A polyhedral equivalent modeling method and device for a distributed energy cluster

Abstract

A polyhedral equivalent modeling method and device of a distributed energy cluster, the method comprising: establishing a corresponding mathematical model for describing the operating characteristics of different distributed energies; establishing a generalized model of the distributed energy for unified description based on the established mathematical model, and obtaining an individual polyhedral feasible region model of the distributed energy according to the variable controllable characteristics; using a homogeneous polyhedron to perform internal approximation in the individual polyhedral feasible region model of all the distributed energies, and calculating the Minkowski sum of the approximation results to obtain an aggregated model; adopting a double-layer optimization method to express the construction process of the aggregated model as a multi-objective optimization process, searching for an optimal homogeneous polyhedron shape in the upper layer, searching for the internal approximation results of all the individual feasible regions in the lower layer, and using a firefly algorithm to perform optimization so as to maximize the accuracy of the aggregated model. The present application can solve the problems that different characteristic distributed energies cannot be described by using a unified model and the model accuracy is poor.

Description

Technical Field

[0001] The present invention belongs to the field of electrical engineering, and more specifically, relates to a polyhedron equivalent modeling method and device for a distributed energy cluster. Background Art

[0002] An integrated energy system (IES) achieves efficient energy utilization and management by integrating different types of energy resources, such as electricity, heat, cooling, and gas. Distributed energy resources (DERs) are key components of this system, providing diverse flexibility to meet system needs and ensure system stability and reliability. By integrating different forms of energy, IES can effectively recycle and reuse energy. For example, a combined cooling, heating, and power (CCHP) system can simultaneously provide electricity, heat, and cooling, improving overall energy efficiency. Furthermore, by utilizing lower-cost energy resources, such as renewable energy (wind and solar) and waste energy, IES can reduce overall energy costs. IES also helps optimize energy management and scheduling, improving system operational efficiency. The diversity and flexibility of DERs enhances the reliability and resilience of the energy system. By comprehensively utilizing multiple energy forms, DERs improve the energy system, reduce dependence on a single energy source, and enhance the stability of energy supply. Therefore, developing IES is a crucial step in achieving my country's energy modernization and promoting sustainable development in the energy sector.

[0003] However, integrated energy systems encompass a wide variety of distributed energy resources, and accurately collecting and processing data from these diverse sources is a complex task. Ensuring data quality and timeliness is a significant challenge, especially given the large volume and diverse sources of data. Furthermore, integrated energy systems involve numerous energy types and complex interactions between their components. Building a comprehensive and accurate cluster model requires a deep understanding of the operating mechanisms and interactions of each subsystem. Therefore, establishing a unified modeling description for the various types of distributed energy clusters within an integrated energy system is not only a key means of achieving efficient energy utilization and management, but also an important path to driving the energy industry's transition toward a green, low-carbon future. Summary of the Invention

[0004] In response to existing technical defects and improvement needs, the present invention proposes a polyhedron equivalent modeling method and device for distributed energy clusters, aiming to solve the problems in existing technologies that distributed energy with different characteristics in integrated energy systems cannot be described using a unified model and the model accuracy is poor.

[0005] To achieve the above objectives, the present invention adopts the following technical solutions:

[0006] A polyhedron equivalent modeling method for a distributed energy cluster, characterized by comprising the following steps:

[0007] According to the operating characteristics of different distributed energy resources, corresponding mathematical models are established to describe them;

[0008] Based on the established mathematical model, a generalized model of distributed energy is established for unified description, and the individual polyhedron feasible domain model of distributed energy is obtained according to the controllable characteristics of variables;

[0009] In the individual polyhedron feasible domain models of all distributed energy resources, homogeneous polyhedrons are used for inner approximation, and the Minkowski sum of the approximation results is calculated to obtain the aggregate model;

[0010] A two-layer optimization method is used to formulate the aggregation model construction process as a multi-objective optimization process. An optimal homogeneous polyhedron shape is sought in the upper layer, and the inner approximation results of all individual feasible domains are sought in the lower layer. The moth-to-flame algorithm is used to perform the optimization to maximize the accuracy of the aggregation model.

[0011] Furthermore, the distributed energy includes energy storage units, temperature-controlled loads, and interruptible loads. The established mathematical model and constraints are as follows:

[0012] (1.1) Energy storage unit modeling and constraints:

[0013] ;

[0014] Equations (1), (2), and (3) represent the power and energy constraints of energy storage. and are the charging power and discharging power of energy storage respectively, and are the maximum charging and discharging powers of the energy storage, respectively, and are the upper and lower limits of energy storage respectively;

[0015] ;

[0016] Formula (4) is the climbing power constraint, where is the upper limit of the ramp power, and Equation (5) shows that the storage energy cannot be charged and discharged simultaneously;

[0017] ;

[0018] Equation (6) is the energy charge and discharge constraint, which represents the relationship between power and energy, where is the energy dissipation rate of stored energy, is the charging efficiency of energy storage, is the discharge efficiency of energy storage;

