Unit combination symmetry elimination acceleration method and device based on convex hull polymerization relaxation
By constructing the mixed integer programming model of thermal power units into a convex hull form, dividing the aggregation group and designing public and private constraints, a convex hull aggregation relaxation model of the units is generated. This solves the problem of low solution efficiency caused by the symmetry of unit combination in traditional methods, and achieves efficient solution of unit combination problems and accuracy of optimization results.
Patent Information
- Application Number
- CN202510818258.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-18
- Publication Date
- 2025-11-14
AI Technical Summary
Traditional methods are inefficient in solving unit combination problems with symmetry. Existing methods for eliminating symmetry in unit combination have relaxation errors or increase model complexity, resulting in slow solution speed and inaccurate results.
A convex hull-based aggregation relaxation method is adopted to construct the mixed integer programming model of thermal power units into a convex hull form. By dividing the aggregation group and designing public and private constraints, integer variables are eliminated, generating a convex hull aggregation relaxation model of the unit, thus reducing the model size.
It accelerates the solution speed of unit combination problems, improves solution efficiency, ensures the accuracy of optimization results and the compactness of the model, and is applicable to unit combination problems of large-scale power systems.
Smart Images
Figure CN120955792A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of power system optimization technology, and more specifically, to a method and apparatus for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation. Background Technology
[0002] In actual power systems, there are a large number of generating units with the same parameters. These units can be regarded as symmetrical units. The feasible solutions of symmetrical units can be exchanged without changing the objective function value. This property will affect the solution of the unit combination problem.
[0003] Traditional branch and bound algorithms, when dealing with unit combination problems involving symmetry, cannot prune branches because the symmetric nature of the units means that equivalent feasible solutions may exist simultaneously in multiple branches. This leads to a significant reduction in solution efficiency. In addition, commercial optimization solvers are also affected by the symmetry of the units when solving unit combination problems, resulting in slower solution speeds for optimization problems.
[0004] There are currently two methods for eliminating symmetry in unit combination, and no method based on unit convex hull aggregation is available in academia: unit aggregation models and symmetry breaking constraints. Unit aggregation often introduces relaxation errors, making it impossible to accurately characterize the continuous output range of aggregated units. Some unit models that can guarantee the feasibility of scheduling results introduce a large number of variables, resulting in a large model size. While symmetry breaking inequalities eliminate unit symmetry, they also increase the difficulty of solving the model, and the solution efficiency increases with the scale of the unit combination problem. In addition, some symmetry elimination models are only applicable to units with certain specific parameters, and symmetry remains one of the factors affecting the solution efficiency of unit combination.
[0005] The method of aggregating units divides units into two types. However, the aggregated models differ for different types of units, and the complexity of the models increases significantly, especially for units with slow ramp-up speeds. The variable matrix and model size increase dramatically, making the search for feasible solutions very difficult. Furthermore, the results of the aggregated optimization problem may differ from the original problem. For the method of introducing symmetry breaking constraints, since the unit combination problem has minimum start-up and shutdown time constraints, forcibly specifying the start-up priority of units has already broken the feasible region of the original problem. This may cut off the optimal solution of the original problem, resulting in unsolvable or non-optimal optimization results. In addition, for multi-period scheduling problems, symmetry breaking constraints need to be introduced for each scheduling period of all symmetric units. The number of constraints increases with the number of symmetric units. Summary of the Invention
[0006] To address the problem of low solution efficiency for large-scale unit combination problems in power systems caused by unit symmetry, this application provides a method and apparatus, a computer device, and a storage medium for accelerating unit combination symmetry elimination based on convex hull aggregation relaxation.
[0007] The embodiments of this application are implemented as follows:
[0008] In a first aspect, this application provides a method for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation, including:
[0009] The mixed integer programming model of thermal power units is constructed as a convex hull form to eliminate integer variables in the model;
[0010] Units with the same parameters are grouped into cluster k, and the cluster variable is defined as total output. Number of machines turned on Number of startups and the number of shutdowns
[0011] Construct public constraints for the aggregation group, including start / stop logic state transition relationships, minimum start / stop time constraints, and output lower limit constraints;
[0012] Based on the unit's ramp-up characteristics, the aggregation groups are classified, and private constraints are designed for each type of aggregation group to tighten the upper bound of output, generating a unit convex hull aggregation relaxation model.
[0013] In one possible implementation, the unit is constructed as a convex hull model, generating the unit's optimal state space (p, u, v, w, T), representing the unit's output peak, operating state, start command, shutdown command, and duration, respectively. The method for eliminating integer variables is as follows:
[0014] ∑ i∈S x(i,1)=1;
[0015]
[0016] x(i,1)≥0,i∈S.
