A scheduling method and system based on high-dimensional Bessel body segmentation

Abstract

The application discloses a kind of based on high-dimensional Bessel body segmentation scheduling method and system.Method comprising: real-time acquisition of power generator and distribution operator's offer data, unit parameter and network constraint information;The above data is input into the preset electric carbon coupling transaction model, reconstruct the double-layer non-convex game problem in model using high-dimensional Bessel body segmentation technology, and constraint reduction is carried out based on external contraction approximation algorithm, to obtain the simplified optimization model, solve optimization model by combining iterative optimization method, output power generator and distribution operator's optimal generator output and carbon quota transaction volume, and dispatch power generator and distribution operator.The application provides a kind of based on high-dimensional Bessel body segmentation scheduling method and system, to solve the technical problems that the quality of solution is unstable, it is difficult to meet market real-time clearing and fast scheduling decision demand when solving the game problem of electric carbon coupling transaction in existing method.

Description

Technical Field

[0001] This invention relates to the field of optimization methods for electricity-carbon coupling trading strategies, and in particular to a scheduling method and system based on high-dimensional Bessel volume segmentation. Background Technology

[0002] With increasing emphasis on the coordinated operation of carbon and electricity markets, the multi-entity carbon-electricity coupling trading problem in transmission and distribution networks has gradually become a research hotspot. To fully reflect the distribution, independence, and autonomy of each market participant, this type of problem is usually described using the Nash-Stackelberg game model, which mathematically belongs to a class of bi-level, non-convex, strongly NP-hard problems.

[0003] Currently, solutions to this type of two-level game problem mainly fall into three categories: classical mathematical algorithms, heuristic algorithms, and reinforcement learning algorithms. In mathematical algorithms, the two-level game model is typically transformed into a mixed-integer programming problem for solution. However, the introduction of a large number of discrete variables significantly increases the computational burden, making it unsuitable for large-scale real-time decision-making scenarios. Heuristic algorithms, such as genetic algorithms and ant colony algorithms, rely on empirical rules for search. While they possess some generality, they suffer from poor robustness, unstable solution quality, and difficulty in guaranteeing convergence to the global optimum. Reinforcement learning algorithms, although possessing strong environmental adaptability, lack interpretability in their decision-making process and struggle to guarantee the strict feasibility of the obtained solution, limiting their application in high-reliability scenarios such as electricity-carbon coupling trading. Therefore, existing technologies for solving the Nash-Stackelberg game problem in electricity-carbon coupling trading in power transmission and distribution networks generally suffer from low computational efficiency, unstable solution quality, and difficulty in balancing optimality and feasibility. This results in the inability to generate scheduling strategies that meet the real-time clearing requirements of the electricity-carbon market within a reasonable timeframe, failing to support the rapid and accurate scheduling decision-making needs of market participants. Summary of the Invention

[0004] This invention provides a scheduling method for electric carbon based on high-dimensional Bessel body partitioning, which solves the technical problems of low computational efficiency, unstable solution quality, and difficulty in meeting the requirements of real-time market clearing and rapid scheduling decision-making in existing methods for solving game problems of electric carbon coupled trading.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a scheduling method based on high-dimensional Bessel volume segmentation, comprising: Real-time acquisition of bidding data, unit parameters, and network constraint information from power generators and distribution operators in the power transmission and distribution network; The bidding data, unit parameters, and network constraint information are input into a preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-layer non-convex game problem in the electricity-carbon coupling trading model, resulting in a single-layer optimization problem. The constraint reduction processing of the single-layer optimization problem is performed based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume of generators and distribution operators are output. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory. Dispatch of power generators and distribution operators is based on optimal generator output and carbon quota trading volume.

[0006] This invention, through the construction of a Nash-Stackelberg game-based electricity-carbon coupling trading model, clearly illustrates the bidding behavior and market clearing mechanism of multiple stakeholders in the power transmission and distribution network. By introducing a high-dimensional Bessel volume partitioning technique, the complex two-layer non-convex game problem is reconstructed into an easily solvable single-layer optimization problem, effectively overcoming the technical bottleneck of traditional methods in handling such strongly NP-hard problems. An external shrinkage approximation algorithm is used to reduce constraints on the reconstructed single-layer optimization problem, significantly reducing the problem size and improving solution efficiency. An iterative optimization method is employed, aiming to maximize the profits of each market participant, ensuring the economic viability and feasibility of the obtained solution. Ultimately, the optimal generator output and carbon quota trading volume are output, providing reliable technical support for meeting the needs of real-time market clearing and rapid dispatch decision-making.

[0007] Furthermore, the construction process of the electricity-carbon coupling trading model based on Nash-Stackelberg game theory includes: Obtain historical bidding data, historical unit parameters, and historical network constraint information of power generators and distribution operators in the transmission and distribution network. The historical bidding data includes the upper and lower limits of electricity market bidding, carbon market bidding, the upper and lower limits of cleared electricity volume of power generator units, and the upper and lower limits of carbon quota winning bids. The historical unit parameters include unit power generation cost, unit output upper and lower limits, and carbon quota data. Based on the bidding data, unit parameters, and network constraint information of power generators and distribution operators in the transmission and distribution network, a first upper-level model with the goal of maximizing the profits of distribution network operators, a second upper-level model with the goal of maximizing the profits of power generators, a first lower-level model with the goal of maximizing the social welfare of the electricity market, and a second lower-level model with the goal of maximizing the social welfare of the carbon market are established. The constraints of the first and second upper-level models include bidding constraints, carbon quota constraints, generator unit constraints, and network operation constraints. The constraints of the first and second lower-level models include market clearing constraints and network security constraints. Based on the first upper-level model, the second upper-level model, the first lower-level model, and the second lower-level model, an electricity-carbon coupling trading model is constructed.

[0008] This approach, employing a Nash-Stackelberg game theory framework comprising two upper-level and two lower-level models, comprehensively describes the multi-agent decision-making process of electricity-carbon coupled trading in power transmission and distribution networks. The upper-level models aim to maximize the profits of distribution network operators and power generators, reflecting the economic rationality of market participants. The lower-level models aim to maximize the social welfare of the electricity and carbon markets, reflecting the efficiency requirements of market clearing. The practicality of the model and the feasibility of the solution are ensured through the inclusion of multiple constraints, including bidding constraints, carbon quota constraints, generator unit constraints, network operation constraints, market clearing constraints, and network security constraints.

[0009] Furthermore, the bidding data, unit parameters, and network constraint information are input into a pre-defined electricity-carbon coupling trading model. This allows the model to reconstruct the bi-layer non-convex game problem using high-dimensional Bessel volume segmentation technology, resulting in a single-layer optimization problem, including: Based on the input of quotation data, unit parameters and network constraint information into the preset electricity-carbon coupling trading model, the mathematical definition of the lower-level optimization problem is obtained from the electricity-carbon coupling trading model, including the objective function and constraints of the lower-level optimization problem; Based on the mathematical definition of the lower-level optimization problem, control points are selected in the decision space composed of upper-level decision variables, and the lower-level optimization problem is solved at each control point to obtain the corresponding dataset of upper-level decisions and lower-level optimal responses. Based on the corresponding dataset of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points, and an approximate explicit optimal response function is derived. For the explicit optimal response function, the maximum absolute error optimization problem is solved to obtain the maximum absolute error; If the maximum absolute error exceeds the set allowable error, then recursively segment and locally reconstruct the high-dimensional Bessel volume to obtain multiple approximate optimal response functions; Based on the multi-piece approximate optimal response function, the result of the multi-piece approximate optimal response function is used as the result of the lower-level optimization problem in the two-layer nonconvex game problem, so as to reconstruct the two-layer nonconvex game problem into a single-layer optimization problem.

