Power system unit commitment acceleration method and system based on dynamic generation of cut plane

Abstract

The application relates to the technical field of power systems, and discloses a power system unit combination acceleration method and system based on a dynamic generation of a cut plane. When solving a linear programming relaxation problem of a branch and bound feasible node, a dual multiplier sequence at an optimal solution is extracted, so that discarded dual information is retained and used for subsequent cut plane construction; a global optimal cut plane is constructed based on an optimal objective function value, the dual multiplier sequence and branch history information. In the solution of a relaxation problem of a subsequent node, the cut plane determines a lower bound of an objective function through the value of a decision variable of the subsequent node. When the lower bound of the objective function is greater than the original optimal objective function value, the cut plane constitutes an effective constraint, eliminates the original optimal solution of the relaxation problem, promotes the optimal objective function value to at least the lower bound, and systematically narrows the feasible region of the relaxation problem, so that the pruning is triggered in advance, the lower bound promotion process is accelerated, and the solving efficiency of a large-scale security constrained unit commitment problem is improved.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to a method and system for accelerating the combination of power system units based on dynamic generation of cutting planes. Background Technology

[0002] Power system market clearing and dispatch planning rely on the efficient solution of security-constrained unit combination models. In the solution process, it is necessary to determine the start-up and shutdown status and output of each unit under the premise of meeting load demand and complex power grid physical constraints, so as to minimize the total operating cost of the system.

[0003] Currently, existing solvers based on mixed integer programming mainly employ the branch and bound and cutting plane method. This method obtains a global lower bound by solving a series of linear programming relaxation problems to relax integer constraints, and then searches for feasible solutions (i.e., a global upper bound) by continuously branching and discretizing decision variables. Simultaneously, cutting planes are added to cut the non-integer solution space to tighten the relaxed boundary, repeating this process until the upper and lower bounds converge to find the optimal integer solution. However, traditional heuristic upper bound optimization methods can only update the global upper bound and cannot adjust the global lower bound. Therefore, the global lower bound convergence of traditional branch and bound search trees is extremely slow, resulting in low solution efficiency in large-scale SCUC (Security Constrained Unit Commitment) scenarios.

[0004] Therefore, how to accelerate the solution of power system unit combinations is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] This application provides a method and system for accelerating the combination of power system units based on dynamic generation of cutting planes, so as to improve the solution efficiency of power system unit combination.

[0006] In a first aspect, this application provides a method for accelerating the combination of power system units based on dynamic generation of cutting planes, including: In the branch-and-bound solution process of the power system's safety-constrained unit combination model, if the linear programming relaxation problem of the current node is feasible, the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables are obtained; the decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output. The global optimal cutting plane is constructed based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of a set of discrete decision variable indices that have been fixed to 1 and a set of discrete decision variable indices that have been fixed to 0 under the current branch strategy. Add the global optimal cut plane to the global cut pool of the branch and bound algorithm; In the linear programming relaxation problem of subsequent nodes, after loading the global optimal cutting plane in the global cut pool, the branch and bound solution process is continued to obtain the optimal unit combination scheme. In solving the linear programming relaxation problem of subsequent nodes, the global optimal cutting plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cutting plane constitutes an effective constraint. After eliminating the original optimal solution, the solution continues to be solved. The optimal objective function value of the subsequent nodes after the solution is resolved is at least raised to the lower bound of the objective function.

[0007] Optionally, if the linear programming relaxation problem of the current node is feasible, then obtaining the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables includes: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved by a solver; the solver is used to determine the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained; if there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and pruning operation is performed on the current node.

[0008] Optionally, the constraints include: physical constraints, first branch constraints, second branch constraints, and slack variable range constraints; wherein, the first branch constraints are constraints satisfied by discrete decision variables that have been fixed to 1 on the branch path where the current node is located, the second branch constraints are constraints satisfied by discrete decision variables that have been fixed to 0 on the branch path where the current node is located, and the slack variable range constraints are value constraints satisfied by discrete decision variables after they have been relaxed to continuous variables.

[0009] Optionally, obtaining the sequence of dual multipliers at the optimal solution includes: Obtain the dual multipliers corresponding to each constraint of the linear programming relaxation problem at the optimal solution of the decision variables of the current node, and obtain the dual multiplier sequence; the dual multiplier sequence includes the dual multipliers of the physical constraint, the dual multipliers of the first branch constraint, the dual multipliers of the second branch constraint, and the dual multipliers of the relaxation variable range constraint.

[0010] Optionally, constructing the globally optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node includes: Based on the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the branch history information of the current node, construct the global optimal cutting plane of the current node according to the cutting plane construction rules. The cutting plane construction rule is an effective inequality construction rule derived from the strong duality theorem in the duality theory of linear programming. The effective inequality construction rule takes the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the fixed discrete decision variable index set in the branch history information as input parameters to construct an effective inequality as the global optimal cutting plane. The global optimal cutting plane is used to quantify the cost penalty for deviating from the fixed discrete decision variables in the subsequent branching process.

[0011] Optionally, the cutting plane construction rule is: ; in, For the current node's first A discrete decision variable, For indexing discrete decision variables, For the set of discrete decision variable indices where the current node is fixed at zero, For node indexing, This is the set of discrete decision variable indices, where the current node is fixed at one. Let be the dual multiplier vector of the first branch constraint. for The One element, Let be the dual multiplier vector of the second branch constraint. for The One element, Let be the objective function. For discrete decision variables of unit start-up and shutdown states, For the unit's output, it is a continuous decision variable. The objective function value for the linear programming relaxation problem of the current node is given.

[0012] Optionally, the branch-and-bound solution process for the power system's safety-constrained unit combination model also includes: Based on the current global upper and lower bounds, check whether the Gap tolerance condition is met; If the conditions are not met, then solve the linear programming relaxation problem for the current node.

[0013] Optionally, in the linear programming relaxation problem of subsequent nodes, after loading the globally optimal cut plane from the global cut pool, the branch and bound solution process continues, including: All globally optimal cutting planes in the global cut pool are added as additional constraints to the constraint set of the linear programming relaxation problem of subsequent nodes; The solver is invoked to solve the linear programming relaxation problem of subsequent nodes loaded with global optimal cutting planes. The solver must satisfy each global optimal cutting plane while minimizing the objective function in order to obtain the optimal objective function value of the subsequent nodes. Obtain the optimal objective function value of the linear programming relaxation problem for subsequent nodes; if the optimal objective function value is greater than or equal to the current global upper bound, perform a pruning operation on the subsequent nodes; if the optimal objective function value is less than the current global upper bound, continue to perform a branching operation on the subsequent nodes until the optimal unit combination scheme is output.

[0014] Secondly, this application provides a power system unit combination acceleration system based on dynamic generation of a cutting plane, comprising: The linear programming relaxation solution module is used in the branch and bound solution process of the power system's safety-constrained unit combination model. If the linear programming relaxation problem of the current node is feasible, it obtains the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables. The decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output. The cutting plane construction module is used to construct the global optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of a set of discrete decision variable indexes that have been fixed to 1 and a set of discrete decision variable indexes that have been fixed to 0 under the current branch strategy. The cutting plane addition module is used to add the globally optimal cutting plane to the global cut pool of the branch and bound algorithm; The branch and bound execution module is used to continue the branch and bound solution process in the linear programming relaxation problem of subsequent nodes after loading the global optimal cut plane in the global cut pool, so as to obtain the optimal unit combination scheme. Specifically, when solving the linear programming relaxation problem of subsequent nodes, the global optimal cut plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cut plane constitutes an effective constraint, and the original optimal solution is eliminated before continuing to solve the problem. The optimal objective function value of the subsequent nodes after resolving is at least raised to the lower bound of the objective function.

