Convex hull construction method, system and equipment for single-unit combination problem and medium
By transforming the combination problem of single-unit units of the power system from mixed integer planning to linear planning and building a convex hull model, the problems of difficulty in solving and low computing efficiency in traditional methods are solved, and efficient optimal solution is achieved.
Patent Information
- Application Number
- CN202411051314.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-01
- Publication Date
- 2025-02-18
AI Technical Summary
The traditional power system unit combination optimization method characterizes the problem as a mixed integer programming, resulting in difficulty in solving and low computational efficiency.
Through mathematical equivalent transformation, the mixed integer programming problem is converted into linear programming problem, and a convex hull model is built to reduce the solution difficulty and improve the computational efficiency.
The single unit unit combination problem is transformed from mixed integer planning to linear planning, which significantly reduces the solution difficulty and improves the calculation efficiency, so that the optimal solution can be obtained within a reasonable time.
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Figure CN119482694A_ABST
Abstract
Description
Technical Field
[0001] The embodiments of the present application relate to the technical field of power systems, and in particular to a method, system, device and medium for constructing a convex hull for a single unit combination problem. Background Art
[0002] The optimization of power system unit combination is an important issue in the field of power engineering. Its main goal is to determine the best power generator start-stop strategy to meet power demand while taking into account multiple constraints and optimization objectives. Traditional modeling methods usually use binary discrete variables to characterize the start-stop status and start-stop actions of the unit, and then construct a mixed integer programming model with the goal of minimizing operating costs. In other words, the traditional modeling method characterizes the unit combination problem as a mixed integer linear programming problem containing discrete variables. It faces the problem of "curse of dimensionality" which makes it very difficult to solve the problem. Because its solution time increases exponentially with the increase of discrete variables, it is usually impossible to solve the model within a reasonable time. Even though the discrete optimization technology is very mature today, it has not changed its NP-hard nature, and it is still challenging to efficiently obtain the optimal solution to the mixed integer programming problem. Summary of the invention
[0003] The embodiments of the present application provide a convex hull construction method, system, device and medium for a single-unit combination problem. The construction method converts the original mixed integer programming problem into a linear programming problem through an equivalent transformation in mathematical form, thereby reducing the difficulty of solving the single-unit combination problem and significantly improving the computational efficiency of the single-unit combination problem.
[0004] To solve the above technical problems, in the first aspect, an embodiment of the present application provides a convex hull construction method for a single-unit combination problem, comprising the following steps: first, based on the single-unit combination state, a unit combination mixed integer programming model is constructed; then, based on the unit combination mixed integer programming model and the minimum start and stop time constraint, a state transition space is constructed; next, based on the state transition space, a dynamic programming model is constructed; finally, the dynamic programming model is transformed to obtain a linear programming model.
[0005] In some exemplary embodiments, the single unit unit combination state is characterized by the unit start-stop state and the unit start-stop state duration.
[0006] In some exemplary embodiments, the expression of the state transition space is as follows:
[0007]
[0008]
[0009] Among them, Si and S j Indicates the start / stop status or start / stop duration of a certain unit; Indicates the start / stop status of the unit and the start / stop duration S i The state set of all possible unit start and stop states and start and stop durations transferred; Represents a collection of all unit start / stop states and start / stop durations.
[0010] In some exemplary embodiments, the Bellman equation is used to construct a dynamic programming model, and the expression of the dynamic programming model is as follows:
[0011]
[0012] Where v represents the cost from the starting state to the ending state; v i and v j Both represent the cost of a certain unit from start-up / stop state to termination state or the cost of start-up / stop duration to termination state; V i and V j Respectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
[0013] In some exemplary embodiments, transforming the dynamic programming model to obtain a linear programming model includes: transforming the dynamic programming model according to a transformation relationship to obtain a linear programming model; the transformation relationship is:
[0014]
[0015] Where v represents the cost from the starting state to the ending state; v n It represents the cost from the start-stop state to the terminal state of the nth unit or the cost from the start-stop duration to the terminal state; v0 represents the cost of the unit's initial state.
