model, replacing the original complex nonlinear components. This process aims to transform the initial model into a target two-stage chance-constrained optimization model, making it easier to solve while maintaining the key features and optimization objectives of the original model. Through this series of steps, the planning system ultimately obtains a simplified and easy-to-solve target optimization model, providing efficient support for flexible interconnection planning of distribution substations.

[0067] Step S40 , converting the probabilistic chance constraints in the target two-stage chance-constrained optimization model into deterministic bilinear constraints by using a sampling average approximation method, thereby obtaining a deterministic approximate model.

[0068] It's important to note that the Sample Average Approximation (SAA) method is used to handle optimization problems with uncertainty. It uses Monte Carlo sampling techniques to generate a sample set of random variables and uses the sample average to approximate the true expected value of the random variable. This method simulates uncertainty by introducing sample scenarios, allowing the optimization model to be solved on a limited sample set, thereby improving the model's solvability and computational efficiency.

[0069] Probabilistic chance constraints refer to constraints in an optimization model that are allowed to be violated with a certain probability, rather than being strictly satisfied. In this embodiment, these constraints are typically related to the uncertainty of distributed renewable energy output and load power. For example, a constraint might require that, with a certain probability (e.g., 95%), the system operating state meet specific requirements, such as the transformer not being overloaded or the renewable energy consumption rate not falling below a certain threshold. This constraint allows uncertainty to be accounted for in the optimization process while controlling the level of risk.

[0070] Deterministic bilinear constraints are constraints that transform probabilistic chance constraints into deterministic constraints using the sampling average approximation method. In this embodiment, these constraints are expressed by introducing binary variables and sample scenarios, allowing the probability of constraint violations to be controlled within a finite set of samples. This constraint form facilitates solution in the optimization model while maintaining the original model's ability to handle uncertainty.

[0071] The deterministic approximation model refers to an optimization model obtained by converting probabilistic chance constraints into deterministic bilinear constraints through the sampling average approximation method. It is an improved two-stage chance-constrained optimization model. By introducing sample scenarios and binary variables, it makes the solution of the optimization problem more efficient and can effectively control the risk level.

[0072] It is understandable that, first, the planning system generates a large number of random sample scenarios through Monte Carlo sampling technology. These scenarios simulate the uncertainty of distributed renewable energy output and load power. Each sample scenario represents a possible operation situation. Its number and distribution are determined according to the statistical characteristics of the prediction error (such as a Gaussian distribution with a mean of zero and a standard deviation of 3.33% of the predicted value) to ensure that the sample can fully reflect the uncertainty in actual operation. Secondly, for each sample scenario, the planning system calculates the satisfaction of the probabilistic chance constraint and introduces a binary variable To identify whether each scene meets the constraints. Specifically expressed as:

[0073]

[0074] in, represents the probability of event A occurring; is an indicator variable that represents whether event A occurs or not. Indicates that an event has occurred. Indicates that the event did not occur; is a binary variable representing whether event A occurs or not, Indicates that an event has occurred. Indicates that the event did not occur.

[0075] Specifically, if the constraints in a certain scenario are met, the corresponding binary variable takes the value of 1; otherwise, it takes the value of 0. In this way, the probabilistic constraints are transformed into deterministic bilinear constraints, that is, the probability-based constraints in the original model are transformed into linear constraints based on sample scenarios. The deterministic bilinear constraint formula is as follows:

[0076]

[0077]

[0078] Where b represents the coefficient matrix and constant term vector defining the polyhedron boundary; z m represents a binary variable (identifier variable) associated with node i, which is used to indicate whether the node is considered in the model; m refers to a sample scenario; M refers to a set of random scenarios with equal probability; α represents the minimum absorption ratio of new energy; and They represent the maximum active power of photovoltaic and wind power equipment w in time period t respectively; the interpretation of other variables is consistent with the linearization constraint formula and the penalty cost formula for curtailment of wind and solar power.

[0079] In deterministic bilinear constraints, means culling scene m to allow it to violate the constraint, Indicates that the scenario m must strictly satisfy the chance constraint. To maintain consistency with the violation probability setting in the original chance constraint, the number of scenarios that meet the constraint is required to be no less than :

[0080] ; simplified to:

[0081] Among them, ε represents a small positive number, which is used to ensure the feasibility of the constraint and allow a certain violation probability; the other variables are explained in the same way as in the deterministic bilinear constraint formula.

[0082] Therefore, the objective function of the running phase is reconstructed as:

[0083]

[0084] Among them, E represents expectation; other variables are consistent with the explanations in the deterministic bilinear constraint formula and the operation phase objective function formula.

[0085] Assume that the decision variables in the first stage are , the decision variables in the second stage under scenario m are expressed as , then the reconstructed two-stage chance-constrained optimization model can be further transformed into the following compact form:

[0086] ; ;

[0087] ; ;

[0088]

[0089] in, and They represent the cost coefficient vector of the first stage and the cost coefficient vector of the second stage under scenario m respectively; 、 and 、 denote the constraint coefficient matrix and constraint lower bound vector of the first and second stages respectively; and represents the coupling constraint matrix of the first and second stages, represents the lower bound vector of the joint constraint; 、 and They represent the coefficient matrices of the first- and second-stage variables in the opportunity constraint and the corresponding right-hand constant terms, respectively. The interpretations of other variables are the same as above.

[0090] Finally, the planning system integrates these deterministic bilinear constraints into the optimization model, replacing the original probabilistic chance constraints, resulting in a deterministic approximate model. This improved model transforms the uncertainty problem into a deterministic one, making it easier to solve using traditional optimization methods. By controlling the number and distribution of sample scenarios, the model's feasibility and reliability in practical applications are ensured, significantly improving its solvability and computational efficiency.

[0091] Step S50 , iteratively solving the deterministic approximate model through a column constraint generation decomposition algorithm to obtain a target interconnection group solution.

[0092] It should be noted that the Column-and-Constraint Generation (CCG) algorithm is an iterative algorithm for solving large-scale optimization problems, particularly well-suited for two-stage optimization models involving chance constraints. In this embodiment, the algorithm decomposes the original problem into a main problem and multiple subproblems, alternately solving the main problem and subproblems. The main problem optimizes decision variables (such as interconnected lines and renewable energy consumption rates), while the subproblems verify the feasibility of these decisions under different scenarios. By dynamically adding cut constraints during the iteration process (cut constraints are constraints dynamically added to the main problem in an optimization algorithm to gradually approach the optimal solution, used to eliminate infeasible solutions or push the solution towards a better solution, thereby gradually narrowing the space of feasible solutions), the algorithm gradually approaches the global optimal solution. It can significantly reduce the computational complexity of the model, improve solution efficiency, and is suitable for handling uncertain optimization problems.

[0093] The target interconnection group scheme refers to the final flexible interconnection planning scheme for distribution substations obtained by solving the optimization model. In this embodiment, the scheme includes the specific interconnection line deployment (such as which substations are interconnected and the specific parameters of the interconnection lines), the new energy consumption rate parameters, and other relevant decision variables. These decision variables are gradually determined during the iterative process of the column constraint generation and decomposition algorithm, ultimately forming an economical and reliable interconnection scheme. The target interconnection group scheme aims to achieve power mutual assistance and load balancing between distribution substations, while improving the level of new energy consumption and ensuring the stable operation of the system under uncertain conditions.