[0017] Where x(i,t) / x(i,T) represents the dual variable of the constraint corresponding to the linear programming model;
[0018] When x(i,t) / x(i,T)=1, it means that the unit is in state i at time t / T, and S is the set of optimal states of the unit;
[0019] Therefore, the unit output, start-up and shutdown status, start-up actions, and shutdown actions can be expressed as:
[0020]
[0021] Where, p t This represents the output of the thermal power unit at time t; u t This indicates the start-up and shutdown status of the generator unit at time t; v t and w t These represent whether the thermal power unit starts up or stops at time t.
[0022] In one possible implementation, the start / stop logic state transition relationship is represented as follows:
[0023]
[0024] In one possible implementation, the minimum start / stop time constraint is expressed as:
[0025]
[0026] In one possible implementation, the lower limit constraint on output is expressed as:
[0027]
[0028] In one possible implementation, the aggregation group classification includes K T-F K T-R and K T-L , is represented as:
[0029]
[0030] Where C0, C1, and C2 are different conditions, respectively:
[0031]
[0032] in, This represents the floor function.
[0033] In one possible implementation, the K T-F The private constraints of the aggregation group are:
[0034]
[0035] Where, [·]+=max{0,·}. The private constraint above couples the start-stop indicator variables of the aggregated thermal power unit group, tightening the upper bound of output.
[0036] In one possible implementation, the K T-R The private constraints of the aggregation group are:
[0037] The upper limit of the output of the polymer unit is expressed as:
[0038]
[0039] The aggregate ramp constraint is expressed as:
[0040]
[0041] In one possible implementation, the K T-L The private constraints of the aggregation group are:
[0042]
[0043] Secondly, this application provides a unit combination symmetry elimination acceleration device based on convex hull aggregation relaxation, comprising:
[0044] The single-unit convex hull conversion module converts the unit into a convex hull model, eliminating integer variables;
[0045] The unit aggregation module is used to group units with the same parameters into aggregation groups k, defining the aggregation group variable as total output. Number of machines turned on Number of startups and the number of shutdowns
[0046] The public constraint construction module is used to construct the public constraints of the aggregation group, including start-stop logic state transition relationships, minimum start-stop time constraints, and output lower limit constraints.
[0047] A private constraint building module is used to classify aggregate groups into K groups based on the unit ramp-up characteristics. T-F K T-R and K T-L And design private constraints for each type of aggregation group to tighten the upper bound of output force;
[0048] The aggregation model building module is used to integrate all constraints and functions to build a unit convex hull aggregation relaxation model.
[0049] This application provides a method and apparatus for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation. By designing compact constraints, it realizes the aggregation relaxation of the unit's convex hull, which speeds up the solution of the unit combination problem. The aggregation reduces the model size, thereby accelerating the solution. Attached Figure Description
[0050] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0051] Figure 1This is a schematic flowchart illustrating an exemplary embodiment of the present application of a method for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation;
[0052] Figure 2 This is a schematic diagram of an exemplary embodiment of the present application illustrating a unit combination symmetry elimination acceleration device based on convex hull polymerization relaxation.
[0053] Figure label:
[0054] 1. Single unit convex hull transformation module; 2. Aggregate unit partitioning module; 3. Public constraint construction module; 4. Private constraint construction module; 5. Aggregate model construction module. Detailed Implementation
[0055] To make the objectives, implementation methods and advantages of this application clearer, the exemplary implementation methods of this application will be clearly and completely described below with reference to the accompanying drawings of the exemplary embodiments of this application. Obviously, the exemplary embodiments described are only some embodiments of this application, and not all embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.
[0056] It should be noted that the brief descriptions of terms in this application are only for the convenience of understanding the embodiments described below, and are not intended to limit the embodiments of this application. Unless otherwise stated, these terms should be understood in their ordinary and common meaning.
[0057] The terms "first," "second," "third," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar or related objects or entities, and do not necessarily imply a specific order or sequence, unless otherwise specified. It should be understood that such terms are interchangeable where appropriate.
[0058] The terms “comprising” and “having”, and any variations thereof, are intended to cover but not exclude inclusion, for example, a product or device that includes a range of components is not necessarily limited to all of the components that are clearly listed, but may include other components that are not clearly listed or that are inherent to such product or device.
[0059] Before explaining the acceleration method for eliminating unit combination symmetry based on convex hull aggregation relaxation provided in the embodiments of this application, the application scenarios and implementation environment of the embodiments of this application will be introduced first.
