CN116957170B - Constraint intensive reduction method and system for power system optimization problem - Google Patents
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Abstract
The invention relates to the technical field of power systems and discloses a constraint intensive reduction method and a constraint intensive reduction system for an optimization problem of a power system.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a constraint intensive reduction method and a constraint intensive reduction system for power system optimization.
Background
At present, the resource allocation optimization problem in the electric power spot market needs to be solved through modeling as a mixed integer programming problem, and meanwhile, the problem to be solved in the electric power spot market is larger and larger in scale, and the requirement on solving efficiency is more stringent. The pre-solving module is used as an important component of the mixed integer programming solver, can eliminate redundant constraint in the problem, reduces the problem scale, tightens up the problem feasible region, and has a key effect on improving the solving efficiency.
Currently, the pre-solving scheme applied to the power market optimization problem is commonly derived from a built-in default algorithm of a general mathematical programming solver and mainly comprises infeasibility detection, constraint upper and lower bound tightening, constraint coefficient tightening and various classical reduction methods. Although the method has applicability to any mixed integer, in a special optimization scene of power market optimization, the general method is difficult to effectively utilize complex relations between problem constraints and variables, so that a large number of redundant constraints which are not easy to detect are omitted, quick solution is not facilitated, and the solution efficiency is adversely affected.
Disclosure of Invention
The invention provides a constraint intensive reduction method and a constraint intensive reduction system for an electric power system optimization problem, which solve the technical problems that the complex relation between problem constraints and variables is difficult to effectively utilize at present, so that a large number of redundant constraints which are difficult to detect are omitted, quick solution is not facilitated, and the solution efficiency is adversely affected.
In view of this, the first aspect of the present invention provides a constraint-intensive subtraction method for an optimization problem of an electric power system, including the steps of:
based on a preset optimization problem of the power system, determining a plurality of constraint reduction to be reduced, and constructing a constraint reduction set to be reduced;
Taking each participation variable to be reduced as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram;
performing node topology sequencing on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram;
traversing each node in the directed sequence diagram according to the node topology sequencing result, performing redundant edge elimination processing, and performing constraint reduction on the constraint reduction set according to the redundant edge elimination processing result.
Preferably, the step of determining a plurality of constraints to be reduced based on a preset optimization problem of the power system and constructing a set of constraints to be reduced specifically includes:
determining a constraint set of the power system based on a preset optimization problem of the power system;
based on the constraint set of the power system, the constraint comprising 0-1 decision variables is screened out as constraint to be reduced, and the constraint set to be reduced is constructed.
Preferably, each participation variable to be reduced is taken as a node, node connection is carried out according to the sequence relation of the participation variables, and before the step of constructing the directed sequence diagram, the method further comprises the following steps:
and carrying out mathematical deformation on each constraint to be reduced in the constraint set to be reduced to obtain a participation variable and a participation variable sequence relation of each constraint to be reduced.
Preferably, the step of mathematically deforming each constraint to be reduced in the constraint set to be reduced to obtain a participation variable of each constraint to be reduced and a sequence relationship of the participation variable specifically includes:
and carrying out mathematical deformation on each constraint to be reduced in the constraint set to be reduced to obtain a sequence constraint, wherein the sequence constraint is an inequality constraint and comprises a participation variable and a participation variable sequence relation.
Preferably, the step of performing node topology sequencing on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram specifically includes:
initializing a topology ordering list;
traversing each node in the directed sequence diagram by using a breadth/depth first search algorithm, and inserting the node with the smallest degree in the directed sequence diagram into the topological ordered list;
deleting the inserted nodes and the linked edges thereof from the directed sequence diagram based on the nodes inserted in the topological sorting list, and updating the degree of entry of each node in the directed sequence diagram;
and based on the updated degree of incidence of the remaining nodes in the directed sequence diagram, the step of inserting the node with the smallest degree of incidence in the directed sequence diagram into the topological sorting list is re-executed until all nodes in the directed sequence diagram are sequentially inserted into the topological sorting list, and a node topological sorting result is obtained.
Preferably, the step of traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing, and performing constraint reduction on the constraint reduction set according to the redundant edge elimination processing result specifically includes:
traversing each node in the directed sequence diagram according to the node topology sequencing result and performing redundant edge elimination processing to obtain a transmission reduction diagram;
comparing the transfer reduced graph with the directed sequence graph to determine reduced redundant edges;
and reducing the corresponding constraint to be reduced in the constraint set to be reduced according to the redundant edge to be reduced.
Preferably, traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing to obtain a transmission reduction graph, which specifically comprises the following steps:
traversing each node in the directed sequence diagram in turn according to a node topology sequencing result, and determining the linked edges between every two nodes in the directed sequence diagram;
traversing each edge in the directed sequence diagram in turn according to the node topology sequencing resultWherein e represents an edge, u represents a departure node, v represents an arrival node, and whether other edges except the edge e exist in the directed sequence diagram or not is judged from the departure node u to the arrival node v;
And if the fact that other edges except the edge e can reach the node v from the starting node u is judged in the directed sequence diagram, deleting the edge e from the directed sequence diagram, and obtaining a transfer reduction diagram.