[0094] As you can understand, the planning system first initializes the solution process of the deterministic approximate model using a column constraint generation decomposition algorithm. Next, the system alternates between solving the main problem (optimizing decision variables such as interconnection routes and renewable energy consumption rates) and subproblems (verifying the feasibility of decision variables under different scenarios). If a subproblem is infeasible or suboptimal, cut constraints are added to the main problem, and the decision variables are updated. Finally, when the main problem no longer requires additional cut constraints, the current solution (the solution to the main problem) becomes the target interconnection group solution, including decision variables such as specific interconnection routes and renewable energy consumption rate parameters, and is output as the optimal solution.

[0095] This embodiment provides a method for planning flexible interconnection clusters of distribution substations for energy mutualization. First, the planning system selects pairs of substations that meet preset load rate conditions or excess output conditions based on distribution network topology parameters, substation loads, and renewable energy output data, and constructs an initial interconnection set. This step, by screening substation pairs that meet these conditions, preliminarily identifies substations that may need to be interconnected, effectively narrowing the optimization scope and improving the efficiency of subsequent optimization processes. Next, based on the initial interconnection set, an initial two-stage opportunity-constrained optimization model is constructed, encompassing both planning and operation phases. The planning phase determines the interconnection strategy and renewable energy consumption rate with the goal of minimizing investment costs and penalty costs. The operation phase verifies the feasibility of the interconnection strategy based on random scenarios. This step simultaneously considers the requirements of both the planning and operation phases, ensuring that the optimization solution balances economic efficiency and reliability. Then, the nonlinear constraints in the initial two-stage opportunity-constrained optimization model are linearized using polyhedral approximations, and the power flow model is reconstructed into a compact form to obtain the target two-stage opportunity-constrained optimization model. This step improves solution efficiency by simplifying the model's complexity. Next, the probabilistic chance constraints in the target two-stage chance-constrained optimization model are converted into deterministic bilinear constraints using the sampling average approximation method, resulting in a deterministic approximate model. This step enables the optimization model to be solved on a finite set of samples, significantly improving the model's solvability and computational efficiency. Finally, the deterministic approximate model is iteratively solved using a column constraint generation decomposition algorithm to obtain the target interconnection cluster solution. This algorithm dynamically adds cut constraints to gradually approach the optimal solution, improving solution efficiency and accuracy. The resulting target interconnection cluster solution achieves efficient energy sharing and load balancing between distribution stations.

[0096] Based on the first embodiment of the present application, in the second embodiment of the present application, the same or similar contents as those in the above embodiment 1 can be referred to the above introduction and will not be described in detail later. Figure 3 , Figure 3 This is a flow chart of a second embodiment of the method for planning a flexible interconnected group of distribution stations for energy mutual assistance in this application. Step S20 of the method for planning a flexible interconnected group of distribution stations for energy mutual assistance includes steps S21 to S24:

[0097] Step S21 : defining a planning stage objective function according to the initial interconnection set, wherein the planning stage objective function represents minimization of the sum of interconnection line investment cost, wind and solar power curtailment penalty cost, and distribution transformer overload penalty cost.

[0098] It should be noted that the planning phase objective function refers to a mathematical expression used to measure and optimize the economic and feasibility of the plan during the planning phase of the flexible interconnection cluster planning of distribution substations. It comprehensively considers the economic investment in building interconnection lines, the penalties for curtailing wind and solar power due to insufficient renewable energy consumption, and the additional costs caused by transformer overload operation. The planning phase objective function formula is as follows:

[0099]

[0100] Where C is the total cost of flexible interconnection group planning for distribution substations; It refers to the investment cost of interconnection lines; Refers to the penalty cost for curtailing wind and solar power; It is the penalty cost for overload of distribution transformer.

[0101] Please refer to Figure 4 , Figure 4 A schematic diagram of the change in total system cost under different violation probabilities is provided for Example 2 of the planning method for flexible interconnected groups of distribution substations for energy mutual assistance in this application. In the figure, the horizontal axis represents the violation probability ε, and the vertical axis represents the total cost of the system. As the violation probability decreases, that is, the system's tolerance for uncertainty decreases, the total system cost also increases. This is because a lower violation probability requires that the system design must be more conservative to ensure that the predetermined goals and constraints can still be met under a wider range of uncertainty conditions, resulting in increased planning costs. The curve in the figure shows that when the violation probability increases from 0 to 0.1, the total system cost drops from approximately 11,100 to approximately 10,700. This shows that by appropriately adjusting the violation probability, it is possible to effectively control costs while ensuring system reliability and achieve a balance between cost and reliability. This trend is consistent with the expected results of the two-stage opportunity constraint model proposed in the briefing book, and verifies the cost-benefit analysis of the model under different violation probability settings. Interconnection line investment cost The formula is as follows:

[0102]

[0103] in, It refers to the annualized investment cost per unit length of interconnection line, which is a constant; Representing interconnected sets The interconnection priority of the p-th area pair in ; is a binary variable representing whether the p-th substation pair is interconnected (1 indicates interconnection, 0 indicates no interconnection); L p represents the actual electrical distance between the p-th substation pair, which is used to calculate the physical length of the interconnection line; r represents the discount rate; Indicates the economic service life of the interconnection line. Penalty cost for curtailed wind and solar power The formula is as follows:

[0104]

[0105] in, The unit penalty cost for wind and solar curtailment is the penalty amount to be paid for each unit of unabsorbed renewable energy generation. represents the optimal new energy consumption rate, and Respectively represent the maximum available capacity of photovoltaic and wind power of renewable energy unit w at time t; T is the total time period considered; W is the set of all wind power and photovoltaic equipment. The formula is as follows:

[0106]

[0107] in, represents the penalty cost per unit distribution transformer overload, i.e., the penalty amount required to be paid for each unit of overloaded transformer capacity; T is the total time period considered; N is the set of all substations; It represents the load rate of the station i at time t, Indicates the rated capacity of the transformer in station i.

[0108] The investment cost of interconnected lines refers to the economic investment required to build interconnected lines within the flexible interconnection planning of distribution substations, including material costs, construction costs, and related maintenance costs. In this embodiment, its calculation depends on the initial interconnection set, namely, which substations require interconnection. The penalty cost for wind and solar curtailment refers to the additional costs incurred due to the inability to fully accommodate distributed renewable energy within the flexible interconnection planning of distribution substations. When the power generation of renewable energy equipment exceeds the absorption capacity of the substation, some renewable energy will be abandoned (wind or solar curtailment), resulting in penalty costs. The penalty cost for distribution transformer overload refers to the additional costs incurred due to transformer load factors exceeding a preset threshold (e.g., 80%) within the flexible interconnection planning of distribution substations. When the distribution transformer load factor in a substation exceeds this threshold, the transformer will overload, increasing the risk of equipment damage and operating costs.