[0060] In actual power systems, there are a large number of generating units with the same parameters. These units can be regarded as symmetrical units. The feasible solutions of symmetrical units can be exchanged without changing the objective function value. This property will affect the solution of the unit combination problem.
[0061] Traditional branch and bound algorithms, when dealing with unit combination problems involving symmetry, cannot prune branches because the symmetric nature of the units means that equivalent feasible solutions may exist simultaneously in multiple branches. This leads to a significant reduction in solution efficiency. In addition, commercial optimization solvers are also affected by the symmetry of the units when solving unit combination problems, resulting in slower solution speeds for optimization problems.
[0062] There are currently two main methods for eliminating symmetry in unit combination: unit aggregation models and symmetry breaking constraints. Unit aggregation often introduces relaxation errors, making it impossible to accurately characterize the continuous output range of aggregated units. Some unit models that can guarantee the feasibility of scheduling results introduce a large number of variables, resulting in a large model size. While symmetry breaking inequalities eliminate unit symmetry, they also increase the difficulty of solving the model, and the solution efficiency increases with the scale of the unit combination problem. Furthermore, some symmetry elimination models are only applicable to units with certain specific parameters, and symmetry remains one of the factors affecting the efficiency of unit combination solution.
[0063] Unit combination is a typical mixed-integer programming problem. Its goal is to minimize the operating and start-up costs of units by selecting appropriate units and operating strategies, while satisfying load balance and unit operating constraints. Currently, the most commonly used unit combination model is the 3-integer variable unit combination model, and the most general algorithm is the branch and bound algorithm.
[0064] In real-world power systems, generating units exhibit a great deal of symmetry. There are many identical generating units within the system, which may be located in the same power plant (i.e., on the same node in the network) or on different nodes.
[0065] The impact of unit symmetry on the solution of the unit combination branch and bound algorithm has the following three aspects:
[0066] 1. Search space expansion: Symmetry causes the branch and bound algorithm to generate a large number of equivalent solutions during the search process, making the search space huge and increasing the complexity of solving the problem.
[0067] 2. Pruning Difficulty: Symmetry makes the pruning process difficult. Traditional branch and bound algorithms reduce the search space and improve solution efficiency through pruning. However, in unit combination problems with symmetric solutions, the pruning conditions often cannot be met due to the existence of symmetry, resulting in the inability to effectively prune equivalent solutions and thus reducing the effectiveness of pruning.
[0068] 3. Redundant Computation: Symmetry can lead to redundant computation. Due to symmetry, units with the same parameters are equivalent, but branch and bound algorithms often fail to recognize these equivalences. Therefore, during the search process, the algorithm may repeatedly compute the same subproblems, increasing computation time and resource consumption.
[0069] Currently, there is no convex hull aggregation method in academia. Common methods for eliminating unit combination symmetry include:
[0070] 1. Aggregated Units: A method is proposed to aggregate identical units to eliminate unit symmetry. The main idea is to add the output of units with the same parameters and convert them into an equivalent unit, thus eliminating unit symmetry.
[0071] 2. Symmetry violation inequality: A method to eliminate unit symmetry by introducing symmetry violation constraints is proposed. The main idea is to forcibly define the start-up priority of the same units.
[0072] The method of aggregating units divides units into two types. However, the aggregated models differ for different types of units, and the complexity of the models increases significantly, especially for units with slow ramp-up speeds. The variable matrix and model size increase dramatically, making the search for feasible solutions very difficult. Furthermore, the results of the aggregated optimization problem may differ from the original problem. For the method of introducing symmetry breaking constraints, since the unit combination problem has minimum start-up and shutdown time constraints, forcibly specifying the start-up priority of units has already broken the feasible region of the original problem. This may cut off the optimal solution of the original problem, resulting in unsolvable or non-optimal optimization results. In addition, for multi-period scheduling problems, symmetry breaking constraints need to be introduced for each scheduling period of all symmetric units. The number of constraints increases with the number of symmetric units.
[0073] Based on this, this application provides a method and apparatus for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation. It can accurately aggregate units to eliminate model symmetry without constructing a complex model, and at the same time reduce the model size. It can efficiently solve unit combination models with symmetry problems in power systems, so as to achieve the goals of power system operating efficiency, power supply reliability and economy.
[0074] Next, the technical solutions of this application and how they solve the aforementioned technical problems will be described in detail through embodiments and in conjunction with the accompanying drawings. The embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this application.
[0075] Figure 1 This is a schematic flowchart illustrating an exemplary embodiment of the present application of a method for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation.
[0076] In one exemplary embodiment, such as Figure 1As shown, a method for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation is provided. In this embodiment, the method may include the following steps:
[0077] Step 100: Construct the mixed integer programming model of the thermal power unit into a convex hull form to eliminate integer variables in the model.
