Two-stage stochastic programming method for power-traffic coupled network based on improved logical benders decomposition

Abstract

This invention discloses a two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition, belonging to the field of power system and transportation planning technology. The method includes: obtaining a set of stochastic traffic flow scenarios to describe demand uncertainty; constructing a two-stage stochastic programming model considering multi-source carbon emissions, where the first stage is charging station site selection planning and the second stage is coordinated operation optimization; linearizing and reconstructing the model using minimal positive correction terms, logarithmic transformation, piecewise linearization, and second-order cone transformation techniques; and using the improved logical Benders decomposition algorithm to perform master-slave structure splitting on the reconstructed model and iteratively solving it alternately. During the iteration process, an optimal cut reinforcement mechanism based on flow contribution and a feasible cut generation strategy based on the minimum infeasible set are executed, dynamically generating high-quality cut planes to accelerate upper and lower bound convergence. This invention achieves deep synergy between the economic efficiency and low-carbon characteristics of power-transportation systems, significantly improving the solution efficiency and convergence stability of large-scale coupled models with integer variables.

Description

Technical Field

[0001] This invention relates to the field of power system and intelligent transportation planning technology, and more specifically, to a two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition. Background Technology

[0002] With the large-scale development of electric vehicles (EVs), the coupling between the power system and the transportation system is becoming increasingly close. Under the dual carbon objectives, comprehensively considering the spatiotemporal distribution uncertainty of traffic flow and multi-source carbon emissions, rationally planning the site selection and capacity configuration of charging stations is crucial to ensuring the economical and low-carbon operation of the power-transportation coupled network.

[0003] Existing research on power-transportation coupled network planning typically faces the following challenges: First, real traffic flow is influenced by various uncertainties, and power system operation must balance strict AC power flow security with low carbon emissions, resulting in co-planning models exhibiting typical nonlinear, mixed-integer, and high-dimensional characteristics. Second, for such complex two-stage stochastic programming models, directly using commercial solvers (such as CPLEX and Gurobi) for global solution often suffers from the "curse of dimensionality," making it difficult to find the global optimum within a reasonable timeframe. Finally, while the conventional Benders decomposition algorithm can decouple the main problem (planning) from the subproblems (running), the presence of numerous nonlinear and discrete variables in the original problem makes it difficult to accurately obtain the dual information of the subproblems. This leads to a weak cutting plane in the traditional Benders algorithm, extremely slow iterative convergence, and a tendency to get trapped in local optima or oscillations. Summary of the Invention

[0004] To address the problems of low solution efficiency and difficulty in balancing uncertainty and low carbon emissions in existing power-transport coupled planning models, this invention provides a two-stage stochastic planning method for power-transport coupled networks based on improved logical Benders decomposition. The aim is to achieve accurate and efficient solutions to complex high-dimensional coupled models through an improved cutting plane generation mechanism.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: A two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition includes the following steps: S1: Obtain a set of stochastic traffic flow scenarios for the power-transportation coupled network to describe the uncertainty of traffic demand; S2: Construct a two-stage stochastic programming model that takes into account multi-source carbon emissions; in the first stage, the location of charging station construction is used as the decision variable, and the objective is to minimize the expected total cost; in the second stage, under the given location decision, the power-transportation cooperative operation optimization is carried out for each stochastic scenario, and the objective is to minimize the total system operating cost. S3: Linearize and reconstruct the two-stage stochastic programming model, use the minimum positive correction term and logarithmic transformation to process the nonlinear term of carbon emissions, and use piecewise linearization and second-order cone transformation techniques to transform the original model into a mixed integer linear programming model. S4: Decompose the linearized and reconstructed model into a main problem and sub-problems, solve the main problem to generate candidate schemes for charging station site selection, and determine the global lower bound of the total system cost; S5: Solve subproblems under given candidate schemes to evaluate the optimal operating cost of each stochastic scenario, update the global upper bound of the total system cost, and perform alternating iterations of cutting plane feedback to the main problem based on heuristic enhancement strategy until the relative difference between the upper and lower bounds meets the preset convergence accuracy, and output the optimal addressing decision and cooperative operation scheme.

[0006] Furthermore, in step S2, the expected total cost includes carbon emission costs, which satisfy the following: in, This indicates the length of each regular road. Indicates the road travel time of a gasoline-powered vehicle. Indicates the flow rate of fuel-powered vehicles; Indicates the average speed of the road; This indicates the carbon emissions per kilometer per hour for a single gasoline-powered vehicle. It is a carbon dioxide emission factor; and These represent carbon emissions from the transportation network and the power distribution network, respectively.

[0007] Furthermore, in step S2, the expected total cost includes the transportation network travel cost, which satisfies the following: in, It is the unit time value coefficient; It is a collection of regular and detour routes; It is a charging road collection; This refers to the travel time on regular roads; It refers to the travel time on the charging route; It is with the busbar Charging fees at connected fast charging stations; This refers to the charging energy requirements of EVs; This indicates the traffic flow on the charging route.

[0008] Furthermore, in step S2, the expected total cost includes the distribution network operating cost, which satisfies the following: in, This refers to the active power output of the generator. The main online purchase volume; and This is the power generation cost coefficient; This represents the electricity purchase cost coefficient.

[0009] Furthermore, in step S2, the cooperative operation optimization is subject to traffic network constraints, which include travel time constraints, wherein: The travel time on conventional roads is described using the BPR function, whose mathematical expression satisfies: The travel time on charging routes is described by a travel time function based on queuing theory, and its mathematical expression satisfies: In the formula, Indicates the free passage time on regular roads; Indicates road The maximum traffic flow limit; Indicates the free passage time of the charging road; This indicates the maximum vehicle capacity of the charging road. Indicates charging power. The need to charge electric vehicles.

[0010] Furthermore, in step S2, the cooperative operation optimization is subject to distribution network constraints, which include line capacity constraints, voltage amplitude constraints, and generator output constraints, respectively satisfying: In the formula: Indicates the upper limit of the line's apparent power; , These represent the upper and lower limits of the node voltage, respectively. , These represent the upper and lower limits of the generator's active power output, respectively. , These represent the upper and lower limits of the generator's reactive power output, respectively.