[0016] In some exemplary embodiments, the linear programming model is expressed as:
[0017]
[0018] Where v represents the cost from the starting state to the ending state; v i and v j Both represent the cost of a certain unit from start-up / stop state to termination state or the cost of start-up / stop duration to termination state; V i and V jRespectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
[0019] In some exemplary embodiments, the linear programming model is the tightest convex relaxation of the single-unit unit combination problem of the power system, which realizes the transformation of the single-unit unit combination problem from a mixed integer programming model to a linear programming model.
[0020] In the second aspect, an embodiment of the present application also provides a convex hull construction system for a single unit combination problem, comprising: a unit combination mixed integer programming model construction module, a state transfer space construction module, a dynamic programming model construction module and a model transformation module connected in sequence; wherein the unit combination mixed integer programming model construction module is used to construct a unit combination mixed integer programming model according to the single unit unit combination state; the state transfer space construction module is used to construct a state transfer space according to the unit combination mixed integer programming model and the minimum start and stop time constraint; the dynamic programming model construction module is used to construct a dynamic programming model according to the state transfer space; the model transformation module is used to transform the dynamic programming model to obtain a linear programming model.
[0021] In addition, the present application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the convex hull construction method for the above-mentioned single-unit combination problem.
[0022] In addition, the present application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the convex hull construction method for the above-mentioned single-unit unit combination problem.
[0023] The technical solution provided by the embodiments of the present application has at least the following advantages:
[0024] The embodiment of the present application provides a convex hull construction method, system, device and medium for a single-unit combination problem, the method comprising the following steps: first, based on the single-unit combination state, a unit combination mixed integer programming model is constructed; then, based on the unit combination mixed integer programming model and the minimum start and stop time constraint, a state transition space is constructed; next, based on the state transition space, a dynamic programming model is constructed; finally, the dynamic programming model is transformed to obtain a linear programming model.
[0025] The present application aims at the technical problem that the model cannot be solved within a reasonable time in the prior art, and provides a convex hull construction method for a single unit combination problem. By abstracting the start and stop state and start and stop duration of the unit combination, a state transition space that can be used to represent the start and stop characteristics of the unit combination and reflect the start and stop duration constraints of the unit combination is constructed; then, a dynamic programming model is established through the constructed state transition space, and the dynamic programming model is equivalently converted into a linear programming model. The obtained linear programming model is the tightest convex relaxation of the single unit combination problem of the power system, and the conversion of the unit combination mixed integer programming model to the linear programming model is realized. After experimental verification, the unit combination result obtained by the convex hull model constructed in the present application is consistent with the unit combination result obtained by the mixed integer programming model, and the calculation time required for solving the convex hull model is significantly reduced compared with the calculation time required for the mixed integer programming model, which is significantly better than the time-consuming solution of the traditional method, and significantly improves the computational efficiency of the single unit combination problem. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] One or more embodiments are exemplarily described by pictures in the corresponding drawings, and these exemplifications do not constitute limitations on the embodiments. Unless otherwise stated, the pictures in the drawings do not constitute proportional limitations.
[0027] Figure 1 A flow chart of a convex hull construction method for a single unit combination problem provided in one embodiment of the present application;
[0028] Figure 2 A structural schematic diagram of a convex hull construction system for a single unit combination problem provided in one embodiment of the present application;
[0029] Figure 3 A schematic diagram of comparing the unit commitment results of the convex hull model obtained by the construction method of the present application and the unit commitment results of the mixed integer programming model of the traditional method provided in one embodiment of the present application;
[0030] Figure 4 A schematic diagram of the time required to solve the constructed convex hull model provided in one embodiment of the present application;
[0031] Figure 5 A schematic diagram of the structure of an electronic device provided in one embodiment of the present application. DETAILED DESCRIPTION
[0032] As can be seen from the background technology, the traditional modeling method has the technical problem that it cannot be solved within a reasonable time.
[0033] Since the traditional modeling method is to characterize the unit combination problem as a mixed integer linear programming problem containing discrete variables, its solution time increases exponentially with the increase of discrete variables. Therefore, the mixed integer programming model faces the problem of "curse of dimensionality", which makes the problem very difficult to solve. Even though the discrete optimization technology is very mature, it has not changed the nature of its NP-hard problem, and it is still challenging to efficiently obtain the optimal solution to the mixed integer programming problem. By constructing the convex hull of the unit combination problem, its advantage is that the mixed integer programming problem that originally describes the unit combination problem is equivalently converted into a linear programming problem, which changes the nature of the optimization problem. The existing solution technology is very friendly to linear programming problems, and there are very mature algorithms with polynomial time complexity, which makes it easy to obtain the optimal solution to the unit combination problem.