[0010] By selecting control points in the decision space of the lower-level optimization problem and solving the lower-level optimization problem at each control point, a mapping dataset between upper-level decisions and lower-level optimal responses is established. A high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points. An approximate explicit optimal response function is derived through interpolation matrices, achieving explicit approximation of the implicit optimal response function. Solving and evaluating the maximum absolute error optimization problem ensures that the accuracy of the approximate optimal response function meets the requirements. Through recursive partitioning and local reconstruction of the high-dimensional Bessel volume, a piecewise accurate approximation of the complex response function is achieved, ultimately reconstructing the complex bi-level non-convex game problem into an easily solvable single-level optimization problem.

[0011] Furthermore, the basis solves the lower-level optimization problem at each control point to obtain the corresponding dataset of upper-level decisions and lower-level optimal responses, including: The upper-level decision vector represented by each control point is used as a given parameter, and the lower-level optimization problem is solved by substituting it into the solution. Based on the solution obtained from the lower-level optimization problem, record the upper-level decision vector and the obtained lower-level optimal response vector corresponding to each control point; Iterate through all control points, integrate the upper-level decision vectors corresponding to all control points with the obtained lower-level optimal response vectors, and obtain the corresponding datasets of upper-level decisions and lower-level optimal responses.

[0012] By obtaining the complete mathematical definition of the lower-level optimization problem, an accurate mathematical foundation is provided for subsequent control point selection and problem solving. Selecting multiple control points in the decision space ensures the representativeness and reasonable distribution of the sampling points. By substituting the upper-level decision vectors corresponding to the control points as parameters into the lower-level optimization problem, a precise decision-response mapping relationship is established. Recording and integrating the corresponding data of all control points forms a complete training dataset, providing ample data support for the subsequent construction of high-dimensional Bezier volumes.

[0013] Furthermore, based on the corresponding datasets of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points to derive an approximate explicit optimal response function, including: Based on the corresponding dataset of upper-level decisions and lower-level optimal responses, the Bernstein polynomial basis functions are determined. Based on the defined Bernstein polynomial basis functions and control points, a high-dimensional Bessel volume is constructed. Calculate the interpolation matrix corresponding to the high-dimensional Bessel volume, and based on the interpolation matrix and the lower-level optimal response vector in the corresponding dataset of upper-level decisions and lower-level optimal responses, derive an explicitly expressed approximate optimal response function through linear computation.

[0014] This provides the necessary data foundation for constructing high-dimensional Bessel volumes by obtaining a complete decision-response mapping dataset. Defining Bernstein polynomial basis functions for the simplex provides mathematical tools for function approximation in high-dimensional spaces. Constructing high-dimensional Bessel volumes using basis functions and control points enables geometric modeling of complex response surfaces. By calculating the interpolation matrix and combining it with the lower-level optimal response vector for linear computation, an explicitly expressed approximate optimal response function is derived, facilitating subsequent optimization solutions.

[0015] Furthermore, the single-layer optimization problem is constrained by an external shrinkage approximation algorithm, resulting in a simplified optimization model, including: Based on the current approximate feasible region, iteratively solve the mixed integer linear programming problem until the optimal objective function value output by the current iteration satisfies the preset conditions, and output the approximate feasible region corresponding to the current iteration. The approximate feasible region at the first iteration is determined based on the single-layer optimization problem. In each iteration, the approximate feasible region of the previous iteration is cut according to the hyperplane to obtain the approximate feasible region of the current iteration. The hyperplane is generated based on the mixed integer linear programming problem. Based on the approximate feasible region of the output, the simplified optimization model is obtained.

[0016] This approach quickly identifies infeasible regions within the feasible region by setting an initial approximate feasible region and solving the mixed-integer linear programming problem. By generating a hyperplane and cutting the current approximate feasible region, infeasible regions are gradually eliminated, achieving an accurate approximation of the feasible region. Iteratively solving the mixed-integer linear programming problem and updating the approximate feasible region ensures that the final approximate feasible region accurately describes the feasible region of the original problem, while significantly reducing the number of constraints, thus accelerating the solution of the optimization problem.

[0017] Furthermore, combining iterative optimization methods, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated price deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume are then output, including: Based on the optimization model and the bidding data of generators and distribution operators in the power transmission and distribution network, the simplified form of the single-layer optimization problem is solved iteratively until the optimal bid set output by the current iteration meets the preset conditions. The optimal bid set corresponding to the current iteration is then output. The optimal bid set in the first iteration is determined based on the initial bid data. The preset condition is whether the deviation norm between the current optimal bid and the previous optimal bid is less than the convergence threshold. In each iteration, the optimal bid set from the previous iteration is updated based on the bidding decisions of other entities to obtain the optimal bid set for the current iteration. The update is performed based on a simplified form of a single-level optimization problem. Based on the set of optimal bids output, the optimal generator output and carbon quota trading volume are obtained.

[0018] This approach, by solving a simplified form of a single-level optimization problem for each agent, achieves the solution of a multi-agent game problem. Real-time updates of all agents' bidding decisions ensure the dynamism and real-time nature of the game process. Checking whether the bid deviation norm is less than the convergence threshold determines whether the algorithm has reached convergence, guaranteeing the stability and reliability of the solution results. Finally, based on the optimal bids, electricity market clearing data, and carbon market clearing data, the optimal generator output and carbon quota trading volume are output, providing direct evidence for the economic dispatch of the power transmission and distribution network.

[0019] Another embodiment of the present invention also provides a scheduling system based on high-dimensional Bessel volume segmentation, comprising: The acquisition module is used to acquire in real time the bidding data, unit parameters and network constraint information of power generators and distribution operators in the transmission and distribution network; The solution module is used to input the bidding data, unit parameters, and network constraint information into the preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-level non-convex game problem in the electricity-carbon coupling trading model, resulting in a single-level optimization problem. The single-level optimization problem is then constrained and reduced based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The module outputs the optimal generator output and carbon quota trading volume for power generators and distribution operators. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory. The scheduling module is used to schedule power generators and distribution operators based on the optimal generator output and carbon quota trading volume.

[0020] This invention employs a modular design, decomposing the complex electricity-carbon coupling trading problem into three clearly defined functional modules: data acquisition, model solving, and scheduling execution. The data acquisition module ensures the integrity and accuracy of the input data, providing a reliable data foundation for subsequent optimization. The solving module integrates core algorithms such as high-dimensional Bessel volume segmentation and external contraction approximation. Through efficient collaboration within the module, it transforms the complex two-level game problem into a rapidly solvable optimization problem, demonstrating the system's powerful ability to handle complex computational tasks. The scheduling module ensures that the optimization results are executed accurately and promptly, forming a closed loop from decision-making to execution. This system architecture not only has clearly defined responsibilities and low coupling, facilitating maintenance and upgrades, but also, through the collaborative work of each module, achieves efficient, accurate, and automated processing of the electricity-carbon coupling trading problem, meeting the power system's requirements for real-time decision-making and high reliability.

[0021] Another embodiment of the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of any of the methods described above.

