Constraint set reduction method and system for electric power system optimization problem

Abstract

The present invention relates to the technical field of electric power systems. Disclosed are a constraint set reduction method and system for an electric power system optimization problem. The present method comprises: determining from a preset optimization problem of an electric power system a constraint set to be reduced; taking as nodes participating variables of each constraint to be reduced, and connecting the nodes according to an order relationship between the participating variables, so as to construct a directed order graph; using the in-degree of each node in the directed order graph to perform node topology sorting on all nodes; and traversing the nodes in the directed order graph on the basis of a node topology sorting result, performing redundant-edge elimination processing, and performing constraint reduction on said constraint set on the basis of a redundant-edge elimination processing result. Therefore, relationships between problem constraints and variables are effectively utilized, and the omission of a large number of redundant constraints, which cannot be easily detected, is prevented, thereby facilitating fast solving and improving the solving efficiency.

Description

A constraint reduction method and system for power system optimization problems

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on September 20, 2023, with application number 202311211715.7 and invention name “A Constrained Intensive Reduction Method and System for Power System Optimization Problems”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention relates to the technical field of power systems, and in particular to a constraint intensive reduction method and system for power system optimization problems. Background Art

[0003] Currently, resource allocation optimization in the electricity spot market is modeled as a mixed-integer programming problem. Simultaneously, the scale of problems in the electricity spot market is increasing, and the requirements for solution efficiency are becoming increasingly stringent. The pre-solver module, as a key component of the mixed-integer programming solver, eliminates redundant constraints, reduces the problem size, and tightens the feasible domain, playing a key role in improving solution efficiency.

[0004] Currently, pre-solutions for power market optimization problems generally come from the built-in default algorithms of general mathematical programming solvers. These primarily include infeasibility detection, tightening of upper and lower bounds on constraints, tightening of constraint coefficients, and various classical reduction methods. Although these methods are applicable to any mixed integer problem, in the specific optimization scenario of power market optimization, these general-purpose methods often fail to effectively exploit the complex relationships between problem constraints and variables, leading to the omission of numerous difficult-to-detect redundant constraints, hindering rapid solution and negatively impacting solution efficiency.

[0005] Summary of the Invention

[0006] The present invention provides a constraint intensive reduction method and system for power system optimization problems, which solves the current technical problem that it is difficult to effectively utilize the complex relationship between problem constraints and variables, resulting in the omission of a large number of redundant constraints that are difficult to detect, which is not conducive to rapid solution and has an adverse impact on solution efficiency.

[0007] In view of this, a first aspect of the present invention provides a constraint reduction method for power system optimization problems, comprising the following steps:

[0008] Based on a preset optimization problem of the power system, multiple constraints to be reduced are determined and a set of constraints to be reduced is constructed;

[0009] Take each participating variable of the constraint to be reduced as a node, and connect the nodes according to the order of the participating variables to construct a directed order graph;

[0010] Performing node topological sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph;

[0011] Each node in the directed order graph is traversed according to the node topology sorting result and redundant edge elimination processing is performed, and constraint reduction is performed on the constraint set to be reduced according to the redundant edge elimination processing result.

[0012] Preferably, based on a preset optimization problem of the power system, the steps of determining a plurality of constraints to be reduced and constructing a set of constraints to be reduced specifically include:

[0013] Determine the constraint set of the power system based on the preset optimization problem of the power system;

[0014] Based on the constraint set of the power system, constraints containing two decision variables of 0-1 are screened out as constraints to be reduced, and a constraint set to be reduced is constructed.

[0015] Preferably, each participating variable of the constraint to be reduced is taken as a node, and the nodes are connected according to the order relationship of the participating variables. Before the step of constructing a directed order graph, the method further includes:

[0016] Perform mathematical transformation on each constraint to be reduced in the constraint set to be reduced to obtain participating variables and participating variable order relationships of each constraint to be reduced.

[0017] Preferably, the step of performing mathematical transformation on each constraint to be reduced in the constraint set to be reduced to obtain the participating variables and the order relationship of the participating variables of each constraint to be reduced specifically includes:

[0018] Performing mathematical transformation on each to-be-reduced constraint in the to-be-reduced constraint set to obtain an order constraint, wherein the order constraint is an inequality constraint and the order constraint includes participating variables and an order relationship of the participating variables.

[0019] Preferably, the step of performing node topological sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph specifically includes:

[0020] Initialize the topologically sorted list;

[0021] Using a breadth / depth-first search algorithm to traverse each node in the directed sequence graph, inserting the node with the smallest in-degree in the directed sequence graph into the topological sorting list;

[0022] Based on the node inserted in the topologically sorted list, the inserted node and the edges linked to it are deleted from the directed sequence graph, and the in-degree of each node in the directed sequence graph is updated;

[0023] Based on the in-degrees of the remaining nodes in the updated directed order graph, the step of inserting the node with the smallest in-degree in the directed order graph into the topological sorting list is re-executed until all nodes in the directed order graph are inserted into the topological sorting list in sequence, thereby obtaining a node topological sorting result.

[0024] Preferably, the steps of traversing each node in the directed ordered graph and performing redundant edge elimination processing according to the node topological sorting result, and performing constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result specifically include:

[0025] Traversing each node in the directed order graph according to the node topological sorting result and performing redundant edge elimination processing to obtain a transitive reduction graph;

[0026] Comparing the transitive reduction graph with the directed order graph to determine the reduced redundant edges;

[0027] The corresponding to-be-reduced constraints in the to-be-reduced constraint set are reduced according to the reduced redundant edges.

