Construction method, system and equipment of single unit combination convex polyhedron and medium
By constructing a convex polyhedral model of unit combination problem, the mixed integer programming problem is converted into linear programming problem using state transfer relationship, which solves the problem of inefficient calculation of the NP-hard problem and achieves efficient solution.
Patent Information
- Application Number
- CN202411077158.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-07
- Publication Date
- 2024-12-17
AI Technical Summary
In the prior art, the mixed integer programming problem is considered to be an NP-hard problem, which leads to inefficient calculations when solving the unit combination problem, especially in large-scale problems, which is difficult to effectively solve.
By constructing a convex polyhedral model of unit combination problem, using state transfer relationships to convert mixed integer programming problems into linear programming problems, and using backward dynamic programming and dual model transformation, a convex polyhedral model that can be solved by polynomial time is obtained.
It improves the solution efficiency of unit combination problems, significantly improves the calculation efficiency, and can solve the original NP-hard problem in polynomial time.
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Abstract
Description
Technical Field
[0001] The present application relates to the technical field of power systems, and in particular to a method, system, equipment and medium for constructing a convex polyhedron of a single-machine unit combination. Background Art
[0002] Unit commitment (UC) is an important part of power system operation. It is often used to determine the start and stop status of generators in the future. It is widely used in power dispatching, power market settlement, reliability assessment, expansion planning and other occasions that require power system operation simulation. Generally speaking, considering the key physical characteristics of the generator, such as output power range, minimum on / off time, climbing limit, etc., the UC problem is usually established as a mixed integer linear programming model, which will involve online status, start instructions, shutdown instructions (binary variables) and power output (continuous variables). However, it is well known that mixed integer programming problems are considered to be NP-hard problems. It is generally believed that there is no polynomial time solution algorithm for its solution, so it often faces the challenge of difficult solution.
[0003] Considering that optimizing within the feasible domain of the unit commitment problem based on the mixed integer programming form is equivalent to optimizing within the convex hull of its feasible domain, the unit commitment problem is established as a linear programming problem by constructing the convex hull of the feasible domain of the unit commitment problem, and is solved using the existing polynomial time solution algorithm. The construction of the unit combination convex polyhedron is essentially to construct the convex hull of the feasible domain of the mixed integer programming problem, which belongs to the category of computational geometry. At present, there are many algorithms for obtaining the convex hull, such as the Graham scanning method, the Jarvis stepping method, etc. However, some studies of this type of method have proposed some calculation methods to describe the convex hull of the feasible domain of the mixed integer programming problem, such as the Graham scanning method, the Jarvis stepping method, etc.
[0004] Although these methods are theoretically very effective in constructing convex polyhedra for mixed integer programming problems, they still have defects in describing practical problems and are difficult to use directly in practical applications. Moreover, the unit combination problem generally contains integer variables that represent the start and stop status and continuous variables that represent the unit output. The optimization model that describes this problem is usually a mixed integer programming problem. Generally speaking, since mixed integer programming problems are considered NP-hard problems, there is generally no applicable polynomial time solution algorithm. As the problem becomes more complex, the time required to solve it will increase exponentially, especially when solving large-scale problems, the disadvantage in computational efficiency is prominent. Summary of the invention
[0005] The embodiments of the present application provide a method, system, device and medium for constructing a convex polyhedron of a single-machine unit combination, construct a convex polyhedron model of the feasible domain of the unit combination problem based on state transfer, and use the unit combination convex hull model to replace the original unit combination mixed integer programming model to improve the solution efficiency.
[0006] To solve the above technical problems, in a first aspect, an embodiment of the present application provides a method for constructing a convex polyhedron of a single-unit combination, comprising the following steps: first, based on the unit state, a single-unit combination model in the form of a mixed integer linear programming is constructed; then, based on the single-unit combination model in the form of a mixed integer linear programming, a state space is obtained, and a state transition relationship between all states in the state space is generated; next, based on the state transition relationship, a backward dynamic programming model of the single-unit combination problem is constructed; then, using an equivalent transformation method, the backward dynamic programming model is transformed into a linear programming model to obtain a dual model of the linear programming; finally, based on the dual model of the linear programming, a convex polyhedron model of the single-unit combination is obtained.
[0007] In some exemplary embodiments, the unit state includes the state of the unit in each period; the state of the unit in each period includes the unit output, the unit start-up and stop state, the unit startup action, the unit shutdown action and the duration of the current start-up and stop state of the unit; the single unit unit combination model in the form of mixed integer linear programming is expressed as follows:
[0008]
[0009] x t P min ≤p t ≤x t P max ,t∈{1,...,T} (2)
[0010] u t +d t ≤1,t∈{1,...,T} (3)
[0011] u t -d t =x t -x t-1 ,t∈{2,...,T} (4)
[0012] p t -p t-1 ≤R+u t (R′-R),t∈{2,...,T} (5)
[0013] p t-1 -p t ≤R+d t(R′-R),t∈{2,...,T} (6)
[0014]
[0015] Among them, C u and C d Respectively represent the startup cost and shutdown cost of the unit; u t and d t They represent the start-up and shutdown actions of the unit in time period t respectively; p t represents the active power of the unit in time period t; x t represents the start and stop status of the unit in time period t; f(p t ,x t ) represents the linearized secondary coal consumption cost curve; Π t represents the node electricity price at time t; P min and P max Respectively represent the minimum technical output and maximum technical output of the unit; T on and T off They represent the minimum start-up time and minimum shutdown time of the unit respectively; T represents the length of the scheduling cycle; where f(p t ,x t ) is as follows:
[0016] f(p t ,x t )≥K i (p t -P i x t )+H i x t ,∈{1,...,T},i∈{1,...,I} (10)
[0017] Among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
[0018] In some exemplary embodiments, a state space is obtained based on a single-unit unit combination model in the form of a mixed integer linear programming, including: obtaining an output set containing all possible optimal outputs based on a single-unit unit combination model in the form of a mixed integer linear programming; obtaining a state space of a single-unit unit combination based on an output set containing all possible optimal outputs; wherein, obtaining an output set containing all possible optimal outputs based on a single-unit unit combination model in the form of a mixed integer linear programming includes: obtaining an optimal output decision result based on a single-unit unit combination model in the form of a mixed integer linear programming; obtaining an output set containing all possible optimal outputs based on the optimal output decision result; for a single-unit unit combination model in the form of a mixed integer linear programming, a cell (p, x, u, d, l) is used to represent the unit state; wherein p, x, u, d and l represent the unit output, the unit start-up and stop state, the unit startup action, the unit shutdown action, and the duration of the current start-up and stop state of the unit, respectively; in the optimal output decision result, the output in the startup state belongs to the following discrete finite set:
[0019] p t ∈Ω p ={Ω p 1∪Ω p 2∪Ω p 3∪Ω p 4} (11)
[0020] in,
[0021]
[0022] Among them, the set Ω p represents the set of all possible optimal outputs; Ω p 1 means that the output set related to the minimum technical output is included; Ω p 2 means that the output set related to the maximum technical output is included; Ω p 3 represents the output set including startup ramp constraints; Ω p 4 indicates that it contains the output set related to the piecewise linearization segmentation points.