[0022] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described above. Attached Figure Description

[0023] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating a scheduling method based on high-dimensional Bessel volume segmentation provided in an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the specific implementation process of a scheduling method based on high-dimensional Bessel volume segmentation provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a scheduling device based on high-dimensional Bessel volume segmentation provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the invention, are intended to cover non-exclusive inclusion.

[0027] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0028] See Figure 1 To address the technical problems of low computational efficiency, unstable solution quality, and difficulty in meeting the requirements of real-time market clearing and rapid scheduling decisions in existing methods for solving the game theory problem of electricity-carbon coupling trading, an embodiment of the present invention provides a scheduling method based on high-dimensional Bessel volume partitioning, comprising: S1 obtains real-time bidding data, unit parameters, and network constraint information from power generators and distribution operators in the power transmission and distribution network.

[0029] The bidding data refers to the prices submitted by power generators and distributors in the electricity and carbon markets, i.e., their bidding strategies; unit parameters refer to key operating parameters such as the upper and lower limits of active / reactive power output, unit generation cost, carbon emission intensity, and carbon quotas of each generating unit; network constraint information includes physical conditions that ensure the safe operation of the power grid, such as node voltage limits, line transmission capacity, and power flow constraints. By collecting the above data in real time, an accurate input foundation is provided for subsequently constructing an electricity-carbon coupled trading model and solving for the optimal scheduling strategy.

[0030] S2 inputs the bidding data, unit parameters, and network constraint information into the preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-layer non-convex game problem in the electricity-carbon coupling trading model, resulting in a single-layer optimization problem. The constraint reduction processing of the single-layer optimization problem is performed based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume of the generator and distribution operator are output. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory.

[0031] The system inputs real-time acquired bidding data, generator parameters, and network constraint information into a power transmission and distribution network carbon coupling trading model based on Nash-Stackelberg game theory. This model first uses an approximation technique based on high-dimensional Bessel volume segmentation to reconstruct the original two-layer non-convex game problem into an easily solvable single-layer optimization problem. Second, it employs an accelerated solution technique based on an external contraction approximation algorithm, constructing a hyperplane to iteratively cut the infeasible space and approximating the feasible region with a few constraints, thereby reducing the constraints of the single-layer optimization problem and obtaining a simplified optimization model. Finally, combined with an iterative optimization method, with the goal of maximizing the profits of each market participant, the bidding strategy is repeatedly updated and the simplified model is solved. If the deviation between the current bid and the previous bid is less than the convergence threshold, the optimal generator output and optimal carbon quota trading volume for each participant are output, completing the scheduling decision for the power-carbon coupling trading.

[0032] The objective function of the distribution network operator k is to maximize its total profit in all markets, as defined below: (1) In the formula, T is the set of all operating time periods; i is the generator set number; Let k be the set of all the units in the distribution network. Let n be the marginal electricity price at node n during time period t. Let n be the set of units on node n; Let i be the unit power generation cost of unit i in distribution network k during time period t; Let be the active power generated by unit i in distribution network k during time period t; The duration of the time period; For the carbon market to clear carbon prices; Let represent the carbon quota trading volume of unit i in distribution network k.

[0033] The constraints of the distribution network operator bidding model are as follows: Network flow constraints are as follows: (2) (3) In the formula, Let k be the set of nodes in the distribution network. Let i be the reactive power generated by unit i in distribution network k during time period t. and These represent the active and reactive loads at node n during time period t; and These are the real and imaginary parts of the element at (n, m) in the nodal admittance matrix, respectively. and These represent the voltage amplitude and phase angle at node m in the distribution network during time period t.

[0034] The generator set constraints are as follows: (4) (5) (6) In the formula, and These represent the lower and upper limits of the active power output of unit i in distribution network k, respectively. and These represent the lower and upper limits of reactive power output of unit i in distribution network k, respectively. Let i be the upper limit of the tradable electricity volume of unit i in distribution network k; Let i be the power generation of unit i when it meets the load demand of distribution network k.

[0035] The node voltage constraints are as follows: (7) In the formula, and These are the lower and upper limits of the voltage amplitude at node m, respectively; and These are the lower and upper limits of the voltage phase angle at node m, respectively.

[0036] The line transmission capacity constraints are as follows: (8) In the formula, and These represent the lower and upper limits of the transmission power of transmission lines m and n, respectively.

[0037] The pricing constraints are as follows: (9) (10) In the formula, and These represent the bids of unit i in the electricity market and carbon market, respectively, for the distribution network k. and These represent the lower and upper limits of the electricity market bid price for unit i in distribution network k during time period t; and These represent the lower and upper limits of the bid price for unit i in the carbon market within distribution network k.

[0038] Carbon quota constraints are as follows: (11) In the formula, The upper limit of the saleable carbon allowances for unit i in distribution network k; The initial free carbon allowance allocated to unit i in distribution network k; Let represent the carbon emission intensity of traditional generating unit i in distribution network k.

[0039] The objective function of generator g is to maximize its total profit across all markets, specifically defined as follows: (12) In the formula, j is the generator set number; The collection consisting of all the generating units of generator g; The unit power generation cost of generator unit j of generator g during time period t; The active power generation of generator unit j of generator g during time period t; The carbon quota trading volume of generator unit j for generator g.

[0040] The constraints of the generator bidding model are as follows: The pricing constraints are as follows: (13) (14) In the formula, and These are the electricity market and carbon market bids for generator unit j of generator g, respectively. and These represent the lower and upper limits of the electricity market bids for generator unit j of generator g during time period t; and The lower and upper limits of the price quoted by generator g's unit j in the carbon market.

[0041] Carbon quota constraints are as follows: (15) In the formula, The upper limit of the saleable carbon allowances for generator unit j of generator g; The initial free carbon allowance allocated to generator unit j of generator g; The carbon emission intensity of traditional unit j of generator g.

[0042] After receiving the declaration information from distribution network operators and power generators, transmission network operators clear the electricity market with the goal of minimizing negative social welfare. The objective function is as follows: (16) In the formula, A collection of distribution networks; A collection of power generation companies.

[0043] The constraints of the electricity market clearing model are as follows: DC power flow constraints are as follows: (17) In the formula, It is the set of all nodes connected to node n; Let n be the line conductance between node n and node m; Let n be the voltage phase angle at node n during time period t. This is the set of nodes in the power transmission network.

[0044] The upper and lower limits of the winning bid quantity are constrained as follows: (18) (19) In the formula, and These are the upper and lower limits of the cleared power output of unit j in generator g.

[0045] The line transmission capacity constraints are as follows: (20) The voltage phase angle constraint is as follows: (twenty one) In the formula, and These are the lower and upper limits of the voltage phase angle at node n, respectively.

[0046] After receiving the declaration information from distribution network operators and power generators, the carbon market clears out its participants with the goal of minimizing negative social welfare. The objective function is shown below: (twenty two) The constraints of the carbon market clearing model are as follows: The carbon quota balance constraints are as follows: (twenty three) The carbon quota allocation constraints are as follows: (twenty four) (25) S3 schedules power generators and distribution operators based on optimal generator output and carbon quota trading volume.

[0047] The system schedules the generating units of each market participant based on the optimal generating unit output and carbon quota trading results, and actually arranges the generating unit output plans and carbon quota delivery of power generators and distribution operators, so as to realize the implementation of the power-carbon coupled scheduling strategy.