[0028] Preferably, the step of traversing each node in the directed ordered graph according to the node topological sorting result and performing redundant edge elimination processing to obtain a transfer reduction graph specifically includes:

[0029] Traversing each node in the directed sequence graph in sequence according to the node topological sorting result, and determining the edges connecting any two nodes in the directed sequence graph;

[0030] Traverse each edge e=(u,v) in the directed ordered graph in sequence according to the node topological sorting result, where e represents an edge, u represents a departure node, and v represents an arrival node, and determine whether there is any edge other than edge e in the directed ordered graph that can go from the departure node u to the arrival node v;

[0031] If it is determined that there are other edges in the directed sequence graph except the edge e that can go from the departure node u to the arrival node v, then the edge e is deleted from the directed sequence graph to obtain a transitive reduction graph.

[0032] Preferably, the step of comparing the transitive reduction graph with the directed order graph to determine the step of reducing redundant edges specifically includes:

[0033] The transitive reduction graph is compared with the directed order graph, and edges that exist in the directed order graph but do not exist in the transitive reduction graph are screened out as reduced redundant edges.

[0034] Preferably, the step of reducing the corresponding to-be-reduced constraints in the to-be-reduced constraint set according to the reduced redundant edges specifically includes:

[0035] Obtaining nodes on both sides of the reduced redundant edge;

[0036] Based on the mapping relationship between nodes and participating variables, corresponding participating variables and their corresponding to-be-reduced constraints are matched in the to-be-reduced constraint set through the nodes on both sides of the reduced redundant edge;

[0037] The matched constraints to be reduced are deleted from the set of constraints to be reduced.

[0038] In a second aspect, the present invention further provides a constraint reduction system for power system optimization problems, comprising:

[0039] A reduction constraint acquisition module is used to determine multiple constraints to be reduced based on a preset optimization problem of the power system and to construct a set of constraints to be reduced;

[0040] A graph construction module is used to take each participating variable of the constraint to be reduced as a node and connect the nodes according to the order relationship of the participating variables to construct a directed order graph;

[0041] A node topology sorting module is used to perform node topology sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph;

[0042] The constraint reduction module is used to traverse each node in the directed order graph according to the node topology sorting result and perform redundant edge elimination processing, and perform constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result.

[0043] In a third aspect, the present invention further provides an electronic device comprising a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus;

[0044] Memory for storing computer programs;

[0045] The processor is configured to implement the above method steps when executing the program stored in the memory.

[0046] In a fourth aspect, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above-mentioned method steps when executed by a processor.

[0047] It can be seen from the above technical solutions that the present invention has the following advantages:

[0048] The present invention determines a set of constraints to be reduced from a preset optimization problem of an electric power system, connects participating variables of each constraint to be reduced as nodes according to the order relationship of the participating variables, constructs a directed order graph, performs node topology sorting on all nodes using the in-degree of each node in the directed order graph, traverses each node in the directed order graph according to the node topology sorting result and performs redundant edge elimination processing, and performs constraint reduction on the set of constraints to be reduced according to the redundant edge elimination processing result, thereby effectively utilizing the relationship between problem constraints and variables, avoiding missing a large number of redundant constraints that are difficult to detect, facilitating rapid solution, and improving solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a schematic diagram of the output range of a hydropower unit;

[0050] Figure 2 is a schematic diagram of the order relationship of the variables on both sides of the constraint;

[0051] FIG3 is a flow chart of a constraint set reduction method for a power system optimization problem provided by one embodiment of the present invention;

[0052] FIG4 is a schematic diagram of eliminating redundant edges in a directed sequence graph provided by an embodiment of the present invention;

[0053] FIG5 is a flowchart of a constraint set reduction method for a power system optimization problem provided by another embodiment of the present invention;

[0054] FIG6 is a schematic diagram of an IEEE 6 node connection topology structure according to an embodiment of the present invention;

[0055] FIG7 is a directed sequence graph provided by an embodiment of the present invention;

[0056] FIG8 is a schematic diagram of a topological sorting process according to an embodiment of the present invention;

[0057] FIG9 is a transfer reduction diagram provided by an embodiment of the present invention;

[0058] FIG10 is a simplified directed sequence graph provided by an embodiment of the present invention;

[0059] FIG11 is a schematic structural diagram of a constraint reduction system for power system optimization problems provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0060] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0061] Currently, pre-solutions for power market optimization problems generally come from the built-in default algorithms of general mathematical programming solvers. These primarily include infeasibility detection, tightening of upper and lower bounds on constraints, tightening of constraint coefficients, and various classical reduction methods. Although these methods are applicable to any mixed integer problem, in the specific optimization scenario of power market optimization, these general-purpose methods often fail to effectively exploit the complex relationships between problem constraints and variables, leading to the omission of numerous difficult-to-detect redundant constraints, hindering rapid solution and negatively impacting solution efficiency.

[0062] The unit commitment problem, one of the most critical issues in power market clearing, aims to determine the start and stop states of individual units. Due to the complexities of practical scenarios, the mathematical model for the unit commitment problem requires numerous constraints to capture the complex business logic. These constraints are often crucial factors in determining the efficiency of the problem.