[0019] (1.2) Temperature control load modeling and constraints:

[0020] ;

[0021] Equations (7) and (8) represent the power and energy constraints of the temperature control load, where is the power of the temperature control load, The power upper limit of the temperature control load. and are the lowest and highest operating temperatures of the temperature control load, is the current temperature of the temperature-controlled load;

[0022] ;

[0023] Formula (9) is a differential equation derived from the heat balance equation, which describes the working process of the temperature control load. is the thermal resistance of the temperature control load, is the heat capacity of the temperature control load, for The outdoor temperature at the moment;

[0024] (1.3) Modeling and constraints of interruptible loads:

[0025] ;

[0026] Formula (10) describes the principle of interruptible load reduction, where is the original load size, is the load reduction factor, and Equation (11) describes the operating range of the interruptible load. and are the minimum and maximum values ​​of the interruptible load in time period t, respectively.

[0027] Furthermore, the operation process and constraints of the generalized model are as follows:

[0028] ;

[0029] Equations (12), (13), and (14) are the power and energy constraints of the generalized model, where superscripts represent upper bounds and subscripts represent lower bounds;

[0030] ;

[0031] Formula (15) is the auxiliary service constraint condition of the generalized model, The frequency regulation range that distributed energy can provide, indicating the maximum acceptable change when increasing or decreasing its power, in units of , For the upper limit of frequency regulation, equation (16) is For the maximum regulation capability of the distributed energy, equation (17) aims to ensure that the superposition of active power and regulation service does not exceed the upper / lower limit of the active power operating range, and equation (18) describes that the energy storage should reserve sufficient remaining energy margin to at least continuously provide auxiliary services hours;

[0032] In addition, the generalized model of the distributed energy is subject to the following constraints:

[0033] ;

[0034] Among them, equation (20) is the power ramping constraint, and equation (21) is the model remaining energy and charging / discharging constraint.

[0035] Further, the individual polyhedral feasible region model of the distributed energy obtained according to the variable controllable characteristics specifically includes:

[0036] Considering the active power and the frequency regulation capability As controllable variables, the generalized model of the distributed energy is sorted into an individual polyhedral feasible region model:

[0037] ;

[0038] In the formula, is the individual generalized model feasible region of the distributed energy, represents the vector form of the controllable variable, 、 and are the matrix forms of the above constraint conditions.

[0039] The polyhedral equivalent modeling method of the distributed energy cluster, characterized in that, the individual polyhedral feasible region model of all distributed energies is internally approximated using a homogeneous polyhedron, and the Minkowski sum of the approximation result is calculated to obtain an aggregated model, specifically including:

[0040] For a set of known feasible region generalized models of distributed energies, the feasible region is represented by the Minkowski sum of all individual distributed energies, and the calculation method is:

[0041] ;

[0042] In equation (23), is the aggregated feasible region, is the Minkowski sum calculation;

[0043] An aggregation method based on a homogeneous polyhedron is used to calculate a set of approximate polyhedrons limited to the same structure,

[0044] The principle is to use basic isomorphic polyhedrons to approximate the polyhedron feasible domain of distributed energy. By scaling and translating the basic isomorphic polyhedrons, an internal approximate polyhedron feasible domain is calculated for each distributed energy polyhedron feasible domain. The mathematical method is expressed as:

[0045] ;

[0046] Formula (24) gives the feasible domain of the basic isomorphic polyhedron, and Formula (25) represents the feasible domain of the basic isomorphic polyhedron after scaling and translation. is the scaling factor, is the translation factor, is a basic isomorphic polyhedron, and is the coefficient matrix of the feasible region polyhedron, and its structure is the same as that in Eq. (22) and same, and By averaging the parameters of all distributed energy resources in the aggregator, we can get:

[0047] ;

[0048] For the distributed energy feasible domain from the same homogeneous polyhedron, the Minkowski sum calculation is simplified to:

[0049] .

[0050] Furthermore, the two-level optimization method is used to express the aggregation model construction process as a multi-objective optimization process, which specifically includes: solving the optimal shape of the basic isomorphic polyhedron without a given basic isomorphic polyhedron shape, and constructing the aggregation feasible domain process is described by a two-level optimization, and its upper-level objective function is designed as: constructing a basic isomorphic polyhedron shape of a special shape ; The lower objective function is designed as follows: for the basic isomorphic polyhedrons with special shapes proposed by the upper layer At this time, the moth-to-fire algorithm is used in the upper and lower optimization layers to iterate out a shape with the largest approximate area within the feasible region of the cluster.

[0051] A polyhedron equivalent modeling device for a distributed energy cluster, comprising:

[0052] The distributed energy mathematical model building module is used to build corresponding mathematical models to describe the operating characteristics of different distributed energy resources;

[0053] Individual polyhedron feasible domain model building module, used to establish a generalized model of distributed energy based on the established mathematical model for unified description, and obtain the individual polyhedron feasible domain model of distributed energy according to the controllable characteristics of variables;

[0054] An aggregation model building module is used to use homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculate the Minkowski sum of the approximation results to obtain the aggregation model;

[0055] The aggregation model optimization module is used to express the aggregation model construction process as a multi-objective optimization process using a two-layer optimization method. It searches for an optimal homogeneous polyhedron shape in the upper layer and the inner approximation results of all individual feasible domains in the lower layer. The moth-to-flame algorithm is used to perform optimization to maximize the accuracy of the aggregation model.