[0011] Furthermore, in step S2, the collaborative operation optimization is subject to charging station constraints, which include: Constraints on the number of charging stations planned and constructed: , ; Feasibility constraints restrict electric vehicles to charging only at planned and constructed charging station nodes, satisfying the following: Total active power load requirement of the system: ; In the formula: A collection of candidate charging stations; These are binary variables for the first stage; It refers to the number of charging stations planned and constructed. For the first The active charging demand of electric vehicles gathered at each charging station; This is an inherent requirement of the node; It is a very large positive number.

[0012] Furthermore, the linearization reconstruction in step S3 includes: To address the nonlinear terms in the carbon emission function, a minimum positive number is introduced as a correction term to avoid the singularity of the zero point of the logarithmic function and to perform a logarithmic transformation. At the same time, an auxiliary variable is introduced to convert the transformed nonlinear terms into a set of linear equality constraints. The nonlinear terms in the conventional road travel time function and carbon emission model are piecewise linearized by using type 2 special ordered set SOS2 constraints. The power flow constraints in the branch power flow model of the distribution network are transformed into a standard second-order cone programming form using the second-order cone transformation technique.

[0013] Furthermore, the cutting plane enhancement strategy in step S5 includes constructing an enhanced optimal cut, specifically including: Based on the results of the sub-problems in all scenarios, the calculation is performed for each planned charging station. Expected traffic : All charging stations are sorted in descending order of their expected traffic volume, and the top-ranked charging stations are identified as the critical charging station set. Key charging station cluster The sum of the cumulative expected traffic reaches a preset proportion of the total expected traffic. ; The enhanced optimal cut satisfies: .

[0014] Furthermore, the cutting plane enhancement strategy in step S5 includes generating enhanced feasible cuts, specifically including: The decision-making scheme given by the main problem If the blanket problem is deemed infeasible, then a collection of charging stations that are not planned for construction will be tested. For each charging station in the problem, determine whether it alone makes the subproblem infeasible, and generate corresponding enhanced feasibility cut constraints accordingly: Enhanced feasible cut constraints force the corresponding charging station to be included in the construction plan in subsequent iterations; if no single site is found to be infeasible, then a basic feasible cut based on complete combinations is adopted to enter the next iteration.

[0015] Compared with the prior art, the present invention has the following advantages: 1. Achieving deep synergy between economic efficiency and low carbon emissions in the power-transportation coupled system. Existing technologies often focus solely on minimizing total system cost or consider low carbon indicators only within a single network. This invention systematically constructs a unified multi-source carbon emission model encompassing the main power grid, distributed power sources, and fuel-powered vehicles. Within a two-stage planning framework, it achieves joint optimization decision-making for the economic efficiency and low carbon emissions of charging station site selection planning and the coordinated operation scheme of the coupled system.

[0016] 2. It balances addressing uncertainty risks with reducing the expected operating cost of the system. Existing robust optimization methods often suffer from high operating costs due to conservative assumptions in dealing with the uncertainties in the spatiotemporal distribution of mixed traffic flows. This invention employs a two-stage, multi-scenario stochastic programming method, which can more accurately balance optimization decisions and operational risks. Especially in extreme traffic scenarios with both high load and fluctuating demand, compared to traditional deterministic models, this invention can significantly reduce the expected operating cost of the system.

[0017] 3. Significantly improves the solution efficiency and stability of large-scale coupled models with integer variables. Addressing the limitations of traditional logistic Benders decomposition algorithms in handling large-scale mixed-integer programming, which suffer from limited cut constraint information and slow convergence, this invention proposes a heuristically enhanced logistic Benders decomposition method. By introducing an optimal cut reinforcement mechanism based on flow contribution and a feasible cut generation strategy based on the minimum infeasible set, it can dynamically generate higher-quality cut planes with richer information. While strictly ensuring the optimality of the site selection planning results, this method significantly reduces the number of alternating iterations between principal and subproblems and significantly shortens the computation time in complex stochastic scenarios. Attached Figure Description

[0018] Figure 1This is a diagram of a power-transportation coupled network system.

[0019] Figure 2 To improve the logical benders decomposition algorithm process.

[0020] Figure 3 This is the power distribution network structure analyzed in this example.

[0021] Figure 4 This is the traffic network structure analyzed in this example.

[0022] Figure 5 The simulation results for the two algorithms are shown under different random scenarios.

[0023] Figure 6 To improve the comparison chart of iteration counts with the basic algorithm.

[0024] Figure 7 A comparison chart showing the solution time for different scenario scales.

[0025] Figure 8 This is a map showing the vehicle path traffic distribution under UE status.

[0026] Figure 9 A chart comparing the travel costs of different types of vehicles.

[0027] Figure 10 This represents the optimal power flow result for the distribution network.

[0028] Figure 11 This is the sensitivity analysis curve for the carbon tax coefficient.

[0029] Figure 12 This is a cost comparison between the stochastic model and the deterministic model. Detailed Implementation

[0030] The present invention will be further described in detail below with reference to the embodiments.

[0031] Example: A two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition (LBBD) is proposed, constructing a stochastic programming model for the power-transport coupled network. Figure 1 This is the framework of the power-transportation coupled system in this embodiment. In the distribution network, the inherent load and the charging station load are jointly supplied by the upstream power grid and distributed power sources; in the transportation network, GVs and EVs together constitute a mixed traffic flow. As a key coupling node between the power and transportation systems, the charging station's charging price affects the route selection and charging behavior of electric vehicles, and the resulting charging load is connected to the distribution network, thus affecting the system's operating costs.

[0032] Based on this, a unified model is constructed for the multi-source carbon emissions of the system, which includes the main power grid, distributed generation (DG) and fuel vehicles. Furthermore, a two-stage stochastic programming model that takes into account traffic flow uncertainty is constructed to minimize the expected total cost of the system.

[0033] In this embodiment, the optional data processing rules for improving computational efficiency are as follows: 1) The State of Charge (SoC) of electric vehicle batteries is simplified, meaning that the electric vehicle always has sufficient power during the journey to reach any fast charging station (FCS) in the network and fully charge the battery at the charging station.

[0034] 2) Treat the charging behavior of electric vehicles as homogeneous, that is, all electric vehicles use the same rated power for charging, so their single charging time and charging demand are similar. All remain consistent.