[0109] It can be understood that, first, the planning system clarifies the potential construction location and scale of the interconnected lines based on the information of the substation pairs in the initial interconnection set, thereby determining the specific calculation method for the investment cost of the interconnected lines. This is estimated based on the electrical distance and line parameters between the substation pairs in the initial interconnection set. Secondly, the system combines the output data of new energy equipment and the absorption capacity of the substation to calculate the possible wind and solar power curtailment, and estimates the penalty costs for curtailment based on this. This step is to assess the economic impact of insufficient new energy absorption. Finally, based on the distribution transformer load rate data of the substation, the system identifies transformers that may be overloaded and calculates the corresponding distribution transformer overload penalty costs. This step is to assess the risks and additional costs brought about by overloaded transformer operation. By adding and minimizing these three costs, the planning system defines the objective function of the planning stage, which aims to reduce the overall planning cost by optimizing the interconnection strategy and the new energy absorption rate, and ensure the balance between the economy and reliability of the plan.

[0110] Step S22: Setting planning phase constraints based on the physical laws and safety standards of the distribution network.

[0111] It should be noted that the physical laws of distribution networks refer to the fundamental physical laws that describe the transmission and conversion of electrical energy in distribution networks, including Ohm's law and Kirchhoff's laws. These laws determine the relationship between current, voltage, and power in distribution networks and serve as the basis for constructing linear power flow constraints and AC / DC power balance constraints for distribution networks, ensuring that the model accurately reflects the operating characteristics of the distribution network. Safety standards refer to the technical specifications and safety requirements that must be adhered to during the operation and planning of distribution networks, including equipment rated capacity limits, voltage and current safety ranges, and equipment overload protection requirements. Planning-stage constraints refer to a series of mathematical constraints set during the planning phase of flexible interconnection cluster planning for distribution substations to ensure the feasibility and safety of the optimization solution. These constraints include voltage source converter capacity constraints, AC / DC power balance constraints, distribution network linear power flow constraints, safe operation constraints, and new energy consumption rate constraints. In this embodiment, planning-stage constraints are used to limit the value range of optimization variables. Voltage source converter capacity constraints refer to constraints that limit the active power and reactive power transmitted by the voltage source converter at a given moment to not exceed its rated capacity. The AC / DC power balance constraint refers to the power balance relationship between the AC system and the DC system in the distribution area, ensuring that at each node, the input active power and reactive power are equal to the output power, thereby maintaining the power balance of the system. The AC / DC power balance constraint requires that the active power and reactive power of the distribution network node i and the distribution area i are balanced. The formula is as follows:

[0112]

[0113]

[0114] in, and They represent the active power and reactive power flowing out of the distribution network node i at time t, and They represent the active power and reactive power of AC load in area i at time t, and They represent the photovoltaic output and wind power output of the new energy unit w at time t, represents the total power demand of DC loads in distribution area i during time period t, It represents the transmission power of the interconnection line between the station pair p at time t, and They represent the set of distributed renewable energy sources connected to area i and the set of all areas interconnected with area i.

[0115] The linear power flow constraint of a distribution network refers to the linearized equation that describes the power flow and voltage distribution in the distribution network, ensuring that the power flow in the distribution network conforms to the laws of physics. Specifically, it describes the power transmission relationship between each node through the matrix form of the power flow equation, ensuring that the power flow of the system is within a safe range. The formula is as follows:

[0116]

[0117]

[0118]

[0119] in, represents the reactive power transmitted by the distribution network line ij at time t; represents the sum of all reactive powers flowing from node j to its directly connected node k in time period t; represents the reactive power demand or generated power of node j itself in time period t; and Respectively represent the parent node and child node set of node j; Represents all network nodes except the source node. Since node 0 is the feeder starting point and the system power injection point, it only performs the power supply function and does not need to meet the power flow balance constraint, so it is eliminated in the constraint modeling; represents the active power demand or generated power of node j itself in time period t; represents the sum of all active powers flowing from node j to its directly connected node k in time period t; It refers to the active power transmitted by the distribution network line ij at time t; represents the voltage amplitude of node i at time t, and They represent the resistance and reactance of the distribution network line ij respectively.

[0120] Safe operation constraints refer to a series of constraints set during the operation of the distribution network to ensure safe and stable operation of the system, including transformer load rate not exceeding the preset threshold, interconnected line transmission power not exceeding the maximum allowed value, node voltage not exceeding the limit, etc. The formula is as follows:

[0121] ;

[0122]

[0123] in, represents the load rate of node i in time period t; represents the active power of node i in time period t; represents the reactive power of node i in time period t; represents the rated capacity of the transformer at node i (apparently on the high-voltage side); Indicates the maximum load rate allowed by the distribution transformer. Indicates the reactance value of line p, which is used to calculate the transmission capacity of the line; Indicates the maximum power allowed to be transmitted through the interconnection lines in the substation area. represents the transmission power of line p in time period t; and They represent the upper and lower limits of the voltage allowed at node i at time t respectively; represents the voltage amplitude of node i in time period t.

[0124] The new energy consumption rate constraint refers to the constraint that the power generation of new energy must be effectively consumed within a certain proportion in the distribution area, ensuring that the power generation of new energy equipment will not be abandoned due to insufficient consumption, thereby improving the utilization efficiency of new energy. The new energy consumption level should not be lower than the optimal consumption rate. , the formula is as follows:

[0125] ;

[0126] in, It refers to the optimal absorption rate; represents the power generation of photovoltaic device w in time period t; represents the power generation of wind turbine w in time period t; represents the abandoned power of photovoltaic equipment w in time period t; It represents the abandoned power of wind power equipment w in time period t.

[0127] As you can understand, first, based on the physical laws of distribution networks, such as Ohm's law and Kirchhoff's law, the relationship between voltage drop and node power balance in the lines is clarified, thereby setting AC / DC power balance constraints and distribution network linear power flow constraints. This step ensures that the optimization model accurately reflects the operating characteristics of the distribution network and that the relationship between current, voltage, and power conforms to physical laws. Second, based on safety standards such as the equipment's rated capacity and safe operating range, voltage source converter capacity constraints and safe operating constraints are set to ensure that the equipment operates within a safe range and avoid damage or system instability caused by overload or voltage exceeding the limit. Finally, based on the renewable energy consumption target, a renewable energy consumption rate constraint is set to ensure the effective utilization of renewable energy, avoid wind and solar power curtailment, and improve the economic and environmental performance of the system. Through these steps, based on the physical laws and safety standards of distribution networks, comprehensive constraints are set during the planning phase to ensure that the optimization plan meets both physical characteristics and safety requirements while achieving the effective consumption of renewable energy.

[0128] Step S23: generating planning stage decision variables based on the planning stage objective function and the planning stage constraints.

[0129] It should be noted that planning-stage decision variables refer to the set of variables used for optimization decisions during the planning phase of flexible interconnection cluster planning for distribution substations. In this embodiment, these decision variables include the interconnection strategy binary variable and the renewable energy absorption rate. These variables are the core components of the optimization model. By adjusting their values, the optimal planning solution can be found while satisfying the planning-stage objective function and constraints. Specifically, by optimizing these decision variables, system investment costs and penalty costs can be minimized while ensuring safe system operation and effective renewable energy absorption.

