Branching method and apparatus for accelerating the solution of power system safety constraint unit combination

Abstract

This application relates to the field of power system technology and discloses a branching method and apparatus for accelerating the solution of power system safety-constrained unit combinations. During the branching process, if the relaxation problem of the target node is unsolvable, instead of simple single-point pruning, a network constraint minimum violation model is constructed. If the network constraint results in no solution, a globally feasible cut is generated using the Lagrange multiplier at the optimal solution. This globally feasible cut represents the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem. Adding the globally feasible cut to the branching cut pool allows for the removal of infeasible solutions for similar specific unit combination modes in the future, avoiding a large number of repetitive and invalid explorations during the branching process, thereby accelerating the solution and ensuring the safety and economy of power grid dispatch. In this application, the globally feasible cut is strictly based on strong duality theory, ensuring that feasible or optimal solutions are not erroneously removed, fundamentally guaranteeing the feasibility and optimality of the solution results for safety-constrained unit combinations.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a branch cutting method and apparatus for accelerating the solution of power system safety constraint unit combination. Background Technology

[0002] In electricity market operation and day-ahead grid dispatch, the Security-Constrained Unit Commitment (SCUC) is the core optimization model and decision-making basis supporting market clearing and the preparation of day-ahead dispatch plans. The SCUC needs to optimize the start-up and shutdown status and output plan of each generating unit while satisfying various system operating constraints, in order to minimize system operating costs.

[0003] In traditional approaches, solving large-scale SCUC problems using solvers primarily relies on the Branch-and-Cut (B&C) algorithm framework. This method systematically explores the integer solution space and combines it with cutting plane techniques to find the optimal solution. During B&C, the algorithm solves the linear programming relaxation problem at each node, performs branching operations based on the relaxation solutions, and forms a search tree. However, when the system network constraints are tight, the LP relaxation problems at many nodes may become infeasible due to network constraints, leading to a large number of invalid searches and severely impacting solution efficiency. This is especially true for systems with severe network congestion, where it is often difficult to obtain a satisfactory solution within the market clearing time window, directly affecting the safety and economy of power grid dispatch.

[0004] Therefore, how to improve the solution efficiency of the power system security constraint unit combination problem and ensure the safety and economy of power grid dispatch is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] This application provides a branching method and apparatus for accelerating the solution of power system security-constrained unit combination problems, so as to improve the solution efficiency of power system security-constrained unit combination problems and ensure the safety and economy of power grid dispatch.

[0006] Firstly, this application provides a branching method for accelerating the solution of power system security constraint unit combination. The branching method is applied to a solver and includes: determining the SCUC model of the power system to be solved; solving the relaxation problem of each node during the branching and bounding process; wherein the relaxation problem of each node is determined based on the SCUC model; if the relaxation problem of the target node has no solution, constructing a network constraint minimum violation model based on the relaxation problem of the target node; solving the network constraint minimum violation model to determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model; if the objective function value determines that the reason for the unsolvability of the target node is a network constraint, generating a globally feasible cut based on the Lagrange multipliers at the optimal solution according to Lagrange duality theory; wherein the globally feasible cut is a constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem; adding the globally feasible cut to the branching and bounding cut pool, pruning nodes that do not satisfy the globally feasible cut; and obtaining the unit combination result after the branching and bounding process.

[0007] Optionally, constructing a network constraint minimum violation model based on the relaxation problem of the target node includes: constructing a network constraint minimum violation model based on the relaxation problem of the target node, wherein the network constraint minimum violation model is constructed as a linear programming problem, and the network constraint minimum violation model includes: an objective function and various constraints, wherein each constraint includes: unit operation constraints after removing network constraints, equality constraints and inequality constraints, and each constraint has a corresponding Lagrange multiplier vector.

[0008] Optionally, the objective function is: ;in, It is a column vector whose elements are all 1s. This represents the upper limit slack for the positive power flow of each line. This represents the upper limit slack for the reverse power flow of each line. The objective function value, This represents the sum of the upper limit slack for power flow across all routes. This indicates taking the transpose of the vector.

[0009] The unit operation constraints for removing network constraints are: ;in, This is the first coefficient matrix. This is the second coefficient matrix. This is the third coefficient matrix. For the active contribution of each unit, For the start-up and shutdown state variables of each unit in the network constraint minimum violation model; is the first Lagrange multiplier vector; the active power output of each unit, the start-stop state variables of each unit, the upper limit slack of the forward power flow, and the upper limit slack of the reverse power flow are all column vectors.

[0010] The equality constraint is: ; ;in, For unit indexing, for The Middle Start-up and shutdown status variables of individual generating units 1 indicates the first Each unit is started. 0 indicates the first One unit was shut down; This is the set of binary variable indices that are fixed to 1 at the current node through a branch operation. For the second Lagrange multiplier, express The multipliers corresponding to the equality constraints of the start-stop state variables of the unit, which are fixed at 1. This is the set of binary variable indices that are fixed to 0 at the current node through a branch operation. It is the third Lagrange multiplier. express The multiplier corresponding to the equality constraint of the start-stop state variables of the unit that is fixed at 0.

[0011] The inequality constraint is: ; ; ; ; ;in, For the set of all binary variable indices, It is the fourth Lagrange multiplier. express The multipliers corresponding to the inequality constraints on the upper limit of the start-stop state variables of the units that are not fixed. It is the fifth Lagrange multiplier. express The multiplier corresponding to the lower bound inequality constraint of the start-stop state variables of the unit that is not fixed; The power transfer distribution factor matrix, For load vector, This is the vector representing the upper limit of line transmission capacity. It is the sixth Lagrange multiplier vector. It is the seventh Lagrange multiplier vector.

[0012] in, For the positive power flow capacity constraint of the line. This is a constraint on the negative power flow capacity of the line.

[0013] Optionally, solving the network constraint minimum violation model and determining the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model includes: determining the optimization variables of the network constraint minimum violation model; wherein, the optimization variables include: the active power output of each unit, the start-up and shutdown state variables of each unit, the upper limit slack of the forward power flow of each line, and the upper limit slack of the reverse power flow of each line; determining the optimal solution of each optimization variable at the point where it satisfies each constraint and the function value calculated by the objective function is minimized, thereby obtaining the objective function value at the optimal solution; determining the Lagrange multiplier vector of each constraint at the optimal solution, wherein the Lagrange multiplier vector of each constraint is used to represent the marginal influence of each constraint on the objective function value at the optimal solution.

[0014] Optionally, determining that the reason for the unsolvability of the target node is a network constraint based on the objective function value includes: determining whether the objective function value is greater than zero; if so, determining that the reason for the unsolvability of the target node is a network constraint.

[0015] Optionally, based on the Lagrange multiplier at the optimal solution, a globally feasible cut is generated according to the Lagrange duality theory, including: obtaining the Lagrange multiplier at the optimal solution of the network constraint minimum violation model; and determining the globally feasible cut based on the Lagrange multiplier at the optimal solution, the global feasible cut determination rule, and the coefficient determination rule.

[0016] Optionally, the global feasible cut determination rule is: ;in, As the first coefficient, Let be the unit start-up and shutdown variable vector in the SCUC model. This is the second coefficient.

[0017] Optionally, the coefficient determination rule is as follows: ; ;in, Let be the second Lagrange multiplier vector at the optimal solution. Let be the third Lagrange multiplier vector at the optimal solution. Let be the first Lagrange multiplier vector at the optimal solution. This is the third coefficient matrix. The sixth Lagrange multiplier vector at the optimal solution. The seventh Lagrange multiplier vector at the optimal solution. This is the vector representing the upper limit of line transmission capacity. The power transfer distribution factor matrix, For load vector, Let be the fourth Lagrange multiplier vector at the optimal solution.