[0035] To minimize the expected total cost of the system under all stochastic scenarios in the context of traffic flow uncertainty, a two-stage stochastic programming model is constructed. The first stage determines the site selection for charging stations, and the second stage, given the charging station site selection plan, optimizes the coordinated operation of the power-transportation system under stochastic scenarios based on traffic demand.

[0036] The objective function for the first stage is as follows: The planning decisions in the first stage indirectly determine the long-term operating cost of the system by influencing the system's operation in the second stage. Therefore, its objective function is characterized by the expected value of the operating cost in the second stage. In particular, this embodiment adopts a simplified scenario where the total investment in charging station construction is given and the investment cost of each charging station is the same. Therefore, the number of charging stations to be planned and constructed in the first stage is determined, and the total investment in construction is not considered in the objective function.

[0037] This stage focuses on the decision variables for charging station site selection. To optimize variables. Among them, For binary variables: This indicates that charging stations will be built in the area; when This indicates that no construction will be carried out; the objective function for the first stage is shown below, where the subscripts are... Representing random scenarios: (1) In the formula: A set of random scenes; Random variables that represent the uncertainty of a system, such as Indicates the first Random traffic flow demand in random scenarios; For the scene The probability of occurrence; The second-stage value function is the minimum system operating cost obtained by solving the power-transportation coupled collaborative optimization problem.

[0038] Formula (1) represents the objective of minimizing the total expected cost of the system obtained by weighted summation under all random scenarios.

[0039] The second-stage objective function provides an explicit expression of the first-stage value function under a given stochastic scenario. The second-stage problem aims to minimize the total system cost, including transportation network travel costs, distribution network operating costs, and system carbon emission costs. Considering the extended network structure built for GVs and EVs within the transportation network, roads in the transportation system can be categorized into three types: conventional roads, detour roads, and charging roads.

[0040] In summary, given the first-stage decision and specific random scene parameters Below, the objective function for each random scenario in the second stage. The definition is as follows: (2) In the formula: The cost of travel on the transportation network, consisting of the cost of travel on regular roads. and travel costs on charging roads composition; For distribution network operating costs; and These are the carbon emissions from transportation and power distribution networks, respectively. This refers to a carbon tax. In the following discussion, all parameters are based on the given first-stage decision. and specific random scene parameters The following are the premise definitions; for simplicity, explicit annotations are omitted. .

[0041] 1) Transportation network travel costs: (3) (4) In the formula, It is the unit time value coefficient; It is a collection of regular and detour routes; It is a charging road collection; This refers to the travel time on regular roads; It refers to the travel time on the charging route; It is with the busbar Charging fees at connected fast charging stations; This refers to the charging energy requirements of EVs; This indicates the traffic flow on the charging route.

[0042] and It is derived from the time function constraints and complementary conditions of the transportation network under the premise of user equilibrium, through Beckmann equivalent transformation, and is represented by an equivalent potential function that characterizes the travel time burden.

[0043] 2) Distribution network operating costs: (5) In the formula, This refers to the active power output of the generator. The main online purchase volume; and This is the power generation cost coefficient; This represents the electricity purchase cost coefficient.

[0044] The total operating cost of the distribution network includes two parts: the cost of distributed generation (DG) in the distribution network and the cost of purchasing electricity from the upstream power grid.

[0045] 3) Carbon emission costs: This embodiment uses a macroscopic carbon emission model, as shown in the following formula: (6) (7) (8) In the formula, This indicates the length of each regular road. Indicates the road travel time of a gasoline-powered vehicle. Indicates the flow rate of fuel-powered vehicles; Indicates the average speed of the road; This indicates the carbon emissions per kilometer per hour for a single gasoline-powered vehicle. As a carbon dioxide emission factor, the traditional distributed power source and the main power grid in this embodiment... same.

[0046] and These represent the carbon emissions from the transportation network and the power distribution network, respectively. The carbon emission function for the transportation network is... It exhibits high nonlinearity, which significantly increases the computational complexity of the model.

[0047] The model constructed in this embodiment considers three sets of constraints: traffic network, power distribution network, and charging network, as detailed below: Traffic network constraints: To uniformly model the travel behavior of GVs and EVs, travel roads are divided into three categories: regular roads, which are road segments used by all vehicles; and two types of virtual roads—charging roads and detour roads. Among them, charging roads are used to represent the queuing and charging process of electric vehicles at charging stations; detour roads are used by vehicles that choose not to charge.

[0048] Based on the above path classification method, the traffic network constraints considered in this embodiment are shown in equations (9)-(18). To facilitate the description of the following constraints, we first introduce the definition of a path that plays a core role in the user equilibrium problem: for a pair of origin-destination (OD) points... Between fuel-powered vehicles and electric vehicles, a feasible path is marked as It is a path consisting of continuous roads from the starting point r to the ending point d. In the given first-stage decision... and specific random scene parameters The constraints of the transportation network are as follows: 1) Traffic flow conservation constraint: (9) (10) (11) (12) In the formula: This indicates the traffic volume on regular roads; Indicates OD pair Between GV or EV in the path Traffic on the internet; These represent the traffic flow demand of any OD for GV and EV, respectively. Indicates whether GV or EV has traversed the path. A certain section of road If the path is passed, its value is 1; if it is not passed, its value is 0.

[0049] The above equation describes the flow conservation relationship in the traffic network. Specifically, constraints (9) to (10) define the mapping relationship between segment flow and path flow, and constraints (11) and (12) indicate that the traffic flow of any OD for all paths is equal to its traffic demand.

[0050] 2) Travel time constraints: (13) (14) In the formula: Indicates the free passage time on regular roads; Indicates road The maximum traffic flow limit; Indicates the free passage time of the charging road; This indicates the maximum vehicle capacity of the charging road. This indicates the charging power.

[0051] The above formula describes the travel time for different types of roads. Specifically: for regular roads, constraint (13) uses the classic BPR (Bureau of Public Roads) function to describe the nonlinear relationship between travel time and road traffic volume, which gradually increases with the increase of traffic volume; for charging roads, constraint (14) uses a travel time function based on queuing theory, whose delay term is determined by the charging demand of electric vehicles. With the power supply capacity of the charging station Decide.

[0052] 3) Travel cost constraints: (15) (16) In the formula, , These represent the paths of GV and EV bicycles, respectively. Travel costs.