[0056] Furthermore, the distributed energy includes energy storage units, temperature-controlled loads, and interruptible loads. The established mathematical model and constraints are as follows:

[0057] (1.1) Energy storage unit modeling and constraints:

[0058] ;

[0059] Equations (1), (2), and (3) represent the power and energy constraints of energy storage. and are the charging power and discharging power of energy storage respectively, and are the maximum charging and discharging powers of the energy storage, respectively, and are the upper and lower limits of energy storage respectively;

[0060] ;

[0061] Formula (4) is the climbing power constraint, where is the upper limit of the ramp power, and Equation (5) shows that the storage energy cannot be charged and discharged simultaneously;

[0062] ;

[0063] Equation (6) is the energy charge and discharge constraint, which represents the relationship between power and energy, where is the energy dissipation rate of stored energy, is the charging efficiency of energy storage, is the discharge efficiency of energy storage;

[0064] (1.2) Temperature control load modeling and constraints:

[0065] ;

[0066] Equations (7) and (8) represent the power and energy constraints of the temperature control load, where is the power of the temperature control load, The power upper limit of the temperature control load. and are the lowest and highest operating temperatures of the temperature control load, is the current temperature of the temperature-controlled load;

[0067] ;

[0068] Formula (9) is a differential equation derived from the heat balance equation, which describes the working process of the temperature control load. is the thermal resistance of the temperature control load, is the heat capacity of the temperature control load, for The outdoor temperature at the moment;

[0069] (1.3) Modeling and constraints of interruptible loads:

[0070] ;

[0071] Formula (10) describes the principle of interruptible load reduction, where is the original load size, is the load reduction factor, and Equation (11) describes the operating range of the interruptible load. and are the minimum and maximum values ​​of the interruptible load in time period t, respectively.

[0072] Furthermore, the operation process and constraints of the generalized model are as follows:

[0073] ;

[0074] Equations (12), (13), and (14) are the power and energy constraints of the generalized model, where superscripts represent upper bounds and subscripts represent lower bounds;

[0075] ;

[0076] Formula (15) is the auxiliary service constraint condition of the generalized model, The frequency regulation range that distributed energy can provide, indicating the maximum acceptable change when increasing or decreasing its power, in units of , is the upper limit of frequency regulation, in formula (16), is the maximum regulation capacity of distributed energy, and Equation (17) aims to ensure that the superposition of active power and regulation services does not exceed the upper / lower limit of the active operation range. Equation (18) describes that the energy storage should retain sufficient residual energy margin to continuously provide auxiliary services for at least Hour;

[0077] In addition, the generalized model of distributed energy is subject to the following constraints:

[0078] ;

[0079] Among them, formula (20) is the power ramp constraint, and formula (21) is the model remaining energy and charge and discharge constraints.

[0080] Furthermore, the aggregation model building module uses homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculates the Minkowski sum of the approximation results to obtain the aggregation model, specifically including:

[0081] For a generalized model of distributed energy resources with a known feasible domain, the feasible domain is represented by the Minkowski sum of all individual distributed energy resources, which is calculated as:

[0082] ;

[0083] In formula (23), is the aggregate feasible region, Calculate for the Minkowski sum;

[0084] A clustering method based on isomorphic polyhedra is used to calculate a set of approximate polyhedra limited to the same structure.

[0085] The principle is to use basic isomorphic polyhedrons to approximate the polyhedron feasible domain of distributed energy. By scaling and translating the basic isomorphic polyhedrons, an internal approximate polyhedron feasible domain is calculated for each distributed energy polyhedron feasible domain. The mathematical method is expressed as:

[0086] ;

[0087] Formula (24) gives the feasible domain of the basic isomorphic polyhedron, and Formula (25) represents the feasible domain of the basic isomorphic polyhedron after scaling and translation. is the scaling factor, is the translation factor, is a basic isomorphic polyhedron, and is the coefficient matrix of the feasible region polyhedron, and By averaging the parameters of all distributed energy resources in the aggregator, we can get:

[0088] ;

[0089] For the distributed energy feasible region from the same homogeneous polyhedron, the Minkowski sum calculation is simplified as:

[0090] .

[0091] Compared with the prior art, the above technical scheme provided by the present application can achieve the following effects:

[0092] 1. A generalized model of distributed energy and a polyhedral equivalent modeling method thereof are proposed, solving the problem of large difference in distributed energy models.