[0048] Furthermore, such as Figure 2 As shown, this application provides a specific implementation process for a scheduling method based on high-dimensional Bessel volume segmentation. First, the constructed electricity-carbon coupling trading model is initialized: the convergence threshold, polynomial order n, and the dimension of the dynamic response function's state space are input. N x The number of Bezier bodies generated is set. n e = 1. Number of iterations i f = 0, Initial quote vector x Construct a two-layer solution example based on high-dimensional Bessel volume segmentation.

[0049] Next, we proceed to the high-dimensional Bessel body construction and iterative optimization stage: based on the leader constraints (2)-(11), (13)-(15) and the follower constraints, we generate... N x +1 initial vertex control point; generate equidistant points on each edge based on the vertex control points. Each edge control point; based on s A control point is used to construct a high-dimensional Bessel volume according to equation (36); based on s For each control point, construct the interpolation matrix of the tracker according to equation (37). Under the upper-level decision-making corresponding to each control point, the tracker solves its own optimization problem to obtain the optimal response value, and constructs the tracker's optimal response vector according to equation (38). Based on interpolation matrix and optimal response vector Based on equation (39), the approximate dynamic response function expression in a high-dimensional Bessel volume is derived. Solve the optimization problems (41)-(43) to obtain the maximum absolute error. The state with the largest absolute error The number of Bezier bodies whose recording error does not meet the requirements. n dIf the error of a certain Bessel solid does not meet the requirements, then a new node corresponding to the constraint state is added, and it is divided into... N x +1 sub-Bessel body and repeat the above construction process.

[0050] Then, the constraint reduction stage based on the external shrinkage approximation algorithm is entered: solving the mixed integer linear programming problem (55)-(60) to obtain the optimal objective function value. p * Based on the solutions to problems (55)-(60), generate a hyperplane; use this hyperplane to cut the current approximate feasible region. ,make i f = i f +1, to get the first i f The approximate feasible region formed after the iteration is obtained; based on the approximate feasible region after the iteration, the simplified form of the optimization problem (31)-(34) is obtained.

[0051] Finally, the iterative solution and output stage of the optimization problem begins: Under the condition that the bidding decisions of other subjects remain unchanged, the subject solves the simplified form of optimization problem (31)-(34) to determine its optimal bid; based on the solution results, the bid vector is... x h Update the data; determine whether the deviation between the current bid and the previous bid is less than the convergence threshold; if the convergence condition is met, output the optimal bid, optimal generator output, and optimal carbon quota trading volume for each entity, and schedule the generators of each market entity according to the optimal generator output, thereby completing the entire process of electricity-carbon coupling trading.

[0052] To construct a high-dimensional Bessel body, the Bernstein polynomial over the triangular domain is first generalized to obtain the nth-order Bernstein polynomial over the N-dimensional simplex. : (35) In the formula, This is the p-th weight coefficient; nth order In the Bernstein polynomial The index; and These are the exponent vector and the weight coefficient vector, respectively. , ; The Manhattan norm of a vector is denoted by .

[0053] Based on the nth-order Bernstein polynomial on the N-dimensional simplex defined above, the state space of the response function is described as a high-dimensional Bessel volume. : (36) In the formula, For state The dimension; nth order Bernstein polynomials; This is the p-th weight coefficient; for middle The index; and These are the exponent vector and the weight coefficient vector, respectively. , ; The Manhattan norm of a vector; Representing high-dimensional Bessel bodies The control points, among which The vertex is the control point, and the rest are edge control points.

[0054] To construct an approximately optimal response function, based on high-dimensional Bessel volumes... Construct the interpolation matrix from the control points in the matrix. . The expression is shown in the following formula: (37) In the formula, Representing high-dimensional Bessel bodies The i-th control point; Denotes the j-th basis function; The value of the basis function j at the i-th control point is represented by s; s represents the construction of the high-dimensional Bessel volume. The number of control points required.

[0055] Based on the above-constructed high-dimensional Bessel body The follower *l* solves its own lower-level optimization problem under different states to obtain the optimal response value in the current state. The optimal response vector is constructed from the optimal response value. As shown below: (38) In the formula, Indicates the i-th control point Under the corresponding higher-level decision, follower l solves its own optimization problem to obtain the optimal response value.

[0056] Based on the interpolation matrix constructed above With the optimal response vector The exported Bezier body The approximate optimal response function expression is shown below: (39) In the formula, Let be a vector composed of basis functions, and its expression is: .

[0057] To evaluate the approximate optimal response function The approximate effect introduces absolute error. Quantification With exact value function The deviation between them. Bessel body middle The maximum absolute error can be obtained by solving the following optimization problem: (40) In the formula, Represents Bessel form middle The maximum absolute error; This indicates the state when the absolute error is at its maximum.

[0058] Note that for convex real-valued functions , and The relationship between them is Then the optimization problem (40) can be equivalently transformed into: (41) (42) (43) In the formula, Indicates the leader's decision The optimal decision set for follower l; Let Lagrangian function represent the optimization problem corresponding to follower l; and This represents the multiplier vector.

[0059] For the reconstructed two-level game problem (31)-(34), the constraints (33)-(34) can be uniformly expressed in the following form: (44) In the formula, For the decision variables of all followers; and Leader decision variables and follower decision variables The corresponding coefficient matrix; It is a constant vector; These are dual variables.

[0060] According to duality theory, feasible region The expression is shown in the following formula: (45) In the formula, For dual space; This represents the set of vertices in the dual space.

[0061] From equation (45), it can be seen that if Then the following inequality holds: (46) Comparing equations (45) and (46), it can be found that there exists a hyperplane that strictly separates the feasible and infeasible regions. Hyperplane The expression is shown in the following formula: (47) From equations (45)-(47), it can be seen that the feasible region is described. The key lies in searching the dual space. All vertices in the equation. However, the reconstructed two-level game problem contains numerous constraints, and corresponding dual variables. For high-dimensional vectors, the dual space is traversed by enumeration. It becomes impractical to construct all vertices in the feasible region, therefore an external contraction approximation algorithm is proposed to efficiently construct the feasible region. .

[0062] Given any sufficiently large initial space .for The problem of verifying whether inequality (46) holds can be expressed as follows: (48) (49) In the formula, Indicates the first The approximate feasible region obtained after the iteration.

[0063] From optimization problems (48)-(49), we know that when When inequality (46) holds, it indicates that in the current space ,Right now It contains infeasible regions. Conversely, when optimizing the optimal objective function value of problem (48)-(49) When, it indicates any point in the current space. All are located within the feasible region within, that is At this point, the external shrinkage approximation algorithm terminates.

[0064] Note that the objective function (48) of the above optimization problem is of nonlinear form, while the dual space in the constraint (49) and They are independent of each other. To facilitate the solution, the optimization problem (48)-(49) is transformed into an integer linear programming problem (55)-(60), and the specific transformation process is as follows: (50) (51) In the formula, and For constructing an approximate feasible region The coefficient matrix and constant vector; The dual variable corresponding to constraint (51).

[0065] The KKT conditions for the internal problems of optimization problems (50)-(51) are: (52) (53) According to equations (52)-(53), the following equations hold: (54) Using the above equations, the objective function of (48) is linearized, and the Big M method is used to decompose the nonlinear inequality (53) into a linear inequality. Finally, problems (48)-(49) are transformed into mixed-integer linear programming problems: (55) (56) (57) (58) (59) (60) In the formula, It is a sufficiently large constant; The binary variable introduced for the Big M method.