[0053] 4) Complementary constraints: (17) (18) Formulas (17) and (18) represent the user equilibrium conditions for gasoline-powered vehicles and electric vehicles, respectively. Taking gasoline-powered vehicles as an example, when the flow rate of a certain path is greater than 0, that is... ,but The corresponding trip cost is equal to the minimum travel cost under that OD pair; if the flow is 0, that is... ,but The cost of this route is greater than the minimum travel cost. The same logic can be applied to electric vehicles.

[0054] The aforementioned complementary constraints characterize the user equilibrium state in the transportation network. This embodiment does not aim to characterize the socially optimal configuration of the transportation system, but rather to prioritize travelers' path selection based on their perceived travel costs. Through Beckmann's equivalent transformation, the user equilibrium problem is expressed as a potential function to characterize traffic flow allocation under given network structure and price conditions. It should be noted that the economic cost of carbon emissions is not included in the traveler's perceived path selection cost, but is included in the objective function without affecting the formation of traffic flow user equilibrium, and is coordinated with the power system operation decision for optimization. In summary, based on the transformation formula of the traffic equilibrium allocation model proposed by Beckmann, this embodiment transforms the formulas (17) and (18) of the nonlinear complementary constraint form of the hybrid user equilibrium criterion to obtain the equivalent model, as shown in formulas (3)-(4).

[0055] Distribution network constraints: Distribution networks typically operate with a radial structure. In this embodiment, its topology can be represented by a graph theory model. Precise description, in which For a set of nodes, This is a set of branches. To accurately describe the operating state of the distribution network, this embodiment uses the widely used Branch Flow Model (BFM) to represent the relationship between line power flow and node voltage in the network. In the given first-stage decision... and specific random scene parameters The mathematical model of the power distribution network is as follows. In this embodiment, the power flow direction of the branches is defined as pointing from the upstream node to the downstream node: (19) (20) (twenty one) (twenty two) In the formula, and ( and These are the active (reactive) power flows on the branch, respectively. ( )and ( These represent the active (reactive) output power and active (reactive) demand of the generators at the nodes, respectively. and These represent the line resistance and reactance, respectively. Line current; Represents a node The square of the voltage amplitude.

[0056] Equations (19) to (22) together constitute the power flow model of the power distribution network. Equations (19) and (20) describe the power balance relationship of the nodes, while equations (21) and (22) respectively give the constraint expressions between line voltage, current and power.

[0057] In addition, distribution network constraints also include line capacity constraints, voltage amplitude constraints, and generator output constraints, as detailed below: (twenty three) (twenty four) (25) In the formula: Indicates the upper limit of the line's apparent power; , These represent the upper and lower limits of the node voltage, respectively. , These represent the upper and lower limits of the generator's active power output, respectively. , These represent the upper and lower limits of the generator's reactive power output, respectively.

[0058] Formula (22) can be further transformed into the standard second-order cone programming form shown below: (26) Through this second-order cone transformation, the optimal power flow model can be transformed into a second-order cone programming problem.

[0059] Charging station constraints: Charging station constraints include power-traffic coupling constraints and charging station planning constraints. In the given first-stage decision... and specific random scene parameters The specific constraints are as follows: (27) (28) (29) (30) In the formula: A collection of candidate charging stations; These are binary variables for the first stage; It refers to the number of charging stations planned and constructed. For the first The active charging demand of electric vehicles gathered at each charging station; This is an inherent requirement of the node; It is a very large positive number.

[0060] Equation (27) describes the quantity constraint of planned construction of charging stations; Equation (29) describes the feasibility constraint that electric vehicles can only be charged at the planned charging station nodes; Equation (30) represents the total active power load demand of the system.

[0061] To handle the various nonlinear terms in the model, the carbon emission function and traffic time function will be linearized and reconstructed. Subsequently, an improved logistic Benders decomposition algorithm is proposed for the stochastic programming problem scenario and structure established in this embodiment.

[0062] Logarithmic Transformation and Reconstruction of Carbon Emission Function: Targeting Nonlinear terms are defined as auxiliary variables. The specific formula is as follows: (31) right Take the natural logarithm, and at the same time avoid exist The singularity problem approaching zero is addressed by introducing the minimum positive number. After making corrections, we obtain the following equation: (32) This logarithmic transformation converts the original expression into a summation of nonlinear terms in logarithmic function form. To further separate these nonlinear characteristics for subsequent linearization, a set of auxiliary variables is introduced, and equation (32) is equivalently expressed as the following set of constraint equations (33a)-(33d): (33a) (33b) (33c) (33d) Through the above transformation, a linear equality constraint can be introduced to associate each auxiliary variable in the form of equation (33e): (33e) Based on this, the nonlinear characteristics in equations (33a)-(33d) are processed by piecewise linearization, thereby transforming the overall model into a mixed integer linear programming problem.

[0063] Piecewise linearization of nonlinear terms in traffic network models: The time functions in the constraint set formulas (8)-(9) contain fractional and high-power terms, which can be processed by piecewise linearization, as follows: (34) This embodiment introduces SOS2, or Type 2 Special Ordered Set Constraint, into the model to achieve effective piecewise linearization of the nonlinear function. The nonlinear terms (33a)-(33e) in the transportation network carbon emission model can be handled using a similar method.

[0064] Based on the aforementioned model construction, this embodiment establishes a mixed-integer two-stage stochastic programming model that includes charging station site selection decision-making and multi-scenario optimization operation, and solves it using the logical Benders decomposition framework. Within this framework, the main problem determines the first-stage site selection scheme, and the sub-problems evaluate the operational status and cost of each stochastic scenario given the scheme. Furthermore, considering the structural characteristics of the power-transportation coupled optimization problem, the cutting plane generation mechanism in traditional LBBD is specifically improved.

[0065] Two-stage master-slave structure decomposition of the model: 1) Main Problem: The main problem, within the Benders decomposition framework, is responsible for strategic decision-making. Its model contains only the decision variables from the first stage and the cutting plane constraints generated by feedback from subproblems. The objective of the main problem is to minimize the lower bound of the total system cost and generate new candidate solutions for subproblem evaluation in each iteration. Its mathematical model is shown below.