[0018] Secondly, this application provides a branching device for accelerating the solution of power system safety constraint unit combination. The branching device is applied to a solver and includes: a first determining module for determining the SCUC model to be solved in the power system; a first solving module for solving the relaxation problem of each node during the branching and bounding process; wherein the relaxation problem of each node is determined based on the SCUC model; a construction module for constructing a network constraint minimum violation model based on the relaxation problem of the target node if the target node's relaxation problem has no solution; and a second solving module for minimizing the network constraints. The system employs a constraint violation model solution to determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum constraint violation model. A generation module is used to determine that the reason for the unsolvability of the target node is a network constraint based on the objective function value, and to generate a globally feasible cut based on the Lagrange multipliers at the optimal solution according to Lagrange duality theory. The globally feasible cut is a constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem. An adding module is used to add the globally feasible cut to the branch-and-bound cut pool and prune nodes that do not satisfy the globally feasible cut. A second determination module is used to obtain the unit combination result after branch-and-bound is completed.

[0019] Optionally, the construction module is specifically used to: construct a network constraint minimum violation model based on the relaxation problem of the target node. The network constraint minimum violation model is constructed as a linear programming problem. The network constraint minimum violation model includes: an objective function and various constraints. Each constraint includes: unit operation constraints after removing network constraints, equality constraints, and inequality constraints. Each constraint has a corresponding Lagrange multiplier vector.

[0020] Compared with the prior art, the above-mentioned technical solutions provided in this application have the following advantages: This application provides a branch cutting method and device for accelerating the solution of power system safety constraint unit combination. In this scheme, during the branch-and-bound process, if the solver finds that the relaxation problem of the target node is unsolvable, it no longer simply performs single-point pruning. Instead, it constructs a network constraint minimum violation model. If the unsolvability is found to be due to network constraints, a globally feasible cut is generated using the Lagrange multipliers at the optimal solution. This globally feasible cut represents the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem. After the globally feasible cut is added to the cut pool of the branch-and-bound process, it can be used to prune infeasible solutions of similar specific unit combination modes. In this way, a large number of repeated invalid explorations are avoided in the branch-and-bound process, thereby greatly accelerating the solution and ensuring the safety and economy of power grid dispatch. Furthermore, this application uses Lagrange duality theory to extract specific unit combination modes that lead to infeasibility and generates a globally feasible cut that can exclude specific unit combination modes. The globally feasible cut is strictly based on strong duality theory, ensuring that feasible or optimal solutions are not erroneously removed, fundamentally guaranteeing the feasibility and optimality of the SCUC solution results. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0024] Figure 1 This is a schematic flowchart of a branch cutting method for accelerating the solution of power system safety constraint unit combination provided in an embodiment of this application;

[0025] Figure 2 This is a schematic diagram of the system topology provided in the embodiments of this application;

[0026] Figure 3 A branch-delimiter decision tree provided in this application embodiment;

[0027] Figure 4This is a schematic diagram of a branch cutting device for accelerating the solution of power system safety constraint unit combination, provided in an embodiment of this application. Detailed Implementation

[0028] This specific embodiment is merely an explanation of this application and is not intended to limit it. After reading this specification, those skilled in the art can make modifications to this embodiment without contributing any inventive step, but such modifications are protected by patent law as long as they are within the scope of this application.

[0029] It should be noted that, in the optional embodiments of this application, the data related to object information, when applied to specific products or technologies, requires the permission or consent of the object. Furthermore, the collection, use, and processing of this data must comply with the relevant laws, regulations, and standards of the relevant countries and regions. In other words, if the embodiments of this application involve data related to an object, it must be obtained with the object's authorization and consent, the authorization and consent of relevant departments, and in accordance with the relevant laws, regulations, and standards of the country and region. If the embodiments involve personal information, the acquisition of all personal information requires the individual's consent. If sensitive information is involved, the separate consent of the information subject is required. The embodiments also need to be implemented with the object's authorization and consent.

[0030] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Furthermore, the term "and / or" in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship. To better understand and illustrate the solutions of the embodiments of this application, some technical terms involved in the embodiments of this application are briefly explained below.

[0032] Security Constrained Unit Commitment (SCUC): This is a core optimization problem in day-ahead power system dispatching planning. It involves determining the start-up and shutdown status and output level of each generating unit while meeting system operating constraints, in order to minimize system operating costs. Abbreviated as SCUC.

[0033] Branch and bound algorithm: Branch and bound is a classic algorithm for integer programming problems. It finds the optimal solution by systematically exploring all branches of candidate solutions and using upper and lower bound information for pruning. Abbreviated as B&B.

[0034] Branch and Cut: The Branch and Cut method is a mixed-integer programming solution that introduces cutting plane technology based on the Branch and Bound (B&C) method. It is the core framework of modern commercial solvers. Abbreviated as B&C.

[0035] Linear Programming Relaxation (LP relaxation) refers to the process of relaxing the integer variable constraints in a mixed integer programming problem into continuous variable constraints, resulting in a linear programming problem.

[0036] Infeasible optimization problem: An infeasible optimization problem means that there are contradictions in the constraints of the optimization problem, and it is impossible to find a solution that satisfies all the constraints.

[0037] Network constraints: Network constraints refer to the physical constraints of the power system's transmission network, mainly referring to the limitations on line transmission capacity, and are key constraints in the SCUC problem.

[0038] Specifically, Security-Constrained Unit Combination (SCUC) is a core optimization problem for electricity market clearing and day-ahead dispatching. It requires optimizing the start-up and shutdown status and output plan of each generating unit while satisfying various system operating constraints, in order to minimize system operating costs. SCUC is essentially a large-scale mixed-integer linear programming (MILP) problem, containing numerous binary variables (unit start-up and shutdown status) and continuous variables (unit output), as well as complex constraints (unit operation constraints, network transmission constraints, reserve constraints, etc.).

[0039] In real-world power systems, the SCUC problem is extremely large in scale. Taking a provincial power grid as an example, its day-ahead spot market clearing model (SCUC) contains nearly 200,000 decision variables, including nearly 3,000 integer variables, facing a considerable optimization challenge, especially under severe network congestion, where congestion removal becomes the most time-consuming computational step. The day-ahead market of a System Independent Operator (MISO) requires optimizing the operating plans of approximately 1,000 generating units over 24 time periods, involving hundreds of thousands of variables and constraints. Each system operator has strict requirements for solution time and accuracy; for example, a provincial power market requires a solution with 1% gap within 900 seconds, while the MISO requires a solution with 0.1% gap within 1,200 seconds.

[0040] Existing operations research optimization methods for solving SCUC (Simplified Chinese Programming Complexity) problems are mainly based on the Branch-and-Cut (B&C) algorithm framework. The B&C algorithm is a core technology of modern commercial solvers (such as Gurobi and CPLEX), finding the optimal solution by systematically exploring the integer solution space and combining it with the cutting plane technique. In the B&C process, the algorithm solves a linear programming (LP) relaxation problem at each node, performs branching operations based on the relaxed solution, and forms a search tree. However, when the system network constraints are tight, the LP relaxation problems of many nodes may become infeasible due to network constraints, leading to a large number of invalid searches and severely impacting the solution efficiency.

[0041] Regarding the efficiency problem in solving SCUC, existing acceleration methods based on B&C theory mainly fall into two categories:

[0042] (1) Heuristic method: In the first scheme, for the SCUC problem that is prone to line congestion, the contribution of the units to line congestion is calculated and ranked to solve the induced problem with most integer variables fixed, aiming to obtain a better feasible solution and thus accelerate the reduction of the upper bound in the B&C process. Although this method can improve the upper bound and accelerate convergence, its effectiveness depends heavily on the SCUC modeling characteristics because the SCUC objective function it constructs contains network constraint over-limit relaxation, and it cannot be applied to general SCUC solutions. In the second scheme, the relaxation reinforcement neighborhood search algorithm or metaheuristic algorithm can be adaptively selected according to the difference between the root node relaxation solution and the optimal solution, and the solution process can be accelerated by dynamically adjusting the search strategy. Although this method can intelligently select the appropriate algorithm according to the problem characteristics, the judgment of the quality of the relaxation solution depends on the preset threshold, and it degenerates into the traditional metaheuristic algorithm when the quality of the relaxation solution is poor, which may get stuck in local optima and make it difficult to guarantee the optimality of the result.