[0066] In one embodiment, the construction process of the electricity-carbon coupling trading model based on Nash-Stackelberg game theory includes steps S201 to S203, each of which is detailed below: S201, obtain historical bidding data, historical unit parameters and historical network constraint information of power generators and distribution operators in the transmission and distribution network. Among them, the historical bidding data includes the upper and lower limits of electricity market bidding, the upper and lower limits of carbon market bidding, the upper and lower limits of cleared electricity volume of power generator units and the upper and lower limits of carbon quota winning bids. The historical unit parameters include unit power generation cost, upper and lower limits of unit output and carbon quota data.

[0067] In the transmission and distribution network carbon coupling trading method based on high-dimensional Bessel volume segmentation, obtaining historical data is a fundamental step in model construction and solution. Specifically, it requires obtaining historical bidding data, historical unit parameters, and historical network constraint information of power generators and distribution operators in the transmission and distribution network. Historical bidding data includes upper and lower limits for electricity market bids, carbon market bids, clearing power volumes of power generators and their units, and carbon quota winning bids, used to characterize the bidding behavior boundaries of market participants under different market environments. Historical unit parameters include unit generation costs, upper and lower limits for unit output, and carbon quota data, used to construct cost and operational constraints for power generators and distribution operators. Historical network constraint information includes grid physical operating conditions such as node voltage and line transmission capacity, ensuring the feasibility and security of the trading strategy. This historical data provides necessary input support for constructing the Nash-Stackelberg game model, generating high-dimensional Bessel volume control points, and subsequently approximate optimal response functions, and is an important prerequisite for achieving efficient and accurate solutions to the carbon coupling trading strategy.

[0068] S202. Based on the bidding data, unit parameters, and network constraint information of power generators and distribution operators in the transmission and distribution network, a first upper-level model with the goal of maximizing the profits of distribution network operators, a second upper-level model with the goal of maximizing the profits of power generators, a first lower-level model with the goal of maximizing the social welfare of the electricity market, and a second lower-level model with the goal of maximizing the social welfare of the carbon market are established. The constraints of the first and second upper-level models include bidding constraints, carbon quota constraints, generator unit constraints, and network operation constraints. The constraints of the first and second lower-level models include market clearing constraints and network security constraints.

[0069] Based on the bidding data of power generators and distribution operators in the transmission and distribution network, unit parameters, and network constraint information, the following four coupled models are established: The first upper-level model aims to maximize the profit of the distribution network operator. Its objective function is defined as the total profit obtained by the distribution network operator in each market. The specific expression is the objective function of the distribution network operator k, which is defined as follows: In the formula, T is the set of all operating time periods; i is the generator set number; Let k be the set of all the units in the distribution network. Let n be the marginal electricity price at node n during time period t. Let n be the set of units on node n; Let i be the unit power generation cost of unit i in distribution network k during time period t; Let be the active power generated by unit i in distribution network k during time period t; The duration of the time period; For the carbon market to clear carbon prices; Let represent the carbon quota trading volume of unit i in distribution network k.

[0070] The second upper-level model aims to maximize the profits of the power generator g. Its objective function is defined as the total profit obtained by the power generator g in each market. The specific expression of the objective function of power generator g is as follows: In the formula, j is the generator set number; The collection consisting of all the generating units of generator g; The unit power generation cost of generator unit j of generator g during time period t; The active power generation of generator unit j of generator g during time period t; The carbon quota trading volume of generator unit j for generator g.

[0071] The first lower-level model aims to maximize the social welfare of the electricity market. Transmission grid operators, on the other hand, clear the electricity market to minimize negative social welfare. The specific expression of its objective function is the objective function of the transmission market clearing model, defined as follows: In the formula, K is the set of distribution networks; G is the set of power generators.

[0072] The second lower-level model aims to maximize the social welfare of the carbon market, while the carbon market clears itself with the goal of minimizing negative social welfare. Its objective function is specifically expressed as the objective function of the carbon market clearing model, defined as follows: In the formula, The carbon quota trading volume of unit i in distribution network k; For the carbon market to clear carbon prices; The carbon quota trading volume of generator unit j for generator g.

[0073] The constraints of the first and second upper-level models include pricing constraints, carbon quota constraints, generator unit constraints, and network operation constraints; the constraints of the first and second lower-level models include market clearing constraints and network security constraints, thus fully constructing a transmission and distribution network carbon coupling trading model based on Nash-Stackelberg game theory.

[0074] S203. Based on the first upper-level model, the second upper-level model, the first lower-level model, and the second lower-level model, construct an electricity-carbon coupling trading model.

[0075] Specifically, an electricity-carbon coupling trading model is constructed based on the first upper-level model, the second upper-level model, the first lower-level model, and the second lower-level model. This model is essentially a multi-time-period, bi-level non-convex optimization problem, which can be concisely described as the mathematical expression of an upper-level game problem and a lower-level game problem. The upper-level models include a distribution network operator bidding model and a power generator bidding model, while the lower-level models include a transmission market clearing model and a carbon market clearing model.

[0076] This embodiment effectively characterizes the competition and cooperation among multiple stakeholders in the electricity-carbon market by constructing a complete Nash-Stackelberg game model. Based on acquired historical bidding data, generator parameters, and network constraint information, the established two-layer game model accurately describes the profit maximization objectives of distribution network operators and generators, as well as the social welfare maximization objectives of the electricity and carbon markets. Furthermore, by encompassing various constraints such as bidding, carbon quotas, generator and network operation, the model's practicality and feasibility are ensured, laying a solid foundation for subsequent efficient solutions based on high-dimensional Bessel volume partitioning. This enhances the rationality and operability of the overall electricity-carbon coupling trading strategy.

[0077] In one embodiment, the bidding data, unit parameters, and network constraint information are input into a preset electricity-carbon coupling trading model. This allows the electricity-carbon coupling trading model to reconstruct the bi-layer non-convex game problem using a high-dimensional Bessel volume segmentation technique, resulting in a single-layer optimization problem. This includes steps S301 to S306, each step as follows: S301 inputs a preset electricity-carbon coupling trading model based on quotation data, unit parameters, and network constraint information. It then obtains the mathematical definition of the lower-level optimization problem from the electricity-carbon coupling trading model, including the objective function and constraints of the lower-level optimization problem.

[0078] The process involves inputting a pre-defined electricity-carbon coupling trading model based on bidding data, unit parameters, and network constraints. The mathematical definition of the lower-level optimization problem is then derived from this model. This lower-level optimization problem comprises a first lower-level model and a second lower-level model. The first lower-level model is a transmission market clearing model, whose objective function is to minimize negative social welfare during electricity market clearing. The second lower-level model is a carbon market clearing model, whose objective function is to minimize negative social welfare during carbon market clearing. The constraints of the lower-level optimization problem include market clearing constraints and network security constraints. Specifically, these encompass the DC power flow constraints, upper and lower limits of winning bids, line transmission capacity constraints, and voltage phase angle constraints of the electricity market clearing model, as well as the carbon quota balance constraints and carbon quota winning bid constraints of the carbon market clearing model. This completes the mathematical definition of the lower-level optimization problem.

[0079] S302, based on the mathematical definition of the lower-level optimization problem, selects control points in the decision space composed of upper-level decision variables, and solves the lower-level optimization problem at each control point to obtain the corresponding dataset of upper-level decisions and lower-level optimal responses.