Preferably, the step of comparing the transfer reduction graph with the directed sequence graph to determine a reduction redundancy edge specifically includes:
comparing the transfer reduction graph with the directed sequence graph, and screening out edges which exist in the directed sequence graph and are not in the transfer reduction graph as reduced redundancy edges.
Preferably, the step of reducing the constraint to be reduced corresponding to the constraint set to be reduced according to the reduced redundancy edge specifically includes:
acquiring nodes on two sides of the reduced redundant edge;
based on the mapping relation between the nodes and the participation variables, the corresponding participation variables and the corresponding constraint to be reduced are matched in the constraint set to be reduced through the nodes on the two sides of the redundant edge to be reduced;
and deleting the matched constraint to be reduced in the constraint set to be reduced.
In a second aspect, the present invention also provides a constraint reduction system for power system optimization problem, comprising:
the constraint reduction acquisition module is used for determining a plurality of constraint reduction to be reduced based on a preset optimization problem of the power system and constructing a constraint reduction set to be reduced;
The diagram construction module is used for taking each participation variable to be reduced and constrained as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram;
the node topology sequencing module is used for carrying out node topology sequencing on all the nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram;
and the constraint reduction module is used for traversing each node in the directed sequence diagram according to the node topology sequencing result, performing redundant edge elimination processing, and performing constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result.
In a third aspect, the present invention further provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, where the processor, the communication interface, and the memory complete communication with each other through the communication bus;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
In a fourth aspect, the present invention also provides a computer readable storage medium having stored therein a computer program which when executed by a processor implements the above-mentioned method steps.
From the above technical scheme, the invention has the following advantages:
according to the method, the constraint reduction set to be reduced is determined from the preset optimization problem of the electric power system, each participation variable to be reduced constraint is used as a node to be connected according to the sequence relation of the participation variables, a directed sequence diagram is constructed, node topology sequencing is carried out on all nodes by utilizing the degree of ingress of each node in the directed sequence diagram, each node in the directed sequence diagram is traversed according to the node topology sequencing result, redundant edge elimination processing is carried out, constraint reduction is carried out on the constraint reduction set to be reduced according to the redundant edge elimination processing result, therefore, the relation between problem constraint and variable is effectively utilized, a large number of redundant constraint which is not easy to detect are avoided, quick solving is facilitated, and solving efficiency is improved.
Drawings
FIG. 1 is a schematic diagram of the output interval of a hydroelectric generating set;
FIG. 2 is a schematic diagram of the order relationship of constraining two side variables;
FIG. 3 is a flow chart of a constraint set reduction method for power system optimization problem according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a redundant edge elimination scenario in a directed sequence diagram according to an embodiment of the present invention;
FIG. 5 is a flow chart of a constraint set reduction method for power system optimization problem according to another embodiment of the present invention;
Fig. 6 is a schematic diagram of an IEEE6 node connection topology according to an embodiment of the present invention;
FIG. 7 is a directed sequence diagram provided by an embodiment of the present invention;
FIG. 8 is a schematic diagram of a topology ordering process according to an embodiment of the present invention;
FIG. 9 is a reduced-scale view of a transfer provided by an embodiment of the present invention;
FIG. 10 is a simplified directed sequence diagram provided by an embodiment of the present invention;
fig. 11 is a schematic structural diagram of a constraint intensive subtraction system for power system optimization problem according to an embodiment of the present invention.
Detailed Description
In order to make the present invention better understood by those skilled in the art, the following description will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Currently, the pre-solving scheme applied to the power market optimization problem is commonly derived from a built-in default algorithm of a general mathematical programming solver and mainly comprises infeasibility detection, constraint upper and lower bound tightening, constraint coefficient tightening and various classical reduction methods. Although the method has applicability to any mixed integer, in a special optimization scene of power market optimization, the general method is difficult to effectively utilize complex relations between problem constraints and variables, so that a large number of redundant constraints which are not easy to detect are omitted, quick solution is not facilitated, and the solution efficiency is adversely affected.
Among them, the unit combination problem is one of the most critical problems in the power market, and the purpose of the unit combination problem is to determine the start-stop state of each unit. Because the actual problem scene is complex, a great deal of constraints are required to be introduced into the mathematical model of the unit combination problem for describing complex business logic. These constraints are often important factors in determining the efficiency of problem solving.
In most cases, the fewer the number of constraints used to characterize the same business logic, the higher the efficiency of the mixed integer programming solver in solving the problem. Especially when the problem root node is difficult to solve, if a more compact and simple representation of the problem feasible region can be found, the solver can fully utilize the property to accelerate the calculation speed of the subsequent modules.
In the unit combination problem, the unit start-stop and hydropower vibration area is the basic business logic, and the constraint used for describing the logic occupies a larger proportion in all model constraints, so that the scale of the optimization problem is increased, and the solving efficiency of the optimization problem is influenced.