[0043] (2) Cutting Plane Method: In one approach, a pricing subproblem is defined and a cutting plane constraint for a single unit is generated and added to the original model to enhance its compactness, thereby improving the quality of linear relaxation and accelerating the solution process. Essentially, this is a more compact modeling method centered around unit operation constraints, without improving the B&C process. In another approach, infeasible discrete variable combinations can be generated by setting a threshold and rounding the relaxation solution, and a feasible cutting plane can be constructed to eliminate invalid search spaces. While this method effectively avoids repeated searches of infeasible regions, the setting of the rounding threshold lacks rigorous theoretical basis, and the generation of feasible cuts occurs during the modeling phase, without utilizing solution information to improve the algorithm during the B&C process.

[0044] The shortcomings of the aforementioned prior art are as follows.

[0045] (1) Fundamental defects of heuristic methods: Heuristic acceleration methods essentially sacrifice optimality for solution speed. Since these methods are based on empirical rules or local search strategies, their performance is highly dependent on the specific problem instance. On the one hand, there are parameter sensitivity issues, such as the threshold setting in the second scheme, where key parameters require extensive experimental adjustment and may need recalibration under different system scales and load levels. Inappropriate parameter selection can severely affect algorithm performance and even lead to solution failure. On the other hand, there is insufficient scalability and generalization ability. For example, the first scheme heavily relies on specific SCUC modeling features (the objective function includes network constraint relaxation), limiting its application scope. More importantly, these methods lack theoretical guarantees and cannot ensure the quality of the found solution. When the quality of the relaxed solution is poor or the system network constraints are complex, neighborhood search may get trapped in local optima, and variable-fixed strategies may exclude the global optimum, which poses a risk in power system dispatching requiring high reliability.

[0046] (2) Limitations of the existing cutting plane method: The current cutting plane method is essentially focused on the SCUC modeling stage, paying attention to the strengthening of individual unit constraints, improving the description of the feasible region of unit operation by adding various effective inequalities, and removing infeasible unit start-up and shutdown states by adding cutting planes before solving. The current method has the following two key problems.

[0047] First, existing methods fail to deeply engage in the branch and bound (B&C) solution process, thus offering limited improvement to the core efficiency of the algorithm. When encountering infeasible linear programming (LP) relaxation problems, current methods merely employ simple pruning strategies, failing to fully exploit the deeper information inherent in the infeasibility. In fact, the infeasibility of LP relaxation problems reveals the global infeasibility characteristics of relevant decision variable combinations. Effective extraction and utilization of this information would significantly accelerate the subsequent search process.

[0048] Secondly, existing methods lack a systematic exploration and utilization of the inherent physical characteristics of the SCUC problem. Of particular concern is the neglect of the systematic characteristics manifested in network constraint violations during the B&C solution process. Power system network constraints not only have explicit physical meaning but also contain unique mathematical structures. When specific unit start-up and shutdown combinations lead to network constraint violations, this infeasibility typically exhibits structured propagation characteristics: it not only affects the current search node but may also render all nodes containing the same or similar unit start-up and shutdown patterns infeasible. However, existing methods fail to effectively identify and utilize this crucial characteristic, causing the algorithm to repeatedly encounter essentially the same infeasibility in different branches of the search tree. Each time, feasibility assessments and pruning operations are required, resulting in a large amount of redundant computation and severely limiting the improvement of solution efficiency.

[0049] Therefore, in this scheme, to address the problem of low efficiency of current solvers in solving large-scale SCUC problems, a method for accelerating SCUC solutions that considers global feasible cut generation and embedded branch and bound is proposed. By mining and utilizing the information of infeasible node LP relaxation problems in the branch and bound process, the network constraint violation characteristics are analyzed. Based on Lagrange duality theory, a global feasible cut is constructed and embedded into the branch and bound solution framework, which significantly reduces the search space, accelerates the convergence process, and achieves efficient solution of SCUC problems.

[0050] In this embodiment, to facilitate understanding of the SCUC model and relaxation problem, power dispatch is used as an example to explain the SCUC model and relaxation problem.

[0051] First, the SCUC model is designed to solve the "safety-constrained generator unit combination" problem. Simply put, it determines which generator units to start and which to shut down (a yes / no integer decision) and how much electricity each unit generates (a continuous variable decision) while meeting the city's electricity demand for tomorrow and ensuring grid safety (e.g., preventing line overload), in order to minimize the total generation cost. This complex problem is the SCUC model. The SCUC model represents a unique and complete problem that needs to be solved; it is predetermined and fixed throughout the entire solution.

[0052] Secondly, the branch and bound method is an intelligent trial and error process for eliminating solutions. Simply put, since the SCUC model is too complex to be solved directly, the branch and bound method is like an intelligent trial and error system, and its process is as follows.

[0053] Step 1: Relaxing the Difficult Problem for Quick Estimation: Temporarily ignore the most difficult integer constraint—that the units must be either on or off—allowing the units to be in a illusory "partially on, partially off" state (e.g., 0.3 units operating). This transforms a complex mixed-integer problem into a simple linear programming problem involving only continuous variables. In this trial-and-error system, whenever a possible scheduling scenario (i.e., a branch node) is considered in depth, such a relaxed linear programming problem is established and solved; this linear programming problem is known as the relaxation problem.

[0054] Step 2: Analyze the estimation results: Calculate the minimum cost of this "half-on, half-off" solution (relaxation problem). This cost value has two key references: Ideal lower bound: Because the constraints are relaxed, this cost is the best (lowest) level that can be achieved in this scenario, the "ideal version" of the real-world cost. Problem identification: If, in the calculated optimal solution, some units are still "half-on, half-off" (not 0 or 1), then this solution is not feasible in reality and needs to be addressed.

[0055] Step 3: Branching and Bounding: Branching: For scenarios involving units that are "partially on and partially off," we conduct "case-by-case discussions." For example, for Unit 1, we create two new scenario nodes: one that forces it to be on (=1), and another that forces it to be off (=0). Then, we perform the "relaxation estimation" (i.e., solving new relaxation problems) from Step 1 again for these two new nodes. Bounding: Throughout the process, we record the best cost among all feasible solutions that meet the integer requirement (i.e., all units are explicitly on or off). When the calculated "ideal cost" of a node (relaxation problem) is worse than the "best realistic cost" we have, it means that no better realistic solution can be found for any scenario represented by this node, and we can directly stop exploring this branch, greatly saving computation.

[0056] As can be seen, the node relaxation problem in this application is dynamically generated. It is a temporary linear relaxation model automatically created by the branch and bound algorithm for each searched node during the solution of the SCUC model. Each relaxation problem originates from the SCUC model, but relaxes the integer constraints and inherits some decision constraints from its parent node. The fixed unit start-up and shutdown situations are different for different nodes.

[0057] Therefore, the generation and solution of relaxation problems is the core automatic process of the branch and bound algorithm. The solution acceleration scheme provided in this paper is embedded in this process. By intelligently utilizing the information provided by these automatically generated relaxation problem models (such as the structure of their solutions), the algorithm is guided to search more efficiently, thereby solving the original SCUC model faster.

[0058] In this application, the nodes in the branch and bound search tree represent each "partially determined scheduling scheme to be analyzed" within the branch and bound "intelligent trial and error elimination system." Each node corresponds to an optimization problem (relaxation problem). It records which generator sets have been forcibly "turned on" or "turned off" so far.

[0059] The search tree starts at the root node, representing the initial state where no mandatory on / off decisions have been made for any units. Solving the relaxation problem at this point is a fully relaxed problem that allows all units to be "half-on, half-off." The process of creating child nodes (branching) occurs when a node's relaxation solution shows unit 1 as "half-on, half-off" (0.3), which is unacceptable. Therefore, a "case-by-case discussion" is performed: Node A (left child): inherits all existing decisions from its parent node and adds a new decision: force unit 1 to start (=1). Node B (right child): inherits all existing decisions from its parent node and adds a new decision: force unit 1 to shut down (=0). Thus, nodes A and B represent two more specific and constrained scheduling scenarios. Nodes A and B then correspond to new optimization problems P2_A and P2_B, respectively. The tree growth process continues indefinitely. Each node represents a decision path. For example, a deep node might mean "It has been decided: Unit 1 is turned on, Unit 2 is turned off, Unit 3 is turned on... Now please analyze how to optimally arrange the remaining units under this premise."