[0080] Based on the mathematical definition of the lower-level optimization problem, control points are selected in the decision space composed of upper-level decision variables. Specifically, initial vertex control points are generated according to the constraints of the leader and followers, and edge control points are generated at equal intervals on each edge based on the vertex control points. The total number of control points and the total number of edges are determined by the polynomial order and the dimension of the state space. Under the upper-level decision corresponding to each control point, the follower solves its own optimization problem to obtain the optimal response value, thus obtaining a dataset corresponding to the upper-level decision and the lower-level optimal response. This dataset is used to construct the follower's optimal response vector, providing a data foundation for subsequently constructing an approximate optimal response function.

[0081] S303, based on the corresponding dataset of upper-level decisions and lower-level optimal responses, uses Bernstein polynomial basis functions and control points to construct a high-dimensional Bessel volume and derive an approximate explicit optimal response function.

[0082] Based on the corresponding datasets of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points. First, the Bernstein polynomial over the triangular domain is generalized to obtain an nth-order Bernstein polynomial over an N-dimensional simplex. Based on this, the state space of the response function is described as a high-dimensional Bessel volume. Using the control points in the constructed high-dimensional Bessel volume, an interpolation matrix is ​​constructed, its expression consisting of the values ​​of the basis functions at the control points. Based on the interpolation matrix and the optimal response vector, an approximate optimal response function expression in the Bessel volume is derived. This expression is represented by a vector of basis functions, thus obtaining an explicitly describable approximate optimal response function.

[0083] S304 solves the maximum absolute error optimization problem for the explicit optimal response function, and obtains the maximum absolute error.

[0084] Specifically, for the explicitly optimal response function, a maximum absolute error optimization problem is solved. To evaluate the approximation effect of the approximate optimal response function, an absolute error is introduced to quantify the deviation between the approximate optimal response function and the exact function. The maximum absolute error of the approximate optimal response function in the Bezier volume is obtained by solving an optimization problem whose objective function is to minimize the absolute error between the approximate function and the exact function.

[0085] S305, if the maximum absolute error exceeds the set allowable error, then recursively segment and locally reconstruct the high-dimensional Bessel volume to obtain multiple approximate optimal response functions.

[0086] The process involves adding vertex control points corresponding to the state with the maximum absolute error, and generating edge control points at equal intervals based on these vertex control points, thus dividing the original Bézier body into several sub-Bézier bodies. Then, a new interpolation matrix and optimal response vector are constructed for each sub-Bézier body, and based on these, the approximate optimal response function and corresponding maximum absolute error on each sub-Bézier body are derived. This recursive segmentation process is repeated until the maximum absolute error in all Bézier bodies meets the given allowable error, ultimately yielding multiple approximate optimal response functions.

[0087] S306, based on the multi-piece approximate optimal response function, uses the result of the multi-piece approximate optimal response function as the result of the lower-level optimization problem in the two-layer nonconvex game problem, so as to reconstruct the two-layer nonconvex game problem into a single-layer optimization problem.

[0088] Among them, based on the multi-piece approximate optimal response function, the result of the multi-piece approximate optimal response function is used as the result of the lower-level optimization problem in the two-layer nonconvex game problem. The optimal response function is used to quantify the impact of the leader's decision on the followers, and the approximate optimal response function is generated based on the high-dimensional Bessel volume segmentation, thereby decoupling the two-layer game problem. Thus, the complex dynamic game problem is reconstructed into a single-layer optimization problem, providing a feasible way to solve the model.

[0089] This embodiment transforms a complex bi-layer non-convex game problem into a solvable single-layer optimization problem using a high-dimensional Bessel volume partitioning technique. An approximate optimal response function is constructed using Bernstein polynomials, and recursive partitioning and error control mechanisms ensure approximate accuracy. This significantly reduces computational complexity while maintaining the optimality of the solution, effectively overcoming the shortcomings of traditional methods such as high computational burden and poor convergence. It provides a reliable and efficient solution approach for the electricity-carbon coupling trading model.

[0090] In one embodiment, the lower-level optimization problem is solved at each control point to obtain the corresponding dataset of the upper-level decision and the lower-level optimal response, including steps S401 to S403, each step of which is as follows: S401 uses the upper-level decision vector represented by each control point as a given parameter, substitutes it into the lower-level optimization problem, and solves the problem.

[0091] In this process, under the upper-level decision-making corresponding to each control point, the follower solves its own optimization problem to obtain the optimal response value, thereby obtaining the optimal response value in the current state, and constructs the optimal response vector based on this, providing a data foundation for the subsequent construction of an approximate optimal response function.

[0092] S402, based on the solution obtained from the lower-level optimization problem, records the upper-level decision vector and the obtained lower-level optimal response vector corresponding to each control point.

[0093] In this context, under the upper-level decision corresponding to each control point, the follower solves its own optimization problem to obtain the optimal response value, and constructs the optimal response vector from the optimal response value, thus forming a corresponding dataset of upper-level decision and lower-level optimal response.

[0094] S403: Traverse all control points, integrate the upper-level decision vectors corresponding to all control points with the obtained lower-level optimal response vectors, and obtain the corresponding datasets of upper-level decisions and lower-level optimal responses.

[0095] In this process, under the upper-level decision corresponding to each control point, the follower solves its own optimization problem to obtain the optimal response value. The optimal response vector is constructed from the optimal response value, thus obtaining the corresponding dataset of the upper-level decision and the lower-level optimal response, providing a complete data foundation for the subsequent construction of an approximate optimal response function.

[0096] This embodiment systematically solves the lower-level optimization problem at each control point and accurately records the correspondence between upper-level decisions and lower-level optimal responses, constructing a complete dataset that provides crucial data support for the subsequent construction of high-dimensional Bessel bodies. This method ensures the accuracy and comprehensiveness of the approximate optimal response function, thus laying a reliable foundation for the effective reconstruction and efficient solution of two-level game problems.

[0097] In one embodiment, based on the corresponding dataset of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points to derive an approximate explicit optimal response function, including steps S501 to S503, each step of which is as follows: S501, based on the corresponding dataset of upper-level decisions and lower-level optimal responses, determines the Bernstein polynomial basis functions.

[0098] This step first generalizes the Bernstein polynomial over the triangular domain to obtain an nth-order Bernstein polynomial over the N-dimensional simplex. Its expression is defined by the exponent vector and the weight coefficient vector, thus constructing the Bernstein polynomial basis function.

[0099] S502 constructs a high-dimensional Bessel volume based on the defined Bernstein polynomial basis functions and control points.

[0100] Specifically, this step involves describing the state space of the response function as a high-dimensional Bessel volume, which contains vertex control points and edge control points, and forming a complete mathematical description of the state space through the combination of basis functions and weight coefficients.

[0101] S503, calculate the interpolation matrix corresponding to the high-dimensional Bessel volume, and based on the interpolation matrix and the lower-level optimal response vector in the corresponding dataset of upper-level decisions and lower-level optimal responses, derive an explicitly expressed approximate optimal response function through linear computation.

[0102] The process involves constructing an interpolation matrix based on control points, the expression of which consists of the values ​​of the basis functions at the control points. Based on the interpolation matrix and the optimal response vector, an approximate optimal response function expression in the Bezier volume is derived. This expression is represented by a vector of basis functions, thus obtaining an approximate optimal response function that can be explicitly described.