[0093] 2. The proposed approximation method in the feasible region has the characteristics of fast calculation speed and high model accuracy, and can be used for real-time regulation and control. The model of the distributed energy cluster is the Minkowski sum of all individual feasible regions, but due to the different types and parameters of the distributed energy, the shapes of the feasible regions are also different. However, the calculation of the Minkowski sum of a polyhedron of any shape is an NP-hard problem, which is difficult to achieve in mathematics and has a large calculation cost. In the present application, the Minkowski sum of a polyhedron of the same shape only needs to be calculated by addition, greatly simplifying the calculation complexity.

[0094] 3. The proposed double-layer optimization method has the characteristics of easy operation, strong expandability, and high accuracy of the aggregated model of distributed energy after optimization compared with existing mathematical optimization methods. According to the establishment process of the equivalent aggregated model, it can be concluded that the shape of the homogeneous polyhedron has a great influence on the model accuracy. In order to improve the accuracy of the equivalent aggregated model, an optimal homogeneous polyhedron shape is found in the upper layer of the double-layer optimization, and the polyhedron vertex coordinates are determined. In the lower layer, the inner approximation results of all individual feasible regions are found. The upper layer iteration result is based on the aggregated model accuracy of the homogeneous polyhedron proposed in the upper layer in the cluster. The firefly algorithm is used to execute the double-layer optimization process, maximizing the accuracy of the aggregated model. BRIEF DESCRIPTION OF DRAWINGS

[0095] Figure 1 The flowchart of the polyhedral equivalent modeling method of the distributed energy cluster provided by the embodiment of the present application;

[0096] Figure 2 The polyhedral aggregation model calculation method of the distributed energy cluster in the embodiment of the present application;

[0097] Figure 3 The principle diagram of the firefly algorithm in the embodiment of the present application;

[0098] Figure 4 All possible positions of a firefly in the execution of the firefly algorithm in the embodiment of the present application;

[0099] Figure 5 Flowchart of the execution of the double-layer optimization algorithm proposed in the embodiment of the present invention;

[0100] Figure 6 The polyhedron feasible region of the generalized model of distributed energy in the embodiment of the present invention;

[0101] Figure 7 Iterative results of the moth-to-flame algorithm in the dual-layer optimization of the embodiment of the present invention;

[0102] Figure 8 The inner approximation result of the double-layer optimization in the embodiment of the present invention;

[0103] Figure 9 Schematic diagram of cluster energy dynamic response using double-layer optimized polyhedrons and random trapezoidal polyhedrons in an embodiment of the present invention. DETAILED DESCRIPTION

[0104] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0105] like Figure 1 As shown, the present invention provides a polyhedron equivalent modeling method for distributed energy clusters, which includes the following steps:

[0106] Step 1: Establish corresponding mathematical models to describe the operating characteristics of different distributed energy sources.

[0107] The distributed energy includes energy storage units, temperature-controlled loads, and interruptible loads. The established mathematical model and constraints are as follows:

[0108] (1.1) Energy storage unit modeling and constraints

[0109]

[0110] Equations (1), (2), and (3) represent the power and energy constraints of energy storage. and are the charging power and discharging power of energy storage respectively, and are the maximum charging and discharging powers of energy storage, and are the upper and lower limits of energy storage respectively.

[0111]

[0112] Formula (4) is the climbing power constraint, where is the upper limit of the ramp power, and Equation (5) shows that the storage energy cannot be charged and discharged at the same time.

[0113]

[0114] Equation (6) is the charge and discharge constraint of energy, which represents the relationship between power and energy, where is the energy dissipation rate of stored energy, is the charging efficiency of energy storage, is the discharge efficiency of energy storage.

[0115] (1.2) Temperature control load modeling and constraints

[0116]

[0117] Equations (7) and (8) represent the power and energy constraints of the temperature control load, where is the power of the temperature-controlled load. Generally speaking, the temperature-controlled load can only be charged, so its charging power must be greater than 0. The power upper limit of the temperature control load. and are the lowest and highest operating temperatures of the temperature control load, The current temperature of the temperature-controlled load.

[0118]

[0119] Formula (9) is a differential equation derived from the heat balance equation, which describes the working process of the temperature control load. is the thermal resistance of the temperature control load, is the heat capacity of the temperature control load, for The outdoor temperature at the moment.

[0120] (1.3) Modeling and constraints of interruptible loads

[0121]

[0122] Formula (10) describes the principle of interruptible load reduction, where is the original load size, is the load reduction factor, and Equation (11) describes the operating range of the interruptible load. and are the minimum and maximum values ​​of the interruptible load in time period t, respectively.

[0123] Step 2: A generalized model of distributed energy is established based on the established mathematical model to uniformly describe the distributed energy, and the individual polyhedral feasible region model of the distributed energy is obtained according to the controllable characteristics of the variables.

[0124] In order to concentrate on the modeling of the aggregation regulation of the distributed energy, a generalized model of the distributed energy is proposed, and the operation process and constraint conditions thereof are as follows:

[0125]

[0126] Equations (12), (13) and (14) are power and energy constraints of the generalized model, wherein the upper index represents the upper limit, the lower index represents the lower limit, and the same applies below.