[0060] See Figure 1 This is a schematic flowchart of a branching method for accelerating the solution of power system safety constraint unit combinations, provided in an embodiment of this application. The branching method is applied to the solver and includes:

[0061] S101. Determine the SCUC model of the power system to be solved.

[0062] This application discloses a solution scheme for the safety constraint unit combination of power systems. Based on this scheme, a globally feasible cut embedded branch and bound SCUC acceleration framework is designed and integrated as a plug-in into an open-source solver. In the branch and bound node processing flow, it triggers the complete algorithm flow of building the minimum violation model of network constraints, generating and adding global cuts, and achieving compatibility and integration with existing open-source solvers. This results in a substantial acceleration of the solution of SCUC problems, which is particularly suitable for large-scale power systems with severe network congestion and provides strong technical support for meeting market clearing time requirements.

[0063] Therefore, in this application, the entity executing the above solution scheme is the solver. When solving the SCUC model of the power system, the solver improves the solution efficiency through the integrated SCUC acceleration framework, thereby ensuring the safety and economy of the power grid system.

[0064] Specifically, the SCUC (Safety Constrained Unit Combination) model to be solved in this application is a pre-constructed SCUC model derived from the actual physical requirements of the power system (load forecasting, unit parameters, network topology, etc.), which is the ultimate goal to be solved. It remains fixed in this scheme and is input into the solver.

[0065] To facilitate the explanation of this scheme, a compact SCUC optimization model is established as an example. This SCUC model aims to minimize the total system operating cost, comprehensively considering unit operating constraints and system hierarchical constraints. The SCUC model includes:

[0066]

[0067] The objective function of the SCUC model is Equation (1), which represents minimizing the total system operating cost, including the unit power generation cost. and start-up / stop costs ;in, This is the vector of unit output variables; This is the unit start-up and shutdown variable vector; This is a matrix of power generation cost coefficients. The start-up and shutdown cost coefficient matrix; the constraint formula (2) of the constraint conditions includes the unit operation constraints (segmented linear output boundary constraints, output and segmented variable relationship constraints and output upper and lower limit constraints) and system level constraints (power balance constraints and network constraints) that SCUC needs to consider. , , The corresponding coefficient matrix; where the coefficient matrices of the SCUC model in this application, and the coefficient matrices of the relaxation problem for each node, are all marked with a sign in the upper right corner ( This symbol does not have any practical meaning; its function is to distinguish the coefficient matrices in the SCUC model and the relaxation problem of each node from the coefficient matrices in the network constraint minimum violation model. Constraint formula (3) is a 0-1 variable constraint, indicating that... The i-th element It is a binary variable consisting of 0 and 1. This is the set of indices for all binary variables.

[0068] This application refers to the SCUC model composed of formulas (1) and (3) as... Its decision variables are: unit output variable vector. Unit start-up and shutdown variable vector .

[0069] S102. Solve the relaxation problem for each node during the branch and bound process; wherein the relaxation problem for each node is determined based on the SCUC model.

[0070] In this application, for each node explored during branch and bound, a node LP relaxation problem needs to be solved. In this embodiment, the LP relaxation problem that needs to be solved for each search tree node during the branch and bound process may include:

[0071]

[0072] in, and Let represent the sets of binary variable indices that are fixed to 1 and 0 respectively through the branch operation at the current node. Constraint formulas (6) and (7) respectively indicate that the relevant variables are fixed to 1 and 0 in the branch, and constraint formula (8) indicates the upper and lower bound constraints that the unfixed binary variables must satisfy. In this embodiment, the node LP relaxation problem composed of formulas (4)-(8) is called . .

[0073] If a node is found to be infeasible in the LP relaxation problem, i.e., there is no solution, then that node is treated as the target node. In traditional schemes, the B&C method simply prunes the node, while in this application, the reasons for infeasibility are further analyzed, especially identifying whether the infeasibility is caused by network constraints.

[0074] S103. If the relaxation problem of the target node has no solution, then construct a network constraint minimum violation model based on the relaxation problem of the target node.

[0075] S104. Solve the network constraint minimum violation model to determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model.

[0076] It should be noted that if the relaxation problem of the target node is unsolvable, this application needs to construct a network constraint minimum violation model based on the relaxation problem of the target node, and determine whether the reason for the unsolvability is network constraint after solving it.

[0077] Specifically, the network constraint minimum violation model is not pre-defined, but dynamically constructed during the branch and bound algorithm's execution. Its construction depends entirely on the specific data of the LP relaxation problem corresponding to the target node currently being processed, which is being pruned due to network constraint violations. That is, when solving the relaxation problem corresponding to the target node and finding it infeasible (i.e., without a solution), a new model aimed at "minimizing the violation" is generated in real-time based on the relaxation problem's data and constraint information. This new model is the network constraint minimum violation model, from which dual information is extracted to generate globally feasible cuts.

[0078] Optionally, the process of constructing a network constraint minimum violation model based on the relaxation problem of the target node in this embodiment includes: constructing a network constraint minimum violation model based on the relaxation problem of the target node, wherein the network constraint minimum violation model is constructed as a linear programming problem, and the network constraint minimum violation model includes: an objective function and various constraints, wherein the constraints include: unit operation constraints after removing network constraints, equality constraints, and inequality constraints, and each constraint has a corresponding Lagrange multiplier vector. Specifically, to accurately identify the root causes of network constraint infeasibility, the following network constraint minimum violation model is constructed, and the objective function in the network constraint minimum violation model is:

[0079] (9)

[0080] in, It is a column vector whose elements are all 1s. This represents the upper limit slack for the positive power flow of each line. This represents the upper limit slack for the reverse power flow of each line. The objective function value, This represents the sum of the upper limit slack for power flow across all routes. This indicates taking the transpose of the vector.

[0081] The unit operation constraints for removing network constraints are:

[0082] (10)

[0083] in, This is the first coefficient matrix. This is the second coefficient matrix. This is the third coefficient matrix. For the active contribution of each unit, For the start-up and shutdown state variables of each unit in the network constraint minimum violation model; is the first Lagrange multiplier vector; the active power output of each unit, the start-stop state variables of each unit, the upper limit slack of the forward power flow, and the upper limit slack of the reverse power flow are all column vectors.

[0084] It should be noted that in this invention, the symbols marked by colons after each constraint represent the Lagrange multipliers corresponding to that constraint. The bolded form represents a Lagrange multiplier vector, and each element within this vector is called a Lagrange multiplier. This is a professional notation in the field of mathematical optimization. Lagrange multipliers are auxiliary variables in optimization theory, reflecting the marginal influence of the corresponding constraint on the optimal objective function value; that is, the change in the optimal objective function value when the right-hand side of the constraint is relaxed by one unit. The equality constraint is:

[0085] (11)

[0086] (12)

[0087] in, For unit indexing, for The Middle Start-up and shutdown status variables of individual generating units 1 indicates the first Each unit is started. 0 indicates the first One unit was shut down; This is the set of binary variable indices that are fixed to 1 at the current node through a branch operation. For the second Lagrange multiplier, express The multipliers corresponding to the equality constraints of the start-stop state variables of the unit, which are fixed at 1. This is the set of binary variable indices that are fixed to 0 at the current node through a branch operation. It is the third Lagrange multiplier. express The multiplier corresponding to the equality constraint of the start-stop state variables of the unit that is fixed at 0.

[0088] The inequality constraint is:

[0089] (13)

[0090] (14)

[0091] (15)

[0092] (16)

[0093] (17)

[0094] in, For the set of all binary variable indices, It is the fourth Lagrange multiplier. express The multipliers corresponding to the inequality constraints on the upper limit of the start-stop state variables of the units that are not fixed. It is the fifth Lagrange multiplier. express The multiplier corresponding to the lower bound inequality constraint of the start-stop state variables of the unit that is not fixed; The power transfer distribution factor matrix, For load vector, This is the vector representing the upper limit of line transmission capacity. It is the sixth Lagrange multiplier vector. It is the seventh Lagrange multiplier vector.

[0095] in, For the positive power flow capacity constraint of the line. For negative power flow capacity constraints, these two constraints mean that the power flow (forward or reverse) of each line should not exceed its capacity limit. Introducing slack variables allows for a certain degree of... , Exceeding the limit.