[0103] This embodiment transforms the implicit optimal response relationship into an explicit functional expression by using Bernstein polynomial basis functions and high-dimensional Bessel bodies. Based on linear calculations of the interpolation matrix and the lower-level optimal response vector, it achieves a mathematically explicit description of complex game behavior, providing a clear functional relationship for subsequent optimization and significantly improving the algorithm's interpretability and computational efficiency.

[0104] In one embodiment, the single-layer optimization problem is subjected to constraint reduction processing based on the external shrinkage approximation algorithm to obtain a simplified optimization model, including steps S601 to S603, each of which is as follows: S601, based on the current approximate feasible region, iteratively solve the mixed integer linear programming problem until the optimal objective function value output by the current iteration satisfies the preset conditions, and output the approximate feasible region corresponding to the current iteration. The approximate feasible region at the first iteration is determined based on the single-layer optimization problem.

[0105] The process involves solving a mixed-integer linear programming problem to obtain the optimal objective function value. If the optimal objective function value is 0, a simplified form of the optimization problem is obtained based on the approximate feasible region. Otherwise, a hyperplane is generated based on the solution, and the hyperplane is used to cut the current approximate feasible region to obtain the approximate feasible region formed after a new round of iterations. This process is repeated until the optimal objective function value meets the preset conditions.

[0106] S602, in each iteration, the approximate feasible region of the previous iteration is cut according to the hyperplane to obtain the approximate feasible region of the current iteration. The hyperplane is generated based on the mixed integer linear programming problem.

[0107] In this process, a hyperplane is generated based on the solution to the mixed integer linear programming problem. The hyperplane is then used to cut the current approximate feasible region to obtain the approximate feasible region formed after the i-th iteration. Thus, the true feasible region is gradually approximated through the iterative shrinkage process.

[0108] S603, based on the output approximate feasible region, obtains the simplified optimization model.

[0109] In this process, a simplified form of the optimization problem is obtained based on the approximate feasible region. This simplified form uses an external shrinkage approximation algorithm to iteratively cut the infeasible space with a hyperplane and approximates the feasible region with fewer constraints, thereby effectively reducing the size of the constraint set and accelerating the solution of the optimization problem.

[0110] This embodiment employs an external shrinkage approximation algorithm, utilizing iterative cutting of the infeasible space with a hyperplane to gradually approximate the true feasible region, thereby efficiently describing complex feasible regions with fewer constraints. This method significantly reduces the constraint scale of the optimization problem, greatly improving computational efficiency while maintaining solution quality, and effectively solving the problem of solution difficulties caused by excessive constraints in traditional methods.

[0111] In one embodiment, an iterative optimization method is used to solve a simplified optimization model with the goal of maximizing the profits of each market participant, until the calculated price deviation meets a preset convergence condition. The optimal generator output and carbon quota trading volume are then output, including steps S701 to S703, each step of which is detailed below: S701, based on the optimization model and the bidding data of generators and distribution operators in the transmission and distribution network, iteratively solves the simplified form of the single-layer optimization problem until the optimal bid set output by the current iteration satisfies the preset conditions, and outputs the optimal bid set corresponding to the current iteration. The optimal bid set in the first iteration is determined based on the initial bid data. The preset condition is whether the deviation norm between the current optimal bid and the previous optimal bid is less than the convergence threshold.

[0112] In this process, under the condition that the bidding decisions of other entities remain unchanged, the entity solves the simplified form of the optimization problem, determines its own optimal bid, and updates the bid vector. If the deviation between the current bid and the previous bid is less than the convergence threshold, the entity outputs the optimal bid, the optimal generator output, and the optimal carbon quota trading volume for each entity. Otherwise, it continues to iterate until the convergence condition is met.

[0113] S702, in each iteration, the optimal bid set of the previous iteration is updated based on the bid decisions of other entities to obtain the optimal bid set of the current iteration. The update is performed based on a simplified form of a single-layer optimization problem.

[0114] In this process, the subject solves an optimization problem while keeping the bidding decisions of other subjects unchanged, determines its own optimal bid, and updates the bid vector based on the current optimal bid, thereby obtaining the optimal bid set for the current iteration.

[0115] S703, based on the output of the optimal bid set, obtains the optimal generator output and carbon quota trading volume.

[0116] The system outputs the optimal generator output and optimal carbon quota trading volume for each entity based on the optimal bid set, and schedules the generators of each market entity based on the optimal generator output, thus completing the entire process of electricity-carbon coupled trading decision-making.

[0117] This embodiment employs an iterative optimization method to continuously update bidding strategies until convergence, while ensuring the maximization of profits for each market participant. The final output is the optimal generator output and carbon quota trading volume. This method effectively coordinates the competitive relationships among multiple participants, ensuring rapid convergence and strategy stability, and providing reliable and efficient decision support for electricity-carbon coupling trading.

[0118] Based on the same inventive concept, this application also provides a scheduling system for implementing the above-mentioned scheduling system based on high-dimensional Bezier volume segmentation. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more scheduling device embodiments based on high-dimensional Bezier volume segmentation provided below can be found in the limitations of the scheduling method based on high-dimensional Bezier volume segmentation described above, and will not be repeated here.

[0119] In one exemplary embodiment, such as Figure 3 As shown, a scheduling system based on high-dimensional Bessel volume segmentation is provided, including: The acquisition module 101 is used to acquire in real time the bidding data, unit parameters and network constraint information of power generators and distribution operators in the transmission and distribution network; The solution module 102 is used to input the bidding data, unit parameters and network constraint information into the preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-layer non-convex game problem in the electricity-carbon coupling trading model to obtain a single-layer optimization problem. The constraint reduction processing of the single-layer optimization problem is performed based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume of the generator and the distribution operator are output. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory. The scheduling module 103 is used to schedule power generators and distribution operators based on the optimal generator output and carbon quota trading volume.

[0120] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of a scheduling method based on high-dimensional Bessel volume segmentation as described above.

[0121] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0122] This technical solution deeply integrates high-dimensional Bessel volume segmentation technology with the Nash-Stackelberg game model and introduces an external contraction approximation algorithm to construct a highly efficient solution system specifically for power-carbon coupled scheduling in transmission and distribution networks. Its core advantage lies in overcoming the limitations of existing methods in solving two-level non-convex game problems, which suffer from low computational efficiency and unstable solution quality. It achieves rapid and high-precision optimization of bidding strategies for various stakeholders in complex market environments. Users can proactively adjust the electricity and carbon market bids of power generators and distribution network operators through this algorithm and obtain the optimal power generation output and carbon quota scheduling scheme in real time. This provides reliable theoretical support and decision-making tools for power-carbon coordinated scheduling, achieving a leap from "difficult to solve" to "highly efficient optimization." Simultaneously, this solution fully leverages the respective advantages of high-dimensional Bessel volume segmentation in constructing approximate response functions and the external contraction algorithm in constraint reduction, solving the problems of low computational efficiency, unstable solution quality, and difficulty in meeting the needs of real-time market clearing and rapid scheduling decisions in traditional optimization methods.

[0123] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative, wherein the components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0124] The above embodiments merely illustrate several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the embodiments of this application, and these all fall within the protection scope of the embodiments of this application.

Claims

1. A scheduling method based on high-dimensional Bessel volume segmentation, characterized in that, include: Real-time acquisition of bidding data, unit parameters and network constraint information from power generators and distribution operators in the power transmission and distribution network; The bidding data, unit parameters, and network constraint information are input into a preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-layer non-convex game problem in the electricity-carbon coupling trading model, resulting in a single-layer optimization problem. The constraint reduction processing of the single-layer optimization problem is performed based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume of generators and distribution operators are output. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory. Dispatch of power generators and distribution operators is based on optimal generator output and carbon quota trading volume.