For example: in the unit start-stop constraint, the unit start-stop constraint can be represented by three types of variables, wherein the three types of variables comprise I, W and Y, I represents the start-stop state of each unit in different time periods, I is a direct decision variable of an optimization problem, W and Y respectively represent the start-stop decision of each unit in different time periods, and the three types of variables jointly model the start-stop constraint of the unit combination problem:
；
；
Wherein i is the serial number of the unit, t is the timeThe decision dimension is defined as the dimension of the decision,decision on the start-up status of the unit i over the period t, -for the unit i>Decision on stop state of unit i over period t, < >>For the start-stop state of the unit i over the period t,is the start-stop state of the unit i in the t-1 period.
The first constraint characterizes the change of the start-stop state of the unit when the unit makes a start-up or shut-down decision; the second constraint limits the unit to be unable to be powered on and off simultaneously at the same time.
For convenience of description, we omit subscripts of the time dimension, converting the second constraint expression into a form as:
is a constraint of (a).
Besides the basic constraint of starting and stopping of the unit, similar constraints can be introduced to the description of the hydropower vibration area in the electric power market: unlike thermal power units, the output interval of the hydroelectric power unit is discontinuous, as shown in FIG. 1, FIG. 1 illustrates the output interval of the hydroelectric power unit, and we need to introduce 0-1 variableThe method is characterized in that whether the output force of the water motor unit is in a certain interval is indicated, and the following constraint is introduced to ensure that the output force of the unit is in a certain interval, wherein the constraint expression is as follows:
；
in the formula, S represents the number of units.
Without loss of generality, auxiliary can be added The variables simplify the summation of a plurality of 0-1 variables, and further apply the two types of constraintsxUnified representation as
；
Or (b)
Wherein->、/>The start-stop decision of the units at the same time is respectively carried out, and the constraint is adjusted to introduce +.>This auxiliary constraint, we can further rewrite the constraint to a shape like:
；
or (b)
Order constraint of (2), wherein->Representing a difference from +.>Is a start-stop decision of (2).
In order constraint, the direction of the inequality sign determines that the variables on two sides of the constraint logically have sequence, wherein the relationship between the direction of the inequality sign and the sequence relationship of the variables on two sides of the constraint is set by itself, such asSecondary of constraint two-sided variable under constraintThe sequence relationship is shown in fig. 2.
In the power market clearing optimization problem, the following phenomena can be observed: when there are precedence relationships between three or more variables, redundant logical relationships often exist in the mathematical model. Taking three variables as examples of what constraints are, inOf these three constraints, +.>，/>The +.A. can be implicitly represented by the transitivity of the inequality>We can therefore remove it from the problem without affecting its equivalence to the original problem, this reduction process is also called the transfer reduction method.
While the three constraint reduction process for the three variables described above is intuitively simple, it is very difficult to manually find all constraints that can be passed on the reduction when the number of variables and constraints is large. In the combined model of the electric spot market machine set in the south area, variables and constraints are in the millions, and the reducible constraints are difficult to distinguish by virtue of manual logic deduction, so that a systematic solution is required to be provided, and the reducible tasks are completed by virtue of a computer. However, as the transmission reduction needs to consider the connection among a plurality of constraints at the same time, it is difficult to directly realize logical reasoning on algebraic level and traverse each combination in a computer, and the general method often has difficulty in effectively utilizing complex relations between problem constraints and variables, so that a large number of redundant constraints which are not easy to detect are omitted, the quick solution is not facilitated, and the solution efficiency is adversely affected.
For this reason, referring to fig. 3, the constraint set reduction method for the power system optimization problem provided by the present invention includes the following steps 101 to 104, specifically including the following steps:
101. based on a preset optimization problem of the power system, a plurality of constraint reduction constraints are determined, and a constraint reduction set is constructed.
Wherein the preset optimization problem of the power system is set up based on variables of the power system, the optimization problem generally comprises an objective function and constraint conditions, and an order constraint set requiring reduction is determined from the objective function and the constraint conditions.
102. And taking each participation variable to be reduced and constrained as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram.
The method comprises the steps that after constraint to be reduced is determined, a participation variable and a participation variable order relation are obtained based on a variable in a constraint formula to be reduced, wherein the participation variable refers to a decision variable in the constraint to be reduced, the participation variable order relation refers to a precedence order relation among the participation variables, the participation variable order relation can be mapped based on a size relation among the participation variables, and the participation variable order relation is set automatically based on the size relation among the participation variables.
Specifically, variables participating in constraint reduction to be reduced can be taken as nodes, and directed edges are connected among the nodes according to the order relation of the participating variables. After constructing according to the rule, a directed graph with the number of nodes equal to the number of variables and the number of edges equal to the number of constraints can be obtained. Assuming that no loops are present in the available graph (otherwise a series of inequality constraints forming loops would be converted to equations), a directed acyclic graph is formed based on graph theory.