[0096] It should be noted that the network constraint minimum violation model aims to minimize the total violation of network constraints. The optimization variables of the network constraint minimum violation model include: the active power output of each unit. Start-up and shutdown status variables of each unit Upper limit slack of positive power flow for each route Upper limit slack of reverse current flow for each line All four types of optimization variables are column vectors, such as the l-th component of the relaxation vector. and These represent the slack values ​​for the upper limits of the forward and reverse power flow of the l-th line, respectively. The power transfer distribution factor matrix, For load vector, Let be the upper limit vector of line transmission capacity. Constraint formula (10) represents the constraint after removing the network constraint from constraint formula (2). Constraint formulas (15) and (16) represent the network constraints after relaxing the upper and lower limits of the line, respectively. Constraint formula (17) is the constraint condition for the relaxed variable. For the Lagrange multipliers corresponding to the inequality constraints, Let be the Lagrange multiplier corresponding to the equality constraint. Let the network constraint minimum violation model constructed from equations (9) to (17) be . , for The objective function value corresponding to the optimal solution, and the Lagrange multipliers at the optimal solution are: .

[0097] In this application, bold text represents vectors or matrices, and non-bold text represents scalars, i.e., the element values ​​of vectors. Furthermore, the objective function is only related to slack variables. , Directly related, reflecting the degree of relaxation of network constraints, but the optimal value of the objective function is determined by all constraints. The Lagrange multipliers corresponding to the above constraints are used to generate subsequent feasible cuts.

[0098] Optionally, this application solves the network constraint minimum violation model to determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model, including: determining the optimization variables of the network constraint minimum violation model; wherein, the optimization variables include: the active power output of each unit, the start-up and shutdown state variables of each unit, the upper limit slack of the forward power flow of each line, and the upper limit slack of the reverse power flow of each line; determining the optimal solution of each optimization variable at the point where it satisfies each constraint and the function value calculated by the objective function is minimized, thereby obtaining the objective function value at the optimal solution; determining the Lagrange multiplier vector of each constraint at the optimal solution, wherein the Lagrange multiplier vector of each constraint is used to represent the marginal influence of each constraint on the objective function value at the optimal solution.

[0099] Specifically, the network constraint minimum violation model construction in this application is a linear programming problem. Linear programming refers to finding the maximum or minimum value of a linear objective function under a set of linear constraints. Linear programming problems can be directly solved by a solver, which is a generally accepted approach in the industry. Therefore, this application can directly solve the network constraint minimum violation model using a solver based on the simplex method or interior point method, such as Gurobi or CPLEX. The solver can directly obtain the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model. The solution principle can be understood as follows: Determine the optimization variables of the network constraint minimum violation model, and determine the optimal solution where each optimization variable satisfies all constraints and the function value calculated by the objective function is minimized. This optimal solution represents the value of each optimization variable found by the network constraint minimum violation model that satisfies two conditions: first, the current value of each optimization variable satisfies all constraints; second, based on the forward power flow upper limit relaxation and the reverse power flow upper limit relaxation of each line in the current optimization variables, and the objective function, the calculated function value is the minimum value. That is, when the values ​​of each optimization variable are other values, the calculated function value is greater than the function value at the optimal solution. This application refers to the function value calculated at the optimal solution as the objective function value.

[0100] It should be noted that the above two conditions are mutually influential. For example, when changing the start-stop state variables of each unit, the active power output of each unit is changed by formula (10). After the active power output of each unit changes, the upper limit relaxation of the forward power flow and the upper limit relaxation of the reverse power flow of each line can be determined by formula (15) and formula (16). Then, based on the upper limit relaxation of the forward power flow and the upper limit relaxation of the reverse power flow of each line, the new function value can be determined by formula (9). Then, the start-stop state variables of each unit are changed again, and the new function value is determined again by the above process. After multiple calculations, it is checked which value of the start-stop state variables of each unit has the smallest function value. After finding the smallest function value, the optimal solution of the network constraint minimum violation model can be determined, and the objective function value is obtained.

[0101] Meanwhile, during the solution process, it is also necessary to determine the Lagrange multiplier vectors of each constraint at the optimal solution. The Lagrange multiplier vectors of each constraint are used to represent the marginal influence of each constraint on the objective function value at the optimal solution. That is, when the right-hand side of the constraint is relaxed by one unit, the change in the optimal objective function value is the Lagrange multiplier. Furthermore, the number of elements in the Lagrange multiplier vector corresponds to the number of units. Here, we will only use formulas (11) and (12) as examples for explanation: If there are 6 units, each Lagrange multiplier vector contains 6 elements. At a certain node, through formulas (11) and (12), the start-stop state variables of the first and second units are fixed at 1, and the start-stop state variables of the third unit are fixed at 0. Then, in the generated second Lagrange multiplier vector, only the first and second elements have a value of 1, while the values ​​of the remaining elements are all zero. In the generated third Lagrange multiplier vector, only the third element has a value of 1, while the values ​​of the remaining elements are all zero.

[0102] Based on the optimal solution of the minimum violation model of network constraints, this application can determine the value of s in constraint formulas (15) and (16). The elements in the slack variable vector s are either 0 or greater than 0. For example, if the 6th element is greater than 0, it means that the 6th path in the corresponding network constraint formula (15) or (16) is not feasible. The reason is that this model introduces a slack variable vector. and This is used to quantify the power flow violation limits for each line. In the optimal solution, each component of the s vector (e.g., the k-th component) or The value of ) directly indicates the violation status of the corresponding line: if =0 and =0: This indicates that on the k-th path, the power flow fully satisfies the safety constraints, and there are no violations. If >0 or >0: This clearly indicates that the power flow has exceeded the limit on the k-th line, which is a key constraint that makes the entire system infeasible at this node.

[0103] Therefore, this application can accurately pinpoint the specific lines causing infeasibility by simply examining the non-zero elements of the s vector in the optimal solution, thereby identifying the root cause of network constraint conflicts. Thus, the network constraint violation feature analysis method for the node LP relaxation problem proposed in this scheme, by constructing a network constraint minimum violation model, can accurately quantify and analyze the degree of network constraint violation when node LP relaxation is infeasible, precisely identify the network constraints causing infeasibility, and generate a globally feasible cut. This allows for the direct removal of infeasible solutions for specific unit combination modes that subsequently exhibit similar globally feasible cuts.

[0104] S105. If the reason for the unsolvability of the target node is determined to be network constraint through the objective function value, then according to the Lagrange duality theory, a globally feasible cut is generated based on the Lagrange multiplier at the optimal solution; wherein, the globally feasible cut is the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem.

[0105] In this application, determining that the reason for the unsolvability of the target node is a network constraint based on the objective function value includes: determining whether the objective function value is greater than zero; if so, determining that the reason for the unsolvability of the target node is a network constraint.

[0106] In other words: if Then, a globally feasible cut for SCUC branch and bound is generated. In this application, based on Lagrange duality theory, a globally feasible cut is generated based on the Lagrange multipliers at the optimal solution, including: obtaining the Lagrange multiplier vector at the optimal solution of the network constraint minimum violation model; and determining the globally feasible cut based on the Lagrange multiplier vector at the optimal solution, the globally feasible cut determination rule, and the coefficient determination rule.

[0107] In this application, the rule for determining the globally feasible cut is as follows:

[0108] (18)

[0109] in, As the first coefficient, Let be the unit start-up and shutdown variable vector in the SCUC model. This is the second coefficient.

[0110] Among them, coefficient The rules for determining the coefficients that must be satisfied are as follows:

[0111] (19)

[0112] (20)

[0113] in, Let be the second Lagrange multiplier vector at the optimal solution. Let be the third Lagrange multiplier vector at the optimal solution. Let be the first Lagrange multiplier vector at the optimal solution. This is the third coefficient matrix. The sixth Lagrange multiplier vector at the optimal solution. The seventh Lagrange multiplier vector at the optimal solution. This is the vector representing the upper limit of line transmission capacity. The power transfer distribution factor matrix, For load vector, Let be the fourth Lagrange multiplier vector at the optimal solution.