2. The scheduling method based on high-dimensional Bezier volume segmentation as described in claim 1, characterized in that, The construction process of the electricity-carbon coupling trading model based on Nash-Stackelberg game theory includes: Obtain historical bidding data, historical unit parameters, and historical network constraint information of power generators and distribution operators in the transmission and distribution network. The historical bidding data includes the upper and lower limits of electricity market bidding, carbon market bidding, the upper and lower limits of cleared electricity volume of power generator units, and the upper and lower limits of carbon quota winning bids. The historical unit parameters include unit power generation cost, unit output upper and lower limits, and carbon quota data. Based on the bidding data, unit parameters, and network constraint information of power generators and distribution operators in the transmission and distribution network, a first upper-level model with the goal of maximizing the profits of distribution network operators, a second upper-level model with the goal of maximizing the profits of power generators, a first lower-level model with the goal of maximizing the social welfare of the electricity market, and a second lower-level model with the goal of maximizing the social welfare of the carbon market are established. The constraints of the first and second upper-level models include bidding constraints, carbon quota constraints, generator unit constraints, and network operation constraints. The constraints of the first and second lower-level models include market clearing constraints and network security constraints. Based on the first upper-level model, the second upper-level model, the first lower-level model, and the second lower-level model, an electricity-carbon coupling trading model is constructed.

3. The scheduling method based on high-dimensional Bezier volume segmentation as described in claim 2, characterized in that, The bidding data, unit parameters, and network constraint information are input into a preset electricity-carbon coupling trading model. This model then uses high-dimensional Bessel volume segmentation technology to reconstruct the two-layer non-convex game problem within the electricity-carbon coupling trading model, resulting in a single-layer optimization problem, including: Based on the input of quotation data, unit parameters and network constraint information into the preset electricity-carbon coupling trading model, the mathematical definition of the lower-level optimization problem is obtained from the electricity-carbon coupling trading model, including the objective function and constraints of the lower-level optimization problem; Based on the mathematical definition of the lower-level optimization problem, control points are selected in the decision space composed of upper-level decision variables, and the lower-level optimization problem is solved at each control point to obtain the corresponding dataset of upper-level decisions and lower-level optimal responses. Based on the corresponding dataset of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points, and an approximate explicit optimal response function is derived. For the explicit optimal response function, the maximum absolute error optimization problem is solved to obtain the maximum absolute error; If the maximum absolute error exceeds the set allowable error, then recursively segment and locally reconstruct the high-dimensional Bessel volume to obtain multiple approximate optimal response functions; Based on the multi-piece approximate optimal response function, the result of the multi-piece approximate optimal response function is used as the result of the lower-level optimization problem in the two-layer nonconvex game problem, so as to reconstruct the two-layer nonconvex game problem into a single-layer optimization problem.

4. The scheduling method based on high-dimensional Bessel volume segmentation as described in claim 3, characterized in that, Solve the lower-level optimization problem at each control point to obtain the corresponding dataset of upper-level decisions and lower-level optimal responses, including: The upper-level decision vector represented by each control point is used as a given parameter, and the lower-level optimization problem is solved by substituting it into the solution. Based on the solution obtained from the lower-level optimization problem, record the upper-level decision vector and the obtained lower-level optimal response vector corresponding to each control point; Iterate through all control points, integrate the upper-level decision vectors corresponding to all control points with the obtained lower-level optimal response vectors, and obtain the corresponding datasets of upper-level decisions and lower-level optimal responses.

5. A scheduling method based on high-dimensional Bezier volume segmentation as described in claim 3, characterized in that, Based on the corresponding dataset of upper-level decisions and lower-level optimal responses, a high-dimensional Bessel volume is constructed using Bernstein polynomial basis functions and control points to derive an approximate explicit optimal response function, including: Based on the corresponding dataset of upper-level decisions and lower-level optimal responses, the Bernstein polynomial basis functions are determined. Based on the defined Bernstein polynomial basis functions and control points, a high-dimensional Bessel volume is constructed. Calculate the interpolation matrix corresponding to the high-dimensional Bessel volume, and based on the interpolation matrix and the lower-level optimal response vector in the corresponding dataset of upper-level decisions and lower-level optimal responses, derive an explicitly expressed approximate optimal response function through linear computation.

6. The scheduling method based on high-dimensional Bessel volume segmentation as described in claim 1, characterized in that, The constraint reduction process for the single-layer optimization problem is performed based on the external shrinkage approximation algorithm, resulting in a simplified optimization model, including: Based on the current approximate feasible region, iteratively solve the mixed integer linear programming problem until the optimal objective function value output by the current iteration satisfies the preset conditions, and output the approximate feasible region corresponding to the current iteration. The approximate feasible region at the first iteration is determined based on the single-layer optimization problem. In each iteration, the approximate feasible region of the previous iteration is cut according to the hyperplane to obtain the approximate feasible region of the current iteration. The hyperplane is generated based on the mixed integer linear programming problem. Based on the approximate feasible region of the output, the simplified optimization model is obtained.

7. The scheduling method based on high-dimensional Bessel volume segmentation as described in claim 1, characterized in that, Using an iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated price deviation meets the preset convergence condition. The optimal generator output and carbon quota trading volume are then output, including: Based on the optimization model and the bidding data of generators and distribution operators in the power transmission and distribution network, the simplified form of the single-layer optimization problem is solved iteratively until the optimal bid set output by the current iteration meets the preset conditions. The optimal bid set corresponding to the current iteration is then output. The optimal bid set in the first iteration is determined based on the initial bid data. The preset condition is whether the deviation norm between the current optimal bid and the previous optimal bid is less than the convergence threshold. In each iteration, the optimal bid set from the previous iteration is updated based on the bidding decisions of other entities to obtain the optimal bid set for the current iteration. The update is performed based on a simplified form of a single-level optimization problem. Based on the set of optimal bids output, the optimal generator output and carbon quota trading volume are obtained.

8. A scheduling system based on high-dimensional Bessel volume segmentation, characterized in that the system... include: The acquisition module is used to acquire in real time the bidding data, unit parameters and network constraint information of power generators and distribution operators in the transmission and distribution network; The solution module is used to input the bidding data, unit parameters, and network constraint information into the preset electricity-carbon coupling trading model. The electricity-carbon coupling trading model uses high-dimensional Bessel volume segmentation technology to reconstruct the two-level non-convex game problem in the electricity-carbon coupling trading model, resulting in a single-level optimization problem. The single-level optimization problem is then constrained and reduced based on the external contraction approximation algorithm to obtain a simplified optimization model. Combined with the iterative optimization method, the simplified optimization model is solved with the goal of maximizing the profits of each market participant until the calculated bidding deviation meets the preset convergence condition. The module outputs the optimal generator output and carbon quota trading volume for power generators and distribution operators. The electricity-carbon coupling trading model is constructed based on Nash-Stackelberg game theory. The scheduling module is used to schedule power generators and distribution operators based on the optimal generator output and carbon quota trading volume.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, The steps of implementing the method of any one of claims 1 to 7 when the processor executes a computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When a computer program is executed by a processor, it implements the steps of the method of any one of claims 1 to 7.

Images