[0023] In some exemplary embodiments, the state space is a set of states of the units in each time period of the optimal scheduling result of the single unit combination;
[0024] The state space expression is as follows:
[0025] Ω s =Ω s_on ∪Ω s_off (16)
[0026] Among them, Ω s represents the state space; Ω s_onRepresents the state space containing all power-on states; Ω s_off Represents the state space containing all shutdown states; according to the minimum startup time of the unit, the state space Ω containing all startup states s_on Including the following two situations: When the minimum startup time of the unit meets T on =1:
[0027] Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×1} (17)
[0028] When the minimum startup time of the unit meets T on >1:
[0029] Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×{1,...,T on}} (18)
[0030] Among them, when l=1, u=1; otherwise l>1, u=0;
[0031] According to the minimum shutdown time of the unit, the state space Ω containing all shutdown states s_off There are two cases: When the minimum shutdown time of the unit meets T off =1:
[0032] Ω S_off ={(p,x,u,d,l)∈0×0×0×B×1} (19)
[0033] When the minimum shutdown time of the unit meets T off >1:
[0034] Ω S_off ={(p,x,u,d,l)∈0×0×0×B×{1,...,T off}} (20)
[0035] Among them, when l=1, d=1; otherwise l>1, d=0.
[0036] In some exemplary embodiments, generating a state transition relationship between all states in the state space includes: generating a state transition relationship between all states in the state space based on the unit output range, the unit start-stop logic, the unit climbing limit and the minimum start-stop time requirement; wherein the state transition relationship is generated according to the following rules: when the unit is turned on and the minimum start-up time of the unit meets T on=1, the state transfer relationship is: when the unit state is (p, 1, 1, 0, 1), when |p′-p|≤R, the unit state transfers to the state (p′, 1, 0, 0, 1), where R is the unit climbing limit; when the unit state is (p, 1, 0, 0, 1), when |p′-p|≤R, the unit state transfers to the state (p′, 1, 0, 0, 1) or (0, 0, 0, 1, 1); when the unit is turned on and the minimum unit start-up time meets T on >1, the state transition relationship is: when the unit state is (p, 1, 1, 0, 1), the unit state is transferred to the state (p', 1, 0, 0, 2) when |p'-p| ≤ R; when the unit state is (p, 1, 0, 0, l), 1 < l < T on When |p′-p|≤R, the unit state is transferred to the state (p′,1,0,0,l+1); when the unit state is (p,1,0,0,T on ), when |p′-p|≤R, the group state is transferred to the state (p′,1,0,0,T on ) or when |p|≤R′, the unit state is transferred to state (0,0,0,1,1); when the unit is shut down and the minimum shutdown time of the unit meets T off =1, the state transition relationship is: when the unit state is (0,0,0,1,1), the unit state is transferred to the state (0,0,0,0,1); when the unit state is (0,0,0,0,1), the unit state is transferred to the state (0,0,0,0,1) or when |p′|≤R′, the unit state is transferred to the state (p′,1,1,0,1), where R′ is the relaxation climbing limit of the unit state change; when the unit is shut down and the minimum shutdown time of the unit meets T off >1, the state transfer relationship is: when the unit state is (0,0,0,1,1), the unit state transfers to state (0,0,0,0,1); when the unit state is (0,0,0,0,l), 1<l<T off , the unit state is transferred to the state (0,0,0,0,l+1); when the unit state is (0,0,0,0,T off ), the unit state is transferred to the state (0,0,0,0,T off ) or when |p′|≤R′, the group state is transferred to state (p′, 1,1,0,1).
[0037] In some exemplary embodiments, based on the state transition relationship, a backward dynamic programming model for a single unit unit combination problem is constructed, including: based on the state transition relationship, converting the single unit unit combination model in a mixed integer linear programming form into a backward dynamic programming model to obtain a backward dynamic programming model for the single unit unit combination problem; the expression of the backward dynamic programming model for the single unit unit combination problem is as follows:
[0038] vDP =min{v DP (i,1)|i∈Ω s} (twenty one)
[0039] v DP (i,t)=min{V(i,t)+v DP (j,t+1)|j∈Ω s_from (i)},i∈Ω s ,t∈{1,...,T-1}(22)
[0040] v DP (i,T)=V(i,T),i∈Ω s (twenty three)
[0041] Among them, v DP represents the minimum cost of the corresponding dynamic programming; Ω s represents the state space; v DP (i, t) represents the minimum cost of the corresponding dynamic programming at time t when the unit maintains state i and runs until the end of the scheduling period; v DP (j, t+1) represents the minimum cost of the corresponding dynamic programming at time t+1 when the unit maintains the state j and runs until the end of the scheduling period; v DP (i, T) represents the minimum cost of the corresponding dynamic programming when the unit maintains the state i at time T and runs until the end of the scheduling period; Ω s_from (i) represents the set of all states in the state space that can be transferred from state i; V(i,t) represents the cost when the unit maintains state i at time t; V(i,T) represents the cost when the unit maintains state i at time T, that is:
[0042] V(i,t)=C u u(i)+C d d(i)+f(p(i),x(i))-Π t p(i),i∈Ω s ,t∈{1,...,T} (24)
[0043] Among them, p(i), x(i), u(i) and d(i) respectively represent the unit output, start-stop status, startup action status and shutdown action status of the unit when the unit maintains state i.