[0127]

[0128] Equation (15) is an auxiliary service constraint condition of the generalized model, is the frequency regulation range that can be provided by the distributed energy, represents the maximum acceptable change amount when the power thereof is adjusted upward or downward, and the unit is , is the upper limit of the frequency regulation, in equation (16), is the maximum regulation capacity of the distributed energy, equation (17) aims to ensure that the superposition of active power and regulation service does not exceed the upper / lower limit of the active power operating range, and equation (18) describes that the energy storage should save enough residual energy margin to continuously provide auxiliary services for at least 1 hour.

[0129] In addition, the generalized model of the distributed energy is also subject to the following constraints:

[0130]

[0131] Among them, equation (20) is a power ramping constraint, and equation (21) is a model residual energy and charging / discharging constraint.

[0132] Since different distributed energies have different key parameters, their feasible regions are also different. Considering the active power and the frequency regulation capacity as controllable variables, the above generalized model of the distributed energy can be sorted into an individual polyhedral feasible region model:

[0133]

[0134] In the equation, is the individual generalized model feasible region of the distributed energy, represents the vector form of the controllable variables, , and are the matrix forms of the above constraint conditions.

[0135] Step 3: Use homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculate the Minkowski sum of the approximation results to obtain the aggregate model.

[0136] For a generalized model of distributed energy resources with a known feasible domain, the exact feasible domain can be represented by the Minkowski sum of all individual distributed energy resources, which is calculated as:

[0137]

[0138] In formula (23), is the aggregate feasible region, However, computing the exact Minkowski sum of two arbitrary polyhedra is an NP-hard problem, mainly due to the following reasons:

[0139] (1) Exponential growth in the number of vertices and faces: The number of vertices and faces of the resulting polyhedron from the Minkowski sum may far exceed the number of vertices and faces of the input polyhedron.

[0140] (2) Combinatorial explosion: In the calculation of the Minkowski sum, the number of combinations of faces and vertices of each polyhedron increases exponentially, making it difficult to complete accurate calculations in a short time.

[0141] One feasible method is to calculate a set of approximate polyhedra confined to the same structure. This method is called the aggregation method based on isomorphic polyhedra. Its principle is to use basic isomorphic polyhedra to approximate the polyhedron feasible domain of distributed energy. By scaling and translating the basic isomorphic polyhedra, an internal approximate polyhedron feasible domain is calculated for each distributed energy polyhedron feasible domain. The calculation method process is as follows: Figure 2 As shown, it can be expressed mathematically as:

[0142]

[0143] Formula (24) gives the feasible domain of the basic isomorphic polyhedron, and Formula (25) represents the feasible domain of the basic isomorphic polyhedron after scaling and translation. is the scaling factor, is the translation factor, is a basic isomorphic polyhedron, and is the coefficient matrix of the feasible region polyhedron, and its structure is the same as that in Eq. (22) and same, and It can be obtained by averaging the parameters of all distributed energy resources in the aggregator:

[0144]

[0145] For the distributed energy feasible domain from the same homogeneous polyhedron, the Minkowski sum calculation can be simplified to:

[0146]

[0147] Step 4: A two-layer optimization method is used to formulate the aggregation model construction process as a multi-objective optimization process. An optimal homogeneous polyhedron shape is sought in the upper layer, and the inner approximation results of all individual feasible domains are sought in the lower layer. The moth-to-flame algorithm is used to perform the optimization to maximize the accuracy of the aggregation model.

[0148] (4.1) Moth-to-flame algorithm

[0149] Moth-flame optimization (MFO) is a heuristic search algorithm designed to mimic the way moths move around light sources at night. The algorithm has strong parallel optimization capabilities, good global performance, and is not prone to falling into local extremes.

[0150] During the iteration process, the moth is the search individual moving in the search space, and the flame is the optimal position that the corresponding moth can reach so far. Each moth individual surrounds a flame, and once a better solution is found, it is updated to the position of the flame in the next generation. Figure 3 The spiral flight path of moths is simulated. The mechanism for updating the position of each moth relative to the flame can be expressed as:

[0151]

[0152] In formula (28), Indicates the Only moths; Indicates the flame; S represents a spiral function that satisfies the following conditions: 1) the initial point of the spiral function should start from the moth; 2) the end point of the spiral is the position of the flame; 3) the fluctuation range of the spiral should not exceed its search space.

[0153]

[0154] In formula (29), Indicates the The moth and the The distance between the flames; is the logarithmic spiral shape constant, and the path coefficient t is a random number in [-1, 1]. The expression of D is as follows:

[0155]

[0156] Equation (29) simulates the spiral flight path of a moth. It can be seen that the next position updated by the moth is determined by the flame it surrounds. The coefficients in the spiral function are Indicates the distance between the moth's next position and the flame ( indicates the position closest to the flame, and The spiral equation indicates that the moth can fly around the flames rather than just in the space between them, thus ensuring the algorithm's global search capability and local development capabilities. Figure 4 This is a model for updating the position of a moth around a flame. When a moth flies around a flame, if the fitness value of the updated moth position is better than that of the current flame, then its updated position will be selected as the position of the next generation flame, so the moth has the ability to develop locally. The following features are used when using this model: 1) By modifying the parameters , a moth can converge to any neighborhood of the flame. 2) The smaller it is, the closer the moth is to the flame. 3) As the moth gets closer to the flame, the frequency of its updates around the flame becomes faster and faster.