[0015] Optionally, the linear programming relaxation solution module is specifically used for: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved by a solver; the solver is used to determine the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained; if there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and pruning operation is performed on the current node.

[0016] Compared with the prior art, the above-mentioned technical solution of this application has the following advantages: This application discloses a method and system for accelerating the combination of power system units based on dynamic generation of cutting planes. In the branch and bound solution process, when solving the linear programming relaxation problem of feasible nodes, this application needs to extract the dual multiplier sequence at the optimal solution so that the originally discarded dual information can be retained and used for subsequent cutting plane construction. Based on the optimal objective function value, the dual multiplier sequence and branch history information, this application constructs a global optimal cutting plane. In the solution of the relaxation problem of subsequent nodes, the global optimal cutting plane determines the lower bound of the objective function through the decision variable values ​​of subsequent nodes. When the lower bound of the objective function is greater than the original optimal objective function value, the cutting plane constitutes an effective constraint, eliminates the original optimal solution of the relaxation problem, and promotes its optimal objective function value to be raised to at least the lower bound. This systematically tightens the feasible region of the relaxation problem, so as to trigger pruning in advance, accelerate the lower bound improvement process, and thus improve the solution efficiency of large-scale safety-constrained unit combination problems. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] To more clearly illustrate the technical solutions in the embodiments of this application 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.

[0019] 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.

[0020] Figure 1 A schematic flowchart of a power system unit combination acceleration method based on dynamic generation of cutting planes is provided for an embodiment of this application; Figure 2 A flowchart of the global optimal cut plane embedded branch and bound algorithm provided in this application embodiment; Figure 3 This is a schematic diagram of a power system unit combination acceleration system structure based on dynamic generation of cutting planes, provided as an embodiment of this application. Detailed Implementation

[0021] 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.

[0022] 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.

[0023] 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.

[0024] 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, or 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.

[0025] Security Constrained Unit Commitment (SCUC): The core optimization problem of day-ahead dispatching in a power system. It is used to decide the start-up and shutdown status and output of generating units while satisfying system operating constraints, in order to minimize system operating costs. The start-up and shutdown status are integer variables, and the output level is a continuous variable.

[0026] Branch and Bound (B&B) is a classic algorithm for mixed 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. It is the core framework of the solver.

[0027] Mixed Integer Programming (MIP) is a class of mathematical optimization problems where all constraints are linear, some decision variables must take integer values, while others can take continuous values. It is widely used in practical engineering fields involving discrete decision-making, such as power system dispatching, logistics route planning, and production planning, for yes / no or statistical calculations.

[0028] Linear programming (LP) is one of the most fundamental mathematical optimization methods in operations research. It studies how to find the maximum or minimum value of a linear objective function under constraints consisting of a set of linear equality or inequality equations. In linear programming, all decision variables are continuous. It is often used for problems involving optimal resource allocation, profit maximization, or cost minimization.

[0029] Linear Programming Relaxation (LP Relaxation): refers to relaxing the integer variable constraints in a mixed integer programming problem into continuous variable constraints, resulting in a linear programming problem.

[0030] Dual Multiplier: A core parameter in the duality theory of linear programming. Its physical meaning is the marginal change in the value of the optimal objective function of the system when the right-hand side of the constraint is relaxed by one unit.

[0031] Cutting Plane: An effective inequality dynamically added during the optimization process to tighten the feasible region of the relaxation problem to accelerate convergence without cutting off any integer feasible solutions.

[0032] Feasible Solution and Feasible Node: A solution that satisfies all constraints of an optimization problem is called a feasible solution; in a branch and bound search tree, a node in the LP relaxation problem that has a feasible solution is called a feasible node.

[0033] Upper and Lower Bounds: In branch and bound algorithms, the upper bound refers to the objective function value of the currently found best integer feasible solution; the lower bound refers to the infimum of the objective function values ​​of all nodes in the LP relaxation problem to be explored. The gap between the two is the convergence criterion for the algorithm.

[0034] It should be noted that safety-constrained unit combination is the core engine of electricity market clearing. It aims to find the unit start-up, shutdown, and output schemes that minimize the total system operating cost, which includes generation costs and start-up / shutdown costs, while meeting load demand and complex grid physical constraints. Mathematically, SCUC is a typical large-scale mixed integer programming (MIP) problem. With the advancement of electricity market construction, the requirements for timeliness and accuracy in clearing calculations are becoming increasingly stringent. For example, a traditional unit combination model involves tens of thousands of integer variables and millions of safety constraints, and its dispatch center typically requires calculation to be completed within 2-3 hours, with a convergence gap set within 0.1%. In another scenario, SCUC requires convergence to a 0.1% gap within 2 hours. However, in actual operation, especially in complex large-scale grid scenarios, solvers often struggle to meet these convergence requirements within the specified time window.

[0035] The current mainstream framework for solving large-scale SCUC problems is the Branch and Bound (B&B) and Cutting Plane method, which is also the underlying core of advanced solvers such as COPT, Gurobi, and CPLEX. The B&B and Cutting Plane method obtains a global lower bound by solving a series of linear programming (LP) relaxation problems with relaxed integer constraints. It then searches for feasible solutions by continuously branching and discretizing decision variables: a global upper bound. Simultaneously, it adds effective inequalities from the Cutting Plane to cut the non-integer solution space to tighten the relaxed boundary, repeating this process until the upper and lower bounds converge to find the optimal integer solution. It is worth noting that the traditional Cutting Plane method is essentially a general generative architecture based on pure algebra and mathematical principles. It mainly relies on general mathematical rules to strengthen the model, failing to effectively combine the inherent physical characteristics and specific structure of the SCUC problem for customized design. This often results in it failing to achieve optimal acceleration when dealing with complex large-scale SCUC problems.

[0036] To accelerate the solution of SCUC, traditional schemes within the framework of branch and bound and cutting plane mainly include: (1) Heuristic upper bound optimization methods: These methods mainly focus on using the LP relaxation solution information of the current node, such as the decimal values ​​of variables, to construct a small-scale mixed integer or linear programming subproblem with reduced dimensionality during the branch and bound search process. The aim is to quickly find high-quality integer feasible solutions in the neighborhood of the relaxation solution, thereby reducing the global upper bound. However, these methods mainly focus on improving the upper bound and fail to fundamentally tighten the mathematical boundary of the LP relaxation of the original problem, that is, they make a weak contribution to improving the lower bound.

[0037] (2) Cutting plane method based on static modeling optimization: This type of method focuses on adding enhanced effective inequalities for the operating characteristics of individual units, such as minimum start-up and shutdown time and ramp rate, during the model building stage, i.e. before solving. The purpose is to make the LP relaxation feasible region of the unit more geometrically close to the integer package, thereby improving the quality of the initial lower bound of the root node. However, this type of method only stays in the static preprocessing stage before solving, and fails to deeply intervene in and utilize the rich node information in the dynamic search process of branch and bound; moreover, it focuses more on single unit constraints, fails to combine the unit coupling characteristics at the system-wide level, and lacks in-depth mining of the core integer variable characteristics that cause the solution time.