[0044] In some exemplary embodiments, the linear programming model is expressed as follows:
[0045] LP
[0046] max v(25)
[0047] st vLP ≤v LP (i,1):w(i,1),i∈Ω s (26)
[0048] v LP (i,t)≤V(i,t)+v LP (j,t+1):w(i,j,t),j∈Ω s_from (i),i∈Ω s ,t∈{1,...,T-1}(27)
[0049] v LP (i,T)=V(i,T):w(i,T),i∈Ω s (28)
[0050] Among them, v LP represents the minimum cost of the corresponding linear programming; v LP (i, t) represents the minimum cost of the corresponding linear programming at time t and when the unit maintains state i until the end of the scheduling period; w(i, t) and w(i, j, t) represent the dual variables of the corresponding inequality constraints; the expression of the dual model of the linear programming is as follows:
[0051]
[0052] w(i,1),w(i,j,t),w(i,T)≥0,i∈Ω s ,j∈Ω s_from (i),t∈{1,...,T-1} (34)
[0053] Among them, Ω s_to (i) represents the set of all states in the state space that can be transferred to state i; based on the dual model of linear programming, a convex polyhedron model of a single unit combination is obtained, including: based on the dual model of linear programming, the unit output, the unit start-stop state, the unit start-up action and the unit shutdown action are obtained respectively; based on the unit output, the unit start-stop state, the unit start-up action and the unit shutdown action, a convex polyhedron model of a single unit combination is obtained; the unit output, the unit start-stop state, the unit start-up action and the unit shutdown action are respectively obtained by the following formulas:
[0054]
[0055] Among them, w*(i,t) and w*(i,j,t) are the optimal solutions of the dual variables corresponding to the inequality constraints; the expression of the convex polyhedron model of the single unit unit combination is as follows:
[0056]
[0057] f(p t ,x t )≥K i (p t -P i x t )+H i x t ,∈{1,...,T},i∈{1,...,I} (40)
[0058] (30)-(34)(41)
[0059] (35)-(38)(42)
[0060] Among them, p t 、x t 、u t d t They represent the unit output, unit start and stop status, unit startup action, and unit shutdown action respectively; among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
[0061] In the second aspect, an embodiment of the present application also provides a system for constructing a convex polyhedron of a single-machine unit combination, which uses the construction method of the convex polyhedron of a single-machine unit combination described in the above embodiment to construct a model, and the system includes: a unit combination model construction module, a state space module, a backward dynamic programming model construction module, a dual model construction module and a convex polyhedron model construction module connected in sequence; wherein the unit combination model construction module is used to construct a single-machine unit combination model in the form of a mixed integer linear programming according to the unit state; the state space module is used to obtain the state space according to the single-machine unit combination model in the form of a mixed integer linear programming, and generate the state transition relationship between all states in the state space; the backward dynamic programming model construction module is used to construct a backward dynamic programming model for the single-machine unit combination problem according to the state transition relationship; the dual model construction module is used to transform the backward dynamic programming model into a linear programming model using an equivalent transformation method to obtain a dual model of the linear programming; the convex polyhedron model construction module is used to obtain a convex polyhedron model of a single-machine unit combination according to the dual model of the linear programming.
[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 above-mentioned method of constructing a convex polyhedron of a single-machine unit combination.
[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 above-mentioned method for constructing a convex polyhedron of a single-machine unit combination.
[0064] The technical solution provided by the embodiment of the present application has at least the following advantages:
[0065] The embodiment of the present application provides a method, system, device and medium for constructing a convex polyhedron of a single-unit combination. The method includes the following steps: first, based on the unit state, a single-unit combination model in the form of a mixed integer linear programming is constructed; then, based on the single-unit combination model in the form of a mixed integer linear programming, a state space is obtained, and a state transition relationship between all states in the state space is generated; next, based on the state transition relationship, a backward dynamic programming model of the single-unit combination problem is constructed; then, using an equivalent transformation method, the backward dynamic programming model is transformed into a linear programming model to obtain a dual model of the linear programming; finally, based on the dual model of the linear programming, a convex polyhedron model of the single-unit combination is obtained.
[0066] The present application constructs a convex polyhedron of a single-unit combination model in the form of a traditional mixed integer linear programming through a series of transformations. Generally, mixed integer linear programming models are considered to be NP-hard problems, and it is generally believed that there is no applicable polynomial time solution algorithm for solving them. The convex polyhedron model of the single-unit combination is a linear programming model in form and can be solved by a polynomial time solution algorithm. Therefore, it can play a significant advantage in computational efficiency and is considered to be significantly superior to traditional technology in solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0067] 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.
[0068] Figure 1 A schematic flow chart of a method for constructing a convex polyhedron of a single-machine assembly provided in one embodiment of the present application;
[0069] Figure 2 A schematic diagram of the structure of a system for constructing a convex polyhedron of a single-machine assembly provided in one embodiment of the present application;
[0070] Figure 3 A schematic diagram of the structure of an electronic device provided in one embodiment of the present application. DETAILED DESCRIPTION
[0071] As can be seen from the background technology, in the prior art, mixed integer programming problems are usually considered to be NP-hard problems. Therefore, as the problem becomes more complex, there are technical problems such as the time required to solve the problem increases exponentially and the computational efficiency is significantly reduced when solving large-scale problems.