[0130] It is understandable that, first, based on the definition of the planning phase objective function, the planning system identifies the key indicators that need to be optimized: namely, minimizing the sum of the interconnection line investment cost, the penalty cost for wind and solar curtailment, and the penalty cost for distribution transformer overload. Second, the planning system determines the feasible value range of the decision variables based on the planning phase constraints. Finally, the planning system solves the planning phase objective function using mathematical optimization methods (such as linear programming or mixed integer programming). Subject to satisfying all constraints, it generates the planning phase decision variables, including the interconnection strategy binary variable (determining which substations are interconnected) and the new energy consumption rate (reflecting the utilization efficiency of the power generation of new energy equipment).

[0131] Step S24 , constructing an initial two-stage chance-constrained optimization model including a planning stage and an operation stage according to the decision variables in the planning stage, the load of the substation, and the new energy output data.

[0132] As an example, the steps of constructing an initial two-stage chance-constrained optimization model including a planning stage and an operation stage based on the planning stage decision variables, substation load and new energy output data include: defining an operation stage objective function based on the planning stage decision variables, the operation stage objective function representing the minimization of the sum of the expected values ​​of the interconnection line loss cost and the load shedding cost; setting an operation stage probability constraint based on the operation stage objective function; applying a preset proportion of Gaussian perturbations to the substation load and new energy output data to generate an equal probability random scenario set, and defining an operation stage random scenario variable based on the random scenario set; coupling the planning stage decision variables, the operation stage probability constraints and the operation stage random scenario variables to form an initial two-stage chance-constrained optimization model.

[0133] The operational phase objective function is a mathematical expression used to measure and optimize the operational costs of a flexible interconnection cluster planning scheme during its operational phase. In this embodiment, the objective function is expressed as minimizing the sum of the interconnection line loss cost and the expected value of the load shedding cost. This reflects the economic impact of line transmission losses and potential load shedding in actual operation, and aims to reduce system operating costs by optimizing the operational strategy. The operational phase objective function formula is as follows:

[0134] ;

[0135]

[0136] in, Indicates the expected value, Refers to the comprehensive operating cost, Refers to the interconnection line loss cost, It refers to the load shedding cost;

[0137] Interconnection line loss cost refers to the economic cost incurred due to power loss during the transmission of power across interconnected lines during the operation of flexible interconnection between distribution substations. This cost is related to the transmission power and line parameters of the interconnected lines, reflecting the impact of line loss on system economics. The expected value of load shedding cost refers to the expected value of the economic compensation cost incurred by reducing some user loads due to system operational needs during the operation of flexible interconnection between distribution substations. This cost is related to the amount of load shedding and the unit load shedding cost, reflecting the impact of load shedding on system economics. Operational phase probabilistic constraints refer to a series of probabilistic constraints established during the operational phase of flexible interconnection cluster planning to ensure system reliability and safety. (In addition, the operational phase may also adhere to the planning phase constraints described above, which are not repeated here.) In this embodiment, these constraints include load shedding power constraints, distribution transformer load factor probability constraints, and renewable energy consumption rate probability constraints. These constraints ensure that, under certain probability levels, the transformer load factor does not exceed a safety threshold and the renewable energy consumption rate meets preset standards. Load shedding power constraint refers to the limit imposed on the amount of load that needs to be shelved in an emergency to ensure system stability and safety during power system operation. It ensures that the load power removed does not exceed the total active power available in the system, that is, the sum of the maximum active power on the AC and DC sides. The purpose is to maintain system power balance and voltage stability by shedding part of the load in the event of a system fault or emergency, thereby preventing system collapse or equipment damage. The formula is as follows:

[0138]

[0139] in, and They represent the active power of AC and DC loads in the area i at time t under scenario m, It represents the maximum active power removed when the load is shed at distribution station area i at time t under scenario m.

[0140] The distribution transformer load rate probability constraint refers to a probabilistic constraint set during the operation phase of the flexible interconnection cluster planning of distribution substations to ensure that the transformer load rate does not exceed the safety threshold. By introducing a probabilistic constraint, it allows the transformer load rate to exceed the safety threshold in a small number of scenarios (for example, no more than 5%). The distribution transformer load rate probability constraint formula is as follows:

[0141] ;

[0142] in, represents the probability, and sets the maximum allowed violation probability to , Represents the power vector of distribution station area i in time period t, which is used to describe the comprehensive power status of the area in a specific time period. and They represent the active power and reactive power flowing out of distribution network node i at time t under scenario m, represents the rated capacity of the transformer in distribution station area i, Indicates the maximum allowable load rate.

[0143] The probability constraint of the new energy consumption rate refers to the probabilistic constraint conditions set during the operation phase of the flexible interconnection group planning of the distribution station area to ensure the effective consumption of new energy. It requires that under a certain probability level (such as 95%), the new energy consumption rate is not lower than the preset optimal value (such as 90%). The formula is as follows:

[0144]

[0145] in, and They represent the photovoltaic and wind power outputs of the new energy unit w at time t under scenario m, is the maximum permissible violation probability, Indicates the minimum absorption ratio of new energy. and They represent the abandoned power of photovoltaic and wind power equipment w in time period t, respectively, T is the total time period set considered, and W is the set of all wind power and photovoltaic equipment.

[0146] The preset ratio refers to the perturbation ratio applied to the load and renewable energy output data when generating random scenarios. In this embodiment, the preset ratio is 5%, which means that a ±5% Gaussian perturbation is applied to the original data to simulate the uncertainty of actual operation.

[0147] Gaussian perturbations are random perturbations that conform to a Gaussian distribution (normal distribution) and are applied to load and renewable energy output data. The mean of a Gaussian perturbation is zero, and its standard deviation is a preset proportion of the original data. It effectively reflects random fluctuations in actual operation.

[0148] The equal-probability random scenario set refers to a group of random scenarios generated by applying Gaussian perturbations. The probability of each scenario occurring is equal. This random scenario is used to simulate the uncertainty of distributed renewable energy output and load power, and provide data support for the probability constraints in the operation phase.

[0149] Operational random scenario variables are variables defined during the operation phase based on a set of equally probabilistic random scenarios. They represent the system's operating status under each random scenario. In this embodiment, these variables include substation load, renewable energy output, and interconnected line transmission power for each scenario, reflecting the system's operational status under different random scenarios. By introducing these random scenario variables, the optimization model can effectively perform optimization and risk control under uncertain conditions.

[0150] First, based on the interconnection strategy and renewable energy consumption rate determined during the planning phase, the planning system defines an operational objective function as minimizing the sum of the expected values ​​of interconnection line loss costs and load shedding costs. These costs are quantified through mathematical expressions to optimize operational economics. Then, based on this objective function, probabilistic constraints are set for the operational phase. Specifically, the probability distributions of the distribution transformer load factor and renewable energy consumption rate are determined based on historical data and statistical analysis. The maximum probability of violating these constraints is then set to balance risk and cost. Next, a Gaussian perturbation with a preset ratio is applied to the substation load and renewable energy output data. A large number of random samples are generated through Monte Carlo simulation. These samples constitute a set of equally probabilistic random scenarios, each representing a possible operational state. Finally, the decision variables from the planning phase (such as the binary variables for the interconnection strategy and the renewable energy consumption rate), the operational probabilistic constraints, and the operational random scenario variables are integrated into a unified mathematical model. By introducing binary variables and constraints, the model ensures that the requirements of both the planning and operational phases are considered during the optimization process, thus forming an initial two-stage chance-constrained optimization model.