[0063] In most cases, the fewer constraints used to describe the same business logic, the more efficient the mixed integer programming solver will be. This is especially true when solving the root node of a problem is difficult. If a more compact and concise representation of the feasible domain can be found, the solver can leverage this property to accelerate the computation of subsequent modules.

[0064] In the unit combination problem, unit start and stop and hydropower vibration zone are the basic business logic. The constraints used to characterize this logic account for a large proportion of all model constraints, which increases the scale of the optimization problem and affects the efficiency of solving the optimization problem.

[0065] For example, in the unit start-stop constraint, the unit start-stop constraint can be represented by three types of variables, including I, W and Y. Among them, I represents the start-stop status of each unit in different time periods. I is the direct decision variable of the optimization problem. W and Y represent the start-stop decision of each unit in different time periods. These three types of variables jointly model the start-stop constraint of the unit combination problem as follows: W i,t -Y i,t =I i,t -I i,t-1 ; W i,t -Y i,t ≤1;

[0066] Where i is the unit number, t is the time decision dimension, W i,t is the startup state decision of unit i in period t, Y i,t is the stop state decision of unit i in period t, I i,t is the start and stop status of unit i in period t, I i,t-1 is the start and stop status of unit i in the t-1 period.

[0067] Among them, the first constraint describes the change of the unit's start-up or shutdown status when the unit makes a startup or shutdown decision; the second constraint restricts the unit from being started and shut down at the same time.

[0068] For the sake of convenience, we omit the subscript of the time dimension and transform the second constraint expression into the following form:

[0069] W i +Y i ≤1 constraint.

[0070] In addition to the basic constraint of unit start and stop, the power market also introduces similar constraints on the characterization of hydropower fluctuation zone: Unlike thermal power units, the output range of hydropower units is not continuous, as shown in Figure 1. Figure 1 shows the output range of hydropower units, which requires us to introduce 0-1 variables Indicates whether the output of the hydropower unit is within a certain range, and introduces the following constraints to ensure that the output of the unit is within a certain range. The constraint expression is:

[0071] Where S represents the number of units.

[0072] Without loss of generality, we can add auxiliary variables to simplify the sum of multiple 0-1 variables, and then use x to unify the above two types of constraints into the form:

[0073] The constraints, where x i 、x j The start and stop decisions of the units at the same time are made, and then the above constraints are adjusted to introduce This auxiliary constraint can be further rewritten as follows:

[0074] The order constraint, where Indicates that it is different from x i start-stop decision.

[0075] In the order constraint, the direction of the inequality sign determines the logical order of the variables on both sides of the constraint. The relationship between the direction of the inequality sign and the order of the variables on both sides of the constraint is set by yourself, such as The order relationship of the variables on both sides of the constraint is shown in Figure 2.

[0076] In electricity market clearing optimization problems, the following phenomenon can be observed: when there are precedence relationships between three or more variables, redundant logical relationships often exist in the mathematical model. For example, in the case of three-variable constraints, x1≤x2, x2≤x3, and x1≤x3, x1≤x2 and x2≤x3 can be implicitly expressed as x1≤x3 through the transitive property of inequalities. Therefore, these constraints can be removed from the problem without affecting its equivalence to the original problem. This reduction process is also known as the transitive reduction method.

[0077] Although the reduction process for the three constraints on the three variables described above is intuitively simple, manually finding all constraints that can be transitively reduced is extremely difficult when the number of variables and constraints is enormous. For example, in the unit commitment model for the Southern Regional Electricity Spot Market, both variables and constraints number in the millions. Manual logical deduction is difficult to identify reducible constraints in this situation, so a systematic solution is needed to complete the reduction task with the help of computers. However, because transitive reduction requires considering the connections between multiple constraints simultaneously, it is difficult to directly implement algebraic logical reasoning and traverse each combination in a computer. Generalized methods often fail to effectively exploit the complex relationships between problem constraints and variables, resulting in the omission of numerous difficult-to-detect redundant constraints, which is not conducive to rapid solution and has a negative impact on solution efficiency.

[0078] To this end, referring to FIG3 , the present invention provides a constraint set reduction method for a power system optimization problem, comprising the following steps 101 to 104 , specifically comprising the following steps:

[0079] 101. Based on the preset optimization problem of the power system, determine multiple constraints to be reduced and construct a set of constraints to be reduced.

[0080] Among them, the preset optimization problem of the power system is built based on the variables of the power system. The optimization problem generally includes an objective function and constraints, and determines the order constraint set that needs to be reduced.

[0081] 102. Take each participating variable of the constraint to be reduced as a node, and connect the nodes according to the order relationship of the participating variables to construct a directed order graph.

[0082] Among them, the participating variables and the participating variable order relationship are obtained based on the variables in the constraint formula to be reduced after determining the constraint to be reduced. Among them, the participating variables refer to the variables participating in the decision-making in the constraint to be reduced, and the participating variable order relationship refers to the order relationship between the participating variables. The participating variable order relationship can be mapped based on the size relationship between the participating variables, and the participating variable order relationship is set based on the size relationship between the participating variables.

[0083] Specifically, the variables participating in the constraints to be reduced can be treated as nodes, and directed edges can be connected between the nodes based on the order of the participating variables. After construction according to the above rules, a directed graph can be obtained with the number of nodes equal to the number of variables and the number of edges equal to the number of constraints. Assuming that there are no cycles in the resulting graph (otherwise, the series of inequality constraints that form a cycle will be converted into equality), a directed acyclic graph is formed based on graph theory.