[0072] In order to solve the above technical problems, the embodiment of the present application provides a method, system, device and medium for constructing a convex polyhedron of a single-machine unit combination, the method comprising the following steps: first, based on the unit state, construct a single-machine unit combination model in the form of mixed integer linear programming; then, based on the single-machine unit combination model in the form of mixed integer linear programming, obtain the state space, and generate the state transfer relationship between all states in the state space; next, based on the state transfer relationship, construct a backward dynamic programming model for the single-machine unit combination problem; then, using the equivalent transformation method, transform the backward dynamic programming model into a linear programming model to obtain the dual model of the linear programming; finally, based on the dual model of the linear programming, obtain the convex polyhedron model of the single-machine unit combination. The present application provides a method for constructing a convex polyhedron of a single-machine unit combination, constructs a convex polyhedron model of the feasible domain of the unit combination problem based on state transfer, and uses the unit combination convex hull model to replace the original unit combination mixed integer programming model to improve the solution efficiency.
[0073] 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.
[0074] See also Figure 1 The present application embodiment provides a method for constructing a convex polyhedron of a single-machine unit combination, comprising the following steps:
[0075] Step S1: Based on the unit status, a single unit unit combination model in the form of mixed integer linear programming is constructed.
[0076] Step S2: Based on the single unit unit commitment model in the form of mixed integer linear programming, a state space is obtained, and a state transfer relationship between all states in the state space is generated.
[0077] Step S3: Based on the state transition relationship, a backward dynamic programming model for the single unit unit commitment problem is constructed.
[0078] Step S4: using an equivalent transformation method to transform the backward dynamic programming model into a linear programming model to obtain a dual model of the linear programming.
[0079] Step S5: Based on the dual model of linear programming, a convex polyhedron model of a single unit combination is obtained.
[0080] In some embodiments, the unit status in step S1 includes the status of the unit in each time period; the status of the unit in each time period includes the unit output, unit start and stop status, unit startup action, unit shutdown action and the duration of the unit's current start and stop status.
[0081] This application starts with the smallest indivisible unit of the unit combination, that is, this application starts with a single unit, and proposes a method for constructing a convex polyhedron of a single unit combination. Here, a mixed integer programming model of a single unit combination is first given as the basis for constructing a convex polyhedron unit combination model, that is, a single unit combination model in the form of mixed integer linear programming, and its expression is as follows:
[0082]
[0083] x t P min ≤p t ≤x t P max ,t∈{1,...,T} (2)
[0084] u t +d t ≤1,t∈{1,...,T} (3)
[0085] u t -d t =x t -x t-1 ,t∈{2,...,T} (4)
[0086] p t -p t-1 ≤R+u t (R′-R),t∈{2,...,T} (5)
[0087] p t-1 -p t ≤R+d t (R′-R),t∈{2,...,T} (6)
[0088]
[0089] Among them, C u and C d Respectively represent the startup cost and shutdown cost of the unit; u t and d t They represent the start-up and shutdown actions of the unit in time period t respectively; p t represents the active power of the unit in time period t; xt Indicates the start and stop status of the unit in time period t; t represents the node electricity price at time t; P min and P max Respectively represent the minimum technical output and maximum technical output of the unit; T on and T off They represent the minimum start-up time and minimum shutdown time of the unit respectively; T represents the length of the scheduling cycle.
[0090] In formula (1), f(p t ,x t ) represents the linearized quadratic coal consumption cost curve, which is in the following form:
[0091] f(p t ,x t )≥K i (p t -P i x t )+H i x t ,∈{1,...,T},i∈{1,...,I} (10)
[0092] Among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
[0093] The above model is a single unit combination model in the form of mixed integer linear programming. It is not difficult to see that the state of the unit in each period can be represented by a cell, namely (p, x, u, d, l). Among them, p, x, u, d and l represent the unit output, unit start-up and shutdown status, unit startup action, unit shutdown action and the duration of the unit's current start-up and shutdown status respectively.
[0094] In some embodiments, step S2 obtains a state space based on a single unit unit commitment model in the form of mixed integer linear programming, comprising the following steps:
[0095] Step S201: Based on a single unit unit combination model in the form of mixed integer linear programming, an output set including all possible optimal outputs is obtained.
[0096] Step S202: Based on the output set including all possible optimal outputs, a state space of the single unit combination is obtained.
[0097] Wherein, step S201 obtains an output set including all possible optimal outputs based on a single unit unit combination model in the form of mixed integer linear programming, and includes the following steps:
[0098] Step S2011, based on the single unit combination model in the form of mixed integer linear programming, obtain the optimal output decision result.
[0099] Step S2012: Based on the optimal output decision result, an output set including all possible optimal outputs is obtained.
[0100] It is worth noting that for the above-mentioned single-unit combination model, in its optimal output decision result, the output in the startup state must belong to the following discrete finite set:
[0101] p t ∈Ω p ={Ω p 1∪Ω p 2∪Ω p 3∪Ω p 4} (11)
[0102] in,
[0103]
[0104] Among them, Ω p represents the set of all possible optimal outputs; Ω p 1 means that the output set related to the minimum technical output is included; Ω p 2 means that the output set related to the maximum technical output is included; Ω p 3 represents the output set including startup ramp constraints; Ω p 4 indicates that it contains the output set related to the piecewise linearization segmentation points.
[0105] Depends on the set Ω containing all possible optimal outputs p , the optimal dispatch result of the single unit combination is that the state (p, x, u, d, l) of the unit in each period belongs to the set Ω s , this set can be considered as the state space of the unit. In order to conveniently describe the state space Ω s , the state space is divided into two parts according to the start and stop status of the unit, namely the state space Ω containing all the start states s_on and the state space Ω containing all halt states s_off .
[0106] State space Ω s The expression is as follows:
[0107] Ω s =Ω s_on ∪Ω s_off (16)
[0108] Among them, Ω srepresents the state space; Ω s_on Represents the state space containing all power-on states; Ω s_off represents the state space containing all halting states.
[0109] According to the minimum start-up time T on , containing the state space Ω of all power-on states s_on Including the following two situations.