[0038] It is evident that the traditional solution suffers from the following technical problems: (1) Heuristic methods focus on upper bound optimization, contributing little to lower bound convergence. The core logic of heuristic acceleration methods is to find a better feasible solution, thereby updating the global upper bound. However, the core indicator of convergence in the MIP problem is that the upper and lower bounds are closed, that is, the gap meets the accuracy requirements. In large-scale SCUC, improving the lower bound is also difficult and slow. Current heuristic methods such as fixing local variables and constructing small MIPs cannot fundamentally improve the relaxation tightness of the mathematical model and contribute little to improving the lower bound; moreover, their effectiveness is highly dependent on the data characteristics of the specific power grid and cannot provide strict optimality guarantees and universal acceleration effects.

[0039] (2) The cutting plane method is a static model enhancement and does not delve into the dynamic solution process of branch and bound. Current cutting plane techniques are mostly static model enhancements, optimizing the SCUC model in the modeling stage to improve its compactness, but lacking deep involvement in the dynamic search process of branch and bound. In the branch and bound process, the algorithm evaluates a large number of local node LP relaxation problems. When encountering a feasible node with a high objective function value or even worse than the currently known global upper bound, the conventional operation of current branch and bound is to directly perform single-point pruning or treat it as an ordinary branch node, but the obtained optimal LP solution of the node and the accompanying dual multipliers are completely discarded. In fact, these dual multipliers and the optimal objective value of the LP problem quantify the economic cost of maintaining the current unit start-up and shutdown state. Ignoring the dual information dynamically generated in the branch and bound process will lead to the inability to predict and avoid suboptimal decision combinations that are destined to lead to high operating costs when searching other branches in the future, thus falling into a lot of redundant exploration.

[0040] Therefore, this application addresses the problem that existing methods fail to fully utilize the dynamic solution information of local nodes in the branch and bound search tree and suffer from slow lower bound improvement. It provides a method and system for accelerating power system unit combination based on dynamically generated cut planes. This scheme is an acceleration scheme for power system unit combination based on the generation and embedding of optimal cut planes with integer variables. Unlike traditional methods that treat the calculation of LP relaxation problems for locally suboptimal or branch nodes as a one-time state judgment tool, this application deeply mines the dual information at the underlying level of the LP relaxation problem. When a feasible solution exists for the LP relaxation problem, the dual multipliers at its optimal solution are used to accurately extract the economic cost penalty term that fixes the current unit start-up and shutdown state, and transform it into an optimal cut plane that is effective throughout the entire search tree. This is dynamically embedded into the subsequent solution process, where the current unit start-up and shutdown state corresponds to 0-1 integer variables. This cutting plane can rigidly project the local economic penalty onto the global integer solution space. On the one hand, it can identify and eliminate suboptimal unit combination schemes that are destined not to improve the target value in advance. On the other hand, it can continuously tighten the feasible region of subsequent LP relaxation problems as an explicit hard constraint, thereby greatly accelerating the process of raising the global lower bound of branch and bound.

[0041] See Figure 1 The following is a schematic flowchart of a power system unit combination acceleration method based on dynamic generation of cutting planes, provided in an embodiment of this application, including: S101. In the process of solving the branch and bound problem of the power system's safety-constrained unit combination model, if the linear programming relaxation problem of the current node is feasible, then obtain the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables; the decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output.

[0042] It should be noted that the proposed method for generating the global optimal cutting plane and accelerating the power system unit combination mainly includes the extraction of dual information of the node LP relaxation problem, the construction process of the global optimal cutting plane, and the process of embedding the branch and bound algorithm in the cutting plane.

[0043] In this application, during the branch-and-bound process of solving the power system's safety-constrained unit combination model, the branch-and-bound algorithm branches the discrete decision variables layer by layer, solving the corresponding linear programming relaxation problem at each node. At the current node, the feasibility of the linear programming relaxation problem at that node is first checked. The feasibility of the linear programming relaxation problem means that there exists a solution that satisfies all constraints. If the solution is successful, the linear programming relaxation problem is feasible. If the linear programming relaxation problem at the current node is feasible, the optimal objective function value of the linear programming relaxation problem at the optimal solution of the decision variables is obtained. This optimal objective function value refers to the optimal objective function value corresponding to the optimal solution obtained after solving the linear programming relaxation problem at the current node. At the same time, the sequence of dual multipliers at the optimal solution is obtained. Each constraint in the linear programming relaxation problem corresponds to a dual multiplier, and the dual multipliers corresponding to all constraints constitute the sequence of dual multipliers.

[0044] S102. Construct the global optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of the discrete decision variable index set that has been fixed to 1 and the discrete decision variable index set that has been fixed to 0 under the current branch strategy.

[0045] This step involves constructing a globally optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and branch history information. This allows the dual information of the current node's linear programming relaxation problem to be transformed into constraints that are effective throughout the entire search tree.

[0046] Specifically, this application constructs a globally optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node. The branch history information includes a set of discrete decision variable indices that are fixed to 1 and a set of discrete decision variable indices that are fixed to 0 under the current branch strategy. Discrete decision variables represent the start-up and shutdown states of the unit, taking values ​​of 0 or 1, where 1 indicates the unit is in the start-up state and 0 indicates the unit is in the shutdown state. The discrete decision variable index set records the set of numbers of discrete decision variables assigned definite values ​​along the branch-bound search path. The globally optimal cutting plane is an effective inequality constructed based on the dual information of the linear programming relaxation problem of the current node. Its construction process uses the optimal objective function value, the dual multiplier sequence, the set of discrete decision variable indices fixed to 1, and the set of discrete decision variable indices fixed to 0 as input parameters, generating a mathematical expression in inequality form through computation. The global optimal cutting plane is used to quantify the cost penalty for deviations from the fixed discrete decision variables of the current node during subsequent branching processes. That is, when the discrete decision variables of the global feasible solution are inconsistent with the fixed values ​​of the current node branch, additional cost is required.

[0047] S103. Add the globally optimal cutting plane to the global cut pool of the branch and bound algorithm.

[0048] This step adds the constructed global optimal cut plane to the global cut pool so that the global optimal cut plane continues to be effective in the linear programming relaxation solution of all subsequent nodes.

[0049] Specifically, this application adds the globally optimal cut plane to the global cut pool of the branch and bound algorithm. The global cut pool is a data structure in the branch and bound algorithm used to store all generated valid inequalities. Cut planes stored in the global cut pool are loaded and used as additional constraints in the linear programming relaxation problem of subsequent nodes. After the globally optimal cut plane is added to the global cut pool, it acts as a rigid constraint in the linear programming relaxation problem of all subsequent nodes, thus narrowing the feasible region of the linear programming relaxation problem in subsequent nodes.

[0050] S104. In the linear programming relaxation problem of subsequent nodes, after loading the global optimal cutting plane in the global cut pool, the branch and bound solution process is continued to obtain the optimal unit combination scheme. Among them, when solving the linear programming relaxation problem of subsequent nodes, the global optimal cutting plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cutting plane constitutes an effective constraint. After removing the original optimal solution, the solution continues to be solved. The optimal objective function value of the subsequent nodes after resolving is at least raised to the lower bound of the objective function.

[0051] In this application, the linear programming relaxation problem of subsequent nodes needs to load the global optimal cut plane in the global cut pool before continuing the branch and bound solution process. The purpose is to use the global optimal cut plane to raise the optimal objective function value of the linear programming relaxation of subsequent nodes, thereby prompting earlier pruning.

[0052] Specifically, in the linear programming relaxation problem of subsequent nodes, the global optimal cut plane from the global cut pool is loaded before continuing the branch and bound solution process. Subsequent nodes refer to the branch and bound search tree nodes to be explored after the current node. The global optimal cut plane is added as an additional constraint to the constraint set of the linear programming relaxation problem of subsequent nodes, and this global optimal cut plane must be satisfied simultaneously when solving the linear programming relaxation problem of subsequent nodes.