[0084] 103. Perform node topological sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph.

[0085] In this embodiment, for a directed ordered graph G=(R,E), R and E both represent nodes, and the in-degree of each node R is defined as the number of edges entering R; the out-degree is defined as the number of edges departing from R.

[0086] 104. Traverse each node in the directed order graph according to the node topology sorting result and perform redundant edge elimination processing, and perform constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result.

[0087] It should be noted that the transitive reduction scheme converts the logical reasoning required in the transitive reduction method into the problem of eliminating redundant edges in a directed order graph, as shown in Figure 4. Figure 4 illustrates the elimination of redundant edges in a directed order graph, thereby eliminating the connecting edges between variables x1 and x4. After the eliminated connecting edges are mapped to the set of constraints to be reduced, the edges that can be deleted without changing the reachability of the graph correspond to the redundant and reducible parts in the constraint set.

[0088] It should be noted that the present invention determines the set of constraints to be reduced from the preset optimization problem of the power system, connects the participating variables of each constraint to be reduced as nodes according to the order relationship of the participating variables, constructs a directed order graph, and uses the in-degree size of each node in the directed order graph to perform node topology sorting on all nodes. According to the node topology sorting result, each node in the directed order graph is traversed and redundant edge elimination processing is performed. According to the redundant edge elimination processing result, constraint reduction is performed on the set of constraints to be reduced, thereby effectively utilizing the relationship between the problem constraints and the variables, avoiding missing a large number of redundant constraints that are difficult to detect, facilitating rapid solution, and improving solution efficiency.

[0089] The above is a detailed description of an embodiment of a constrained set reduction method for power system optimization problem provided by the present invention. The following is a detailed description of another embodiment of a constrained set reduction method for power system optimization problem provided by the present invention.

[0090] For ease of understanding, please refer to FIG5 , which shows a constraint set reduction method for a power system optimization problem provided by another embodiment of the present invention, including the following steps:

[0091] 201. Based on a preset optimization problem of the power system, multiple constraints to be reduced are determined, and a set of constraints to be reduced is constructed.

[0092] In one example, step 201 specifically includes:

[0093] 2011. Determine the constraint set of the power system based on the preset optimization problem of the power system.

[0094] 2012. Based on the constraint set of the power system, the constraints containing two decision variables of 0-1 are selected as the constraints to be reduced, and the constraint set to be reduced is constructed.

[0095] It should be noted that the present invention performs transitive reduction on constraints containing two decision variables of 0-1, wherein the constraints of the two decision variables of 0-1 mean that their decisions are 0 or 1, and they cannot make different decisions at the same time. Before the general solver computer group combines the problems, the trivial pre-solution method will be used to reduce the model size and determine the values ​​of some 0-1 variables in advance.

[0096] 202. Perform mathematical transformation on each constraint to be reduced in the constraint set to obtain the participating variables and the order relationship of the participating variables of each constraint to be reduced.

[0097] It should be noted that each constraint to be reduced in the constraint set to be reduced is mathematically transformed through mathematical operations and transformations. For example, the participating variables in the power on / off constraint W1+Y1≤1 are W1 and Y1, and a mapping relationship between constraints and variables is established in the computer for subsequent establishment of an ordered directed sequence graph.

[0098] In one achievable manner, each to-be-reduced constraint in the to-be-reduced constraint set is mathematically transformed to obtain an order constraint, wherein the order constraint is an inequality constraint and includes participating variables and an order relationship of the participating variables.

[0099] It should be noted that after obtaining the set of constraints to be reduced, the constraints to be reduced need to be simplified by introducing auxiliary constraints and merging similar terms and equivalent mathematical transformations, so as to convert the constraints to be reduced into order constraints of inequalities involving only the participating variables. In the order constraint, the direction of the inequality sign determines the logical order of the variables on both sides of the constraint. The relationship between the direction of the inequality sign and the order relationship of the variables on both sides of the constraint is set by yourself, such as The order relationship of the variables on both sides of the constraint is shown in Figure 2.

[0100] In a power optimization problem, there can be multiple constraints containing two decision variables (0-1). For multiple constraints containing two decision variables (0-1), the constraints to be reduced can be sorted according to the number of decision variables. In general, they are sorted in ascending order, that is, according to the difficulty of constraint reduction. The sorted constraints to be reduced form the constraint set to be reduced. In actual applications, if there is a constraint that contains a variable in the constraint set to be reduced, the form is similar to the following:

[0101] In the formula, i represents the unit number, S represents the number of units, and x i represents the 0-1 decision variable of unit i, x i =0 or 1, y represents other decision variables, and b represents the right value of the constraint.

[0102] The constraint form looks like this:

[0103] And perform the following mathematical transformation:

[0104] After completing the above processing, we can obtain a constraint containing only two decision variables.

[0105] 203. Each participating variable of the constraint to be reduced is taken as a node, and the nodes are connected according to the order relationship of the participating variables to construct a directed order graph.

[0106] It should be noted that step 203 in this embodiment is consistent with step 101 in the aforementioned embodiment and will not be described again here.

[0107] 204. Perform node topological sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph.

[0108] Specifically, step 204 includes:

[0109] 2041. Initialize the topologically sorted list.

[0110] After the topological sorting list is initialized, the topological sorting list is empty.