[0034] In order to solve the above technical problems, the embodiments of the present application provide a convex hull construction method, system, device and medium for a single-unit unit combination problem, the method comprising the following steps: first, based on the single-unit unit combination state, a unit combination mixed integer programming model is constructed; then, based on the unit combination mixed integer programming model and the minimum start-stop time constraint, a state transition space is constructed; next, based on the state transition space, a dynamic programming model is constructed; finally, the dynamic programming model is transformed to obtain a linear programming model. The embodiments of the present application provide a convex hull construction method for a single-unit unit combination problem, the construction method converts the original mixed integer programming problem into a linear programming problem through an equivalent transformation in mathematical form, reduces the difficulty of solving the single-unit unit combination problem, and improves the computational efficiency of the single-unit unit combination problem.
[0035] The following will describe the various embodiments of the present application in detail with reference to the accompanying drawings. However, it will be appreciated by those skilled in the art that in the various embodiments of the present application, many technical details are provided in order to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solution claimed in the present application can be implemented.
[0036] See also Figure 1 , the embodiment of the present application provides a convex hull construction method for a single unit combination problem, comprising the following steps:
[0037] Step S1: construct a unit combination mixed integer programming model based on the unit combination status of a single unit.
[0038] Step S2: constructing a state transition space based on the unit commitment mixed integer programming model and the minimum start and stop time constraint.
[0039] Step S3: construct a dynamic programming model based on the state transition space.
[0040] Step S4: transform the dynamic programming model to obtain a linear programming model.
[0041] The unit combination problem of a single unit in a power system generally needs to meet a series of physical constraints related to unit parameters, including output limit constraints, minimum start-stop time constraints, and climbing limit constraints. Step S1 of the present application constructs a mixed integer programming model for unit combination by abstracting the start-stop state and start-stop duration of the unit combination, and then step S2 constructs a state transition space that can represent the start-stop characteristics of the unit combination and reflect the start-stop duration constraint of the unit combination according to the minimum start-stop time constraint.
[0042] In some embodiments, in step S1, the state of the single unit combination is represented by the start-stop state and the start-stop state duration.
[0043] In some embodiments, the expression of the above state transition space is as follows:
[0044]
[0045] Among them, S i and S j Both indicate the start / stop status or start / stop duration of a certain unit; Indicates the start / stop status of the unit and the start / stop duration S i The state set of all possible unit start and stop states and start and stop durations transferred; Represents a collection of all unit start / stop states and start / stop durations.
[0046] After constructing the state transition space, the present application establishes a dynamic programming model based on the constructed state transition space, and converts the dynamic programming model into a linear programming model. The obtained linear programming model is the tightest convex relaxation of the single unit combination problem of the power system, and then realizes the transformation process of the unit combination mixed integer programming model to the linear programming model.
[0047] In some embodiments, in step S3, the Bellman equation is used to construct a dynamic programming model, and the expression of the dynamic programming model is as follows:
[0048]
[0049]
[0050] Where v represents the cost from the starting state to the ending state; v i and v j Both represent the cost of a certain unit from start-up / stop state to termination state or the cost of start-up / stop duration to termination state; V i and V jRespectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
[0051] In some embodiments, in step S4, the dynamic programming model is transformed to obtain a linear programming model, including: according to a transformation relationship, the dynamic programming model is transformed to obtain a linear programming model.
[0052] The transformation relationship is:
[0053]
[0054] Where v represents the cost from the starting state to the ending state; v n It represents the cost from the start-stop state to the terminal state of the nth unit or the cost from the start-stop duration to the terminal state; v0 represents the cost of the unit's initial state.