[0053] The global optimal cutting plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of subsequent nodes. In the linear programming relaxation problem of subsequent nodes, the global optimal cutting plane provides a lower bound of the objective function through inequality constraints for the discrete decision variables corresponding to that node. If the lower bound of the objective function determined by the global optimal cutting plane is greater than the original optimal objective function value of the linear programming relaxation problem of that subsequent node, then the global optimal cutting plane constitutes a valid constraint. After removing the original optimal solution, the solution continues, and the optimal objective function value of the subsequent node after resolving is at least raised to the lower bound of the objective function. After the global optimal cutting plane tightens the problem, the feasible region of the linear programming relaxation problem of the subsequent node shrinks, and the optimal objective function value is raised, making it easier for that node to be pruned because the optimal objective function value is not lower than the global upper bound. The branch and bound algorithm iterates continuously according to the above process until the convergence condition is met, and outputs the optimal unit combination scheme. The optimal unit combination scheme includes the start-up and shutdown status and output level of each unit in each time period. This scheme minimizes the total operating cost of the system while satisfying all system operating constraints.

[0054] For example, in the branch and bound problem-solving process, if a node has an initial optimal solution in its linear programming relaxation problem before the cutting plane is loaded, let the first combination of discrete decision variables in this optimal solution be denoted as the first value, and the corresponding optimal objective function value be the first value. The current global upper bound is the second value. If the first value is less than the second value, then the node does not meet the pruning conditions, and the algorithm needs to continue analyzing or branching it.

[0055] After loading the node with the globally optimal cutting plane, the cutting plane calculates a lower bound for the objective function based on the first combination of values, denoted as the third value. If the third value is higher than the first value, the original optimal solution is excluded because it does not satisfy the cutting plane, and the cutting plane constitutes an effective constraint on the current node. Under the action of the cutting plane, the feasible region of the linear programming relaxation problem of this node is tightened, and a new set of optimal solutions is obtained after resolving the problem. The values ​​of the discrete decision variables in this new optimal solution are denoted as the second combination of values, and the corresponding optimal objective function value is the fourth value, which is not lower than the third value.

[0056] If the third value is higher than the second value, then since the fourth value is not lower than the third value, the fourth value must be higher than the second value. That is, the optimal objective function value after resolving is higher than the current global upper bound, thus triggering pruning of the node. Before the node is pruned, its child nodes may be eliminated one by one because they also do not satisfy the cut plane, resulting in a lot of redundant exploration. However, by loading the cut plane, the node and all its child nodes are pruned together, thereby avoiding invalid exploration of the branch and accelerating the convergence process of branch and bound.

[0057] In summary, this application constructs a globally optimal cutting plane by extracting the dual information of the linear programming relaxation problem during the branch-and-bound process. This transforms the economic penalty information of local nodes into constraints that are effective throughout the entire search tree, narrowing the feasible domain of the linear programming relaxation problem in subsequent nodes and increasing the optimal objective function value of the linear programming relaxation problem. This accelerates the improvement of the global lower bound of branch-and-bound and the pruning of suboptimal branches, thereby improving the solution efficiency for large-scale safety-constrained unit combination problems.

[0058] In another embodiment of this application, if the linear programming relaxation problem of the current node is feasible, obtaining the optimal objective function value and the dual multiplier sequence at the optimal solution of the decision variables of the linear programming relaxation problem includes: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved by a solver; the solver is used to determine the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained; if there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and pruning operation is performed on the current node.

[0059] In this application, during the branch-and-bound solution of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is first determined based on the safety-constrained unit combination model. To clearly illustrate this scheme, the classic mathematical model of the SCUC problem is given here, including the objective function and constraints, where the objective function is given by formula (1) and the constraints are given by formulas (2)-(10).

[0060] (1); (2); (3); (4); (5); (6); (7); (8); (9); (10); In formula (1), the objective function represents minimizing the sum of the unit's power generation cost, start-up cost, and shutdown cost, where i represents the i-th unit. The number of thermal power units; t represents the t-th time period. The number of time periods in the scheduling cycle; This represents the online status of the i-th generating unit during time period t, where, A value of 1 indicates that the device is powered on. A value of 0 indicates that the machine is stopped. This represents the operating status of the i-th generating unit during time period t, where... A value of 1 indicates that the device is powered on at that moment. A value of 0 indicates that the device is not powered on. This represents the shutdown status of the i-th generating unit during time period t, where, A value of 1 indicates that the device is powered off at that moment. A value of 0 indicates that the device is not turned off; Let i be the power output of the i-th generating unit in time period t; Let be the quadratic, primary, and constant coefficients of the power generation cost of the i-th generating unit. Let represent the start-up cost coefficient and shutdown cost coefficient of the i-th unit, respectively.

[0061] Formula (2) represents the upper and lower limits of the unit's output. Let represent the lower limit and upper limit of the output of the i-th unit, respectively; formula (3) represents the unit output ramp-up constraint. Let represent the maximum ramping power of the i-th unit; Equation (4) represents the unit start-up time constraint. This represents the duration for which the i-th generating unit remains powered on before time period t. Let represent the minimum continuous start-up time of the i-th unit; Equation (5) represents the unit shutdown time constraint. This represents the duration for which the i-th generating unit remains shut down before time period t. Let represent the minimum continuous shutdown time of the i-th unit; Equation (6) represents the unit start-up and shutdown state constraints; Equation (7) represents the system power balance constraints. This represents the magnitude of the j-th load in time period t. The number of loads in the system; Formula (8) represents the system's standby constraint. Let be the system's reserve capacity requirement for time period t; formula (9) represents the system's security flow constraints. This is the upper limit of the transmission power of the l-th line. Let i and j represent the power transmission distribution factors of generator set i and load j to line l, respectively; formula (10) represents the logical constraints of the 0-1 variables of the generator set state, and represents... It can only take the value 0 or 1.

[0062] In the above mathematical model, the decision variables include the i-th unit in time period t. , , , ,common Each unit, One time period, the rest are known constants.

[0063] To facilitate the extraction of dual information from the node LP relaxation problem, this application expresses the above SCUC mixed integer programming model formulas (1) to (10) in the following matrix algebraic compact form: (11); (12); (13); The decision variables include discrete decision variables and continuous decision variables. Discrete decision variables are 0-1 discrete vectors representing the start-up and shutdown states of the unit. , express In terms of dimensions, continuous decision variables are vectors of continuous unit output variables. In this application, discrete representations are either 0 or 1, and continuous representations are real numbers; where, The variables corresponding to the above SCUC model , , , correspond ; Let be the objective function, representing the total operating cost of the system, corresponding to the above formula (1). This represents the objective function value at the optimal solution of the SCUC optimization problem; the constraint conditions corresponding to formula (12) are given by the coefficient matrix. With the right-hand item The joint statement indicates that the constraints cover the upper and lower limits of unit output, the ramp-up constraints of unit output, the start-up time constraints of unit, the shutdown time constraints of unit, the start-up and shutdown status constraints of unit, the system power balance constraints, the system reserve constraints, and the system safety power flow constraints, corresponding to the above formulas (2) to (9), with the right-hand side terms... The constant term; the constraint conditions in formula (13) Corresponding formula (10). express Take real numbers as continuous variables. express The dimension, namely: continuous variables The total number; This indicates the transpose of a vector or matrix. The SCUC model represented by formulas (11), (12), and (13) is denoted as P1.