[0111] 2042. Use the breadth / depth-first search algorithm to traverse each node in the directed ordered graph and insert the node with the smallest in-degree in the directed ordered graph into the topologically sorted list.

[0112] Here, in-degree is defined as the number of edges connected to a node.

[0113] 2043. Based on the inserted node in the topologically sorted list, the inserted node and the edges connected to it are deleted from the directed sequence graph, and the in-degree of each node in the directed sequence graph is updated.

[0114] It should be noted that after deleting a node and the edges it links to, the in-degrees of the remaining nodes in the directed sequence graph will also be updated.

[0115] 2044. Based on the in-degrees of the remaining nodes in the updated directed order graph, re-execute the step of inserting the node with the smallest in-degree in the directed order graph into the topological sorting list until all the nodes in the directed order graph are inserted into the topological sorting list in sequence, thereby obtaining a node topological sorting result.

[0116] Among them, if all the nodes in the directed order graph are not empty, then continue to insert the node with the smallest in-degree in the directed order graph into the topological sorting list until all the nodes in the directed order graph are empty. The order in which the nodes are inserted into the topological sorting list in turn is the node topological sorting result.

[0117] In an example, given a directed order graph G, the node topological sorting process is: select the node u with an in-degree of 0 in the directed order graph G and add it to the sorting. Then, for each node v that has not yet been added to the sorting, if there is a directed edge from u to v, we reduce the in-degree of node v by one. Repeat the above process until all nodes are added to the sorting. The sorting result obtained is the node topological sorting result.

[0118] 205. Traverse each node in the directed order graph according to the node topological sorting result and eliminate redundant edges to obtain a transitive reduction graph.

[0119] Specifically, step 205 includes:

[0120] 2051. Traverse each node in the directed sequence graph in sequence according to the node topological sorting result, and determine the edges connecting each two nodes in the directed sequence graph.

[0121] 2052. According to the node topology sorting result, traverse each edge e=(u,v) in the directed sequence graph in sequence, where e represents the edge, u represents the starting node, and v represents the arrival node, and determine whether there are other edges in the directed sequence graph besides the edge e that can go from the starting node u to the arrival node v.

[0122] 2053. If it is determined that there are other edges in the directed sequence graph except edge e that can go from the departure node u to the arrival node v, then delete edge e from the directed sequence graph to obtain a transitive reduction graph.

[0123] It should be noted that if there are edges other than edge e in the directed order graph that can go from the departure node u to the arrival node v, then edge e is a logically redundant edge, that is, a logically redundant constraint in the constraint system.

[0124] In an example, suppose there are three nodes u, v, and z in a directed ordered graph, and the edge relationships between the three are u>v>z and u>z. Since node u can already reach z through the path u>v>z, and u>v or v>z cannot be deleted because u cannot reach v or v cannot reach z after deleting the two paths u>v or v>z, the two paths u>v or v>z cannot be deleted. The edge u>z is an extra edge and can be deleted, which means that the edge u>z is a logically redundant edge, which is also a logically redundant constraint in the constraint system.

[0125] In another example, a transitive reduction graph can also be constructed based on top-down transitive reduction and bottom-up transitive closure. Specifically, the construction of the transitive closure starts from the empty edge set E' and continuously adds new edges. For example, for each node u traversed by topological sorting, for each node v that can be reached by u in the set E, if there is no path from u to v in the set E', then (u, v) is added to the set E'.

[0126] 206. Compare the transitive reduction graph with the directed order graph to determine the reduced redundant edges.

[0127] It should be noted that based on graph theory, when we get the transitive reduction graph G t After that, its edge set can be mapped back to the constraint set, and at this time, due to the direct order graph G and the transitive reduction graph G t With the same transitive closure, the feasible domain range of the constraint expression does not change. t The cardinality of the edge set is generally always smaller than that of the directed ordered graph G, and the transitive reduction graph G t It is also called the transitive reduction graph of the directed ordered graph G.

[0128] At the same time, after obtaining the transfer reduction graph G t After that, it is compared with the directed order graph G, and the edges that exist in the original order graph but do not exist in the reduced order graph are found to be the reduced redundant edges.

[0129] In one achievable manner, the transitive reduction graph is compared with the directed order graph, and edges that exist in the directed order graph but not in the transitive reduction graph are screened out as reduced redundant edges.

[0130] 207. Reduce the corresponding to-be-reduced constraints in the to-be-reduced constraint set according to the reduced redundant edges.

[0131] Specifically, step 207 includes:

[0132] 2071. Obtain the nodes on both sides of the reduced redundant edge.

[0133] 2072. Based on the mapping relationship between nodes and participating variables, the corresponding participating variables and their corresponding to-be-reduced constraints are matched in the to-be-reduced constraint set by reducing the nodes on both sides of the redundant edge.

[0134] It should be noted that in the process of forming a directed order graph, the nodes are connected based on the participating variables, so there is a mapping relationship between the nodes and the participating variables. After determining the nodes on both sides of the reduced redundant edges, the corresponding participating variables and their corresponding constraints to be reduced can be matched in the set of constraints to be reduced based on the mapping relationship between the nodes and the participating variables.

[0135] 2073. Delete the matched constraints to be reduced from the set of constraints to be reduced.

[0136] In order to more clearly illustrate the above-mentioned constraint reduction process of the power system optimization problem, a practical case of power system unit combination is given below for illustration in combination with a constraint reduction method for the power system optimization problem provided by the present invention.