[0055] In some embodiments, the linear programming model in step S4 is expressed as:
[0056]
[0057] Where v represents the cost from the starting state to the ending state; v i and v j Both represent the cost of a certain unit from start-up / stop state to termination state or the cost of start-up / stop duration to termination state; V i and V j Respectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
[0058] See also Figure 2The embodiment of the present application also provides a convex hull construction system for a single unit combination problem, the system comprising: a unit combination mixed integer programming model construction module 101, a state transfer space construction module 102, a dynamic programming model construction module 103 and a model transformation module 104 connected in sequence; wherein the unit combination mixed integer programming model construction module 101 is used to construct a unit combination mixed integer programming model according to the single unit unit combination state; the state transfer space construction module 102 is used to construct a state transfer space according to the unit combination mixed integer programming model and the minimum start and stop time constraint; the dynamic programming model construction module 103 is used to construct a dynamic programming model according to the state transfer space; the model transformation module 104 is used to transform the dynamic programming model to obtain a linear programming model.
[0059] In order to verify the effect of the convex hull construction method for the single-unit unit combination problem provided in the embodiment of the present application, the present application tests the consistency and computational efficiency of the single-unit unit combination convex hull model constructed by the present application and the mixed integer programming model constructed by the traditional method based on the unit data in the IEEE-118 test example and combined with the randomly generated electricity price data. The test results are as follows: Figure 3 and Figure 4 shown. Figure 3 The unit combination calculation results of the convex hull model obtained by the construction method of the present application are presented to illustrate the consistency of the results obtained by the construction method of the present application and the traditional method; Figure 4 The time results for solving the convex hull model obtained by the construction method of the present application are shown to illustrate the superiority of the construction method of the present application compared with the time-consuming solution of the traditional method.
[0060] Verification of the consistency of the unit combination results: 54 single units were established as mixed integer programming models and convex hull models respectively, and the optimal operating cost was calculated in combination with the electricity price curve. The test results are as follows Figure 3 As shown, (a) is the result of the convex hull model unit combination; (b) is the result of the mixed integer programming model unit combination. Figure 3 It can be seen that the unit combination result of the convex hull model obtained by the construction method of the present application is consistent with the unit combination result of the mixed integer programming model obtained by the traditional method.
[0061] The efficiency verification of the unit combination results of the convex hull model of this application: 54 single units are established as mixed integer programming models and convex hull models respectively, and the optimal operating cost is calculated in combination with the electricity price curve. The test results are as follows Figure 4 As shown, it can be seen that the computing time required for solving the convex hull model obtained by the construction method of the present application is significantly reduced compared with the computing time required for the mixed integer programming model, indicating that the construction method of the present application can improve the computational efficiency of the single-unit combination problem.
[0062] In addition, the present application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the convex hull construction method for the above-mentioned single-unit combination problem.
[0063] In addition, the present application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the convex hull construction method for the above-mentioned single-unit unit combination problem.
[0064] See also Figure 5 Another embodiment of the present application provides an electronic device, comprising: at least one processor 110; and a memory 111 communicatively connected to the at least one processor; wherein the memory 111 stores instructions executable by the at least one processor 110, and the instructions are executed by the at least one processor 110 so that the at least one processor 110 can execute any of the above method embodiments.
[0065] Among them, the memory 111 and the processor 110 are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors 110 and the memory 111 together. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are all well known in the art, so they are not further described in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor 110 is transmitted on a wireless medium through an antenna, and further, the antenna also receives data and transmits the data to the processor 110.
[0066] The processor 110 is responsible for managing the bus and general processing, and may also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. The memory 111 may be used to store data used by the processor 110 when performing operations.
[0067] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program, which implements the above method embodiment when executed by a processor.
[0068] That is, those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the above-mentioned method of each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.
[0069] Based on the above technical scheme, the embodiment of the present application provides a convex hull construction method, system, equipment and medium for a single unit combination problem, the method comprising the following steps: first, based on the single unit combination state, a unit combination mixed integer programming model is constructed; then, based on the unit combination mixed integer programming model and the minimum start and stop time constraint, a state transition space is constructed; next, based on the state transition space, a dynamic programming model is constructed; finally, the dynamic programming model is transformed to obtain a linear programming model.