[0151] As an example, the probabilistic chance constraints in the target two-stage chance constraint optimization model are converted into deterministic bilinear constraints through the sampling average approximation method, and the steps of obtaining the deterministic approximation model include: extracting the probabilistic chance constraints in the target two-stage chance constraint optimization model; defining a binary identification variable for each scenario in the equal probability random scenario set; converting the probabilistic chance constraints into bilinear inequalities containing the identification variables; constructing an identification variable sum constraint based on the probability estimation principle of the sampling average approximation method: integrating the bilinear inequality and the identification variable sum constraint, replacing the probabilistic chance constraint, and obtaining a deterministic approximation model.

[0152] In the sampling average approximation method, an identifier variable is a binary variable used to indicate whether each random scenario satisfies a probabilistic chance constraint. By introducing an identifier variable, probabilistic constraints can be converted into linear constraints, facilitating the solution of the optimization model. A bilinear inequality is a linear inequality formed by introducing an identifier variable when converting probabilistic chance constraints into deterministic constraints, consisting of a decision variable and an identifier variable. In this embodiment, a bilinear inequality is used to represent the constraints under each scenario, ensuring that the optimization model can run effectively while satisfying the probabilistic constraints. The probabilistic estimation principle refers to a method for estimating the probability distribution or expected value of a random variable using sample data. Specifically, the probability of satisfying the constraint is approximated by calculating the proportion of scenarios that satisfy the constraint to the total number of scenarios, thereby achieving a deterministic approximation of the probabilistic constraint. In the sampling average approximation method, an identifier variable sum constraint is constructed by summing the identifier variables across all scenarios. In this embodiment, the identifier variable sum constraint is used to ensure that the number of scenarios that satisfy the probabilistic chance constraint across all sample scenarios reaches a preset probability level (e.g., 95%).

[0153] First, probabilistic chance constraints are extracted from the target two-stage chance-constrained optimization model, including probabilistic constraints on the distribution transformer load rate and the renewable energy consumption rate. These constraints allow for violation of the constraints at a certain probability level. Specifically, all probabilistic constraint terms in the model are identified and extracted individually for subsequent processing. Next, a binary flag variable is defined for each scenario in the set of equally probabilistic random scenarios. A value of 1 indicates that the scenario satisfies the constraint, while a value of 0 indicates that it does not. This allows tracking whether each scenario meets the constraint. Next, the probabilistic chance constraints are converted into bilinear inequalities containing the flag variable. By introducing the flag variable and multiplying it with the variables in the original constraint, a bilinear inequality is formed. This step converts the probabilistic constraints into a linear form, making the optimization model easier to solve. Thus, when the flag variable is 0, the constraint is relaxed, and when the flag variable is 1, the constraint must be satisfied. Then, based on the probability estimation principle of the sampling average approximation method, a sum constraint of the identification variables is constructed. The specific operation is to calculate the sum of the identification variables in all scenarios and compare it with the total number of scenarios multiplied by (1 - the allowed violation probability), that is, Σ identification variables ≥ total number of scenarios × (1 - allowed violation probability). This step ensures that the number of scenarios that meet the constraint reaches a preset probability level in all scenarios, thereby approximating the probabilistic constraint in the optimization model. Finally, the bilinear inequality and the sum constraint of the identification variables are integrated into the original model, replacing the original probabilistic chance constraint, to obtain a deterministic approximate model. This step, by adding new constraints to the model and removing the original probabilistic constraints, enables the model to be solved on a finite set of samples, significantly improving the model's solvability and computational efficiency while maintaining the original model's ability to handle uncertainty.

[0154] As an example, the step of iteratively solving the deterministic approximate model through the column constraint generation decomposition algorithm to obtain the target interconnection group solution includes: initializing the parameters of the column constraint generation decomposition algorithm, the parameters including the convergence threshold, the upper bound of the objective function and the lower bound of the objective function; constructing a main problem based on the deterministic approximate model, the main problem including the interconnection strategy variable, the new energy consumption rate variable and the scenario cost upper bound variable; solving the main problem to obtain the optimal solution of the main problem, the optimal solution of the main problem including the interconnection strategy, the new energy consumption rate and the scenario identifier; screening the target random scenario from the equal probability random scenario set according to the scenario identifier; for each of the target random scenarios A scenario constructs a subproblem, wherein the subproblem includes a line transmission power variable and a load shedding variable; the subproblem is solved to obtain a subproblem objective value and a feasibility state; a cut constraint is added to the main problem according to the feasibility state of the subproblem, and the upper bound and the lower bound of the objective function are updated according to the optimal solution of the main problem; when the relative error between the upper bound and the lower bound of the objective function is greater than or equal to the convergence threshold, the step of constructing the main problem based on the deterministic approximate model is returned; when the relative error is less than the convergence threshold, a target interconnection group solution is obtained according to the interconnection strategy and the new energy consumption rate in the optimal solution of the main problem.

[0155] The convergence threshold is a preset value used to determine whether the column constraint generation and decomposition algorithm has converged. In this embodiment, the convergence threshold is set to 0.01, indicating that when the relative error between the upper and lower bounds of the objective function is less than or equal to 0.01, the algorithm is considered to have converged and iterations can be stopped. The upper bound of the objective function is an estimate of the maximum value that the objective function can reach in the column constraint generation and decomposition algorithm. In this embodiment, the upper bound of the objective function is initialized to positive infinity, indicating that there is no limit on the maximum value of the objective function at the beginning of the algorithm. As the algorithm iterates, the upper bound of the objective function is updated based on the currently found optimal solution, gradually approaching the true maximum value of the objective function. The lower bound of the objective function is an estimate of the minimum value that the objective function can reach in the column constraint generation and decomposition algorithm. In this embodiment, the lower bound of the objective function is initialized to negative infinity, indicating that there is no limit on the minimum value of the objective function at the beginning of the algorithm. As the algorithm iterates, the lower bound of the objective function is updated based on the currently found optimal solution, gradually approaching the true minimum value of the objective function. The main problem is the core optimization problem in the column constraint generation decomposition algorithm, which includes decision variables (such as interconnection strategy variables and new energy consumption rate variables) and objective functions. In this embodiment, the goal of the main problem is to optimize the interconnection strategy and new energy consumption rate to minimize the overall cost of the system. The solution to the main problem provides a basis for the sub-problems, and iterative updates are performed through the feedback of the sub-problems. The sub-problem is an optimization problem constructed for each target random scenario in the column constraint generation decomposition algorithm. In this embodiment, the sub-problem includes line transmission power variables and load shedding variables, which are used to verify the feasibility of the solution to the main problem in a specific scenario and optimize its cost. In order to facilitate algorithm implementation and structural analysis, while simplifying the expression and improving the operability of the model, the main problem and sub-problems are written in a compact form. The compact form of the main problem is as follows:

[0156] ; ;

[0157] ;

[0158] in, It represents the average upper bound estimate of the second-stage scenario cost, which is continuously updated to approach the true optimal expected value in each iterative solution of the main and subproblems; is the feasibility indicator of the subproblem, Indicates that all subproblems in the considered scenario are feasible, otherwise, Indicates that there is an infeasible subproblem; represents the optimal solution obtained by the second-stage model under scenario m; represents the set of scenarios for all infeasible subproblems, and the interpretation of other variables is consistent with that in the compact form formulation of the two-stage chance-constrained optimization model.