103. And performing node topological sorting on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram.
In the present embodiment, for the directed sequence diagram g= (R, E), R, E each represents a node, the degree of ingress of each node R of which is defined as the number of edges that enter R; the degree of departure is defined as the number of edges starting from R.
104. Traversing each node in the directed sequence diagram according to the node topology sequencing result, performing redundant edge elimination processing, and performing constraint reduction on the constraint reduction set according to the redundant edge elimination processing result.
It should be noted that, the transfer reduction scheme converts the logic reasoning needed in the transfer reduction method into the problem of eliminating redundant edges in the directed sequence diagram, as shown in fig. 4, fig. 4 illustrates the situation of eliminating redundant edges in the directed sequence diagram, thereby eliminating the variable x 1 And x 4 And after the eliminated connecting edges are corresponding to the constraint set to be reduced, the edges which can be deleted on the premise of not changing the accessibility of the graph correspond to the redundant reducible parts in the constraint set.
It should be noted that, the invention determines the constraint reduction set from the preset optimization problem of the electric power system, connects each participation variable to be constrained as a node according to the sequence relation of the participation variables, constructs a directed sequence diagram, uses the degree of penetration of each node in the directed sequence diagram to carry out node topology sequencing on all nodes, traverses each node in the directed sequence diagram according to the node topology sequencing result and carries out redundant edge elimination processing, and carries out constraint reduction on the constraint reduction set according to the redundant edge elimination processing result, thereby effectively utilizing the relation between the problem constraint and the variable, avoiding missing a large number of redundant constraints which are not easy to detect, being beneficial to quick solution and improving the solving efficiency.
The above is a detailed description of one embodiment of a constraint reduction method for an electric power system optimization problem provided by the present invention, and the following is a detailed description of another embodiment of the constraint reduction method for an electric power system optimization problem provided by the present invention.
For ease of understanding, referring to fig. 5, another embodiment of the present invention provides a constraint set reduction method for power system optimization problem, which includes the following steps:
201. based on a preset optimization problem of the power system, a plurality of constraint reduction constraints are determined, and a constraint reduction set is constructed.
In one example, step 201 specifically includes:
2011. and determining a constraint set of the power system based on a preset optimization problem of the power system.
2012. Based on a constraint set of the power system, the constraint comprising 0-1 decision variables is screened out as a constraint to be reduced, and the constraint set to be reduced is constructed.
It should be noted that, the present invention reduces the constraint comprising two decision variables of 0-1 by transmitting, wherein, the constraint of two decision variables of 0-1 means that the decision is 0 or 1, which cannot make different decisions at the same time, and before the general solver computer group combines the problems, the model scale is reduced by adopting a trivial pre-solving method, and the variable value of 0-1 is determined in advance.
202. And carrying out mathematical deformation on each constraint to be reduced in the constraint set to be reduced to obtain a participation variable and a participation variable sequence relation of each constraint to be reduced.
It should be noted that, each constraint to be reduced in the constraint set to be reduced is mathematically deformed by mathematical operation and deformation, such asThe participation variable in the switch constraint is +.>、/>And establishing a mapping relation between the constraint and the variable in the computer for establishing a directional sequence diagram with sequence in the follow-up.
In one implementation, each constraint to be reduced in the set of constraints to be reduced is mathematically deformed to obtain a sequence constraint, wherein the sequence constraint is an inequality constraint, and the sequence constraint comprises a participation variable and a participation variable sequence relationship.
After the constraint set to be reduced is obtained, the constraint to be reduced is simplified by introducing auxiliary constraints and combining similar items and equivalent mathematical transformation, so that the constraint to be reduced is converted into an order constraint of inequality of only participating variables, wherein the order constraint determines that the two variables of the constraint have a logically sequential order in different sign directions, and the order of the two variables of the constraint is different sign directions and the order of the two variables of the constraint The relationships between relationships being self-setting, e.g.The order relationship of the two side variables of the constraint is shown in fig. 2.
In the power optimization problem, the number of constraints including 0-1 decision variables may be multiple, and for multiple constraints including 0-1 decision variables, the multiple constraints to be reduced may be ordered according to the number of decision variables, in a general example, the constraints to be reduced are ordered in an ascending manner, that is, the ordered constraints are ordered according to the difficulty of constraint reduction, and the ordered multiple constraints to be reduced form a constraint set to be reduced. In practical applications, if there is a constraint contained in the constraint set to be reduced, the variables contained in the constraint set are similar in form to the following:
；
wherein i represents the serial number of the unit, S represents the number of the unit, and x i 0-1 decision variable, x, representing unit i i =0 or 1, y represents the other decision variable, and b represents the constraint right value.
The constraint form is similar as follows:
；
and the mathematical transformation is performed as follows:
；
after the above processing is completed, a constraint containing only two decision variables can be obtained.
203. And taking each participation variable to be reduced and constrained as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram.
It should be noted that, step 203 in this embodiment is identical to step 101 in the foregoing embodiment, and will not be described herein.