[0110] 1) For the state space Ω containing all power-on states s_on :
[0111] (1) When the minimum startup time of the unit meets T on =1:
[0112] Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×1} (17)
[0113] (2) When the minimum startup time of the unit meets T on >1:
[0114] Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×{1,...,T on}} (18)
[0115] Among them, when l=1, u=1; otherwise l>1, u=0.
[0116] According to the minimum shutdown time T of the unit off , the state space Ω containing all halt states s_off Including the following two situations.
[0117] 2) For the state space Ω containing all shutdown states s_off :
[0118] (1) When the minimum shutdown time of the unit meets T off =1:
[0119] Ω S_off ={(p,x,u,d,l)∈0×0×0×B×1} (19)
[0120] (2) When the minimum shutdown time of the unit meets T off >1:
[0121] Ω S_off ={(p,x,u,d,l)∈0×0×0×B×{1,...,T off}} (20)
[0122] Among them, when l=1, d=1; otherwise l>1, d=0.
[0123] At this time, the state space Ω s The state space Ω containing all the startup states can be s_on and the state space Ω containing all halt states s_off It is represented as shown in formula (16).
[0124] In some embodiments, the state transition relationship between all states in the state space is generated in step S2, including: based on the unit output range, unit start and stop logic, unit climbing limit and minimum start and stop time requirements, the state transition relationship between all states in the state space is generated.
[0125] Specifically, according to the unit output range, unit start-stop logic, unit climbing limit and minimum start-stop time requirements, the state transition relationship between all states in the state space can be generated according to the following rules, namely:
[0126] 1) When the unit is turned on and T on =1, then the following state transition relationship exists: ① When the unit state is (p, 1, 1, 0, 1), it can transfer to the state (p′, 1, 0, 0, 1) when |p′-p| ≤ R; ② When the unit state is (p, 1, 0, 0, 1), it can transfer to the state (p′, 1, 0, 0, 1) when |p′-p| ≤ R or transfer to the state (0, 0, 0, 1, 1), where R is the unit climbing limit.
[0127] 2) When the unit is turned on and T on >1, then there exists the following state transition relationship: ① When the unit state is (p, 1, 1, 0, 1), it can be transferred to the state (p′, 1, 0, 0, 2) when |p′-p|≤R; ② When the unit state is (p, 1, 0, 0, l) when 1<l<T on When |p′-p|≤R, it can transfer to the state (p′,1,0,0,l+1); ③ When the unit state is (p,1,0,0,T on ), it can transfer to the state (p′,1,0,0,T on ) when |p′-p|≤R or transfer to state (0,0,0,1,1) when |p|≤R′, where R is the unit climbing limit and R′ is the relaxation climbing limit of the unit state change.
[0128] 3) When the unit is shut down and T off=1, then the following state transition relationship exists: ① When the unit state is (0,0,0,1,1), it can be transferred to the state (0,0,0,0,1); ② When the unit state is (0,0,0,0,1), it can be transferred to the state (0,0,0,0,1) or transferred to the state (p′,1,1,0,1) when |p′|≤R′, where R′ is the relaxation climbing limit of the unit state change.
[0129] 4) When the unit is shut down and T off >1, then there is the following state transition relationship: ① When the unit state is (0,0,0,1,1), it can be transferred to the state (0,0,0,0,1); ② When the unit state is (0,0,0,0,l) in 1<l<T off , it can transfer to the state (0,0,0,0, l+1); ③ When the unit state is (0,0,0,0, T off ), it can transfer to the state (0,0,0,0,T off ) or transfers to the state (p′, 1, 1, 0, 1) when |p′| ≤ R′, where R′ is the relaxation climbing limit of the unit state change.
[0130] In some embodiments, step S3 constructs a backward dynamic programming model for the single unit combination problem based on the state transition relationship, including: based on the state transition relationship, converting the single unit combination model in the mixed integer linear programming form into a backward dynamic programming model to obtain the backward dynamic programming model for the single unit combination problem.
[0131] In order to facilitate subsequent representation, the unit state represented by the cell (p, x, u, d, l) is replaced by the symbols i, j and k. At the same time, according to the above state transfer relationship, the single unit unit commitment problem in the form of mixed integer linear programming can be expressed as the following backward dynamic programming model, that is, the backward dynamic programming model of the single unit unit commitment problem, which is expressed as follows:
[0132] v DP =min{v DP (,1)|i∈Ω s} (twenty one)
[0133] v DP (i, t) = min{V(i, t) + v DP (j, ++1)|j∈Ω s_from (i)},i∈Ω s , t∈{1,...,T-1}(22)
[0134] v DP (i,T)=V(i,T),i∈Ω s (twenty three)
[0135] Among them, v DP represents the minimum cost of the corresponding dynamic programming; Ω s represents the state space; v DP (i, t) represents the minimum cost of the corresponding dynamic programming at time t when the unit maintains state i and runs until the end of the scheduling period; v DP (j, t+1) represents the minimum cost of the corresponding dynamic programming at time t+1 and when the unit maintains the state j until the end of the scheduling period; v DP (i, T) represents the minimum cost of the corresponding dynamic programming when the unit maintains the state i at time T and runs until the end of the scheduling period; Ω s-from (i) represents the set of all states in the state space that can be transferred from state i; V(i,T) represents the cost when the unit maintains state i at time T; V(i,t) represents the cost when the unit maintains state i at time t, that is:
[0136] V(i, t) = C u u(i)+C d d(i)+f(p(i),x(i))-Π t p(i),i∈Ω s , t∈{1,..,T} (24)
[0137] Among them, p(i), x(i), u(i) and d(i) respectively represent the unit output, start-stop status, startup action status and shutdown action status of the unit when the unit maintains state i.