[0159] because The scenario that is considered to be allowed to violate the chance constraint is eliminated and does not participate in the optimization, so this type of scenario does not need to be solved as a sub-problem; for scenarios that meet The compact form of the corresponding sub-problem for scenario m is as follows:

[0160] ; ; ;

[0161] in, It indicates that the optimal solution is obtained by solving the first stage model, and the interpretation of other variables is consistent with the compact form of the main problem.

[0162] Interconnection strategy variables refer to decision variables in the main problem that indicate which substations are interconnected. In this embodiment, these variables are typically binary variables, with a value of 1 indicating that an interconnection line is established between two substations, and a value of 0 indicating that no interconnection line is established. By optimizing these variables, the optimal interconnection strategy can be determined. New energy consumption rate variables refer to decision variables in the main problem that indicate the utilization efficiency of the power generated by new energy equipment. They reflect the system's effective utilization of new energy. By optimizing these variables, the level of new energy consumption can be improved and wind and solar power curtailment can be reduced. Scenario cost upper bound variables refer to variables in the main problem that indicate the upper limit of the system operating cost under each random scenario. These variables are used to ensure that the system operating cost does not exceed a preset upper limit in each scenario, thereby ensuring the system's economic efficiency. Target random scenarios are specific scenarios selected from a set of equally probable random scenarios based on scenario identifiers during the column constraint generation and decomposition algorithm. In this embodiment, the scenario identifier variables for target random scenarios are zero, indicating that these scenarios require further analysis to verify their feasibility or optimize their costs. The line transmission power variable refers to the decision variable used to represent the transmission power of the interconnected lines in the subproblem. It reflects the actual power transmission status of the interconnected lines in a specific scenario. By optimizing these variables, we can ensure that the line transmission power does not exceed its capacity limit. The load shedding variable refers to the decision variable used to represent the amount of load that needs to be reduced in a specific scenario in the subproblem. It reflects the amount of load that may need to be reduced during system operation to ensure safe operation. The subproblem objective value refers to the numerical value of the system operating cost or optimization objective obtained during the subproblem solution process. In this embodiment, the subproblem objective value reflects the actual value of the system operating cost or optimization objective in a specific scenario and is used to evaluate the feasibility and optimization level of the solution to the main problem. The feasibility status refers to the status of whether the current solution satisfies all constraints during the subproblem solution process. If the solution to the subproblem satisfies all constraints, the status is feasible; otherwise, it is infeasible. The feasibility status is used to determine whether to add cut constraints to the main problem.

[0163] First, the parameters of the column constraint generation decomposition algorithm are initialized. The convergence threshold is set to 0.01, the upper bound of the objective function is set to positive infinity, and the lower bound is set to negative infinity. These parameters control the algorithm's iteration process and determine the convergence conditions. Next, a main problem is constructed based on a deterministic approximate model. The main problem contains variables for the interconnection strategy, the renewable energy consumption rate, and the upper bound of the scenario cost. The main problem aims to optimize the interconnection strategy and renewable energy consumption rate while controlling the upper cost limit for each scenario. The main problem is then solved to obtain the optimal solution, including the interconnection strategy, renewable energy consumption rate, and scenario identifier. These results provide the basis for constructing subsequent subproblems. Based on the scenario identifier of the main problem, a target random scenario is selected from a set of equally probable random scenarios. For each target random scenario, a subproblem is constructed to verify the feasibility and optimization cost of the main problem solution in a specific scenario. The subproblem is solved to obtain the subproblem objective value and feasibility status. Add cut constraints to the main problem according to the feasibility status of the subproblem. When the subproblem is infeasible, add feasible cut constraints (this constraint is used to exclude solutions that make the subproblem infeasible, thereby guiding the solution process of the main problem to avoid these infeasible areas); when the subproblem is feasible, add optimal cut constraints (usually constructed based on the objective function value of the subproblem. It introduces new constraints and uses the optimal objective function value of the subproblem as a new lower bound of the objective value of the main problem, thereby guiding the solution process of the main problem to a better solution) to promote the solution to develop in a better direction. At the same time, according to the optimal solution of the main problem, update the upper bound of the objective function (updated to the actual value of the comprehensive cost of the current optimal solution of the main problem, which is calculated by substituting the optimal solution of the main problem into the objective function of the deterministic approximate model) and the lower bound (updated to the current main problem objective value, which refers to the objective function value corresponding to the current optimal solution of the main problem in the column constraint generation decomposition algorithm). When the relative error between the upper and lower bounds of the objective function is greater than or equal to the convergence threshold, the algorithm returns to the step of constructing the main problem and continues iterating. When the relative error is less than the convergence threshold, the algorithm determines the specific interconnection line deployment plan based on the interconnection strategy in the optimal solution to the main problem. This strategy specifies which substations require interconnection lines and their specific parameters. Furthermore, the new energy consumption level of each substation is determined based on the new energy consumption rate to ensure the effective utilization of new energy. Combining this information forms a target interconnection group plan, which includes not only the specific interconnection line deployment but also the optimized new energy consumption strategy. This plan can achieve efficient energy sharing and load balancing between distribution stations, meeting the system's economic and reliability requirements.

[0164] Please refer to Figure 5 , Figure 5This diagram illustrates the evolution of infeasible scenarios, the actual violation probability, and the iterative convergence of the main and subproblems in the CCG algorithm, provided in Example 2 of the method for flexible interconnected cluster planning of distribution substations for energy mutualization. During the CCG algorithm iterations, the upper bound (UB) and lower bound (LB) of the objective function, the number of infeasible scenarios, and the actual violation probability change. In the figure, the horizontal axis represents the iteration number it, the left vertical axis represents the scenario number, and the right vertical axis represents the actual violation probability (%). Blue triangles represent the violation probability, green dots represent eliminated scenarios, and red dots represent infeasible scenarios. As the number of iterations increases, the number of infeasible scenarios gradually decreases, and the violation probability rapidly decreases and stabilizes, ultimately reaching around 4%. This indicates that the algorithm effectively reduces infeasible scenarios and lowers the actual violation probability. UB and LB are represented by red and yellow lines, respectively. As the number of iterations increases, they gradually approach each other, indicating that the algorithm is converging. The inset further illustrates the evolution of the total cost during the first few iterations, showing a rapid initial decrease before stabilizing. These results verify the effectiveness of the CCG algorithm in dealing with uncertain optimization problems. It can gradually approach the optimal solution during the iterative process and improve the computational efficiency and solution performance of the model.

[0165] The formulated solution process of the CCG decomposition algorithm is as follows:

[0166] (1) Initialization: Setting the convergence threshold , iterate index , the lower bound of the objective function , the upper bound of the objective function , the feasibility index of the subproblem , the set of scenarios for all infeasible subproblems .