[0137] As shown in FIG6 , FIG6 illustrates an IEEE 6-node connection topology. A constraint intensive reduction method for a power system optimization problem provided by the present invention is applied to a system of an IEEE 6-node unit combination problem. The system is formed by connecting 6 buses Bus1, Bus2, Bus3, Bus4, Bus5, and Bus6, 3 units G1, G2, and G3, 3 load nodes D1, D2, and D3, and 11 tie lines. Specific data parameters are shown in Tables 1 to 3.

[0138] Table 1 Unit data

[0139] Table 2 Tie line data

[0140] Table 3 Hourly load data

[0141] The mathematical model of the unit commitment problem includes objective function and constraints.

[0142] Among them, the objective function is:

[0143] Where Z is the operating cost, T is the number of optimization periods, PC i (P i,t) is the unit operation quotation, I i,t The unit is in start and stop state, SU i,t , SD i,t are the unit startup and shutdown costs, respectively.

[0144] The following constraints are considered based on the lowest unit operating cost, including:

[0145] 1) Node load balancing constraints are:

[0146] Among them, the constraint requires that the load of each node can be satisfied, I b For all units included in node b, P i,t is the power of unit i at time t, j is the contact line number, is the tie line of input node b, is the tie line leaving node b, TL j,t is the output of tie line j at time period t, D b,t is the load of node b in time period t.

[0147] 2) Unit output constraints are:

[0148] This constraint requires that if unit i is turned on in time period t, the output range must be met, and if it is turned off, the output is 0. i,t 、 are the minimum and maximum output of the unit respectively.

[0149] 3) The unit climbing constraint is:

[0150] This constraint requires that the output change of unit i meets the unit climbing range requirements, and it can only be shut down when it climbs to the minimum output. i 、dr i are the ramp-up rate and ramp-down rate of unit i respectively.

[0151] 4) The minimum start and stop time constraints of the unit are:

[0152] This constraint requires that each time unit i is turned on or off, it must be kept on for a certain minimum on time and minimum off time. Where τ is the maximum start-up and shutdown time, T i down 、T i up are the minimum shutdown time and minimum startup time of unit i respectively.

[0153] 5) Tie line output constraints

[0154] This constraint requires that the tie line output must meet a certain output range. i,t 、 are the minimum output and maximum output of tie line j respectively.

[0155] This patented method focuses on removing redundancy that only contains 0-1 variables, in this case, the minimum start-stop time constraint. Before the general solver solves the combinatorial problem, it uses a trivial pre-solve method to reduce the model size and determine the values ​​of some 0-1 variables in advance. In this example, due to the small scale of the 6-node system, some 0-1 variables can be determined in advance through the following business logic, simulating the trivial pre-solve process of the general solver.

[0156] Use business logic to determine 0-1 variables: At 18, 19, and 20 in the load data table, node 4 and load 1 require a power of more than 160MW. At the same time, node 4 is connected by only two paths, path 1-2-4 and path 1-4. The output limit of all interconnection lines in the two paths is 160MW. Node 1 contains unit G1, and node 2 contains unit G2. If G1 is shut down at 18, 19, and 20, load D1 cannot meet the load demand through the 160MW upper limit of the interconnection line 2-4. Therefore, unit G1 needs to start up and output at 18, 19, and 20, that is, I 1,18 =I 1,19 =I 1,20 = 1. However, the state of unit G2 cannot be determined because G1 can meet the demand of load D1 through two paths 1-2-4 and 1-4 respectively.

[0157] After obtaining the above preprocessing information, the patented method can delete the following redundant constraints. 1,11 -I 1,12 ≤1-I 1,13 I 1,11 -I 1,12 ≤1-I 1,14 I 1,11 -I 1,12 ≤1-I 1,15 I 1,12 -I 1,13 ≤1-I 1,14 I 1,12 -I 1,13 ≤1-I 1,15 I 1,12 -I 1,13 ≤1-I 1,16 I 1,13 -I 1,14 ≤1-I 1,15 I 1,13 -I 1,14 ≤1-I1,16 I 1,13 -I 1,14 ≤1-I 1,17 I 1,14 -I 1,15 ≤1-I 1,16 I 1,14 -I 1,15 ≤1-I 1,17 I 1,14 -I 1,15 ≤1-I 1,18 I 1,15 -I 1,16 ≤1-I 1,17 I 1,16 -I 1,17 ≤1-I 1,18 I 1,16 -I 1,17 ≤1-I 1,19 I 1,16 -I 1,17 ≤1-I 1,20 ;

[0158] Combining the same categories and converting them into mathematics, we finally get the following inequality: I 1,11 -I 1,12 ≤1-I 1,13 I 1,11 -I 1,12 ≤1-I 1,14 I 1,11 -I 1,12 ≤1-I 1,15 I 1,12 -I 1,13 ≤1-I 1,14 I 1,12 -I 1,13 ≤1-I 1,15 I 1,12 -I 1,13 ≤1-I 1,16 I 1,13 -I 1,14 ≤1-I 1,15 I 1,13 -I 1,14 ≤1-I 1,16 I 1,13 -I 1,14 ≤1-I 1,17 I 1,14 -I 1,15 ≤1-I 1,16 I 1,14 -I 1,15 ≤1-I 1,17 I 1,15 -I 1,16 ≤1-I1,17 1-I 1,15 ≤1-I 1,14 1-I 1,16 ≤1-I 1,15 1-I 1,17 ≤1-I 1,16 ;