[0078] Step 200: Divide units with the same parameters into clusters k, and define the cluster variable as total output. Number of machines turned on Number of startups and the number of shutdowns
[0079] Step 300: Construct the public constraints of the aggregation group, including the start-stop logic state transition relationship, minimum start-stop time constraint, and output lower limit constraint.
[0080] Step 400: Classify the aggregate groups according to the ramp characteristics of the unit, and design private constraints for each type of aggregate group to tighten the upper limit of output, generating the unit convex hull aggregate relaxation model.
[0081] In one possible implementation, the specific implementation of the unit combination symmetry elimination acceleration method based on convex hull aggregation relaxation provided in this application is as follows:
[0082] First, the unit is constructed as a convex hull model to generate the optimal state space (p, u, v, w, T), representing the unit's output peak, operating state, start command, shutdown command, and duration, respectively. The method for eliminating integer variables is as follows:
[0083] Σ i∈S x(i,1)=1;
[0084]
[0085] x(i,1)≥0,i∈S.
[0086] Where x(i,t) / x(i,T) represents the dual variable of the constraint corresponding to the linear programming model. When x(i,t) / x(i,T)=1, it means that the unit is in state i at time t / T. S is the set of optimal states of the unit. Therefore, the unit output, start-up and shutdown states, start-up actions, and shutdown actions can be expressed as:
[0087]
[0088] For ease of description, the aggregated scheduling object is called an "aggregate group", and the superscript "A" is used to distinguish the variables within the aggregate group.
[0089] use This represents the set of indices of thermal power units with the same parameters of type k. The variable corresponding to the aggregated unit group k is... These represent the total output of the aggregation unit group k at time t, the number of units in the start-up state, the number of units started, and the number of units shut down, respectively.
[0090] Constraints in a cluster of thermal power units are divided into public constraints and private constraints.
[0091] The public constraint refers to the group of all aggregate machines k∈K T The constraints they all contain are as follows:
[0092] (1) The start-stop logic state variable transformation relationship of the aggregated thermal power unit group
[0093]
[0094] (2) Minimum start-up and shutdown time of the aggregate group
[0095]
[0096] (3) Minimum total output of the aggregation group
[0097]
[0098] Private constraints are more compact constraints designed to accurately characterize the output features of integrated thermal power units.
[0099] Different types of integrated thermal power unit clusters require different private constraints. Therefore, it is necessary to classify the integrated thermal power unit clusters.
[0100]
[0101] Where C0, C1, and C2 are different conditions:
[0102]
[0103] In the formula, This represents the floor function.
[0104] Able to notice set K T-F The ramp-up constraint of the aggregated thermal power unit group can be relaxed within a unit scheduling time.
[0105] Therefore, for set K T-F Within the aggregation group, this paper constructs the following private constraints:
[0106]
[0107] In the formula, [·]+=max{0,·}.
[0108] The private constraints above are coupled with the start-stop indicator variables of the aggregated thermal power unit group, tightening the upper limit of output.
[0109] Set K T-R The coal-fired power units in the system have a sufficiently long minimum start-up time, enabling the unit to increase its output to or near its maximum value within this minimum start-up time. Therefore, the private constraints are as follows:
[0110] (1) Upper limit of output of polymer unit
[0111]
[0112] (2) Aggregate climbing constraint
[0113]
[0114] Set K T-L The aggregation unit group in the middle has high ramping flexibility. Specifically, the private constraints in this part are as follows:
[0115]
[0116] The above constraints can tighten the upper bound of the output of the aggregation group, but there will still be some aggregation relaxation error. Therefore, it is necessary to introduce decomposition constraints and thermal power unit constraints to ensure the feasibility of the aggregation results.
[0117]
[0118] At the same time, in order to eliminate the symmetry in the decomposition process, the following symmetry-breaking inequality needs to be introduced:
[0119]
[0120] Therefore, a convex hull aggregation relaxation model for the unit is constructed.
[0121] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially as indicated, these steps are not necessarily executed in the indicated order. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages in other steps.
[0122] Corresponding to the aforementioned embodiments of the unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation, and employing the same technical concept, this application also provides embodiments of a unit combination symmetry elimination and acceleration device based on convex hull aggregation relaxation.
[0123] Figure 2 This is a schematic diagram of an exemplary embodiment of the present application illustrating a unit combination symmetry elimination acceleration device based on convex hull polymerization relaxation.