[0114] It should be noted that the unit start-up and shutdown variable vector in the global feasible cut is not the same variable as the unit start-up and shutdown variable vector in the network constraint minimum violation model. This is because the unit start-up and shutdown variable vector in the network constraint minimum violation model is no longer a variable after being solved, but a constant value; while the unit start-up and shutdown variable vector in the feasible cut here is consistent with formulas (1) to (3) of the SCUC model, and is a variable, not a constant. That is, this application constructs a feasible cut by solving the network constraint minimum violation model, and the variable of this cut is... These are the unit start-up and shutdown variables in formulas (1) to (3) for the SCUC model.

[0115] As can be seen, this application provides a global feasible cut generation method. Based on the strong duality theorem, this scheme extracts key information from the optimal solution and Lagrange multipliers of the network constraint minimum violation model, and constructs a globally effective inequality that can cut off all the specific infeasible unit combination modes. The specific form of the global cut is formula (18), and the coefficient calculation method is formula (19)-formula (20).

[0116] S106. Add the globally feasible cut to the branch-bound cut pool and prune nodes that do not satisfy the globally feasible cut.

[0117] S107. After the branch delimitation is completed, the unit combination result is obtained.

[0118] As can be seen, this application constructs an SCUC model, and after inputting it into the solver, the branch and bound explores each node and solves the LP relaxation problem of each node. If the relaxation problem is not feasible, the network constraint minimum violation model is constructed, and the optimal objective function value and optimal multiplier are obtained after solving it. If the objective function value > 0, the global feasible cut is generated according to formula (18)-formula (20), and the global feasible cut is added to the cut pool of the branch and bound to cut off the infeasible solutions of subsequent similar specific unit combination modes.

[0119] For example: if the relaxation problem is infeasible at a certain node, a cut is generated based on the constructed network constraint minimum violation model. ( , (All variables are 0-1). That is, a "specific unit combination pattern" is found that leads to grid line overload (i.e., infeasibility): when Unit 1 and Unit 5 are started simultaneously, regardless of adjustments to other units, a critical transmission line will inevitably exceed its power limit. In this case, the solution will not simply discard this node, but will generate a globally feasible cut. Its logical essence is like a new "safety rule" added to the entire search process: "Units 1 and 5 must not be started simultaneously." Subsequently, in subsequent branch-and-bound searches, regardless of which new node is explored, as long as the solver finds that the unit start-up / shutdown decision of that node triggers this "safety rule" (i.e., attempting to start Units 1 and 5 simultaneously), it will directly skip that node because it knows this combination is a "dead end." This avoids repeatedly calculating and wasting time verifying the same pattern that has already been proven infeasible in different branches of the search tree, thus greatly accelerating the solution. This is what is known as "pruning."

[0120] In summary, this application aims to overcome the shortcomings of existing technologies by proposing a unit combination acceleration method based on global feasible cut generation and embedded branch and bound. Addressing the issues that existing cutting plane methods fail to intervene in the B&C solution process and lack systematic utilization of the physical characteristics of the SCUC problem, this application utilizes network constraint violation information from the LP relaxation problem during the B&C process. When a node becomes infeasible due to network constraints, instead of simple single-point pruning, a minimum network constraint violation LP model is constructed. Through Lagrange duality theory, the unit start-up and shutdown combination patterns leading to infeasibility are extracted, generating a globally feasible cut that can exclude similar specific infeasible patterns, thereby avoiding a large amount of repetitive and ineffective exploration during the B&C process.

[0121] It is worth noting that the globally feasible cut constructed in this application is strictly based on strong duality theory, ensuring that feasible or optimal solutions are not erroneously cut off, thus fundamentally guaranteeing the feasibility and optimality of the SCUC solution. Furthermore, this application designs a SCUC acceleration framework with embedded branch and bound in the globally feasible cut, which can be integrated as a plugin into open-source solvers to achieve substantial acceleration of SCUC problem solving. This is particularly suitable for large-scale power systems with severe network congestion, providing strong technical support for meeting market clearing time requirements.

[0122] To facilitate understanding of this solution, a specific embodiment is provided here to explain and illustrate it, which specifically includes the following process.

[0123] See Figure 2 This is a schematic diagram of the system topology provided in an embodiment of this application. This embodiment uses a case study system of 6 units-2 loads-3 lines to illustrate the effectiveness of the proposed globally feasible cut. Figure 2 As shown, the system comprises six generator sets: Unit 1 (G1), Unit 2 (G2), Unit 3 (G3), Unit 4 (G4), Unit 5 (G5), and Unit 6 (G6). The system includes two loads: Load 1 (Load1) and Load 2 (Load2). Load 1 has a capacity of 20 MW, and Load 2 has a capacity of 510 MW. The system is interconnected via transmission lines. The transmission capacity of Line 1 is limited to 115 MW, the transmission capacity of Line 2 is limited to 260 MW, and the transmission capacity of Line 3 is limited to 165 MW. See Table 1 for the generator set parameter information provided in this embodiment.

[0124] Table 1

[0125]

[0126] In this embodiment, the branch and bound process employs a depth-first search strategy for node selection and a minimum score strategy for branching variables during branch operations. Specifically, at each node, the algorithm prioritizes selecting nodes that satisfy the minimum score requirement. Conditional binary variables Branching, where, To obtain a continuous solution value (between 0 and 1) after solving the LP relaxation at the current node, we select the variable with the smallest decimal part that is closest to 0 or 1 in the current solution. Then, we determine whether the current solution is closer to 0 or 1 based on whether this variable is closer to 0 or 1. and The priority of exploration is determined, thereby systematically advancing the search process for integers.

[0127] Based on system parameter information, it is possible to construct It includes the following content.

[0128] Objective function: .

[0129] in, ;

[0130] ;

[0131] ;in, This represents the power value of the i-th unit in the j-th output segment, such as: The elements in the vector represent the power value of the first unit in the first output segment. Represents the total output of the i-th unit, such as This is the total output of the first unit.

[0132] The objective function corresponds to formula (1) above.

[0133] Piecewise linear output boundary constraints:

[0134] ;in, This represents the maximum power value of the i-th unit in the j-th output segment.

[0135] Constraints on the relationship between output and piecewise variables:

[0136] ;

[0137] Output upper and lower limit constraints:

[0138] ;

[0139] Power balance constraints:

[0140] ;

[0141] Network constraints:

[0142] ;

[0143] The piecewise linear output boundary constraints, output and piecewise variable relationship constraints, output upper and lower limit constraints, power balance constraints and network constraints correspond to all the constraints in formula (2) above.

[0144] 0-1 variable constraints:

[0145] ;

[0146] This constraint corresponds to formula (3) above.

[0147] Then The model is input into the solver, and the global cut generation method proposed in this paper is embedded into the solver to obtain a branch and bound decision tree. See [link to relevant documentation]. Figure 3 Figure 1 shows a branch-and-bound decision tree proposed in this application. Each node in the figure corresponds to an LP problem in the method described in this paper. Model. For example... Figure 3 As shown, after solving LP1, the following results are obtained: And so on, obtaining the values ​​of the start-up and shutdown status variables for each unit at each node. Specifically, the values ​​constructed in LP10... For (and) (Differences have been marked)

[0148] Objective function:

[0149] ;

[0150] in, ;

[0151] ;

[0152] ;

[0153] The objective function corresponds to formula (4) above.

[0154] Piecewise linear output boundary constraints:

[0155] ;

[0156] Constraints on the relationship between output and piecewise variables:

[0157] ;

[0158] Output upper and lower limit constraints:

[0159] ;

[0160] Power balance constraints:

[0161] ;

[0162] Network constraints:

[0163] ;

[0164] Among them, the piecewise linear output boundary constraint, the output and piecewise variable relationship constraint, the output upper and lower limit constraint, the power balance constraint, and the network constraint are the constraints corresponding to formula (5) above, and are related to... All constraints are the same.

[0165] Variable constraints:

[0166] ;

[0167] All constraints corresponding to formulas (6) and (7) above.

[0168] ;

[0169] All constraints corresponding to formula (8) above (and) different).

[0170] Solver solves It was found that there was no solution, triggering Build, what is built for:

[0171] Objective function:

[0172] ;

[0173] in , The target formula corresponds to formula (9) above.