[0138] All expressions in backward dynamic programming can be abstracted as "v0 = min{v1, ..., v N}, its role can be represented by the linear programming model “max{v0|v0≤v1, ..., v0≤v N}". Thus, the backward dynamic programming model can be replaced by an equivalent linear programming model, which is in the following form:
[0139] max v LP (25)
[0140] stv LP ≤v LP (i, 1): w(t, 1), i∈Ω s (26)
[0141] v LP (i, t)≤V(i, t)+v LP (j, t+1): w(i, j, t), j∈Ω s_fiom(i),i∈Ω,t∈{1,..,T-1}(27)
[0142] v LP (i, T) = V (i, T): w (i, T), i∈Ω s (28)
[0143] Among them, v LP represents the minimum cost of the corresponding linear programming; v LP (i, t) represents the minimum cost of the corresponding linear programming at time t and when the unit maintains state i until the end of the scheduling period; w(i, t) and w(i, j, t) represent the dual variables of the corresponding inequality constraints respectively.
[0144] Furthermore, the dual model of the above linear programming can be obtained. The expression of the dual model of the linear programming is as follows:
[0145]
[0146] w(i,1),w(i,j,t),w(i,T)≥0,i∈Ω s , j∈Ω s_from (i), t∈{1,...,T-1} (34)
[0147] Among them, Ω s_to (i) represents the set of all states in the state space that can transition to state i.
[0148] Step S4 obtains a convex polyhedron model of a single unit combination based on the dual model of linear programming, including the following steps:
[0149] Step S401: Based on the dual model of linear programming, the unit output, the unit start-stop state, the unit startup action and the unit shutdown action are obtained respectively.
[0150] Step S402: Based on the unit output, the unit start / stop status, the unit startup action and the unit shutdown action, a convex polyhedron model of a single unit combination is obtained.
[0151] Based on the dual model of linear programming, the unit output, unit start-up and shutdown status, unit startup action and unit shutdown action can be inferred by the following formula:
[0152]
[0153] Among them, w*(i,t) and w*(i,j,t) are the optimal solutions of the decision variables of the dual problem, that is, the optimal solutions of the dual variables corresponding to the inequality constraints. Since the dual model is a linear programming model, the convex polyhedron of the single unit combination can be obtained, and its corresponding optimization model is:
[0154] (10)(40)
[0156] (30)-(34)(41)
[0157] (35)-(38)(42)
[0158] Among them, p t 、x t 、u t d t They represent the unit output, unit start and stop status, unit startup action, and unit shutdown action respectively; among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
[0159] Based on this, the embodiment of the present application provides a method for constructing a convex polyhedron of a single-unit unit combination. First, a single-unit unit combination model in the form of mixed integer linear programming is constructed. At the same time, an output set containing all possible optimal outputs is proposed, and a state space of the single-unit unit combination is constructed, and the state transition relationship between all states in the single-unit unit combination state space is generated. The present application also constructs a backward dynamic programming model for the single-unit unit combination problem. By designing an equivalent transformation method from the backward dynamic programming model of the single-unit unit combination problem to the linear programming model, the backward dynamic programming model is transformed into a linear programming model to obtain a dual model of the linear programming; finally, the dual model of the linear programming model is used to establish the relationship between the convex polyhedron model of the single-unit unit combination and the unit output, unit start-up and shutdown status, unit startup action and unit shutdown action, and restore the physical meaning of the unit.
[0160] Compared with the prior art, the method for constructing the convex polyhedron of a single-unit combination provided by the present application has the following advantages: the present application constructs a single-unit combination model in the form of a mixed integer linear programming based on the unit state, and then constructs a convex polyhedron of the single-unit combination model through a series of transformations. The convex polyhedron model of the single-unit combination is a linear programming model in form and can be solved by a polynomial time solving algorithm, so it can play a significant advantage in computational efficiency.
[0161] See also Figure 2The embodiment of the present application also provides a system for constructing a convex polyhedron of a single-machine unit combination, which uses the construction method of the convex polyhedron of a single-machine unit combination described in the above embodiment to construct a model. The system includes: a unit combination model construction module 101, a state space module 102, a backward dynamic programming model construction module 103, a dual model construction module 104 and a convex polyhedron model construction module 105 connected in sequence; wherein the unit combination model construction module 101 is used to construct a single-machine unit combination model in the form of mixed integer linear programming according to the unit state; the state space module 102 It is used to obtain the state space and generate the state transfer relationship between all states in the state space according to the single-unit combination model in the form of mixed integer linear programming; the backward dynamic programming model construction module 103 is used to construct the backward dynamic programming model of the single-unit combination problem according to the state transfer relationship; the dual model construction module 104 is used to transform the backward dynamic programming model into a linear programming model by adopting an equivalent transformation method to obtain the dual model of the linear programming; the convex polyhedron model construction module 105 is used to obtain the convex polyhedron model of the single-unit combination according to the dual model of the linear programming.
[0162] See also Figure 3 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.
[0163] 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.
[0164] 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.
[0165] 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.
[0166] 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.
[0167] Based on the above technical scheme, an embodiment of the present application provides a method, system, equipment and medium for constructing a convex polyhedron of a single-unit combination, and the method includes the following steps: first, based on the unit state, a single-unit combination model in the form of mixed integer linear programming is constructed; then, based on the single-unit combination model in the form of mixed integer linear programming, a state space is obtained, and a state transition relationship between all states in the state space is generated; next, based on the state transition relationship, a backward dynamic programming model of the single-unit combination problem is constructed; then, using an equivalent transformation method, the backward dynamic programming model is transformed into a linear programming model to obtain a dual model of the linear programming; finally, based on the dual model of the linear programming, a convex polyhedron model of the single-unit combination is obtained.
[0168] The present application constructs a convex polyhedron of a single-unit combination model in the form of a traditional mixed integer linear programming through a series of transformations. Generally, mixed integer linear programming models are considered to be NP-hard problems, and it is generally believed that there is no applicable polynomial time solution algorithm for solving them. The convex polyhedron model of the single-unit combination is a linear programming model in form and can be solved by a polynomial time solution algorithm. Therefore, it can play a significant advantage in computational efficiency and is considered to be significantly superior to traditional technology in solution efficiency.