[0064] In this application, the linear programming relaxation problem of the current node includes an objective function and constraints. The objective function is used to determine the total operating cost of the unit based on the decision variables. The decision variables include discrete decision variables of the unit's start-up and shutdown states and continuous decision variables of the unit's output. The constraints include physical constraints, first branch constraints, second branch constraints, and relaxation variable range constraints. Among them, the first branch constraints are the constraints satisfied by the discrete decision variables that have been fixed to 1 on the branch path where the current node is located, the second branch constraints are the constraints satisfied by the discrete decision variables that have been fixed to 0 on the branch path where the current node is located, and the relaxation variable range constraints are the value constraints satisfied by the discrete decision variables after they are relaxed to continuous variables.

[0065] This application solves the linear programming relaxation problem of the current node using a solver. The solver determines the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is deemed feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained. If no solution is found, the linear programming relaxation problem of the current node is deemed infeasible, and pruning operations are performed on the current node. Accordingly, when obtaining the dual multiplier sequence at the optimal solution, this application specifically obtains the dual multipliers corresponding to each constraint at the optimal solution of the decision variables in the linear programming relaxation problem of the current node, resulting in a dual multiplier sequence. The dual multiplier sequence includes the dual multipliers of the physical constraints, the dual multipliers of the first branch constraints, the dual multipliers of the second branch constraints, and the dual multipliers of the relaxation variable range constraints.

[0066] Specifically, in the branch-bound search tree... At each node, discrete decision variables Relaxed into a continuous state At the same time, the branch history information of this node is superimposed: and , and These are the sets of discrete decision variable indices that have been fixed at 1 and 0 under the current branching strategy. Therefore, this application can relax the LP problem of the current node (hereinafter referred to as LP). k The following includes the objective function represented by formula (14) and the constraints represented by formulas (15) to (18): (14); (15); (16); (17); (18); In this context, formula (14) is the objective function, which is the same as that in formula (11). For LP k The optimal objective function value, i.e.: LP k The objective function value at the optimal solution; Formula (15) is the physical constraint condition, which is the same as Formula (12); Formula (16) is the first branch constraint condition, that is: the branch constraint condition of the discrete decision variable that is fixed to 1. Indicates by The sub-vectors formed by the indicated discrete decision variables, Indicates and The corresponding all-1 vector, as shown in formula (16), represents the vector at the current branch node k. The index is in the index set All discrete decision variables All equal to 1; Formula (17) is the second branch constraint, that is: the branch constraint of the discrete decision variable that is fixed to 0. Formula (17) means that at the current branch node k, The index is in the index set All discrete decision variables All equal to 0; Formula (18) represents discrete decision variables. The constraints that need to be satisfied after relaxation; by combining formulas (16) and (18), we can obtain the conditions in the index set. In satisfy Combining formulas (17) and (18), we can obtain the result in the index set. In satisfy ; These are the dual multipliers of formulas (15) to (18), where the dual multiplier represents the change in the optimal objective value of the optimization problem by relaxing the right-hand side of the corresponding constraint by one unit, i.e., increasing by 1. And all dual multipliers are non-negative. In order to facilitate the derivation of the Lagrange dual function, the constraints are all expressed in the form of ≤.

[0067] This application solves the LP of the current node. k The problem is to obtain the optimal objective function value for the current node if the problem is feasible. And extract the dual multiplier sequence corresponding to the optimal solution. .

[0068] in, For the dual multipliers of physical constraints. The dual multiplier for the first branch constraint. For the dual multipliers of the second branch constraint, and It is the dual multiplier for the range constraint of the slack variable.

[0069] It should be noted that the step of determining the objective function value at the optimal solution in this application can be achieved by directly calling the solver to solve the LP. kThe problem is that the objective function and constraints are input into the solver, and the solver automatically outputs the objective function value at the optimal solution. This process is the industry-recognized procedure for solving linear programming problems, and will not be described in detail here. For example, the objective function and all constraints are input into the solver, and the solver searches within the feasible region of the linear programming relaxation problem at the current node. It finds the set of values ​​that minimizes the objective function value among all combinations of optimization variables that satisfy the constraints, and outputs the minimum function value as the objective function value at the optimal solution. For each constraint, the solver outputs the dual multiplier corresponding to the constraint at the same time as outputting the optimal solution. The magnitude of the dual multiplier directly determines the marginal influence of the constraint on the optimal objective function value. The dual multipliers of each constraint together constitute the dual multiplier sequence in this application.

[0070] In this application, the global optimal cutting plane is constructed based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node, including: Based on the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the branch history information of the current node, construct the global optimal cutting plane of the current node according to the cutting plane construction rules. The cutting plane construction rule is an effective inequality construction rule derived from the strong duality theorem in the duality theory of linear programming. The effective inequality construction rule takes the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the fixed discrete decision variable index set in the branch history information as input parameters to construct an effective inequality as the global optimal cutting plane. The global optimal cutting plane is used to quantify the cost penalty for deviating from the fixed discrete decision variables in the subsequent branching process.

[0071] The construction rule for the cutting plane is as follows: ; in, For the current node's first A discrete decision variable, For indexing discrete decision variables, For the set of discrete decision variable indices where the current node is fixed at zero, For node indexing, This is the set of discrete decision variable indices, where the current node is fixed at one. Let be the dual multiplier vector of the first branch constraint. for The One element, Let be the dual multiplier vector of the second branch constraint. for The One element, Let be the objective function. For discrete decision variables of unit start-up and shutdown states, For the unit's output, it is a continuous decision variable. The objective function value for the linear programming relaxation problem of the current node is given.

[0072] In this application, to quantify the economic penalty of deviating from the fixed state of the current discrete decision variables during the branching process, an optimal cutting plane is constructed based on the strong duality theorem. The application examines any feasible solution within the feasible region P1 of the SCUC problem. Since it is a feasible SCUC solution, it satisfies all SCUC physical constraints of formula (12), but may not satisfy the node constraints. The local state branch constraints are, in other words, Equations (16) and (17). This is because branch bounds impose additional mandatory constraints specific to the current node on different search nodes, such as forcing a certain unit to be 0 or 1. However, the integer values ​​of a feasible solution of SCUC may not necessarily satisfy the additional mandatory conditions on this specific node. For example, the feasible solution corresponds to unit 1 being powered on during time period 1, but the branch constraint of a certain node may be that unit 1 is powered off during time period 1. The two are obviously mutually exclusive. This application constructs node LP k The problem's Lagrangian function See formula (19): (19); According to the duality theory of linear programming, since the node LP k This is a linear programming problem, therefore its optimal objective function value is... It can be equivalently expressed as The maximum and minimum values ​​are shown in formula (20): (20); This application will provide a globally feasible solution. With the extracted optimal dual multiplier Substituting this in, since the infimum of the Lagrange function over the entire domain must be less than or equal to its value at a specific feasible solution, and the feasible solution... Strictly meet the physical constraints of SCUC Relaxing constraints , Combining the nonnegativity of the dual multipliers, we can obtain the inequality relationship of formula (21), thereby establishing the mathematical relationship of the cutting plane construction rule shown in formula (22): (twenty one); (twenty two); Here, the proof of formula (22) is explained: Since formula (20) holds, equation (a) in formula (22) also holds. Because node LP k This is a linear programming problem. According to duality theory, about The maximum value is at For optimal dual multipliers Therefore, equation (b) in formula (22) holds. According to the definition of the infimum, the infimum of the Lagrange function over the entire domain must be less than or equal to its value at a specific feasible solution. This means that the feasible solution... Substitution Therefore, inequality (c) holds. Because a feasible solution... Strictly meet the physical constraints of SCUC Relaxing constraints , Given that the dual multipliers are nonnegative, we can obtain the inequality relation of formula (21). Taking the maximum value of all terms on the left side of formula (21), i.e., the right side term is 0, we can obtain the inequality (d) in formula (22). Thus, formula (22) is proved.