[0174] Piecewise linear output boundary constraints:

[0175] ;

[0176] Constraints on the relationship between output and piecewise variables:

[0177] ;

[0178] Output upper and lower limit constraints:

[0179] ;

[0180] Power balance constraints: ;

[0181] Among them, the piecewise linear output boundary constraint, the output and piecewise variable relationship constraint, the output upper and lower limit constraint, and the power balance constraint correspond to all the constraints in formula (10) above.

[0182] Network constraints:

[0183] ;

[0184] The network constraints correspond to all the constraints in formulas (15) and (16) above.

[0185] Variable constraints:

[0186] ;

[0187] All constraints corresponding to formulas (13) and (14) above;

[0188] ;

[0189] All constraints corresponding to formulas (11) and (12) above;

[0190] ;

[0191] All constraints corresponding to formula (17) above.

[0192] Solve According to formulas (18) and (20), the globally feasible cut can be obtained as follows:

[0193] ;

[0194] When solving the branch and bound process up to the linear relaxation problem LP10, which is infeasible, a globally feasible cut is generated based on the proposed method. This cut description When the value is 0, regardless of the start / stop and output of other units, the system cannot meet the network constraints, and the power flow always exceeds the limits. This indicates that ensuring the feasibility of network constraints is crucial. should Add this cut to the subsequent branch and bound process, such as... Figure 3 As shown, in In the right branch, according to the feasible cut It can be seen that, An equal value of 0 necessarily means that the network constraints are infeasible, that is, LP18 has no solution. Therefore, direct pruning is necessary, and thus, the following branches can be effectively pruned: Branch (LP18).

[0195] In summary, the unit combination acceleration method based on global feasible cut generation and embedded branch delimitation proposed in this application has achieved a systematic breakthrough in addressing the shortcomings of existing technologies. Compared with existing technologies, this solution has at least the following beneficial effects.

[0196] Improving Solution Efficiency: This application achieves a fundamental shift from "single-point pruning" to "global exclusion." Traditional B&C methods, when encountering LP relaxation problems where network constraints render them infeasible, only prune the current node. When encountering similar specific unit start-up / shutdown combinations in other branches, the solution and judgment must be repeated. This application, by generating a globally feasible cut, eliminates all search spaces containing specific infeasible patterns at once, fundamentally avoiding redundant exploration. Especially for systems with severe network congestion, this significantly reduces the time to obtain high-quality solutions for large-scale SCUC problems. More importantly, unlike existing cutting plane methods that only add cutting planes during the modeling stage, this application deeply integrates the generation of globally feasible cuts into the core of the B&C solution process, achieving a substantial improvement to the inherent logic of the branch-and-bound algorithm. This deep involvement allows the globally feasible cut to continuously play a role in the search process, constantly strengthening the description of the problem's feasible domain and systematically improving solution efficiency while ensuring solution feasibility.

[0197] Guaranteeing Optimality: This application overcomes the shortcomings of heuristic methods, such as lack of theoretical guarantees and susceptibility to local optima, by deeply engaging in the B&C solution process and establishing rigorous theoretical support. The globally feasible cut constructed based on strong duality and Lagrange duality in this application does not remove any feasible or optimal solutions, which theoretically ensures the feasibility and optimality of the proposed method for solving SCUC.

[0198] This application fully leverages the physical characteristics of the SCUC problem, achieving a deep integration of operations research and optimization with knowledge from the power system domain. By deeply analyzing the systematic characteristics of network constraint violations, it identifies structured infeasibility patterns caused by unit start-up and shutdown combinations. Mathematical representations are extracted using auxiliary LP models and duality theory, transforming infeasibility information discarded after single-point pruning into globally guiding feasible cuts. This approach is particularly effective in systems with severe network congestion, fully utilizing the global characteristics of constraint violations.

[0199] Engineering Application: This application demonstrates excellent engineering feasibility. It can be embedded into existing solvers as callback functions or plugins without modifying the core code, significantly lowering the implementation threshold. The algorithm framework is not limited to specific modeling methods, does not rely on empirical parameters, and maintains stable acceleration effects for power systems of different sizes and characteristics. It is particularly suitable for large-scale systems with complex networks and frequent congestion, providing an effective technical means to meet market clearing time constraints, and can be extended to other mixed-integer programming problems with network constraints.

[0200] In summary, this application, while ensuring optimal solution, also considers solution efficiency, theoretical rigor, and engineering practicality, representing a significant improvement and innovation over existing technologies. It can adapt to large-scale power system scenarios with severe network congestion, providing a theoretically sound and engineering-feasible effective technical means to meet the time requirements for power market clearing.

[0201] The following describes a branch cutting device for accelerating the solution of power system safety constraint unit combination provided by an embodiment of this application. The branch cutting device described below can be referred to in correspondence with the branch cutting method described above.

[0202] See Figure 4 , Figure 4 This application provides a schematic diagram of a branch cutting device for accelerating the solution of power system safety constraint unit combinations. The branch cutting device is applied to the solver and includes:

[0203] The first determining module 11 is used to determine the SCUC model of the power system to be solved;

[0204] The first solution module 12 is used to solve the relaxation problem of each node during the branch and bound process; wherein the relaxation problem of each node is determined based on the SCUC model.

[0205] Module 13 is used to construct a network constraint minimum violation model based on the relaxation problem of the target node if there is no solution to the relaxation problem of the target node.

[0206] The second solution module 14 is used to solve the network constraint minimum violation model and determine the objective function value and Lagrange multiplier at the optimal solution of the network constraint minimum violation model.

[0207] The generation module 15 is used to determine, based on the objective function value, that the reason for the unsolvability of the target node is network constraints, and to generate a globally feasible cut based on the Lagrange multipliers at the optimal solution according to the Lagrange duality theory; wherein, the globally feasible cut is the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem;

[0208] Add module 16 to add the globally feasible cut to the branch delimitation cut pool and prune nodes that do not satisfy the globally feasible cut.

[0209] The second determining module 17 is used to obtain the unit combination result after the branch delimitation is completed.

[0210] In another embodiment of this application, the construction module is specifically used to: construct a network constraint minimum violation model based on the relaxation problem of the target node. The network constraint minimum violation model is constructed as a linear programming problem, and includes: an objective function and various constraints, including: unit operation constraints after removing network constraints, equality constraints, and inequality constraints, and each constraint has a corresponding Lagrange multiplier vector. It should be noted that the specific network constraint minimum violation model can be referred to in the above method embodiment, and will not be elaborated here.

[0211] In another embodiment of this application, the second solution module is specifically used to: determine the optimization variables of the network constraint minimum violation model; wherein, the optimization variables include: the active power output of each unit, the start-stop state variables of each unit, the upper limit relaxation of the forward power flow of each line, and the upper limit relaxation of the reverse power flow of each line; determine the optimal solution of each optimization variable at the point where it satisfies each constraint and the function value calculated by the objective function is minimized, and obtain the objective function value at the optimal solution; determine the Lagrange multiplier vector of each constraint at the optimal solution, wherein the Lagrange multiplier vector of each constraint is used to represent the marginal influence of each constraint on the objective function value at the optimal solution.

[0212] In another embodiment of this application, the generation module includes:

[0213] The judgment unit is used to determine whether the objective function value is greater than zero; if so, it determines that the reason why the objective node has no solution is due to network constraints.

[0214] The acquisition unit is used to acquire the Lagrange multiplier vector at the optimal solution of the network constraint minimum violation model;

[0215] The generation unit is used to determine the globally feasible cut based on the Lagrange multiplier vector at the optimal solution, the global feasible cut determination rule, and the coefficient determination rule. It should be noted that the global feasible cut determination rule and the coefficient determination rule can be referred to in the above method embodiments, and will not be elaborated upon here.

[0216] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. It should be understood that the terminology used herein is for the purpose of describing particular exemplary embodiments only and is not intended to be limiting. Unless the context clearly indicates otherwise, the singular forms “a,” “an,” and “described” used herein may also mean the plural forms. The terms “comprising,” “including,” “containing,” and “having” are inclusive and therefore indicate the presence of the stated features, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, elements, components, and / or combinations thereof. The method steps, processes, and operations described herein are not construed as requiring them to be performed in a specific order described or illustrated, unless the order of performance is explicitly indicated. It should also be understood that additional or alternative steps may be used.