[0066] Objective function: (35) Constraints: (36) (37) Equations (27)-(30) (38) In the formula, auxiliary variables It is the core decision variable in the Benders decomposition of the main problem, equivalent to the lower bound estimate of the system cost in the subproblems, corresponding to the expected cost term in formula (1). Indicates the first Cost estimate for the next iteration; For the first stage, there are two variables, representing the charging station. The construction status; and Each represents a set of historical iterations where all subproblems are either feasible or infeasible. It is in the Candidate solutions for the next iteration The expected cost of the second-stage system is obtained by solving all sub-problems in the scenario. Indicates the first In this iteration, the decision is the set of charging stations to be planned and constructed, i.e. Similarly This indicates a collection of charging stations that are not planned for construction.

[0067] Formula (36) is the Benders optimal cut, which means that if the main problem proposes a new solution in the current iteration... Compared with the previous plan If there is complete consistency in the planning decisions for charging stations, the corresponding summation term will be 0, that is: Thus, cost estimation variables This provides a valid lower bound; if the new scheme changes at any site's planning state, the summation term is not less than 1, and in the case of a larger... Under the influence of the coefficient, this constraint no longer effectively restricts the auxiliary variables in the current iteration. Formula (37) is the Benders feasible cut, which serves to address the candidate solutions proposed in the main problem. If a new solution makes a subproblem infeasible, the solution is excluded. This constraint means that when a new solution is proposed... With failed solutions When they are completely identical, the summation term is 0, the constraint is violated, and the decision is excluded. Conversely, as long as there is a difference in the planning state of the two at at least one site, the summation term is not less than 1, the constraint is satisfied, and the algorithm can explore a new decision space. Since equations (36) and (37) do not introduce additional structural information and are constructed only based on the first-stage decision of the current iteration, this embodiment refers to them as the basic cut.

[0068] 2) Subproblems In the Benders decomposition framework, subproblems are used to solve for the optimal operating cost of the power-transportation coupled network under a given charging station location scheme, and the optimal cut or feasible cut is generated and fed back to the main problem.

[0069] The objective function and constraints of the sub-problems are based on the cooperative operation optimization model established above, and the charging station construction state constraints determined by the main problem are introduced. Their mathematical form is as follows: (39) The constraints include traffic network constraints, power distribution network constraints and charging network constraints, which correspond to equations (6), (9)-(16), (8), (19)-(26) and (27)-(30), respectively.

[0070] Algorithm Flow and Convergence Criterion: The logical Benders decomposition used in this embodiment is an iterative algorithm that gradually tightens the upper and lower bounds of the objective function of the original problem by alternately solving the main problem and subproblems until the convergence criterion is met. The specific implementation flow of the proposed algorithm can be found in [link to implementation details]. Figure 2 In each iteration of this algorithm, the main problem only reflects the expected cost of the second stage, and its optimal objective value is... This forms a lower bound for the true optimum. As iterations progress, the newly added Benders cut continuously tightens the feasible region of the main problem, used to update the global lower bound: (40) The upper bound is provided by the subproblems. When the main problem provides candidate solutions... When feasible in all stochastic scenarios, what is the corresponding expected total cost? This constitutes an upper bound for the optimal value of the original problem. The algorithm uses the minimum expected cost among all feasible solutions as the upper bound and continuously updates it during the iteration process: (41) Therefore, the upper bound is a monotonically non-increasing sequence, and the initial value can be set to positive infinity. The convergence criterion of the algorithm is that the relative difference between the upper and lower bounds is less than the preset convergence accuracy. The algorithm terminates when the specified conditions are met. Specifically, the conditions for algorithm termination are: (42) in It is a very small positive number, used to prevent the denominator from being zero. In this case, make... The candidate solution that reaches the minimum value is the approximate optimal solution to the problem.

[0071] Heuristic Augmentation Strategy for Benders Cut: To improve the convergence efficiency of the logistic Benders decomposition algorithm, this embodiment proposes a heuristic augmentation strategy, aiming to improve the basic cut into a more restrictive augmentation cut. The specific improvements are as follows: 1) Optimal cut enhancement The basic optimal cut only takes effect when the planning states of charging stations are completely identical in adjacent iterations, resulting in a low trigger probability. Considering that the system's operational characteristics are primarily driven by a few key charging stations, even if the planning states of non-key stations change, the system's operational characteristics may still remain similar. Therefore, the triggering conditions of the cut constraint are bound to key charging stations, and heuristic enhancement rules are designed to dynamically identify the set of key charging stations based on the sub-problem results, thereby strengthening the constraint of the optimal cut and improving the algorithm's search efficiency. This method is explained in detail below.

[0072] First, based on the results of the sub-problems in all scenarios, calculate the cost of each planned charging station. Expected traffic : (43) Then, all charging stations are sorted in descending order of their expected traffic. Key charging station set. These charging stations, ranked at the top, were selected based on the criterion that the sum of their cumulative expected traffic volumes reaches a predetermined proportion of the total expected traffic volume. In this way, the basic optimal cut is improved into the following enhanced optimal cut: (44) because It is a collection of planned and constructed charging stations. A subset of the algorithm makes it easier to satisfy the triggering conditions for enhanced cuts, thereby generating effective constraints earlier and accelerating the convergence process of the algorithm.

[0073] 2) Feasible cut reinforcement The basic feasible cut in the main problem can only eliminate specific combinations of charging stations that are infeasible, but it fails to reveal the root cause. For example, in a certain iteration, the main problem gives the set of unbuilt charging stations as follows: This decision renders the subproblem infeasible. However, further analysis shows that the infeasibility is not caused by the entire set, but rather stems from a key subset, such as... It has not been planned or constructed. To enhance the effectiveness of feasible cuts, a heuristic enhancement strategy is proposed. Its core idea is: in the decision schemes given by the main problem... When the quilt problem is deemed infeasible, the algorithm will test the set of charging stations that are not planned for construction. For each charging station in the problem, determine whether it alone makes the subproblem infeasible, and generate corresponding enhanced feasible cut constraints accordingly.

[0074] (45) This cut constraint forces the corresponding charging station to be included in the construction plan in subsequent iterations. If no single site causes infeasibility, it indicates that the infeasibility is caused by a combination of multiple sites. In this case, the basic feasible cut based on the complete combination is used to proceed to the next iteration.

[0075] Example Analysis: The topologies of the power distribution and transportation networks are as follows: Figure 3 and Figure 4 As shown, Figure 4 Road categories I to IV represent different road capacity limits. Detailed data can be found in Tables A1, A2, B1, and B2, where C1-C8 are eight planned charging stations, and the bypass roads have the same capacity as their adjacent roads.