[0073] Then, by rearranging formula (22) and performing algebraic rearrangement, the global optimal cutting plane induced by the dual information of the LP relaxation problem of node k can be obtained. Therefore, the cutting plane construction rule in this application is as shown in formula (23).

[0074] (twenty three); Accordingly, in the linear programming relaxation problem of subsequent nodes, this application continues the branch and bound solution process after loading the globally optimal cut plane from the global cut pool, including: All globally optimal cut planes in the global cut pool are added as additional constraints to the constraint set of the linear programming relaxation problem of subsequent nodes. The solver is invoked to solve the linear programming relaxation problem of subsequent nodes with the globally optimal cut planes loaded. The solver must satisfy all globally optimal cut planes while minimizing the objective function in order to obtain the optimal objective function value of the subsequent nodes. The optimal objective function value of the linear programming relaxation problem of the subsequent nodes is obtained. If the optimal objective function value is greater than or equal to the current global upper bound, a pruning operation is performed on the subsequent nodes. If the optimal objective function value is less than the current global upper bound, the branching operation continues to be performed on the subsequent nodes until the optimal unit combination scheme is output.

[0075] In this application, the globally optimal cutting plane constructed by formula (23) can, on the one hand, provide the absolute minimum cost that is independent of the continuous output of the units under the known start-up and shutdown states of some units; on the other hand, it accurately quantifies the economic penalty brought about by violating the fixed decision of the current discrete decision variables, that is, how much the lower bound of cost will change by changing the start-up and shutdown state of the units under the current node branch constraints: if the SCUC globally feasible solution is relatively fixed at the current node... and The start / stop status of the generator units was flipped, and the variable that was fixed at 1 was changed. The cost of flipping to 0 is the dual multiplier. Variables that are fixed to 0 The cost of flipping to 1 is the dual multiplier. Therefore, the total operating cost of SCUC will inevitably be higher. Based on this, dual multipliers are generated. The economic cost increases. This application adds the cutting plane to the node LP relaxation problem after branch and bound. On the one hand, it can cut off nodes that do not contain the optimal integer solution of the original SCUC problem, compress the search space of branch and bound, and reduce the solution scale of subsequent nodes. On the other hand, the cutting plane effectively tightens the feasible region of the node LP relaxation problem, which is conducive to improving the optimal objective function value of the node LP relaxation problem, thereby accelerating the pruning process of inferior branches in the branch and bound tree.

[0076] In another embodiment of this application, the branch and bound solution process of the power system safety constraint unit combination model further includes: checking whether the gap tolerance condition is satisfied based on the current global upper bound and global lower bound; if not satisfied, solving the linear programming relaxation problem of the current node.

[0077] Specifically, in the branch-and-bound process of the power system's safety-constrained unit combination model, this application checks whether the Gap tolerance condition is met based on the current global upper and lower bounds. The global upper bound refers to the objective function value corresponding to the currently found optimal integer feasible solution during the branch-and-bound search process; this value continuously decreases as better feasible solutions are discovered during the search. The global lower bound refers to the minimum value among the optimal objective function values ​​of the linear programming relaxations for all unexplored nodes during the branch-and-bound search process; this value continuously increases as the search progresses. Gap refers to the relative distance between the global upper and lower bounds, calculated by dividing the difference between the global upper and lower bounds by the absolute value of the global upper bound, and then multiplying by 100% to obtain a percentage Gap value. The Gap tolerance condition means that if the Gap value is less than or equal to a preset tolerance threshold, the convergence condition is considered met. The preset tolerance threshold can be set according to the accuracy requirements of the actual application scenario. For example, in the day-ahead scheduling scenario of the power system, it can be set to 0.1%, which means that when the relative difference between the global upper bound and the global lower bound is less than 0.1%, it is considered that a sufficiently approximate optimal feasible solution has been found. In scenarios with lower accuracy requirements, it can also be set to 0.5% or 1.0%.

[0078] If the Gap tolerance condition is met, the branch and bound algorithm terminates the search, and the feasible solution corresponding to the current global upper bound is output as the optimal unit combination scheme. If the Gap tolerance condition is not met, subsequent steps are executed to solve the linear programming relaxation problem of the current node. The Gap tolerance condition check is performed before each node is evaluated to ensure that the algorithm terminates in time when the preset accuracy requirement is reached, avoiding unnecessary continuation of the solution process.

[0079] As can be seen, by checking the gap tolerance condition before node evaluation, this application enables the branch and bound algorithm to terminate in time when the preset accuracy requirement is met, avoiding redundant calculations. At the same time, the preset tolerance threshold can be flexibly adjusted according to the actual scenario, taking into account both solution accuracy and computational efficiency.

[0080] See Figure 2 This is a flowchart of the global optimal cut plane embedded branch and bound algorithm provided in this application embodiment. This application needs to embed the above-mentioned optimal cut plane generation mechanism into the workflow of the existing branch and bound algorithm (B&B) solution framework, such as... Figure 2 As shown, the branch and bound algorithm process includes the following steps: S201. Establish the SCUC model and pass it as input to the branch and bound algorithm; S202. Start the branch and bound algorithm solution process and check whether the gap tolerance condition is met. If the conditions are met, it is determined that the optimal solution has been found, and there is no need to explore the next node, so the process ends; if the conditions are not met, then S203 continues to be executed. S203. Trigger node evaluation and solve the LP relaxation problem for the current node; S204. Determine whether the LP relaxation problem of the current node is feasible; If not feasible, proceed to S205; if feasible, continue to S206. S205, Perform pruning or backtracking operations on the node; S206. Determine if the LP relaxation problem of the current node has an optimal solution, and obtain the optimal objective function value and the corresponding dual multiplier sequence.

[0081] S207. Generate the globally optimal cutting plane based on the optimal objective function value and the dual multiplier sequence, and dynamically add it to the global cut pool of branch and bound. S208. Continue executing the standard branch and bound algorithm process, adding the newly added global optimal cut plane as a constraint to the LP relaxation problem of subsequent nodes. That is, the newly added optimal cut plane will automatically take effect in the LP relaxation model of subsequent unexplored nodes, acting as a rigid constraint to tighten the feasible region of the LP relaxation problem, raising its objective value to induce earlier pruning, thereby accelerating the convergence process of B&B in solving SCUC.

[0082] In summary, the unit combination acceleration method proposed in this application, which generates optimal cutting planes and incorporates embedded branch and bound, breaks away from the conventional practice of discarding dual information of locally feasible nodes in traditional B&B algorithms by using an economic penalty quantification method based on the integer variable state reversal of node LP relaxation problems. This application proposes to extract the dual multipliers corresponding to the fixed variables of the branches, which can be used to accurately quantify the economic cost of deviating from the current local unit start-up and shutdown state. This application also proposes a global optimal cutting plane construction mechanism: a cutting plane construction form based on a specific effective inequality derived from the Lagrange minima principle, so that the constructed cutting plane can explicitly establish a non-negative algebraic relationship between the total system operating cost and the changes in the local integer variable states of nodes, safely projecting the local cost lower bound into a cutting plane that constrains the global integer solution space. This application proposes an optimal cut plane embedded branch and bound scheme with dynamic lower bound reinforcement and suboptimal avoidance: the optimal cut generation mechanism is embedded as a callback logic into the algorithm framework of the branch and bound process. This framework uses the constructed cost-penalty cut to tighten the feasible region of the LP relaxation problem in advance in the subsequent search, systematically accelerates the raising of the global lower bound of B&B, avoids the ineffective exploration of suboptimal solutions, and thus accelerates the solution of SCUC.