[0159] Now we need to replace the above system variables with only two variables for each constraint based on the patented method, which is defined as: α t =I 1,t -I 1,t+1 β t =1-I 1,t ;

[0160] So the above inequality becomes: α 11 ≤β 13 α 11 ≤β 14 α 11 ≤β 15 α 12 ≤β 14 α 12 ≤β 15 α 12 ≤β 16 α 13 ≤β 15 α 13 ≤β 16 α 13 ≤β 17 α 14 ≤β 16 α 14 ≤β 17 α 15 ≤β 17 β 15 ≤β 14 β 16 ≤β 15 β 17 ≤β 16 ;

[0161] According to the order relationship of the variables in the above inequality, a directed order graph can be constructed as shown in Figure 7.

[0162] Then, nodes are continuously deleted according to the in-degree of the directed graph nodes to obtain a topological sort. The topological sorting process is shown in Figure 8.

[0163] Then, we traverse each node according to the topological sorting to obtain the transitive reduction graph as shown in Figure 9.

[0164] After completing the final transitive reduction graph, the deleted connections can be checked. These connections are the edges where redundant constraints can be deleted, as shown in Figure 10. Figure 10 illustrates the simplified directed order graph, where the dotted lines are the edges that can be deleted.

[0165] Then the edges that can be deleted are mapped to the constraint set, so that the inequality system after redundant filtering can be obtained as follows: 1,11 -I 1,12 ≤1-I 1,13 I 1,11 -I 1,12 ≤1-I 1,15 I 1,12 -I 1,13 ≤1-I 1,16 I 1,13 -I 1,14 ≤1-I 1,17 I 1,14 -I 1,15 ≤1-I 1,17 I 1,15 -I 1,16 ≤1-I 1,17 I 1,14 ≤I 1,15 I 1,15 ≤I 1,16 I 1,16 ≤I 1,17 ;

[0166] Ultimately, this method removed six inequality constraints. Compared to existing general-purpose methods, this method is more applicable to power optimization problems and can identify a large number of redundant constraints that general-purpose methods cannot. In actual power system production environments, this solution has a significant reduction effect. In current practical applications, this method can effectively remove an average of more than 500,000 redundant order constraints from the total constraints (over 500,000), improving computational efficiency by approximately 21%.

[0167] In practical applications, a SCUC problem for six units with 24 periods of operation corresponds to some unit on / off constraints, which contain three redundant constraints. Manual logical deduction is completely unable to identify the reducible constraints. However, by proposing a constraint set reduction method for power system optimization problems through transfer reduction based on a transfer order graph, the three redundant constraints can be easily reduced.

[0168] The above is a detailed description of an embodiment of a constrained set reduction method for a power system optimization problem provided by the present invention. The following is a detailed description of an embodiment of a constrained set reduction system for a power system optimization problem provided by the present invention.

[0169] For ease of understanding, please refer to FIG11 . The present invention further provides a constraint reduction system for power system optimization problems, including:

[0170] The reduction constraint acquisition module 100 is used to determine a plurality of constraints to be reduced based on a preset optimization problem of the power system and to construct a set of constraints to be reduced;

[0171] A graph construction module 200 is used to construct a directed sequence graph by taking each participating variable of the constraint to be reduced as a node and connecting the nodes according to the order relationship of the participating variables;

[0172] A node topology sorting module 300 is configured to perform node topology sorting on all nodes in the directed sequence graph according to the in-degree of each node in the directed sequence graph;

[0173] The constraint reduction module 400 is used to traverse each node in the directed order graph according to the node topology sorting result and perform redundant edge elimination processing, and perform constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result.

[0174] The present invention also provides an electronic device, comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus;

[0175] Memory for storing computer programs;

[0176] The processor is configured to implement the above method steps when executing the program stored in the memory.

[0177] The present invention also provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, the above method steps are implemented.

[0178] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described system, electronic device, and computer-readable storage medium can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0179] In the several embodiments provided by the present invention, it should be understood that the disclosed systems, electronic devices, computer-readable storage media, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of modules is merely a logical function division. In actual implementation, there may be other division methods, such as multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0180] Modules described as separate components may or may not be physically separate, and components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of these modules may be selected to achieve the purpose of this embodiment based on actual needs.

[0181] In addition, the functional modules in various embodiments of the present invention may be integrated into a single processing module, or each module may exist physically separately, or two or more modules may be integrated into a single module. The aforementioned integrated modules may be implemented in the form of hardware or software functional modules.

[0182] If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for executing all or part of the steps of the various embodiments of the method of the present invention through a computer device (which can be a personal computer, server, or network device, etc.). The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (full name: Read-Only Memory, English abbreviation: ROM), random access memory (full name: Random Access Memory, English abbreviation: RAM), magnetic disk or optical disk, and other media that can store program code.

[0183] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A constraint set reduction method for power system optimization problem, characterized in that: The following steps are involved: Based on the preset optimization problem of the power system, multiple constraints to be reduced are determined, and a set of constraints to be reduced is constructed; Take each participating variable of the constraint to be reduced as a node, and connect the nodes according to the order of the participating variables to construct a directed order graph; Performing node topological sorting on all nodes in the directed sequence graph according to the in-degree size of each node in the directed sequence graph; According to the node topology sorting result, each node in the directed order graph is traversed and redundant edge elimination processing is performed, and constraint reduction is performed on the constraint set to be reduced according to the redundant edge elimination processing result.