[0076] Table A1 Parameter Settings for Transportation Network Segments Table A2 User travel demand parameters Table B1 Node Load and Voltage Amplitude Table B2 Distribution Network Branch Impedance The baseline values ​​for traffic flow and electricity demand are 100 veh / h and 100 MVA, respectively; voltage upper and lower limits are 1.05 pu and 0.95 pu, respectively; line capacity is 1 p.u.; and the distributed generation factor is... and The carbon emission factor is 600g / kW, and the carbon tax coefficient is $18 / t. Other parameters: , , .

[0077] The simulation experiments in this embodiment were all completed in the MATLAB R2022a environment, with a hardware configuration of R9-8945HX CPU and 64 GB of memory. The optimization problems involved were solved by calling the Gurobi solver.

[0078] Optimality Verification of the Improved Logical Benders Decomposition Algorithm: Verify whether the proposed improved logical Benders decomposition algorithm can still maintain the optimality of the original algorithm after introducing the enhancement cut strategy. Under the same test case conditions, compare the optimal objective function value and charging station planning decision results obtained by the improved algorithm and the basic logical Benders decomposition algorithm to verify whether the improved algorithm affects the optimal solution while improving the solution efficiency. The convergence criterion of the algorithm is judged according to formula (41). The test cases are selected with 5 and 6 charging stations to be built and 100 random scenarios. The traffic demand under each random scenario is generated based on the normal distribution with the mean of the baseline OD to the traffic flow to characterize the uncertainty of travel demand. The planning results and cost indicators are summarized in Table 1 (in the table: M0 represents the basic algorithm and M1 represents the improved algorithm).

[0079] Table 1 Simulation results for optimality verification Table 1 presents the optimal planning results and cost indicators obtained by the improved algorithm and the basic algorithm under different charging station construction requirements. It can be seen that when planning to build 5 charging stations, both algorithms select nodes C1-C5 for construction; when the planned construction scale expands to 6 stations, the optimal site selection scheme is consistently adjusted to C1, C2, C3, C4, C5, and C8. Under the above two planning and construction requirements, the improved algorithm and the basic algorithm show only minor numerical differences in indicators such as expected total cost, transportation network travel cost, distribution network operating cost, and carbon emission cost of the transportation network and distribution network, and these differences do not affect the selection of the optimal planning scheme. The above results verify the advantages of the proposed improved algorithm in ensuring the optimality of the decision results.

[0080] Furthermore, to verify the impact of the number of random scenes on the performance of the proposed improved algorithm, comparative calculations were performed with 50, 150, and 200 scenes respectively. The results are as follows: Figure 5 As shown in the figure (M0 represents the basic algorithm, and M1 represents the improved algorithm).

[0081] Depend on Figure 5 It can be seen that as the number of scenarios increases, the expected total cost and the cost of each component change slightly. When the number of scenarios increases from 50 to 200, the expected total cost obtained by the improved algorithm changes by 0.10%, while the expected total cost obtained by the basic algorithm changes by 0.48%. Under the same demand distribution, increasing the number of scenarios reduces the random fluctuation of the sample average estimate of the expected target, making the scenario set more fully characterize the traffic demand distribution, thus making the objective function value closer to its true value. Under different scenario scales, the charging station site selection schemes obtained by the improved algorithm and the basic logical Benders decomposition algorithm are consistent, and the differences in various operating results are minimal. The above analysis shows that the proposed improved algorithm has good stability under changes in scenario scale and can obtain reliable solution results under various scenario conditions.

[0082] Convergence verification of the improved logistic Benders decomposition algorithm: The advantages of the proposed improved logistic Benders decomposition algorithm in terms of computational convergence were verified from the aspects of the number of iterations and computation time. The details are as follows.

[0083] Figure 6The iterative convergence of the two algorithms is presented for different charging station construction scales with 100 random scenarios. It can be seen that when planning to build 5 charging stations, the improved algorithm only requires 9 iterations to converge, while the basic algorithm requires 57 iterations. When the number of charging stations increases to 6, the improved algorithm only requires 11 iterations to converge, while the basic algorithm requires 29 iterations. These results show that at this scenario scale, the improved algorithm can always converge within a smaller number of iterations, and its convergence speed is significantly better than the basic logic Benders algorithm. Furthermore, when the number of random scenarios is 50, 150, and 200, the number of iterations for both algorithms remains consistent with the case of 100 scenarios, indicating that the convergence speed of the improved algorithm does not change with the scale of the random scenarios and consistently exhibits better convergence performance.

[0084] Figure 7 The solution times of the improved algorithm and the basic algorithm were compared under the condition of needing to build 6 charging stations, for different scales of random scenarios. As shown in the figure, the solution time of both algorithms exhibits a monotonically increasing trend with the increase of the number of random scenarios. This is because the logistic Benders decomposition requires solving the corresponding subproblems for each random scenario in each iteration, and generating cut planes to feed back to the main problem. When the number of scenarios increases, the scale of the subproblems to be processed in each iteration also increases, leading to a significant increase in the total computational cost of solving subproblems and generating cut planes, thus increasing the overall solution time. The figure also shows that compared to the basic algorithm, the improved algorithm significantly shortens the computation time for all scenario scales: when the number of scenarios is 50, the solution time of the improved algorithm is 538s, while the basic algorithm reaches 1367s; when the number of scenarios increases to 250, the solution time of the improved algorithm is 2511s, only 40% of that of the basic algorithm. This is because the improved algorithm accelerates the information feedback process between the main problem and subproblems by reducing the number of invalid or weak cuts generated, thereby improving the overall convergence efficiency. The advantage of the improved algorithm in terms of computation time is even more pronounced when the scale of the random scenario is large, demonstrating better solution efficiency and scale adaptability.

[0085] The analysis of the operational decision-making results of the power-transportation coupled network includes the analysis of the operational results of the power-transportation coupled network under the baseline scenario, the sensitivity analysis of the carbon tax coefficient, and the necessity analysis of stochastic modeling.

[0086] Analysis of the Power-Traffic Coupling Operation Results in the Baseline Scenario: Under the charging station planning scheme obtained in the first stage, the operation status of the traffic system and the power distribution system in the second stage is closely coupled through the charging behavior of electric vehicles. Therefore, the operation decision results of the coupled system are presented from three levels: traffic flow allocation, vehicle travel costs, and the operation status of the power distribution network. The baseline scenario adopted considers the planned construction of 6 charging stations as the demand, with 100 random scenarios. Traffic flow is generated based on the baseline OD pair using a normal distribution.