[0083] The unit combination acceleration method proposed in this application, which combines global optimal cutting plane generation and embedded branch delimitation, has at least the following beneficial effects: (1) Accelerating the lower bound of branch and bound and reducing the exploration space: One of the core bottlenecks of traditional methods for solving SCUC is that the LP relaxation problem is not tight enough, resulting in an infinite suboptimal branch exploration by the solver due to the lower bound. The optimal cutting plane generated in this application is different from the existing methods that improve the model based on static rules. Instead, it delves into the branch and bound solution process and is driven by the dynamic data (dual multipliers) of the node LP relaxation solution. It conveys to the solver in advance the information that changing the state of these units will face huge economic costs. By continuously accumulating these precise cost penalties in the cutting pool, the LP relaxation problem of subsequent nodes is subject to stricter bounds, forcing the lower bound to rise rapidly. This results in the large-scale, batch removal of suboptimal search spaces that are destined to have no economic advantage, significantly compressing the solution time.

[0084] (2) Based on rigorous mathematical theory, absolute optimality is guaranteed: Unlike heuristic acceleration algorithms (such as local neighborhood search) that lack theoretical guarantees and sacrifice optimality for speed, the optimal cut proposed in this application has a rigorous mathematical foundation. Its derivation is entirely based on the Lagrange strong duality theorem and the inherent physical properties of feasible solutions to the original problem. This means that the generated cutting plane is an absolutely safe and effective inequality. In geometric space, it only cuts the relaxed regions that cannot lead to the optimal solution and will never mistakenly cut the global optimal solution. This is of crucial value for SCUC calculations, which have extremely high requirements for safety and economy.

[0085] (3) High engineering compatibility: Existing B&B algorithms consume a huge amount of computational power in simplex method iteration when dealing with non-optimal but feasible LP nodes, and often only obtain a pruning conclusion. This application realizes for the first time the mining and utilization of the computational results of node LP relaxation problems, transforming the dual information of these originally discarded nodes into effective inequality constraints to guide the global search. In addition, the optimal cut extraction process only relies on the dual multipliers output by the solver, without adding extra complex auxiliary variables to the original SCUC model or reconstructing the model. It can be easily and seamlessly embedded into solvers such as Gurobi and COPT through callback interfaces, with high engineering practice compatibility and great industrial promotion prospects.

[0086] The following describes the power system unit combination acceleration system provided in the embodiments of this application. The power system unit combination acceleration system described below can be referred to in correspondence with the method described above.

[0087] See Figure 3 , Figure 3 A schematic diagram of a power system unit combination acceleration system based on dynamic generation of a cutting plane is provided for an embodiment of this application. The system specifically includes: The linear programming relaxation solution module 11 is used to obtain the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables in the branch and bound solution process of the power system's safety constraint unit combination model. The decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output. The cutting plane construction module 12 is used to construct the global optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of a set of discrete decision variable indexes that have been fixed to 1 and a set of discrete decision variable indexes that have been fixed to 0 under the current branch strategy. The cutting plane addition module 13 is used to add the global optimal cutting plane to the global cut pool of the branch and bound algorithm; The branch and bound execution module 14 is used to continue the branch and bound solution process after loading the global optimal cut plane in the global cut pool in the linear programming relaxation problem of subsequent nodes, so as to obtain the optimal unit combination scheme. In the process of solving the linear programming relaxation problem of subsequent nodes, the global optimal cut plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cut plane constitutes an effective constraint, and the original optimal solution is eliminated and the solution is continued. The optimal objective function value of the subsequent nodes after resolving is at least raised to the lower bound of the objective function.

[0088] As an optional implementation, the linear programming relaxation solution module is specifically used for: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved by a solver. The solver is used to determine the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution of the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained. If there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and pruning operation is performed on the current node.

[0089] As an optional embodiment, the constraints include: physical constraints, first branch constraints, second branch constraints, and slack variable range constraints; The first branch constraint is the constraint satisfied by the discrete decision variable that has been fixed to 1 on the branch path where the current node is located; the second branch constraint is the constraint satisfied by the discrete decision variable that has been fixed to 0 on the branch path where the current node is located; and the slack variable range constraint is the value constraint satisfied by the discrete decision variable after it has been relaxed to a continuous variable.

[0090] As an optional embodiment, the linear programming relaxation solution module is specifically used for: Obtain the dual multipliers corresponding to each constraint of the linear programming relaxation problem at the optimal solution of the decision variables of the current node, and obtain the dual multiplier sequence; the dual multiplier sequence includes the dual multipliers of the physical constraint, the dual multipliers of the first branch constraint, the dual multipliers of the second branch constraint, and the dual multipliers of the relaxation variable range constraint.

[0091] As an optional embodiment, the cutting plane construction module is specifically used for: Based on the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the branch history information of the current node, construct the global optimal cutting plane of the current node according to the cutting plane construction rules. The cutting plane construction rule is an effective inequality construction rule derived from the strong duality theorem in the duality theory of linear programming. The effective inequality construction rule takes the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the fixed discrete decision variable index set in the branch history information as input parameters to construct an effective inequality as the global optimal cutting plane. The global optimal cutting plane is used to quantify the cost penalty for deviating from the fixed discrete decision variables in the subsequent branching process.

[0092] The rules for constructing the cutting plane are as follows: ; in, For the current node's first A discrete decision variable, For indexing discrete decision variables, For the set of discrete decision variable indices where the current node is fixed at zero, For node indexing, This is the set of discrete decision variable indices, where the current node is fixed at one. Let be the dual multiplier vector of the first branch constraint. for The One element, Let be the dual multiplier vector of the second branch constraint. for The One element, Let be the objective function. For discrete decision variables of unit start-up and shutdown states, For the unit's output, it is a continuous decision variable. The objective function value for the linear programming relaxation problem of the current node is given.

[0093] As an optional embodiment, the device further includes: The tolerance check module is used to check whether the gap tolerance condition is met based on the current global upper bound and global lower bound; if not, the linear programming relaxation problem of the current node is solved.

[0094] As an optional embodiment, the branch delimitation execution module is specifically used for: All globally optimal cutting planes in the global cut pool are added as additional constraints to the constraint set of the linear programming relaxation problem of subsequent nodes; The solver is invoked to solve the linear programming relaxation problem of subsequent nodes loaded with global optimal cutting planes. The solver must satisfy each global optimal cutting plane while minimizing the objective function in order to obtain the optimal objective function value of the subsequent nodes. Obtain the optimal objective function value of the linear programming relaxation problem for subsequent nodes; if the optimal objective function value is greater than or equal to the current global upper bound, perform a pruning operation on the subsequent nodes; if the optimal objective function value is less than the current global upper bound, continue to perform a branching operation on the subsequent nodes until the optimal unit combination scheme is output.

[0095] It should be noted that the power system unit combination acceleration system based on dynamic generation of cutting plane described in this application is specifically an execution system that embeds the above-mentioned optimal cutting plane generation mechanism into the existing branch and bound algorithm (B&B) solution framework. This system uses the acceleration method described in any of the above method embodiments to accelerate the solution of the branch and bound algorithm.