[0124] In one exemplary embodiment, such as Figure 2 As shown, the unit combination symmetry elimination acceleration device based on convex hull aggregation relaxation includes:
[0125] Single-unit convex hull conversion module 1 converts the unit into a convex hull model, eliminating integer variables;
[0126] Unit aggregation module 2 is used to divide units with the same parameters into aggregation groups k, and defines the aggregation group variable as total output. Number of machines turned on Number of startups and the number of shutdowns
[0127] Public constraint construction module 3 is used to construct public constraints for the aggregation group, including start-stop logic state transition relationships, minimum start-stop time constraints, and output lower limit constraints.
[0128] Private constraint building module 4 is used to classify aggregate groups into K based on unit ramping characteristics. T-F K T-R and K T-L And design private constraints for each type of aggregation group to tighten the upper bound of output force;
[0129] Module 5, the aggregation model building module, is used to integrate all constraints and functions to construct the unit's convex hull aggregation relaxation model.
[0130] Specific limitations regarding the unit combination symmetry elimination acceleration device based on convex hull aggregation relaxation can be found in the limitations of the unit combination symmetry elimination acceleration method based on convex hull aggregation relaxation described above, and will not be repeated here. Each module in the aforementioned unit combination symmetry elimination acceleration device based on convex hull aggregation relaxation can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.
[0131] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0132] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A method for accelerating the elimination of unit combination symmetry based on convex hull aggregation relaxation, characterized in that, include: The mixed integer programming model of thermal power units is constructed as a convex hull form to eliminate integer variables in the model; Units with the same parameters are grouped into cluster k, and the cluster variable is defined as total output. Number of machines turned on Number of startups and the number of shutdowns Construct public constraints for the aggregation group, including start / stop logic state transition relationships, minimum start / stop time constraints, and output lower limit constraints; Based on the unit's ramp-up characteristics, the aggregation groups are classified, and private constraints are designed for each type of aggregation group to tighten the upper bound of output, generating a unit convex hull aggregation relaxation model.
2. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 1, characterized in that, The unit is constructed as a convex hull model, generating the unit's optimal state space (p, u, v, w, T), representing the unit's output peak, operating state, start command, shutdown command, and duration, respectively. The method for eliminating integer variables is as follows: ∑ i∈S x(i,1)=1; x(i,1)≥0,i∈S. Where x(i,t) / x(i,T) represents the dual variable of the constraint corresponding to the linear programming model; When x(i,t) / x(i,T)=1, it means that the unit is in state i at time t / T, and S is the set of optimal states of the unit; Therefore, the unit output, start-up and shutdown status, start-up actions, and shutdown actions can be expressed as: Where, p t This represents the output of the thermal power unit at time t; u t This indicates the start-up and shutdown status of the generator unit at time t; v t and w t These represent whether the thermal power unit starts up or stops at time t.
3. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 1, characterized in that, The start / stop logic state transition relationship is represented as follows:
4. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 1, characterized in that, The minimum start / stop time constraint is expressed as follows:
5. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 1, characterized in that, The lower limit constraint on output is expressed as follows:
6. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 1, characterized in that, The cluster classification includes K T-F K T-R and K T-L , represented as: Where C0, C1, and C2 are different conditions, respectively: in, This represents the floor function.
7. The unit combination symmetry elimination and acceleration method based on convex hull aggregation relaxation as described in claim 5, characterized in that, The K T-F The private constraints of the aggregation group are: Where, [·]+=max{0,·}. The private constraint above couples the start-stop indicator variables of the aggregated thermal power unit group, tightening the upper bound of output.
8. The method for accelerating unit combination symmetry elimination based on convex hull aggregation relaxation as described in claim 1, characterized in that, The K T-R The private constraints of the aggregation group are: The upper limit of the output of the polymer unit is expressed as: The aggregate ramp constraint is expressed as:
9. The method for accelerating unit combination symmetry elimination based on convex hull aggregation relaxation as described in claim 1, characterized in that, The K T-L The private constraints of the aggregation group are:
10. A unit combination symmetry elimination and acceleration device based on convex hull aggregation relaxation, characterized in that, include: The single-unit convex hull conversion module converts the unit into a convex hull model, eliminating integer variables; The unit aggregation module is used to group units with the same parameters into aggregation groups k, defining the aggregation group variable as total output. Number of machines turned on Number of startups and the number of shutdowns The public constraint construction module is used to construct the public constraints of the aggregation group, including start-stop logic state transition relationships, minimum start-stop time constraints, and output lower limit constraints. A private constraint building module is used to classify aggregate groups into K groups based on the unit ramp-up characteristics. T-F K T-R and K T-L And design private constraints for each type of aggregation group to tighten the upper bound of output force; The aggregation model building module is used to integrate all constraints and functions to build a unit convex hull aggregation relaxation model.