[0169] 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 method for constructing a convex polyhedron of a single-machine unit combination, characterized in that: The following steps are involved: Based on the unit status, a single unit unit commitment model in the form of mixed integer linear programming is constructed; Based on the single-unit unit commitment model in the mixed integer linear programming form, a state space is obtained, and a state transfer relationship between all states in the state space is generated; Based on the state transfer relationship, a backward dynamic programming model for the unit commitment problem of a single unit is constructed; Using an equivalent transformation method, the backward dynamic programming model is transformed into a linear programming model to obtain a dual model of the linear programming; Based on the dual model of the linear programming, a convex polyhedron model of a single unit combination is obtained.
2. The method for constructing a convex polyhedron of a single machine unit combination according to claim 1, characterized in that: The unit status includes the status of the unit in each period; the status of the unit in each period includes the unit output, the unit start and stop status, the unit startup action, the unit shutdown action and the duration of the unit's current start and stop status; The single unit unit combination model in the mixed integer linear programming form is expressed as follows: x t P min ≤p t ≤x t P max ,t∈{1,...,T} (2) u t +d t ≤1,t∈{1,...,T} (3) u t -d t =x t -x t-1 ,t∈{2,...,T} (4) p t -p t-1 ≤R+u t (R′-R),t∈{2,...,T} (5) p t-1 -p t ≤R+d t (R′-R),t∈{2,...,T} (6) Among them, C u and C d Respectively represent the startup cost and shutdown cost of the unit; u t and d t They represent the start-up and shutdown actions of the unit in time period t respectively; p t represents the active power of the unit in time period t; x t represents the start and stop status of the unit in time period t; f(p t ,x t ) represents the linearized secondary coal consumption cost curve; Π t represents the node electricity price at time t; P min and P max Respectively represent the minimum technical output and maximum technical output of the unit; T on and T off They represent the minimum start-up time and minimum shutdown time of the unit respectively; T represents the length of the scheduling cycle; Among them, f(p t ,x t ) is as follows: f(p t ,x t )≥K i (p t -P i x t )+H i x t ,∈{1,...,T},i∈{1,...,I} (10) Among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
3. The method for constructing a convex polyhedron of a single machine assembly according to claim 1, characterized in that: Based on the single unit unit commitment model in the form of mixed integer linear programming, a state space is obtained, including: Based on the single unit unit combination model in the mixed integer linear programming form, an output set including all possible optimal outputs is obtained; Based on the output set including all possible optimal outputs, a state space of the single unit unit combination is obtained; Wherein, based on the single unit unit combination model in the form of mixed integer linear programming, an output set containing all possible optimal outputs is obtained, including: Based on the single unit unit combination model in the mixed integer linear programming form, an optimal output decision result is obtained; Based on the optimal output decision result, an output set including all possible optimal outputs is obtained; For the single-unit unit combination model in the form of mixed integer linear programming, the unit state is represented by a cell (p, x, u, d, l); wherein p, x, u, d and l represent the unit output, the unit start-up and shutdown state, the unit startup action, the unit shutdown action, and the duration of the current start-up and shutdown state of the unit, respectively; In the optimal output decision result, the output in the power-on state belongs to the following discrete finite set: p t ∈Ω p ={Ω p 1∪Ω p 2∪Ω p 3∪Ω p 4} (11) in, Among them, the set Ω p represents the set of all possible optimal outputs; Ω p 1 means that the output set related to the minimum technical output is included; Ω p 2 means that the output set related to the maximum technical output is included; Ω p 3 represents the output set including startup ramp constraints; Ω p 4 indicates that it contains the output set related to the piecewise linearization segmentation points.
4. The method for constructing a convex polyhedron of a single machine assembly according to claim 3, characterized in that: The state space is a set of states of the units in each time period of the optimal dispatch result of the single unit combination; The state space expression is as follows: Oh s =Oh s_on ∪Ω s_off (16) Among them, Ω s represents the state space; Ω s_on Represents the state space containing all power-on states; Ω s_off represents the state space containing all halting states; According to the minimum startup time of the unit, the state space Ω containing all startup states s_on This includes the following two situations: When the minimum startup time of the unit meets T on =1: Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×1} (17) When the minimum startup time of the unit meets T on >1: Ω S_on ={(p,x,u,d,l)∈Ω p ×1×B×0×{1,...,T on }} (18) Among them, when l=1, u=1; otherwise l>1, u=0; According to the minimum shutdown time of the unit, the state space Ω containing all shutdown states s_off This includes the following two situations: When the minimum shutdown time of the unit meets T off =1: Ω S_off ={(p,x,u,d,l)∈0×0×0×B×1} (19) When the minimum shutdown time of the unit meets T off >1: Among them, when l=1, d=1; otherwise l>1, d=0.
5. The method for constructing a convex polyhedron of a single machine assembly according to claim 1, characterized in that: Generate state transition relations between all states in the state space, including: Based on the unit output range, unit start-stop logic, unit climbing limit and minimum start-stop time requirements, the state transition relationship between all states in the state space is generated; wherein, The state transition relationship is generated according to the following rules: When the unit is turned on and the minimum start-up time of the unit meets T on =1, the state transition relationship is: When the unit state is (p, 1, 1, 0, 1), the unit state is transferred to the state (p′, 1, 0, 0, 1) when |p′-p|≤R, where R is the unit climbing limit; When the unit state is (p, 1, 0, 0, 1), when |p′-p|≤R, the unit state is transferred to the state (p′, 1, 0, 0, 1) or (0, 0, 0, 1, 1); When the unit is turned on and the minimum start-up time of the unit meets T on >1, the state transition relationship is: When the unit state is (p, 1, 1, 0, 1), when |p′-p|≤R, the unit state is transferred to the state (p′, 1, 0, 0, 2); When the unit state is (p, 1, 0, 0, l), 1<l<T on , when |p′-p|≤R, the group state is transferred to the state (p′,1,0,0,l+1); When the unit state is (p,1,0,0,T on ), when |p′-p|≤R, the group state is transferred to the state (p′,1,0,0,T on ) or when |p|≤R′, the group state is transferred to state (0,0,0,1,1); When the unit is shut down and the minimum shutdown time of the unit meets T off =1, the state transition relationship is: When the unit state is (0,0,0,1,1), the unit state is transferred to state (0,0,0,0,1); When the unit state is (0,0,0,0,1), the unit state is transferred to the state (0,0,0,0,1) or when |p′|≤R′, the unit state is transferred to the state (p′,1,1,0,1), where R′ is the relaxation climbing limit of the unit state change; When the unit is shut down and the minimum shutdown time of the unit meets T off >1, the state transition relationship is: When the unit state is (0,0,0,1,1), the unit state is transferred to state (0,0,0,0,1); When the unit state is (0,0,0,0,l), 1<l<T off , the unit state is transferred to state (0,0,0,0,l+1); When the unit status is (0,0,0,0,T off ), the unit state is transferred to the state (0,0,0,0,T off ) or when |p′|≤R′, the group state is transferred to state (p′, 1,1,0,1).