[0087] Figure 8 The paper presents the path selection results of different origin-destination (OD) points in the transportation network under the user equilibrium criterion. Notably, charging stations C6 and C7, which were not planned or constructed, experienced no traffic flow.

[0088] Based on the above equilibrium results Figure 9 The travel costs for gasoline-powered vehicles and electric vehicles under 11 origin-destination (OD) pairs are presented separately. The results show that the overall travel cost of electric vehicles is higher than that of gasoline-powered vehicles (the travel cost of gasoline-powered vehicles ranges from $2.11 to $3.84, while the travel cost of electric vehicles ranges from $5.80 to $8.05). The difference mainly comes from the additional costs introduced by charging time and charging fees, which reflects the impact of charging behavior on the economics of electric vehicle travel.

[0089] In terms of power distribution networks, electric vehicle charging behavior manifests as a typical power load, which will significantly affect the network's operating status. Figure 10 The distribution network node voltage distribution and line power flow considering the combined effects of charging load and grid conventional load are presented. It can be seen that the voltage of each node in the system remains within the range of 0.97-1.04 pu. Among them, node 12 has the lowest voltage, mainly because this node handles the charging load from charging station 2, resulting in a higher load level at this node. Node 18, located at the end of the line, has a relatively high voltage level due to the reverse power injection from distributed generation. Meanwhile, some lines exhibit localized reverse transmission phenomena.

[0090] Sensitivity analysis of carbon tax coefficient: Based on the baseline operation results analysis, further sensitivity analysis of the impact of carbon tax coefficient on the operation decision of the power-transportation coupled system is carried out. Figure 11The study presents the changing trends of carbon emissions from transportation and distribution networks under different carbon tax coefficient levels, thus quantifying the impact of carbon emission pricing on the emission reduction effect of the power-transportation coupled system. As shown in the figure, with the gradual increase of the carbon tax coefficient, the emission reduction effect of both the transportation and distribution networks exhibits a monotonically increasing trend. The emission reduction benefit of the transportation network is more significant, increasing from 5.27 tons at a carbon tax of $10 / ton to 7.47 tons at $90 / ton, representing a 41.75% increase in emission reduction benefit. In contrast, the emission reduction of the distribution network is limited, remaining within the range of 1.31-1.72 tons. Furthermore, it is evident that as the carbon tax level continues to increase, the marginal increase in the system's emission reduction effect shows a gradually decreasing trend. When the carbon tax exceeds $60 / ton, the emission reduction growth rate of both the transportation and distribution networks slows significantly, indicating that the system's potential for emission reduction is gradually approaching saturation, and simply relying on further increases in the carbon tax coefficient is no longer sufficient to sustainably obtain higher emission reduction benefits.

[0091] Meanwhile, increasing the carbon tax coefficient will drive up the cost of carbon emissions, thus increasing the financial burden on users. Therefore, in the power-transportation coupled system, the setting of the carbon tax coefficient should strike a reasonable balance between emission reduction effects and socio-economic burden.

[0092] Necessity Analysis of Stochastic Modeling: To verify the necessity of considering traffic flow uncertainty in the modeling process, the differences in system operating costs between the stochastic and deterministic models are compared. In the stochastic model, OD travel demand under different scenarios is randomly generated according to a given distribution and varies. In the deterministic model, the expected traffic demand of each scenario is used as input for solution. The above comparison aims to illustrate that considering the inherent randomness of traffic demand in system optimization operation decisions can improve the model's accuracy in depicting the real operating environment, thereby obtaining more reasonable decisions and reducing system operating costs. To highlight the impact of traffic demand fluctuations on operational decision costs, the stochastic scenarios constructed in this embodiment include general demand scenarios and high-load extreme demand scenarios. By increasing the number of extreme demand scenarios in the scenario set, the system operation results under the two modeling methods are compared and analyzed. The traffic demand in each extreme scenario is twice the traffic flow of the baseline scenario. The total number of scenarios in the scenario set constructed in the example is 50, and the traffic flow is generated by a normal distribution.

[0093] Figure 12The changes in system operating costs for two modeling methods are presented under different numbers of extreme scenarios in the scenario set. It can be seen that as the number of extreme scenarios in the scenario set increases, the system operating cost shows a continuous upward trend in both scenarios, indicating that high traffic demand significantly increases traffic network congestion and the pressure on power distribution network operation. However, under all extreme scenario numbers, the model considering the stochasticity of traffic flow achieves lower expected operating costs. Specifically, when the number of extreme scenarios is 5, the system operating cost obtained by the stochastic model is $714.4, while the cost of the deterministic model is $777.3, with the stochastic model costing approximately 8.1% less. When the number of extreme scenarios increases to 15, the operating costs corresponding to the two models are $1378.1 and $1595.1, respectively, with the stochastic model reducing costs by approximately 13.6% compared to the deterministic model. This difference continues to widen as the proportion of extreme scenarios further increases. When the number of extreme scenarios is 25, the operating costs of the stochastic model and the deterministic model are $2080 and $2508.1, respectively, with a cost reduction of approximately 17.1%. When the number of extreme scenarios is 30, the costs are $2425.5 and $2643, respectively, with the stochastic model still achieving a cost reduction of approximately 8.2%. This indicates that under conditions of high load and demand fluctuations, the stochastic programming model that introduces traffic flow uncertainty has better expected operating economy.

[0094] In summary, this embodiment addresses the planning and coordinated operation problem of a power-transportation coupled system under a low-carbon background. It constructs a two-stage stochastic programming model considering traffic flow uncertainty and multi-source carbon emissions, and proposes an improved logical Benders decomposition algorithm for solving the problem. The effectiveness of the proposed model and algorithm is verified through multi-scenario case studies. The main conclusions are as follows: 1) The established model can effectively characterize the operating characteristics of the power-transportation coupled system. Taking electric vehicle charging behavior as the coupling link, it can be concluded that charging demand will lead to higher travel time costs for electric vehicles and power flow aggregation in the distribution network; the carbon tax coefficient has a greater impact on the emission reduction benefits of the transportation network than on the emission reduction benefits of the distribution system; and stochastic modeling that considers the uncertainty of traffic flow can obtain better decisions with lower costs.