[0157] (4.2) Polyhedron Bi-layer Optimization Method Based on Moth-to-Flame

[0158] According to the calculation process of the Minkowski sum of the aggregation model, the shape of the basic isomorphic polyhedron directly affects the effect of the inner approximation. Therefore, when solving the optimal shape of the basic isomorphic polyhedron without a given basic isomorphic polyhedron shape, the process of constructing the aggregation feasible domain can be described by a two-level optimization. The upper objective function is designed as: construct a basic isomorphic polyhedron shape of a special shape. ; The lower objective function is designed as follows: for the basic isomorphic polyhedrons with special shapes proposed by the upper layer At this time, the moth-to-fire algorithm is used in the upper and lower optimization to iterate a shape with the largest approximate area in the feasible region of the cluster. The specific process is as follows Figure 5 shown.

[0159] Based on the above aggregation calculation method, the accuracy of the aggregation results can be deduced:

[0160]

[0161] In formulas (31) and (32), is the scale factor, the average scale factor of the approximate feasible domain relative to the original feasible domain, which reflects the degree to which the approximate polyhedron retains the information of the original polyhedron. The closer it is to 1 (100%), the higher the model accuracy.

[0162] An embodiment of the present invention further provides a polyhedron equivalent modeling device for a distributed energy cluster, comprising:

[0163] Distributed energy mathematical model building module, used to establish corresponding mathematical models to describe the operating characteristics of different distributed energy resources;

[0164] Individual polyhedron feasible domain model building module, used to establish a generalized model of distributed energy based on the established mathematical model for unified description, and obtain the individual polyhedron feasible domain model of distributed energy according to the controllable characteristics of variables;

[0165] An aggregation model building module is used to use homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculate the Minkowski sum of the approximation results to obtain the aggregation model;

[0166] The aggregation model optimization module is used to express the aggregation model construction process as a multi-objective optimization process using a two-layer optimization method. It searches for an optimal homogeneous polyhedron shape in the upper layer and the inner approximation results of all individual feasible domains in the lower layer. The moth-to-flame algorithm is used to perform optimization to maximize the accuracy of the aggregation model.

[0167] When the parameters of a distributed energy are as shown in Table 1, its individual polyhedron feasible domain model is as follows: Figure 6 The parameters of the moth-to-flame algorithm in this case are shown in Table 2, and the parameters of the simulated distributed energy cluster are shown in Table 3:

[0168] Table 1 Generalized model parameters of distributed energy

[0169]

[0170] Table 2 Moth-to-flame algorithm parameters

[0171]

[0172] Table 3 Distribution parameters of distributed energy clusters

[0173]

[0174] Use Python to build the model environment. The trend of the objective function during the iteration process is as follows: Figure 7 As shown, the final approximation result in the feasible region of aggregation is as follows Figure 8The aggregation process and results are shown in Table 4. The results show that the two-layer optimization can well preserve the information of the feasible domain of the original polyhedron, has higher model accuracy, and can be used for model analysis or predictive control at different time scales. If the specific shape of the homogeneous polyhedron is given, the calculation time is only about 2.6 seconds, which can be used for real-time scheduling. This aggregation method is helpful to achieve the coordinated control of the cluster. Considering a cluster of 100 distributed energy sources to supply and consume new energy stations and loads, Figure 9 It can be seen from the dynamic process shown that the parameters of the cluster under the proposed two-level optimization method are closer to the individual model.

[0175] Table 4. Results of iterative solution of double-layer optimization

[0176]

[0177] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art will be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.

Claims

1. A polyhedron equivalent modeling method for distributed energy clusters, characterized by: The steps include: According to the operating characteristics of different distributed energy resources, corresponding mathematical models are established to describe them; Based on the established mathematical model, a generalized model of distributed energy is established for unified description, and the individual polyhedron feasible domain model of distributed energy is obtained according to the controllable characteristics of variables; In the individual polyhedron feasible domain models of all distributed energy resources, homogeneous polyhedrons are used for inner approximation, and the Minkowski sum of the approximation results is calculated to obtain the aggregate model; A two-level optimization method is used to formulate the aggregation model construction process as a multi-objective optimization process. The upper level searches for an optimal homogeneous polyhedron shape, while the lower level searches for the inner approximation of all individual feasible regions. The moth-to-flame algorithm is used to perform the optimization to maximize the accuracy of the aggregation model. The operation process and constraints of the generalized model are as follows: ； Equations (12), (13), and (14) are the power and energy constraints of the generalized model, where the superscript represents the upper bound and the subscript represents the lower bound; ； Formula (15) is the auxiliary service constraint condition of the generalized model, The frequency regulation range that distributed energy can provide, indicating the maximum acceptable change when increasing or decreasing its power, in units of , is the upper limit of frequency regulation, in formula (16), is the maximum regulation capacity of distributed energy, and Equation (17) aims to ensure that the superposition of active power and regulation services does not exceed the upper / lower limit of the active operation range. Equation (18) describes that the energy storage should retain sufficient residual energy margin to continuously provide auxiliary services for at least Hour; In addition, the generalized model of distributed energy is subject to the following constraints: ； Among them, formula (20) is the power ramp constraint, and formula (21) is the model remaining energy and charge and discharge constraints; The individual polyhedron feasible domain model of distributed energy is obtained according to the controllable characteristics of the variables, specifically including: Considering active power and frequency adjustment capability As a controllable variable, the generalized model of distributed energy is organized into an individual polyhedron feasible domain model: ； Where, is the feasible domain of the individual generalized model of distributed energy, Represents the vector form of the controllable variables, 、 and is the matrix form of the above constraints.