204. And performing node topological sorting on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram.
Specifically, step 204 specifically includes:
2041. initializing a topological ordered list.
After initializing the topology ordering list, the topology ordering list is empty.
2042. Traversing each node in the directed sequence diagram by using a breadth/depth first search algorithm, and inserting the node with the smallest degree in the directed sequence diagram into a topological ordered list.
Wherein the ingress is defined as the number of edges connected to the node.
2043. Based on the inserted nodes in the topological order list, deleting the inserted nodes and the linked edges thereof from the directed sequence diagram, and updating the degree of importation of each node in the directed sequence diagram.
It should be noted that, after deleting the node and the edge linked with the node, the degree of entry of the remaining nodes in the directed sequence graph is updated.
2044. And based on the degree of incidence of the remaining nodes in the updated directed sequence diagram, the step of inserting the node with the smallest degree of incidence in the directed sequence diagram into the topology sequencing list is re-executed until all the nodes in the directed sequence diagram are sequentially inserted into the topology sequencing list, and a node topology sequencing result is obtained.
If all the nodes in the directed sequence diagram are not empty, the node with the smallest degree of penetration in the directed sequence diagram is continuously inserted into the topology sequencing list until all the nodes in the directed sequence diagram are empty, and the sequence in which the nodes are sequentially inserted into the topology sequencing list is the node topology sequencing result.
In one example, given a directed sequence graph G, its node topology ordering process is: selecting a node u with a node degree of 0 in the directed sequence diagram G, adding the node u to the sequence, and then for each node v which is not added with the sequence, subtracting one from the degree of the node v if directed edges from u to v exist, and repeating the above processes until all the nodes are added with the sequence, wherein the obtained sequence result is the node topology sequence result.
205. And traversing each node in the directed sequence diagram according to the node topology sequencing result, and performing redundant edge elimination processing to obtain a transmission reduction diagram.
Specifically, step 205 specifically includes:
2051. and traversing each node in the directed sequence diagram in turn according to the node topology sequencing result, and determining the linked edges between every two nodes in the directed sequence diagram.
2052. Traversing each edge in the directed sequence diagram in turn according to the node topology sequencing result Where e represents an edge, u represents a departure node, v represents an arrival node, and it is determined whether there are edges in the directed sequence diagram other than the edge e from the departure node u to the arrival node v.
2053. If it is determined that the directed sequence diagram has other edges from the departure node u to the arrival node v, deleting the edge e from the directed sequence diagram, and obtaining a transfer reduction diagram.
If there are other edges in the directed sequence diagram, except the edge e, from the departure node u to the arrival node v, the edge e is described as a logically redundant edge, i.e., a logically redundant constraint in the constraint system.
In one example, if there are three nodes u, v, z in the directed sequence diagram, the side relationship of the three is u > v > z and u > z, since node u can already reach z through the path u > v > z, and the two paths u > v or v > z cannot reach z due to the fact that u cannot reach v or v cannot reach z after deletion, the two paths u > v or v > z cannot be deleted, the path u > z is an additional side, and the side u > z is a logically redundant side, that is, a logically redundant constraint in the constraint system.
In another example, the transfer reduction graph may also be constructed based on top-down transfer reduction and bottom-up transfer closure, specifically, the transfer closure is constructed by starting from the empty edge set E ', adding new edges continuously, for example, for each node u traversed in topological order, for each node v reachable by u in set E, adding (u, v) to set E ' if there is no path from u to v in set E '.
206. The transfer reduced graph is compared to the directed sequence graph to determine reduced redundancy edges.
It should be noted that, based on graph theory, when we get the transfer reduction graph G t Thereafter, its edge set may be mapped back to the constraint set, and at this time, the graph G is reduced due to the directed sequence and transfer t With the same transitive closure, there is no change in the feasible region range represented by the constraint. Due to the fact that reduced graph G is transferred t The radix of the edge set of (a) is generally always smaller than the directed sequence graph G, passing the reduction graph G t Also referred to as a transfer reduction graph of the directed sequence graph G.
At the same time, the transfer reduction graph G is obtained t Then, the result is compared with the directed sequence diagram G to find out the edges which exist in the original sequence diagram but do not exist in the reduced sequence diagram, namely the reduced redundancy edges.
In one implementation, the transfer reduction graph is compared to the directed order graph, and edges that exist in the directed order graph and that do not exist in the transfer reduction graph are screened out as reduced redundancy edges.
207. And reducing the corresponding constraint to be reduced in the constraint set to be reduced according to the redundant edge to be reduced.
Specifically, step 207 specifically includes:
2071. nodes on two sides of the reduced redundant edge are obtained.
2072. Based on the mapping relation between the nodes and the participation variables, the corresponding participation variables and the corresponding constraint to be reduced are matched in the constraint to be reduced set through the nodes on the two sides of the redundant edge to be reduced.