6. The method for constructing a convex polyhedron of a single machine assembly according to claim 1, characterized in that: Based on the state transfer relationship, a backward dynamic programming model for the single unit unit commitment problem is constructed, including: Based on the state transfer relationship, converting the single-unit unit commitment model in the mixed integer linear programming form into a backward dynamic programming model to obtain a backward dynamic programming model for the single-unit unit commitment problem; The expression of the backward dynamic programming model of the single unit unit commitment problem is as follows: v DP =min{v DP (i,1)|i∈Ω s } (21) v DP (i,t)=min{V(i,t)+v DP (j,t+1)|j∈Ω s_from (i)},i∈Ωs,t∈{1,...,T-1} (22) v DP (i,T)=V(i,T),i∈Ω s (23) Among them, v DP represents the minimum cost of the corresponding dynamic programming; Ω s represents the state space; v DP (i, t) represents the minimum cost of the corresponding dynamic programming at time t when the unit maintains state i and runs until the end of the scheduling period; v DP (j, t+1) represents the minimum cost of the corresponding dynamic programming at time t+1 when the unit maintains the state j and runs until the end of the scheduling period; v DP (i, T) represents the minimum cost of the corresponding dynamic programming at time T and when the unit maintains state i until the end of the scheduling period; Ω s_from (i) represents the set of all states in the state space that can be transferred from state i; V(i,t) represents the cost when the unit maintains state i at time t; V(i,T) represents the cost when the unit maintains state i at time T, that is: V(i,t)=C u u(i)+C d d(i)+f(p(i),x(i))-Π t p(i),i∈Ω s ,t∈{1,...,T} (24) Among them, p(i), x(i), u(i) and d(i) respectively represent the unit output, start-stop status, startup action status and shutdown action status of the unit when the unit maintains state i.
7. The method for constructing a convex polyhedron of a single machine assembly according to claim 6, characterized in that: The expression of the linear programming model is as follows: LP max v(25) s.t. v LP ≤v LP (i,1):w(i,1),i∈Ω s (26) v LP (i,t)≤V(i,t)+v LP (j,t+1):w(i,j,t),j∈Ω s_from (i),i∈Ω s ,t∈{1,...,T-1}(27) v LP (i,T)=V(i,T):w(i,T),i∈Ω s (28) Among them, v LP represents the minimum cost of the corresponding linear programming; v LP (i, t) represents the minimum cost of the corresponding linear programming at time t and when the unit maintains state i until the end of the scheduling period; w(i, t) and w(i, j, t) represent the dual variables of the corresponding inequality constraints; The dual model of the linear programming is expressed as follows: w(i,1),w(i,j,t),w(i,T)≥0,i∈Ω s ,j∈Ω s_from (i),t∈{1,...,T-1} (34) Among them, Ω s_to (i) represents the set of all states in the state space that can be transferred to state i; Based on the dual model of the linear programming, a convex polyhedron model of a single unit combination is obtained, including: Based on the dual model of the linear programming, the unit output, the unit start-stop state, the unit startup action and the unit shutdown action are obtained respectively; Based on the unit output, the unit start-stop state, the unit startup action and the unit shutdown action, a convex polyhedron model of a single unit combination is obtained; The unit output, the unit start / stop state, the unit startup action and the unit shutdown action are obtained by the following formulas: Among them, w*(i,t) and w*(i,j,t) are the optimal solutions of the dual variables corresponding to the inequality constraints; The expression of the convex polyhedron model of the single unit combination is as follows: f(p t ,x t )≥K i (p t -P i x t )+H i x t ,∈{1,...,T},i∈{1,...,I} (40) (30)-(34)(41)(35)-(38)(42) Among them, p t 、x t 、u t d t They represent the unit output, unit start and stop status, unit startup action, and unit shutdown action respectively; among them, K i and H i P represents the parameter of the i-th segment of the secondary coal consumption cost curve; i It represents the starting position coordinates of the parameters of the i-th segment of the secondary coal consumption cost curve; I represents the total number of segments.
8. A system for constructing a convex polyhedron of a single-machine unit combination, which uses the method for constructing a convex polyhedron of a single-machine unit combination as claimed in any one of claims 1 to 7 to construct a model, characterized in that: include: The unit combination model building module, state space module, backward dynamic programming model building module, dual model building module and convex polyhedron model building module are connected in sequence; wherein, The unit commitment model building module is used to build a single unit unit commitment model in the form of mixed integer linear programming according to the unit status; The state space module is used to obtain a state space according to the single unit unit commitment model in the mixed integer linear programming form, and generate a state transfer relationship between all states in the state space; The backward dynamic programming model building module is used to build a backward dynamic programming model for the single unit unit commitment problem according to the state transfer relationship; The dual model building module is used to transform the backward dynamic programming model into a linear programming model by using an equivalent transformation method to obtain a dual model of the linear programming; The convex polyhedron model building module is used to obtain a convex polyhedron model of a single unit combination according to the dual model of the linear programming.
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 method for constructing a convex polyhedron of a single-machine unit combination 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 method for constructing a convex polyhedron of a single-machine unit combination as described in any one of claims 1 to 7 is implemented.