2. The polyhedron equivalent modeling method for distributed energy clusters according to claim 1 is characterized in that: The distributed energy includes energy storage units, temperature-controlled loads, and interruptible loads. The established mathematical model and constraints are as follows: (1.1) Energy storage unit modeling and constraints: ； Equations (1), (2), and (3) represent the power and energy constraints of energy storage. and are the charging power and discharging power of energy storage respectively, and are the maximum charging and discharging powers of the energy storage, respectively, and are the upper and lower limits of energy storage respectively; ； Formula (4) is the climbing power constraint, where is the upper limit of the ramp power, and Equation (5) shows that the storage energy cannot be charged and discharged simultaneously; ； Equation (6) is the energy charge and discharge constraint, which represents the relationship between power and energy, where is the energy dissipation rate of stored energy, is the charging efficiency of energy storage, is the discharge efficiency of energy storage; (1.2) Temperature control load modeling and constraints: ； Equations (7) and (8) represent the power and energy constraints of the temperature control load, where is the power of the temperature control load, is the upper limit of the power of the temperature control load, and are the lowest and highest operating temperatures of the temperature control load, is the current temperature of the temperature-controlled load; ； Formula (9) is a differential equation derived from the heat balance equation, which describes the working process of the temperature control load. is the thermal resistance of the temperature control load, is the heat capacity of the temperature control load, for The outdoor temperature at the moment; (1.3) Modeling and constraints of interruptible loads: ； Formula (10) describes the principle of interruptible load reduction, where is the original load size, is the load reduction factor, and Equation (11) describes the operating range of the interruptible load. and are the minimum and maximum values ​​of the interruptible load in time period t, respectively.

3. The polyhedron equivalent modeling method for distributed energy clusters according to claim 1 is characterized in that: The method uses homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain model of all distributed energy resources, and calculates the Minkowski sum of the approximation results to obtain the aggregate model, specifically including: For a generalized model of distributed energy resources with a known feasible domain, the feasible domain is represented by the Minkowski sum of all individual distributed energy resources, which is calculated as: ； In formula (23), is the aggregate feasible region, Calculate for the Minkowski sum; A clustering method based on isomorphic polyhedra is used to calculate a set of approximate polyhedra limited to the same structure. The principle is to use basic isomorphic polyhedrons to approximate the polyhedron feasible domain of distributed energy. By scaling and translating the basic isomorphic polyhedrons, an internal approximate polyhedron feasible domain is calculated for each distributed energy polyhedron feasible domain. The mathematical method is expressed as: ； Formula (24) gives the feasible domain of the basic isomorphic polyhedron, and Formula (25) represents the feasible domain of the basic isomorphic polyhedron after scaling and translation. is the scaling factor, is the translation factor, is a basic isomorphic polyhedron, and is the coefficient matrix of the feasible region polyhedron, and its structure is the same as that in Eq. (22) and same, and By averaging the parameters of all distributed energy resources in the aggregator, we can get: ； For the distributed energy feasible domain from the same homogeneous polyhedron, the Minkowski sum calculation is simplified to: 。 4. The polyhedron equivalent modeling method for distributed energy clusters according to claim 1 is characterized in that: The two-level optimization method is used to describe the aggregation model construction process as a multi-objective optimization process, specifically including: solving the optimal shape of the basic isomorphic polyhedron without a given basic isomorphic polyhedron shape, and constructing the aggregation feasible domain process is described by a two-level optimization, and its upper objective function is designed as: constructing a basic isomorphic polyhedron shape of a special shape ; The lower objective function is designed as follows: for the basic isomorphic polyhedrons with special shapes proposed by the upper layer At this time, the moth-to-fire algorithm is used in the upper and lower optimization layers to iterate out a shape with the largest approximate area within the feasible region of the cluster.