It should be noted that, in the process of forming the directed sequence graph, the nodes are connected based on the participation variables as nodes, so that a mapping relationship between the nodes and the participation variables exists, and after the nodes on two sides of the reduced redundancy edge are determined, according to the mapping relationship between the nodes and the participation variables, the corresponding participation variables and the corresponding reduced constraints thereof can be matched in the reduced constraint set.
2073. And deleting the matched constraint to be reduced in the constraint set to be reduced.
In order to more clearly illustrate the constraint intensive subtraction process of the power system optimization problem, the practical case of a power system unit combination is provided below in connection with the constraint intensive subtraction method of the power system optimization problem provided by the invention.
As shown in FIG. 6, FIG. 6 illustrates an IEEE6 node connection topology, and the constraint intensive reduction method for power system optimization problem provided by the invention is applied to a system for IEEE6 node unit combination problem, wherein the system comprises 6 buses Bus1, bus2, bus3, bus4, bus5, bus6 and 3 units G 1 、G 2、 G 3 3 load nodes D 1 、D 2、 D 3 And 11 connecting lines are connected to form, and specific data parameters are shown in tables 1-3.
Table 1 set data
Table 2 tie line data
TABLE 3 hourly load data
The mathematical model of the crew combination problem includes an objective function and constraints.
Wherein, the objective function is:
；
wherein Z is the running cost, T is the number of optimized time periods,quoting for unit operation,/->For the start-stop state of the machine set, < > for>、/>The starting and shutdown costs of the unit are respectively.
The following constraint conditions are considered based on the minimum unit operation cost, and the method comprises the following steps:
1) The node load balancing constraint is:
；
wherein the constraint requires that the load of each node can be satisfied,for all of the sets of sets included in node b,for the power of unit i at time t, +.>For the tie number>For the connection line of input node b +.>For leaving the connection of node b +.>For the output of tie j during period t, < >>Is the load of node b at time period t.
2) The output constraint of the unit is as follows:
；
the constraint requires that the unit i meet the output range if turned on and the output is 0 if turned off in period t.、The minimum output and the maximum output of the machine set are respectively.
3) The unit climbing constraint is as follows:
；
the constraint requires that the output change of the unit i meets the requirement of the climbing range of the unit, and shutdown can be realized only when the climbing reaches the minimum output. Wherein, 、/>The ascending climbing speed and the descending climbing speed of the unit i are respectively.
4) The minimum starting and stopping time constraint of the unit is as follows:
；
the constraint requires that the unit i need to be powered on for a certain minimum on time and minimum off time each time it is powered on or off. Wherein,for maximum time of start-stop->、/>The minimum shutdown time and the minimum startup time of the unit i are respectively.
5) Tie line output constraint
；
The constraint requires that the tie line output be satisfied over a range of outputs. Wherein,、/>the minimum and maximum forces of tie j, respectively.
The method of this patent focuses on eliminating redundancy that contains only 0-1 variables, which in this example is the minimum start-stop time constraint. Before the general solver computer group combines the problem, a trivial pre-solving method is adopted to reduce the model scale, and the variable value of the part 0-1 is determined in advance. In the 6-node system of this example, some 0-1 variables can be determined in advance by the following business logic, simulating the process of trivial pre-solution of a general purpose solver, due to the small scale.
Using business logic to determine the 0-1 variable: at nodes 4 at times 18, 19, 20 in the load data table, the load 1 requires more than 160MW of power. Meanwhile, the node 4 is connected by two paths, namely paths 1-2-4 and paths 1-4. The upper limit of the tie-line output in both paths is 160MW. Wherein the node 1 comprises a unit G 1 Node 2 contains a unit G 2 . If G 1 At 18, 19, 20, the load D 1 The load requirement cannot be met through the upper limit of 160MW of the connecting line between 2 and 4, so the unit G 1 All require power-on output at 18, 19, 20, i.e. But unit G 2 Cannot be determined in a stateBecause G 1 The load D can be satisfied by two paths 1-2-4 and 1-4, respectively 1 Is not limited to the above-mentioned requirements.
After the preprocessing information is obtained, the method can perform redundant constraint pruning on the following constraints.
；
By combining equivalent mathematical transformations of the same kind of terms and simplifying the equivalent mathematical transformations, the following inequality on the right and middle sides is finally obtained:
；
it is now necessary to replace the above-described system variables with only two variables per constraint based on the method of this patent, defined as:
；
so that the above inequality becomes:
；
a directed sequence diagram can be constructed from the variable sequence relationships in the inequality described above as shown in fig. 7.
And then continuously deleting the nodes according to the node degree of the directed graph to obtain the topological ordering, wherein the topological ordering process is shown in fig. 8.
The nodes are then traversed according to the topological ordering, resulting in a transfer reduction graph as shown in fig. 9.
After the final transfer reduction graph is completed, the deleted connections, which are edges where redundant constraints can be subtracted, can be checked, as shown in fig. 10, fig. 10 illustrates a reduced directed sequence graph, where the dashed lines are edges that can be subtracted.