[0167] (2) Solve the main problem: Obtain the objective function value of the main problem , Internet Strategy , optimal absorption rate and scene identification variables , the updated model lower bound is .

[0168] (3) Verification and For all satisfaction The feasibility of the sub-problem in the scenario:

[0169] ①If all subproblems are feasible, then , and obtain the objective function values ​​of all subproblems (cost under scenario m), add the following optimal cut constraint to the main problem:

[0170]

[0171] The interpretation of the variables is the same as above.

[0172] ② If there is an infeasible subproblem, then , set the second stage (operation stage) objective function , get all scenarios of infeasible subproblems and add them to the set , add the following feasible cut constraints to the main problem:

[0173]

[0174] The interpretation of the variables is the same as above (see the compact form of the two-stage chance-constrained optimization model and other formulas).

[0175] (4) Update the upper bound of the model:

[0176]

[0177] in, is the probability that scene m is selected, Refers to the expected cost.

[0178] (5) Convergence judgment: If , the problem converges and returns the optimal solution, obtaining the target interconnected group solution. Otherwise, update And return to (2).

[0179] Please refer to Figure 6 , Figure 6 This diagram shows the flexible interconnection planning results and substation grouping situation for the second embodiment of the flexible interconnection group planning method for energy mutual assistance provided by this application. In the figure, substations are represented by black squares, and low-voltage DC interconnection lines are represented by blue lines. Different distribution substations are connected to form interconnected groups. Each distribution substation is identified by a number, such as Group 1, Group 2, Group 3, and Group 4, and each is represented by a different colored background area. The orange dots in the figure represent substations with excess distributed resources, and the red triangles represent substations with overloaded distribution transformers. Through flexible interconnection, these substations can share resources, optimize power distribution, improve energy utilization efficiency, and reduce distribution transformer overload. For example, when the distributed energy generation of a substation exceeds its load demand, the excess power can be transmitted to other substations via low-voltage DC interconnection lines, thereby achieving energy mutual assistance. This interconnection group planning method helps improve the reliability and economy of the distribution network, especially as the scale of distributed energy access continues to grow. It can effectively address the uncertainty caused by random fluctuations in sources and loads, ensuring the safe and stable operation of the distribution network.

[0180] This embodiment first defines a planning-stage objective function based on the initial interconnection set. This objective function integrates the interconnection line investment cost, wind and solar curtailment penalty costs, and distribution transformer overload penalty costs. By minimizing the sum of these costs, the goal is to find the interconnection strategy with the best economic and reliability. This step ensures that the planning scheme meets system operational requirements while minimizing overall costs. Next, planning-stage constraints are set based on the physical laws and safety standards of the distribution network, including voltage source converter capacity constraints and AC / DC power balance constraints. These constraints ensure that the optimization scheme is physically feasible and meets safety requirements, thereby ensuring the safety and reliability of the system. Then, using the planning-stage objective function and constraints, a mathematical optimization method is used to generate planning-stage decision variables, including the interconnection strategy binary variable and the renewable energy absorption rate. This step optimizes the decision variables to find the lowest-cost interconnection strategy and renewable energy absorption plan while satisfying the constraints. Finally, based on the decision variables in the planning stage, substation load, and renewable energy output data, an initial two-stage chance-constrained optimization model consisting of the planning stage and the operation stage was constructed. This model optimized the interconnection strategy and renewable energy absorption rate in the planning stage, and verified the feasibility of the strategy through random scenarios in the operation stage. This staged optimization method can effectively deal with uncertainty and improve the adaptability and robustness of the system.

[0181] This application also provides a flexible interconnection group planning device for distribution station areas for energy mutual assistance, please refer to Figure 7 The energy-assisted distribution station area flexible interconnection group planning device includes:

[0182] The initial set building module 10 is used to screen the pairs of substations that meet the preset load rate conditions or excess output conditions based on the distribution network topology parameters, substation loads, and renewable energy output data, and build the initial interconnection set;

[0183] A model building module 20 is configured to construct an initial two-stage opportunity-constrained optimization model based on the initial interconnection set, comprising a planning stage and an operation stage. The planning stage determines the interconnection strategy and the new energy consumption rate with the goal of minimizing investment cost and penalty cost. The operation stage verifies the feasibility of the interconnection strategy based on random scenarios.

[0184] a linearization processing module 30 for performing polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model, and reconstructing the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain a target two-stage chance-constrained optimization model;

[0185] An equivalent conversion module 40 is used to convert the probabilistic chance constraints in the target two-stage chance-constrained optimization model into deterministic bilinear constraints by using a sampling average approximation method to obtain a deterministic approximate model;

[0186] The solving module 50 is configured to iteratively solve the deterministic approximate model by using a column constraint generation decomposition algorithm to obtain a target interconnection group solution.

[0187] The present application provides a distribution substation area flexible interconnection group planning device for energy mutual assistance. The distribution substation area flexible interconnection group planning device for energy mutual assistance includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the distribution substation area flexible interconnection group planning method for energy mutual assistance in the above-mentioned embodiment one.

[0188] The present application provides a computer-readable storage medium having computer-readable program instructions (i.e., computer programs) stored thereon, and the computer-readable program instructions are used to execute the method for planning flexible interconnection groups of distribution substations for energy mutual assistance in the above-mentioned embodiment.

[0189] The apparatus, device, and storage medium for planning flexible interconnected groups of distribution substations for energy mutual assistance provided in this application employ the method for planning flexible interconnected groups of distribution substations for energy mutual assistance in the above-mentioned embodiments, and are capable of solving the technical problem of achieving efficient energy mutual assistance and load balancing between distribution substations. Compared with the prior art, the beneficial effects of this apparatus are the same as those of the method for planning flexible interconnected groups of distribution substations for energy mutual assistance provided in the above-mentioned embodiments, and the other technical features of the apparatus for planning flexible interconnected groups of distribution substations for energy mutual assistance are the same as those disclosed in the above-mentioned embodiment methods, and are not further described here.

[0190] The above descriptions are only some embodiments of the present application and do not limit the patent scope of the present application. Anything that is directly or indirectly applied to other related technical fields under the technical concept of the present application is included in the patent protection scope of the present application.

Claims

1. A method for planning flexible interconnection groups of distribution substations for energy mutual assistance, characterized in that: The method comprises: Based on the distribution network topology parameters, substation load, and renewable energy output data, we select substation pairs that meet the preset load rate conditions or excess output conditions and build an initial interconnection set. Based on the initial interconnection set, an initial two-stage chance-constrained optimization model is constructed, which includes a planning stage and an operation stage. The planning stage determines the interconnection strategy and the new energy consumption rate with the goal of minimizing investment cost and penalty cost. The operation stage verifies the feasibility of the interconnection strategy based on random scenarios. performing polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model, and reconstructing the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain a target two-stage chance-constrained optimization model; The probabilistic chance constraint in the target two-stage chance-constrained optimization model is converted into a deterministic bilinear constraint by using a sampling average approximation method, thereby obtaining a deterministic approximate model; The deterministic approximate model is iteratively solved by a column constraint generation decomposition algorithm to obtain a target interconnected group solution.