5. A polyhedron equivalent modeling device for distributed energy clusters, characterized in that: include: Distributed energy mathematical model building module, used to establish corresponding mathematical models to describe the operating characteristics of different distributed energy resources; Individual polyhedron feasible domain model building module, used to establish a generalized model of distributed energy based on the established mathematical model for unified description, and obtain the individual polyhedron feasible domain model of distributed energy according to the controllable characteristics of variables; An aggregation model building module is used to use homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculate the Minkowski sum of the approximation results to obtain the aggregation model; The aggregate model optimization module uses a two-layer optimization method to formulate the aggregate model construction process as a multi-objective optimization process. The upper layer searches for an optimal homogeneous polyhedron shape, and the lower layer searches for the inner approximation of all individual feasible regions. The optimization is performed using a moth-to-flame algorithm to maximize the accuracy of the aggregate model. The operation process and constraints of the generalized model are as follows: ; Equations (12), (13), and (14) are the power and energy constraints of the generalized model, where superscripts represent upper bounds and subscripts represent lower bounds; ； Formula (15) is the auxiliary service constraint condition of the generalized model, The frequency regulation range that distributed energy can provide, indicating the maximum acceptable change when increasing or decreasing its power, in units of , is the upper limit of frequency regulation, in formula (16), is the maximum regulation capacity of distributed energy, and Equation (17) aims to ensure that the superposition of active power and regulation services does not exceed the upper / lower limit of the active operation range. Equation (18) describes that the energy storage should retain sufficient residual energy margin to continuously provide auxiliary services for at least Hour; In addition, the generalized model of distributed energy is subject to the following constraints: ； Among them, formula (20) is the power ramp constraint, and formula (21) is the model remaining energy and charge and discharge constraints; The individual polyhedron feasible domain model of distributed energy is obtained according to the controllable characteristics of the variables, specifically including: Considering active power and frequency adjustment capability As a controllable variable, the generalized model of distributed energy is organized into an individual polyhedron feasible domain model: ； Where, is the feasible domain of the individual generalized model of distributed energy, Represents the vector form of the controllable variables, 、 and is the matrix form of the above constraints.

6. The polyhedron equivalent modeling device for distributed energy clusters according to claim 5, characterized in that: The distributed energy includes energy storage units, temperature-controlled loads, and interruptible loads. The established mathematical model and constraints are as follows: (1.1) Energy storage unit modeling and constraints: ； Equations (1), (2), and (3) represent the power and energy constraints of energy storage. and are the charging power and discharging power of energy storage respectively, and are the maximum charging and discharging powers of the energy storage, respectively, and are the upper and lower limits of energy storage respectively; ； Formula (4) is the climbing power constraint, where is the upper limit of the ramp power, and Equation (5) shows that the storage energy cannot be charged and discharged simultaneously; ； Equation (6) is the energy charge and discharge constraint, which represents the relationship between power and energy, where is the energy dissipation rate of stored energy, is the charging efficiency of energy storage, is the discharge efficiency of energy storage; (1.2) Temperature control load modeling and constraints: ； Equations (7) and (8) represent the power and energy constraints of the temperature control load, where is the power of the temperature control load, is the upper limit of the power of the temperature control load, and are the lowest and highest operating temperatures of the temperature control load, is the current temperature of the temperature-controlled load; ； Formula (9) is a differential equation derived from the heat balance equation, which describes the working process of the temperature control load. is the thermal resistance of the temperature control load, is the heat capacity of the temperature control load, for The outdoor temperature at the moment; (1.3) Modeling and constraints of interruptible loads: ； Formula (10) describes the principle of interruptible load reduction, where is the original load size, is the load reduction factor, and Equation (11) describes the operating range of the interruptible load. and are the minimum and maximum values ​​of the interruptible load in time period t, respectively.

7. The polyhedron equivalent modeling device for distributed energy clusters according to claim 6, characterized in that: The aggregation model building module uses homogeneous polyhedra to perform inner approximation in the individual polyhedron feasible domain models of all distributed energy resources, and calculates the Minkowski sum of the approximation results to obtain the aggregation model, specifically including: For a generalized model of distributed energy resources with a known feasible domain, the feasible domain is represented by the Minkowski sum of all individual distributed energy resources, which is calculated as: ； In formula (23), is the aggregate feasible region, Calculate for the Minkowski sum; A clustering method based on isomorphic polyhedra is used to calculate a set of approximate polyhedra limited to the same structure. The principle is to use basic isomorphic polyhedrons to approximate the polyhedron feasible domain of distributed energy. By scaling and translating the basic isomorphic polyhedrons, an internal approximate polyhedron feasible domain is calculated for each distributed energy polyhedron feasible domain. The mathematical method is expressed as: ； Formula (24) gives the feasible domain of the basic isomorphic polyhedron, and Formula (25) represents the feasible domain of the basic isomorphic polyhedron after scaling and translation. is the scaling factor, is the translation factor, is a basic isomorphic polyhedron, and is the coefficient matrix of the feasible region polyhedron, and By averaging the parameters of all distributed energy resources in the aggregator, we can get: ； For the distributed energy feasible domain from the same homogeneous polyhedron, the Minkowski sum calculation is simplified to: 。

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