[0096] 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.

[0097] 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.

[0098] 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 method for accelerating the combination of power system units based on dynamic generation of cutting planes, characterized in that, include: In the branch-and-bound solution of the power system's safety-constrained unit combination model, if the linear programming relaxation problem of the current node is feasible, the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables are obtained; the decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output. The global optimal cutting plane is constructed based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of a set of discrete decision variable indices that have been fixed to 1 and a set of discrete decision variable indices that have been fixed to 0 under the current branch strategy. Add the global optimal cut plane to the global cut pool of the branch and bound algorithm; In the linear programming relaxation problem of subsequent nodes, after loading the global optimal cutting plane in the global cut pool, the branch and bound solution process is continued to obtain the optimal unit combination scheme. In solving the linear programming relaxation problem of subsequent nodes, the global optimal cutting plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cutting plane constitutes an effective constraint. After eliminating the original optimal solution, the solution continues to be solved. The optimal objective function value of the subsequent nodes after the solution is resolved is at least raised to the lower bound of the objective function.

2. The method for accelerating the combination of power system units according to claim 1, characterized in that, If the linear programming relaxation problem at the current node is feasible, then obtaining the optimal objective function value and dual multiplier sequence at the optimal solution of the decision variables for the linear programming relaxation problem includes: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved by a solver; the solver is used to determine the optimal solution that minimizes the objective function among the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained; if there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and pruning operation is performed on the current node.

3. The method for accelerating the combination of power system units according to claim 2, characterized in that, The constraints include: physical constraints, first branch constraints, second branch constraints, and slack variable range constraints; wherein, the first branch constraints are the constraints satisfied by the discrete decision variables that have been fixed to 1 on the branch path where the current node is located, the second branch constraints are the constraints satisfied by the discrete decision variables that have been fixed to 0 on the branch path where the current node is located, and the slack variable range constraints are the value constraints satisfied by the discrete decision variables after they have been relaxed to continuous variables.

4. The method for accelerating the combination of power system units according to claim 3, characterized in that, Obtaining the sequence of dual multipliers at the optimal solution includes: Obtain the dual multipliers corresponding to each constraint of the linear programming relaxation problem at the optimal solution of the decision variables of the current node, and obtain the dual multiplier sequence; the dual multiplier sequence includes the dual multipliers of the physical constraint, the dual multipliers of the first branch constraint, the dual multipliers of the second branch constraint, and the dual multipliers of the relaxation variable range constraint.

5. The method for accelerating the combination of power system units according to claim 1, characterized in that, Constructing the globally optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node includes: Based on the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the branch history information of the current node, construct the global optimal cutting plane of the current node according to the cutting plane construction rules. The cutting plane construction rule is an effective inequality construction rule derived from the strong duality theorem in the duality theory of linear programming. The effective inequality construction rule takes the optimal objective function value of the linear programming relaxation problem of the current node, the dual multiplier sequence, and the fixed discrete decision variable index set in the branch history information as input parameters to construct an effective inequality as the global optimal cutting plane. The global optimal cutting plane is used to quantify the cost penalty for deviating from the fixed discrete decision variables in the subsequent branching process.

6. The method for accelerating the combination of power system units according to claim 5, characterized in that, The rules for constructing the cutting plane are as follows: ； in, For the current node's first A discrete decision variable, For indexing discrete decision variables, For the set of discrete decision variable indices where the current node is fixed at zero, For node indexing, This is the set of discrete decision variable indices, where the current node is fixed at one. Let be the dual multiplier vector of the first branch constraint. for The One element, Let be the dual multiplier vector of the second branch constraint. for The One element, Let be the objective function. For discrete decision variables of unit start-up and shutdown states, For the unit's output, it is a continuous decision variable. The objective function value for the linear programming relaxation problem of the current node is given.

7. The method for accelerating the combination of power system units according to claim 1, characterized in that, The branch-and-bound solution process for the safety-constrained unit combination model of a power system also includes: Based on the current global upper and lower bounds, check whether the Gap tolerance condition is met; If the conditions are not met, then solve the linear programming relaxation problem for the current node.

8. The method for accelerating the combination of power system units according to any one of claims 1 to 7, characterized in that, In the linear programming relaxation problem of subsequent nodes, after loading the globally optimal cut plane from the global cut pool, the branch and bound solution process continues, including: All globally optimal cutting planes in the global cut pool are added as additional constraints to the constraint set of the linear programming relaxation problem of subsequent nodes; The solver is invoked to solve the linear programming relaxation problem of subsequent nodes loaded with global optimal cutting planes. The solver must satisfy each global optimal cutting plane while minimizing the objective function in order to obtain the optimal objective function value of the subsequent nodes. Obtain the optimal objective function value of the linear programming relaxation problem for subsequent nodes; if the optimal objective function value is greater than or equal to the current global upper bound, perform a pruning operation on the subsequent nodes; if the optimal objective function value is less than the current global upper bound, continue to perform a branching operation on the subsequent nodes until the optimal unit combination scheme is output.

9. A power system unit combination acceleration system based on dynamic generation of cutting planes, characterized in that, include: The linear programming relaxation solution module is used in the branch and bound solution process of the power system's safety-constrained unit combination model. If the linear programming relaxation problem of the current node is feasible, it obtains the optimal objective function value and dual multiplier sequence of the linear programming relaxation problem at the optimal solution of the decision variables. The decision variables include: discrete decision variables of unit start-up and shutdown states and continuous decision variables of unit output. The cutting plane construction module is used to construct the global optimal cutting plane based on the optimal objective function value, the dual multiplier sequence, and the branch history information of the current node; the branch history information consists of a set of discrete decision variable indexes that have been fixed to 1 and a set of discrete decision variable indexes that have been fixed to 0 under the current branch strategy. The cutting plane addition module is used to add the globally optimal cutting plane to the global cut pool of the branch and bound algorithm; The branch and bound execution module is used to continue the branch and bound solution process in the linear programming relaxation problem of subsequent nodes after loading the global optimal cut plane in the global cut pool, so as to obtain the optimal unit combination scheme. Specifically, when solving the linear programming relaxation problem of subsequent nodes, the global optimal cut plane is used to determine the lower bound of the objective function based on the values ​​of the discrete decision variables of the original optimal solution of the subsequent nodes. If the lower bound of the objective function is greater than the original optimal objective function value of the linear programming relaxation problem of the subsequent nodes, the global optimal cut plane constitutes an effective constraint, and the original optimal solution is eliminated before continuing to solve the problem. The optimal objective function value of the subsequent nodes after resolving is at least raised to the lower bound of the objective function.

10. The power system unit combination acceleration system according to claim 9, characterized in that, The linear programming relaxation solution module is specifically used for: In the branch and bound solution process of the safety-constrained unit combination model of the power system, the linear programming relaxation problem of the current node is determined according to the safety-constrained unit combination model; the linear programming relaxation problem includes an objective function and constraints, and the objective function is used to determine the total operating cost of the unit based on the decision variables. The linear programming relaxation problem of the current node is solved using a solver; The solver is used to determine the optimal solution that minimizes the objective function from the values ​​of the decision variables that satisfy the constraints. If the optimal solution for the decision variables is obtained, the linear programming relaxation problem of the current node is determined to be feasible, and the optimal objective function value and dual multiplier sequence at the optimal solution are obtained. If there is no solution, the linear programming relaxation problem of the current node is determined to be infeasible, and a pruning operation is performed on the current node.

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