[0217] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0218] The above are only some embodiments of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A branching method for accelerating the solution of power system safety constraint unit combinations, characterized in that, The branch cutting method is applied to the solver, and the branch cutting method includes: Determine the SCUC model of the power system to be solved; The relaxation problem of each node is solved during the branch and bound process; wherein the relaxation problem of each node is determined based on the SCUC model. If the relaxation problem of the target node has no solution, then a network constraint minimum violation model is constructed based on the relaxation problem of the target node; wherein, the objective function in the network constraint minimum violation model is: ;in, It is a column vector whose elements are all 1s. This represents the upper limit slack for the positive power flow of each line. This represents the upper limit slack for the reverse power flow of each line. The objective function value, This represents the sum of the upper limit slack for power flow across all routes. This indicates taking the transpose of the vector; if =0 and =0 indicates that on the k-th path, the power flow satisfies the safety constraints and there are no violations; if >0 or If the value is >0, it indicates that the power flow limit has been exceeded on the kth line, resulting in a critical constraint that has no solution at the target node; Solve the network constraint minimum violation model to determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model; If the reason for the unsolvability of the target node is determined to be network constraint through the objective function value, then according to the Lagrange duality theory, a globally feasible cut is generated based on the Lagrange multipliers at the optimal solution; wherein, the globally feasible cut is the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem; Add the globally feasible cut to the branch-bound cut pool and prune nodes that do not satisfy the globally feasible cut. After the branch delimitation is completed, the unit combination result is obtained; The step of determining that the reason for the unsolvability of the target node is a network constraint based on the objective function value includes: determining whether the objective function value is greater than zero; if so, then determining that the reason for the unsolvability of the target node is a network constraint.

2. The branch cutting method according to claim 1, characterized in that, Based on the relaxation problem of the target node, a network constraint minimum violation model is constructed, including: Based on the relaxation problem of the target node, a network constraint minimum violation model is constructed. The network constraint minimum violation model is constructed as a linear programming problem. The network constraint minimum violation model includes: objective function and various constraints. Each constraint includes: unit operation constraints after removing network constraints, equality constraints and inequality constraints, and each constraint has a corresponding Lagrange multiplier vector.

3. The branch cutting method according to claim 2, characterized in that, The unit operation constraints for removing network constraints are: ； in, This is the first coefficient matrix. This is the second coefficient matrix. This is the third coefficient matrix. For the active contribution of each unit, For the start-up and shutdown state variables of each unit in the network constraint minimum violation model; is the first Lagrange multiplier vector; the active power output of each unit, the start-stop state variables of each unit, the upper limit slack of the forward power flow and the upper limit slack of the reverse power flow are all column vectors; The equality constraint is: ； ； in, For unit indexing, for The Middle Start-up and shutdown status variables of individual generating units 1 indicates the first Each unit is started. 0 indicates the first One unit was shut down; This is the set of binary variable indices that are fixed to 1 at the current node through a branch operation. For the second Lagrange multiplier, express The multipliers corresponding to the equality constraints of the start-stop state variables of the unit, which are fixed at 1. This is the set of binary variable indices that are fixed to 0 at the current node through a branch operation. It is the third Lagrange multiplier. express The multipliers corresponding to the equality constraints of the start-stop state variables of the unit that are fixed at 0; The inequality constraint is: ； ； ； ； ； in, For the set of all binary variable indices, It is the fourth Lagrange multiplier. express The multipliers corresponding to the inequality constraints on the upper limit of the start-stop state variables of the units that are not fixed. It is the fifth Lagrange multiplier. express The multiplier corresponding to the lower bound inequality constraint of the start-stop state variables of the unit that is not fixed; The power transfer distribution factor matrix, For load vectors, This is the vector representing the upper limit of line transmission capacity. It is the sixth Lagrange multiplier vector. It is the seventh Lagrange multiplier vector; in, For the positive power flow capacity constraint of the line. This is a constraint on the negative power flow capacity of the line.

4. The branch cutting method according to claim 3, characterized in that, Solving the network constraint minimum violation model, determining the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model, including: Determine the optimization variables for the network constraint minimum violation model; among which, the optimization variables include: the active power output of each unit, the start-stop state variables of each unit, the upper limit slack of the forward power flow of each line, and the upper limit slack of the reverse power flow of each line. Determine the optimal solution for each optimization variable at the point where all constraints are satisfied and the function value calculated by the objective function is minimized, and obtain the objective function value at the optimal solution. Determine the Lagrange multiplier vectors of each constraint at the optimal solution. The Lagrange multiplier vectors of each constraint are used to represent the marginal influence of each constraint on the objective function value at the optimal solution.

5. The branch cutting method according to any one of claims 1 to 4, characterized in that, According to Lagrange duality theory, globally feasible cuts are generated based on the Lagrange multipliers at the optimal solution, including: Obtain the Lagrange multiplier vector at the optimal solution of the network constraint minimum violation model; The global feasible cut is determined based on the Lagrange multiplier vector at the optimal solution, the global feasible cut determination rule, and the coefficient determination rule.

6. The branch cutting method according to claim 5, characterized in that, The global feasible cut determination rule is as follows: ； in, As the first coefficient, Let be the unit start-up and shutdown variable vector in the SCUC model. This is the second coefficient.

7. The branch cutting method according to claim 6, characterized in that, The rule for determining the coefficients is as follows: ； ； in, Let be the second Lagrange multiplier vector at the optimal solution. Let be the third Lagrange multiplier vector at the optimal solution. Let be the first Lagrange multiplier vector at the optimal solution. This is the third coefficient matrix. The sixth Lagrange multiplier vector at the optimal solution. The seventh Lagrange multiplier vector at the optimal solution. This is the vector representing the upper limit of line transmission capacity. The power transfer distribution factor matrix, For load vectors, Let be the fourth Lagrange multiplier vector at the optimal solution.

8. A branch cutting device for accelerating the solution of power system safety constraint unit combination, characterized in that, The branch cutting device is applied to the solver, and the branch cutting device includes: The first determining module is used to determine the SCUC model of the power system to be solved; The first solution module is used to solve the relaxation problem of each node during the branch and bound process; wherein the relaxation problem of each node is determined based on the SCUC model. A construction module is used to construct a network constraint minimum violation model based on the relaxation problem of the target node if the relaxation problem of the target node has no solution; wherein, the objective function in the network constraint minimum violation model is: ;in, It is a column vector whose elements are all 1s. This represents the upper limit slack for the positive power flow of each line. This represents the upper limit slack for the reverse power flow of each line. The objective function value, This represents the sum of the upper limit slack for power flow across all routes. This indicates taking the transpose of the vector; if =0 and =0 indicates that on the k-th path, the power flow satisfies the safety constraints and there are no violations; if >0 or If the value is >0, it indicates that the power flow limit has been exceeded on the kth line, resulting in a critical constraint that has no solution at the target node; The second solution module is used to solve the network constraint minimum violation model and determine the objective function value and Lagrange multipliers at the optimal solution of the network constraint minimum violation model. The generation module is used to determine, based on the objective function value, that the reason for the unsolvability of the target node is network constraints, and to generate a globally feasible cut based on the Lagrange multipliers at the optimal solution according to the Lagrange duality theory; wherein, the globally feasible cut is the constraint condition of a specific unit combination mode that leads to the unsolvability of the relaxation problem; An add module is used to add the globally feasible cut to the branch delimitation cut pool and prune nodes that do not satisfy the globally feasible cut. The second determining module is used to obtain the unit combination result after the branch delimitation is completed; The generation module includes: The judgment unit is used to determine whether the objective function value is greater than zero; if so, it determines that the reason why the objective node has no solution is due to network constraints.

9. The branch cutting device according to claim 8, characterized in that, Builder modules are specifically used for: Based on the relaxation problem of the target node, a network constraint minimum violation model is constructed. The network constraint minimum violation model is constructed as a linear programming problem. The network constraint minimum violation model includes: objective function and various constraints. Each constraint includes: unit operation constraints after removing network constraints, equality constraints and inequality constraints, and each constraint has a corresponding Lagrange multiplier vector.

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