2. The method according to claim 1, wherein The step of constructing an initial two-stage chance-constrained optimization model including a planning stage and an operation stage based on the initial interconnection set includes: Defining a planning stage objective function according to the initial interconnection set, wherein the planning stage objective function represents minimization of the sum of interconnection line investment cost, wind and solar power curtailment penalty cost, and distribution transformer overload penalty cost; Setting planning phase constraints based on the physical laws and safety standards of the distribution network; generating planning-stage decision variables based on the planning-stage objective function and the planning-stage constraints; An initial two-stage chance-constrained optimization model including a planning stage and an operation stage is constructed based on the decision variables in the planning stage, the load of the substation and the new energy output data.

3. The method according to claim 2, wherein The step of constructing an initial two-stage chance-constrained optimization model including a planning stage and an operation stage according to the planning stage decision variables, the substation load, and the new energy output data includes: defining an operation phase objective function based on the planning phase decision variables, wherein the operation phase objective function represents minimization of the sum of the interconnection line loss cost and the expected value of the load shedding cost; Setting an operation phase probability constraint based on the operation phase objective function; Applying a preset proportion of Gaussian disturbance to the load and renewable energy output data of the substation area to generate a set of random scenarios with equal probability, and defining random scenario variables in the operation phase based on the random scenario set; The planning stage decision variables, the operation stage probability constraints and the operation stage random scenario variables are coupled to form an initial two-stage chance-constrained optimization model.

4. The method according to claim 3, wherein The step of converting the probabilistic chance constraints in the target two-stage chance-constrained optimization model into deterministic bilinear constraints by using the sampling average approximation method to obtain a deterministic approximate model includes: extracting probabilistic chance constraints in the target two-stage chance-constrained optimization model; defining a binary identification variable for each scenario in the set of equally probable random scenarios; converting the probabilistic chance constraint into a bilinear inequality involving the identification variable; The probability estimation principle based on the sampling average approximation method is used to construct the sum constraint of the identification variable: The bilinear inequality and the identification variable sum constraint are integrated to replace the probabilistic chance constraint to obtain a deterministic approximate model.

5. The method according to claim 3, wherein The step of iteratively solving the deterministic approximate model by using a column constraint generation decomposition algorithm to obtain a target interconnection group solution includes: Initializing parameters of a column constraint generation decomposition algorithm, the parameters including a convergence threshold, an upper bound of an objective function, and a lower bound of an objective function; Constructing a main problem based on the deterministic approximate model, wherein the main problem includes an interconnection strategy variable, a new energy consumption rate variable, and a scenario cost upper bound variable; Solve the main problem and obtain an optimal solution to the main problem, wherein the optimal solution to the main problem includes an interconnection strategy, a new energy consumption rate, and a scenario identifier; According to the scene identifier, a target random scene is selected from the set of random scenes with equal probability; Constructing a sub-problem for each of the target random scenarios, wherein the sub-problem includes a line transmission power variable and a load shedding variable; Solve the subproblem to obtain the subproblem target value and feasibility status; Adding a cut constraint to the main problem according to the feasibility state of the subproblem, and updating the upper bound of the objective function and the lower bound of the objective function according to the optimal solution of the main problem; When the relative error between the upper bound of the objective function and the lower bound of the objective function is greater than or equal to the convergence threshold, returning to the step of constructing the main problem based on the deterministic approximate model; When the relative error is less than the convergence threshold, a target interconnection group solution is obtained according to the interconnection strategy and the new energy consumption rate in the optimal solution of the main problem.

6. The method according to claim 1, wherein The step of selecting pairs of substations that meet a preset load rate condition or an excess output condition based on distribution network topology parameters, substation loads, and renewable energy output data to construct an initial interconnection set includes: Obtaining distribution network topology parameters, substation load, and renewable energy output data, wherein the distribution network topology parameters include distribution network node connection relationships and line impedance parameters, and the substation load includes substation load power; Calculating the distribution transformer load rate of each substation according to the substation load power, and identifying the first type of substation where the distribution transformer load rate exceeds a preset load rate threshold; According to the renewable energy output data, identifying a second type of substation where the wind and solar power output exceeds a preset rated capacity; According to the connection relationship of the distribution network nodes, a target substation pair including at least one of the first type of substation or the second type of substation is selected within the entire range of the distribution network nodes; Calculating the effective electrical distance between the target stations according to the line impedance parameters; Eliminate the to-be-eliminated substation pairs from the target substation pairs to generate an initial interconnection set, wherein the effective electrical distance of the to-be-eliminated substation pairs is greater than a preset distance threshold.

7. The method according to any one of claims 1 to 6, characterized in that The nonlinear constraints include voltage source converter transmission power constraints and distribution transformer load rate constraints, and the power flow model includes distribution network active power flow equation, reactive power flow equation and voltage amplitude equation; The steps of performing polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model and reconstructing the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain the target two-stage chance-constrained optimization model include: Using a polyhedron envelope method to perform linear approximation on the voltage source converter transmission power constraint and the distribution transformer load rate constraint to generate linearized constraint conditions; Constructing an impedance matrix based on line impedance parameters in the distribution network topology parameters; Reconstructing the distribution network active power flow equation, the reactive power flow equation, and the voltage amplitude equation into a node power-voltage matrix relationship according to the impedance matrix; The linearized constraint condition is integrated with the node power-voltage matrix relationship to replace the nonlinear constraint and power flow equation in the initial two-stage chance-constrained optimization model, thereby obtaining a target two-stage chance-constrained optimization model.

8. A flexible interconnection group planning device for distribution substations for energy mutual assistance, characterized in that: The device comprises: The initial set construction module is used to screen the pairs of substations that meet the preset load rate conditions or excess output conditions based on the distribution network topology parameters, substation loads, and renewable energy output data, and construct the initial interconnection set; a model construction module for constructing an initial two-stage chance-constrained optimization model based on the initial interconnection set, comprising a planning stage and an operation stage, wherein the planning stage determines the interconnection strategy and the new energy consumption rate with the goal of minimizing investment cost and penalty cost, and the operation stage verifies the feasibility of the interconnection strategy based on random scenarios; a linearization processing module, configured to perform polyhedron approximate linearization processing on the nonlinear constraints in the initial two-stage chance-constrained optimization model, and reconstruct the power flow model in the initial two-stage chance-constrained optimization model into a compact form to obtain a target two-stage chance-constrained optimization model; An equivalent conversion module, configured to convert the probabilistic chance constraints in the target two-stage chance-constrained optimization model into deterministic bilinear constraints by using a sampling average approximation method, thereby obtaining a deterministic approximate model; The solution module is used to iteratively solve the deterministic approximate model through a column constraint generation decomposition algorithm to obtain a target interconnected group solution.

9. A flexible interconnection group planning device for distribution substations for energy mutual assistance, characterized in that: The device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of the method for planning flexible interconnection groups of distribution substations for energy mutual assistance as described in any one of claims 1 to 7.

10. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the method for planning flexible interconnection groups of distribution substations for energy mutual assistance as described in any one of claims 1 to 7 are implemented.

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