The edges that can be pruned are then mapped into a set of constraint conditions, so that a redundancy filtered system of inequalities can be obtained as:
；
finally, 6 inequality constraints are deleted by the method, and compared with the existing general method, the method has higher applicability to the power optimization problem, and a large number of redundant constraints which cannot be identified by the general method can be identified. In an actual power system production environment, the reduction effect of the scheme is remarkable. In practical application, in the whole constraint (more than 50 ten thousand), the method can effectively delete more than 5% of redundant order constraint on average, and the calculation efficiency is improved by about 21%.
In practical application, the partial unit switching-on and switching-off constraint corresponding to the SCUC problem of one unit of six units of 24 time periods is hidden, and at the moment, the constraint which can be reduced cannot be distinguished completely by manual logic deduction.
The above is a detailed description of an embodiment of a constraint reduction method for an electric power system optimization problem provided by the present invention, and the following is a detailed description of an embodiment of a constraint reduction system for an electric power system optimization problem provided by the present invention.
For ease of understanding, referring to fig. 11, the present invention further provides a constraint reduction system for power system optimization problem, including:
the constraint reduction acquisition module 100 is configured to determine a plurality of constraint reduction to be performed based on a preset optimization problem of the power system, and construct a constraint reduction set to be performed;
the graph construction module 200 is configured to take each participation variable to be reduced and constrained as a node, and connect the nodes according to the order relation of the participation variables to construct a directed order graph;
the node topology ordering module 300 is configured to perform node topology ordering on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram;
and the constraint reduction module 400 is used for traversing each node in the directed sequence diagram according to the node topology sequencing result and performing redundant edge elimination processing, and performing constraint reduction on the constraint reduction set to be reduced according to the redundant edge elimination processing result.
The invention also provides electronic equipment, which comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
The invention also provides a computer readable storage medium, in which a computer program is stored, which when being executed by a processor, implements the above-mentioned method steps.
It will be clearly understood by those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described system, electronic device and computer readable storage medium may refer to corresponding procedures in the foregoing method embodiments, which are not repeated herein.
In the several embodiments provided by the present invention, it should be understood that the disclosed system, electronic device, computer readable storage medium, and method may be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative, e.g., the division of modules is merely a logical function division, and there may be additional divisions of actual implementation, e.g., multiple modules or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed with each other may be an indirect coupling or communication connection via some interfaces, devices or modules, which may be in electrical, mechanical, or other forms.
The modules illustrated as separate components may or may not be physically separate, and components shown as modules may or may not be physical modules, i.e., may be located in one place, or may be distributed over a plurality of network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional module in each embodiment of the present invention may be integrated into one processing module, or each module may exist alone physically, or two or more modules may be integrated into one module. The integrated modules may be implemented in hardware or in software functional modules.
The integrated modules, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in essence or a part contributing to the prior art or all or part of the technical solution in the form of a software product stored in a storage medium, comprising several instructions for executing all or part of the steps of the methods of the embodiments of the present invention by a computer device (which may be a personal computer, a server, or a network device, etc.). And the aforementioned storage medium includes: u disk, mobile hard disk, read-Only Memory (ROM), random access Memory (Random Access Memory, RAM), magnetic disk or optical disk, etc.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (11)
1. A method for constraint intensive reduction of an optimization problem of an electric power system, comprising the steps of:
based on a preset optimization problem of the power system, determining a plurality of constraint reduction to be reduced, and constructing a constraint reduction set to be reduced;
taking each participation variable to be reduced as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram;
performing node topology sequencing on all nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram;
traversing each node in the directed sequence diagram according to a node topology sequencing result, performing redundant edge elimination processing, and performing constraint reduction on the constraint set to be reduced according to a redundant edge elimination processing result;
The step of traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing, and performing constraint reduction on the to-be-reduced constraint set according to the redundant edge elimination processing result comprises traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing to obtain a transmission reduction graph, and specifically comprises the steps of:
traversing each node in the directed sequence diagram in turn according to a node topology sequencing result, and determining the linked edges between every two nodes in the directed sequence diagram;
traversing each edge in the directed sequence diagram in turn according to the node topology sequencing resultWherein e represents an edge, u represents a departure node, v represents an arrival node, and whether other edges except the edge e exist in the directed sequence diagram or not is judged from the departure node u to the arrival node v;
and if the fact that other edges except the edge e can reach the node v from the starting node u is judged in the directed sequence diagram, deleting the edge e from the directed sequence diagram, and obtaining a transfer reduction diagram.
2. The method for reducing constraint set of power system optimization problem according to claim 1, wherein the steps of determining a plurality of constraints to be reduced based on the preset optimization problem of the power system, and constructing a set of constraints to be reduced specifically include:
Determining a constraint set of the power system based on a preset optimization problem of the power system;
based on the constraint set of the power system, the constraint comprising 0-1 decision variables is screened out as constraint to be reduced, and the constraint set to be reduced is constructed.