[0095] 2) Regarding algorithm performance, the proposed improved logical Benders decomposition algorithm effectively enhances the solution efficiency by strengthening the cutting plane generation mechanism. While ensuring optimal convergence, the improved algorithm significantly reduces the number of iterations and the solution time, accelerating the convergence speed of the main problem.

[0096] Building on this foundation, future research could further incorporate source-side uncertainties such as fluctuations in renewable energy output to construct a collaborative stochastic programming model that considers both source-load stochasticity. Simultaneously, the impact of emission reduction guidance mechanisms such as dynamic carbon pricing on system operation could be explored to further tap the low-carbon potential of the power-transportation coupled system.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition, characterized in that, Includes the following steps: S1: Obtain a set of stochastic traffic flow scenarios for the power-transportation coupled network to describe the uncertainty of traffic demand; S2: Construct a two-stage stochastic programming model that takes into account multi-source carbon emissions; in the first stage, the location of charging station construction is used as the decision variable, and the objective is to minimize the expected total cost; in the second stage, under the given location decision, the power-transportation cooperative operation optimization is carried out for each stochastic scenario, and the objective is to minimize the total system operating cost. S3: Linearize and reconstruct the two-stage stochastic programming model, use the minimum positive correction term and logarithmic transformation to process the nonlinear term of carbon emissions, and use piecewise linearization and second-order cone transformation techniques to transform the original model into a mixed integer linear programming model. S4: Decompose the linearized and reconstructed model into a main problem and sub-problems, solve the main problem to generate candidate schemes for charging station site selection, and determine the global lower bound of the total system cost; S5: Solve subproblems under given candidate schemes to evaluate the optimal operating cost of each stochastic scenario, update the global upper bound of the total system cost, and perform alternating iterations of cutting plane feedback to the main problem based on heuristic enhancement strategy until the relative difference between the upper and lower bounds meets the preset convergence accuracy, and output the optimal addressing decision and cooperative operation scheme.

2. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the expected total cost includes carbon emission costs, which satisfy the following: in, This indicates the length of each regular road. Indicates the road travel time of a gasoline-powered vehicle. Indicates the flow rate of fuel-powered vehicles; Indicates the average speed of the road; This indicates the carbon emissions per kilometer per hour for a single gasoline-powered vehicle. It is a carbon dioxide emission factor; and These represent carbon emissions from the transportation network and the power distribution network, respectively.

3. The two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the expected total cost includes the transportation network travel cost, which satisfies the following: in, It is the unit time value coefficient; It is a collection of regular and detour routes; It is a charging road collection; This refers to the travel time on regular roads; It refers to the travel time on the charging route; It is with the busbar Charging fees at connected fast charging stations; This refers to the charging energy requirements of EVs; This indicates the traffic flow on the charging route.

4. The two-stage stochastic programming method for power-transportation coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the expected total cost includes the distribution network operating cost, which satisfies the following: in, This refers to the active power output of the generator. The main online purchase volume; and This is the power generation cost coefficient; This represents the electricity purchase cost coefficient.

5. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the cooperative operation optimization is subject to traffic network constraints, including travel time constraints, wherein: The travel time on conventional roads is described using the BPR function, whose mathematical expression satisfies: The travel time on charging routes is described by a travel time function based on queuing theory, and its mathematical expression satisfies: In the formula, Indicates the free passage time on regular roads; Indicates road The maximum traffic flow limit; Indicates the free passage time on the charging road; This indicates the maximum vehicle capacity of the charging road. Indicates charging power. The need to charge electric vehicles.

6. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the cooperative operation optimization is subject to distribution network constraints, which include line capacity constraints, voltage amplitude constraints, and generator output constraints, respectively satisfying: In the formula: Indicates the upper limit of the line's apparent power; , These represent the upper and lower limits of the node voltage, respectively. , These represent the upper and lower limits of the generator's active power output, respectively. , These represent the upper and lower limits of the generator's reactive power output, respectively.

7. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, In step S2, the collaborative operation optimization is subject to charging station constraints, which include: Constraints on the number of charging stations planned and constructed: , ; Feasibility constraints restrict electric vehicles to charging only at planned and constructed charging station nodes, satisfying the following: Total active power load requirement of the system: ; In the formula: A collection of candidate charging stations; These are binary variables for the first stage; It refers to the number of charging stations planned and constructed. For the first The active charging demand of electric vehicles gathered at each charging station; This is an inherent requirement of the node; It is a very large positive number.

8. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, The linearization reconstruction in step S3 includes: To address the nonlinear terms in the carbon emission function, a minimum positive number is introduced as a correction term to avoid the singularity of the zero point of the logarithmic function and to perform a logarithmic transformation. At the same time, an auxiliary variable is introduced to convert the transformed nonlinear terms into a set of linear equality constraints. The nonlinear terms in the conventional road travel time function and carbon emission model are piecewise linearized by using type 2 special ordered set SOS2 constraints. The power flow constraints in the branch power flow model of the distribution network are transformed into a standard second-order cone programming form using the second-order cone transformation technique.

9. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, The cutting plane enhancement strategy in step S5 includes constructing an enhanced optimal cut, specifically including: Based on the results of the sub-problems in all scenarios, the calculation is performed for each planned charging station. Expected traffic : All charging stations are sorted in descending order of their expected traffic volume, and the top-ranked charging stations are identified as the critical charging station set. Key charging station cluster The sum of the cumulative expected traffic reaches a preset proportion of the total expected traffic. ; The enhanced optimal cut satisfies: 。 10. The two-stage stochastic programming method for power-transport coupled networks based on improved logical Benders decomposition as described in claim 1, characterized in that, The cutting plane enhancement strategy in step S5 includes generating enhanced feasible cuts, specifically including: The decision-making scheme given by the main problem If the blanket problem is deemed infeasible, then a collection of charging stations that are not planned for construction will be tested. For each charging station in the problem, determine whether it alone makes the subproblem infeasible, and generate corresponding enhanced feasibility cut constraints accordingly: Enhanced feasible cut constraints force the corresponding charging station to be included in the construction plan in subsequent iterations; if no single site is found to be infeasible, then a basic feasible cut based on complete combinations is adopted to enter the next iteration.

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