[0070] The present application aims at the technical problem that the model cannot be solved within a reasonable time in the prior art, and provides a convex hull construction method for a single unit combination problem. By abstracting the start and stop state and start and stop duration of the unit combination, a state transition space that can be used to represent the start and stop characteristics of the unit combination and reflect the start and stop duration constraints of the unit combination is constructed; then, a dynamic programming model is established through the constructed state transition space, and the dynamic programming model is equivalently converted into a linear programming model. The obtained linear programming model is the tightest convex relaxation of the single unit combination problem of the power system, and the conversion of the unit combination mixed integer programming model to the linear programming model is realized. After experimental verification, the unit combination result obtained by the convex hull model constructed in the present application is consistent with the unit combination result obtained by the mixed integer programming model, and the calculation time required for solving the convex hull model is significantly reduced compared with the calculation time required for the mixed integer programming model, which is significantly better than the time-consuming solution of the traditional method, and significantly improves the computational efficiency of the single unit combination problem.
[0071] Those skilled in the art can understand that the above-mentioned embodiments are specific examples for implementing the present application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of the present application. Any person skilled in the art can make their own changes and modifications without departing from the spirit and scope of the present application, so the scope of protection of the present application shall be based on the scope defined in the claims.
Claims
1. A convex hull construction method for a single unit unit combination problem, characterized in that: include: Based on the unit commitment status of a single unit, a mixed integer programming model for unit commitment is constructed; Based on the unit commitment mixed integer programming model and the minimum start-stop time constraint, a state transition space is constructed; Based on the state transition space, construct a dynamic programming model; The dynamic programming model is transformed to obtain a linear programming model.
2. The convex hull construction method for the single unit unit combination problem according to claim 1 is characterized in that: The single unit combination state is characterized by the unit start-stop state and the unit start-stop state duration.
3. The convex hull construction method for the single unit unit combination problem according to claim 1 is characterized in that: The expression of the state transition space is as follows: Among them, S i and S j Indicates the start / stop status or start / stop duration of a certain unit; Indicates the start / stop status of the unit and the start / stop duration S i The state set of all possible unit start and stop states and start and stop durations transferred; Represents a collection of all unit start / stop states and start / stop durations.
4. The convex hull construction method for the single unit unit combination problem according to claim 1 is characterized in that: The Bellman equation is used to construct a dynamic programming model, and the expression of the dynamic programming model is as follows: Where v represents the cost from the starting state to the ending state; v i and v j V represents the cost of a certain unit from the start-up / stop state to the end state or the cost of the start-up / stop duration to the end state; i and V j Respectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
5. The convex hull construction method for the single unit unit combination problem according to claim 1, characterized in that: The dynamic programming model is transformed to obtain a linear programming model, including: According to the transformation relationship, the dynamic programming model is transformed to obtain a linear programming model; The transformation relationship is: Where v represents the cost from the starting state to the ending state; v n It represents the cost from the start-stop state to the terminal state of the nth unit or the cost from the start-stop duration to the terminal state; v0 represents the cost of the unit's initial state.
6. The convex hull construction method for the single unit unit combination problem according to claim 1, characterized in that: The linear programming model is expressed as: Where v represents the cost from the starting state to the ending state; v i and v j V represents the cost of a certain unit from the start-up / stop state to the end state or the cost of the start-up / stop duration to the end state; i and V j Respectively represent the start and stop state of the unit and the start and stop time state as S i and S j Costs; Represents the set of costs corresponding to all starting states; Represents a state collection The set of costs corresponding to all states in .
7. The convex hull construction method for the single unit unit combination problem according to claim 1, characterized in that: The linear programming model is the tightest convex relaxation of the single-unit unit combination problem of the power system, and realizes the transformation of the single-unit unit combination problem from a mixed integer programming model to a linear programming model.
8. A convex hull construction system for a single unit unit combination problem, characterized in that: include: A unit combination mixed integer programming model building module, a state transfer space building module, a dynamic programming model building module and a model transformation module are connected in sequence; wherein, The unit combination mixed integer programming model construction module is used to construct a unit combination mixed integer programming model according to the unit combination status of a single unit; The state transfer space construction module is used to construct the state transfer space according to the unit combination mixed integer programming model and the minimum start and stop time constraint; The dynamic programming model construction module is used to construct a dynamic programming model according to the state transfer space; The model transformation module is used to transform the dynamic programming model to obtain a linear programming model.
9. An electronic device, characterized in that: include: at least one processor; as well as, A memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor so that the at least one processor can execute the convex hull construction method for the single-unit unit combination problem as described in any one of claims 1 to 7.
10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the convex hull construction method for the single unit combination problem described in any one of claims 1 to 7 is implemented.