3. The method for reducing constraint on power system optimization problem according to claim 1, wherein each participation variable to be reduced is taken as a node, node connection is performed according to the order relation of the participation variables, and before the step of constructing the directed sequence diagram, the method further comprises:
and carrying out mathematical deformation on each constraint to be reduced in the constraint set to be reduced to obtain a participation variable and a participation variable sequence relation of each constraint to be reduced.
4. The method for reducing constraint set of power system optimization problems according to claim 3, wherein the step of mathematically deforming each constraint to be reduced in the constraint set to be reduced to obtain a participation variable and a participation variable order relation of each constraint to be reduced specifically comprises:
and carrying out mathematical deformation on each constraint to be reduced in the constraint set to be reduced to obtain a sequence constraint, wherein the sequence constraint is an inequality constraint and comprises a participation variable and a participation variable sequence relation.
5. The method for constraint intensive reduction of power system optimization problems according to claim 1, wherein the step of performing node topology sequencing on all nodes in the directed sequence graph according to the degree of ingress of each node in the directed sequence graph comprises:
initializing a topology ordering list;
traversing each node in the directed sequence diagram by using a breadth/depth first search algorithm, and inserting the node with the smallest degree in the directed sequence diagram into the topological ordered list;
deleting the inserted nodes and the linked edges thereof from the directed sequence diagram based on the nodes inserted in the topological sorting list, and updating the degree of entry of each node in the directed sequence diagram;
and based on the updated degree of incidence of the remaining nodes in the directed sequence diagram, the step of inserting the node with the smallest degree of incidence in the directed sequence diagram into the topological sorting list is re-executed until all nodes in the directed sequence diagram are sequentially inserted into the topological sorting list, and a node topological sorting result is obtained.
6. The constraint reduction method for power system optimization problem according to claim 1, wherein the step of traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing, and performing constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result further comprises:
Comparing the transfer reduced graph with the directed sequence graph to determine reduced redundant edges;
and reducing the corresponding constraint to be reduced in the constraint set to be reduced according to the redundant edge to be reduced.
7. The method of constrained intensive reduction of power system optimization problems as claimed in claim 6, wherein the step of comparing the transfer reduced graph with the directed sequence graph to determine reduced redundancy edges comprises:
comparing the transfer reduction graph with the directed sequence graph, and screening out edges which exist in the directed sequence graph and are not in the transfer reduction graph as reduced redundancy edges.
8. The method for reducing constraint set of power system optimization problems according to claim 6, wherein the step of reducing the constraint to be reduced corresponding to the constraint set to be reduced according to the reduced redundancy edge specifically comprises:
acquiring nodes on two sides of the reduced redundant edge;
based on the mapping relation between the nodes and the participation variables, the corresponding participation variables and the corresponding constraint to be reduced are matched in the constraint set to be reduced through the nodes on the two sides of the redundant edge to be reduced;
and deleting the matched constraint to be reduced in the constraint set to be reduced.
9. A constraint intensive mitigation system for an optimization problem of an electrical power system, comprising:
the constraint reduction acquisition module is used for determining a plurality of constraint reduction to be reduced based on a preset optimization problem of the power system and constructing a constraint reduction set to be reduced;
the diagram construction module is used for taking each participation variable to be reduced and constrained as a node, and connecting the nodes according to the sequence relation of the participation variables to construct a directed sequence diagram;
the node topology sequencing module is used for carrying out node topology sequencing on all the nodes in the directed sequence diagram according to the degree of ingress of each node in the directed sequence diagram;
the constraint reduction module is used for traversing each node in the directed sequence diagram according to the node topology sequencing result and carrying out redundant edge elimination processing, and carrying out constraint reduction on the constraint set to be reduced according to the redundant edge elimination processing result;
the step of traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing, and performing constraint reduction on the to-be-reduced constraint set according to the redundant edge elimination processing result comprises traversing each node in the directed sequence graph according to the node topology sequencing result and performing redundant edge elimination processing to obtain a transmission reduction graph, and specifically comprises the steps of:
Traversing each node in the directed sequence diagram in turn according to a node topology sequencing result, and determining the linked edges between every two nodes in the directed sequence diagram;
traversing each edge in the directed sequence diagram in turn according to the node topology sequencing resultWherein e represents an edge, u represents a departure node, v represents an arrival node, and whether other edges except the edge e exist in the directed sequence diagram or not is judged from the departure node u to the arrival node v;
and if the fact that other edges except the edge e can reach the node v from the starting node u is judged in the directed sequence diagram, deleting the edge e from the directed sequence diagram, and obtaining a transfer reduction diagram.
10. The electronic equipment is characterized by comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory are communicated with each other through the communication bus;
a memory for storing a computer program;
a processor for implementing the method steps of any one of claims 1 to 8 when executing a program stored on a memory.
11. A computer readable storage medium, characterized in that a computer program is stored in the computer readable storage medium, which computer program, when being executed by a processor, implements the method steps of any of claims 1-8.
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