2. The constraint set reduction method for power system optimization problem according to claim 1, characterized in that: Based on a preset optimization problem of the power system, a plurality of constraints to be reduced are determined, and steps of constructing a set of constraints to be reduced are specifically included: Determine the constraint set of the power system based on the preset optimization problem of the power system; Based on the constraint set of the power system, constraints containing two decision variables of 0-1 are screened out as constraints to be reduced, and a constraint set to be reduced is constructed.

3. The constraint set reduction method for power system optimization problem according to claim 1, characterized in that: Before the step of taking each participating variable of the constraint to be reduced as a node and connecting the nodes according to the order relationship of the participating variables and constructing a directed order graph, the following steps are also included: Mathematically transform each constraint to be reduced in the constraint set to be reduced to obtain participating variables and participating variable order relationships of each constraint to be reduced.

4. The constraint set reduction method for power system optimization problem according to claim 3, characterized in that: The step of performing mathematical deformation on each to-be-reduced constraint in the to-be-reduced constraint set to obtain participating variables and participating variable order relationships of each to-be-reduced constraint specifically includes: Each to-be-reduced constraint in the to-be-reduced constraint set is mathematically transformed to obtain an order constraint, wherein the order constraint is an inequality constraint and the order constraint includes participating variables and an order relationship of the participating variables.

5. The constraint set reduction method for power system optimization problem according to claim 1, characterized in that: The step of performing node topological sorting on all nodes in the directed sequence graph according to the in-degree size of each node in the directed sequence graph specifically comprises: Initialize the topological sorted list; Using a breadth / depth first search algorithm to traverse each node in the directed sequence graph, inserting the node with the smallest in-degree in the directed sequence graph into the topological sorting list; Based on the node inserted in the topological sorting list, the inserted node and the edge linked to it are deleted from the directed sequence graph, and the in-degree of each node in the directed sequence graph is updated; Based on the updated in-degrees of the remaining nodes in the directed order graph, the step of inserting the node with the smallest in-degree in the directed order graph into the topological sorting list is re-executed until all the nodes in the directed order graph are inserted into the topological sorting list in sequence, thereby obtaining a node topological sorting result.

6. The constraint set reduction method for power system optimization problem according to claim 1, characterized in that: The steps of traversing each node in the directed ordered graph and performing redundant edge elimination processing according to the node topological sorting result, and performing constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result specifically include: Traversing each node in the directed order graph according to the node topological sorting result and performing redundant edge elimination processing to obtain a transitive reduction graph; Comparing the transitive reduction graph with the directed order graph to determine the reduced redundant edges; The corresponding to-be-reduced constraints in the to-be-reduced constraint set are reduced according to the reduced redundant edges.

7. The constraint set reduction method for power system optimization problem according to claim 6, characterized in that: The steps of traversing each node in the directed order graph according to the node topological sorting result and performing redundant edge elimination processing to obtain a transfer reduction graph specifically include: Traversing each node in the directed sequence graph in turn according to the node topological sorting result, and determining the edges connecting each two nodes in the directed sequence graph; According to the node topological sorting result, traverse each edge e=(u,v) in the directed sequence graph in turn, where e represents an edge, u represents a departure node, and v represents an arrival node, and determine whether there are other edges in the directed sequence graph that can go from the departure node u to the arrival node v except the edge e; If it is determined that there are other edges in the directed sequence graph except edge e that can go from the starting node u to When the node v is reached, the edge e is deleted from the directed sequence graph to obtain a transitive reduction graph.

8. The constraint set reduction method for power system optimization problem according to claim 6, characterized in that: The steps of comparing the transitive reduction graph with the directed order graph to reduce redundant edges specifically include: The transitive reduction graph is compared with the directed order graph, and edges that exist in the directed order graph but do not exist in the transitive reduction graph are screened out as reduced redundant edges.

9. The constraint set reduction method for power system optimization problem according to claim 6, characterized in that: The step of reducing the corresponding to-be-reduced constraints in the to-be-reduced constraint set according to the reduced redundant edges specifically includes: Obtaining nodes on both sides of the reduced redundant edge; Based on the mapping relationship between nodes and participating variables, the corresponding participating variables and their corresponding to-be-reduced constraints are matched in the to-be-reduced constraint set through the nodes on both sides of the reduced redundant edge; The matched constraints to be reduced are deleted from the set of constraints to be reduced.

10. A constraint set reduction system for power system optimization problems, characterized in that: include: A reduction constraint acquisition module is used to determine multiple constraints to be reduced based on a preset optimization problem of the power system and to construct a set of constraints to be reduced; A graph construction module is used to take each participating variable of the constraint to be reduced as a node, and connect the nodes according to the order relationship of the participating variables to construct a directed order graph; A node topology sorting module is used to perform node topology sorting on all nodes in the directed sequence graph according to the in-degree size of each node in the directed sequence graph; The constraint reduction module is used to traverse each node in the directed order graph according to the node topology sorting result and perform redundant edge elimination processing, and perform constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result.

11. An electronic device, characterized in that: It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, for executing a program stored in a memory, to implement any one of claims 1 to 9 The method steps are described.

12. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method steps of any one of claims 1 to 9 are implemented.

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