Centralized main-grid and distribution network collaborative robust optimization scheduling method and device
Patent Information
- Application Number
- CN202211269091.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-17
- Publication Date
- 2026-09-25
- Estimated Expiration
- 2042-10-17
AI Technical Summary
[0005]本申请提供一种集中式主配网协同分布鲁棒优化调度方法及装置,以解决相关技术缺乏高效的需求侧灵活性聚合模型,灵活性参数的概率分布难以构建,传统的机会约束难以计算,而抽样平均、场景集优化等方法又难以泛化等问题
[0023]本申请的实施例可以通过搭建确定性主配网协同调度问题的框架,框架包括主网、配网、灵活资源的单体模型;基于确定性主配网协同调度问题的框架,生成配网灵活性聚合模型;使用分布鲁棒机会约束建模新能源出力与配网中灵活性的不确定性,嵌入到主配网协同调度模型中,从而实现一次性求解优化问题得到调度策略,无需迭代,并可以高效地刻画主配网接口处的功率灵活性,约束数量较少,精确度较高。此外,本申请为灵活资源参与大电网的经济调度或市场出清提供决策方案,以在主网调度中兼顾配网安全约束,新能源出力和需求侧资源灵活性的不确定性,最大化地利用需求侧资源的灵活性,提升全网运行的经济性和安全性。由此,解决了相关技术缺乏高效的需求侧灵活性聚合模型,灵活性参数的概率分布难以构建,传统的机会约束难以计算,而抽样平均、场景集优化等方法又难以泛化等问题。
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Figure CN115566687B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of main and distribution network coordinated scheduling technology, and in particular to a centralized main and distribution network coordinated distributed bar optimization scheduling method and device. Background Technology
[0002] The high penetration rate of intermittent renewable energy sources such as wind and solar power has increased the demand for grid regulation capabilities. Against this backdrop, the grid can no longer rely solely on the regulation role of traditional generating units; leveraging the regulation capabilities of flexible demand-side resources is imperative. Some typical flexible demand-side resources include distributed generation, electric vehicles, distributed energy storage, and thermal load control. The participation of flexible demand-side resources in grid regulation can ensure the safe and stable operation of the grid, promote the consumption of new energy sources, and reduce electricity costs for users. However, considering the parameters of all demand-side resources and the network model of the distribution network during transmission grid dispatch leads to excessive computational complexity and is detrimental to protecting the privacy of electricity users. Therefore, transmission grid operators should not consider the operating range of each demand-side resource when calculating their dispatch strategies. Many existing technologies use distributed optimization methods to calculate the primary-distribution coordinated dispatch problem. They decompose the large-scale optimization problem of primary-distribution coordinated dispatch into multiple sub-problems based on entities such as transmission grid operators and distribution grid operators. By solving each sub-problem separately and through some information exchange, they iteratively converge to the global optimum. However, this approach places high demands on computational and communication capabilities.
[0003] The current main mode of power grid operation, namely centralized dispatch, involves aggregating flexible resources to a certain scale before participating in dispatch. In this mode, flexible resource aggregators first submit the feasible domain of total power to the distribution network operator. The distribution network operator then considers the feasible domains reported by all aggregators within its jurisdiction, as well as the security constraints of the distribution network, to calculate the feasible domain of the total power of the distribution network, which is then reported to the main grid operator. After clearing or dispatching calculations are completed, the total power of each distribution network is determined, and this total power is then allocated layer by layer to each flexible resource. Therefore, it is necessary to accurately construct an aggregation flexibility model of flexible resources in the distribution network to ensure smooth allocation without leading to excessive computational complexity. Furthermore, the uncertainty of renewable energy and demand-side flexibility must be considered in dispatching; existing technologies have extensively studied the uncertainty of renewable energy output.
[0004] However, the relevant technologies lack efficient demand-side flexibility aggregation models, the probability distribution of flexibility parameters is difficult to construct, traditional opportunity constraints are difficult to calculate, and methods such as sampling average and scenario set optimization are difficult to generalize, which urgently need to be solved. Summary of the Invention
[0005] This application provides a centralized main and distribution network collaborative distributed optimization scheduling method and device to solve the problems of related technologies, such as the lack of an efficient demand-side flexibility aggregation model, the difficulty in constructing the probability distribution of flexibility parameters, the difficulty in calculating traditional opportunity constraints, and the difficulty in generalizing methods such as sampling average and scenario set optimization.
[0006] The first aspect of this application provides a centralized main and distribution network coordinated sub-Bluerg bar optimization scheduling method, comprising the following steps: constructing a framework for a deterministic main and distribution network coordinated scheduling problem, the framework including individual models of the main network, distribution network, and flexible resources; generating a distribution network flexibility aggregation model based on the framework of the deterministic main and distribution network coordinated scheduling problem; and modeling the uncertainty of new energy output and distribution network flexibility using sub-Bluerg bar opportunity constraints, embedding it into the main and distribution network coordinated scheduling model.
[0007] Optionally, in one embodiment of this application, the framework for constructing a deterministic main and distribution network coordinated scheduling problem includes: determining a deterministic scheduling model for the transmission network, wherein minimizing the total generation cost of the entire system is used as the objective function, and multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the node power balance, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources; constructing the original power flow constraints of the distribution network using the linearized power flow equation, wherein the original power flow constraints include the power balance at the transmission and distribution network interface, the linearized distribution network power flow equation, the active and reactive power balance of the node, the voltage and phase angle at the distribution network balance node, the node voltage limit, and the branch active power transmission capacity limit; and defining the operating range constraints of the distributed flexible resources in the distribution network and the precise model of the distribution network aggregation flexibility.
[0008] Optionally, in one embodiment of this application, the design of the distribution network flexibility aggregation model includes: identifying the flexibility boundary whose probability of operation satisfies preset conditions based on the regularity of power grid operation; and constructing the flexibility aggregation model based on the flexibility boundary.
[0009] Optionally, in one embodiment of this application, constructing the flexibility aggregation model based on the flexibility boundary includes: inputting the number of constraint pairs of the target, shadow price samples, and flexibility parameter samples; calculating an optimization model for all samples, and based on the optimization model, identifying the constraint sets of the power-energy boundary model and the constraint sets of the energy change boundary model that are in effect; calculating the probability of all constraints being in effect, and sorting them to obtain a set of constraint pairs, so as to obtain a price-guided flexibility model.
[0010] Optionally, in one embodiment of this application, the main and distribution network coordinated scheduling model is as follows:
[0011]
[0012] Where, Δ t Indicates the length of time period t; Let each represent a set of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; j∈i indicates that node j is connected to node i. A flexible distribution network connected to node i, consisting of a collection of traditional and renewable energy generating units; P ij,t ,P d,t ,P g,t ,P r,t These represent the active power of line ij, distribution network d, traditional generating unit g, and new energy generating unit r during time period t, respectively. This represents the fixed load of node i; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill gradient for conventional generator sets.
[0013] A second aspect of this application provides a centralized main and distribution network coordinated sub-bar optimization scheduling device, comprising: a construction module for constructing a framework for a deterministic main and distribution network coordinated scheduling problem, the framework including individual models of the main network, distribution network, and flexible resources; a generation module for generating a distribution network flexibility aggregation model based on the framework of the deterministic main and distribution network coordinated scheduling problem; and an embedding module for modeling the uncertainty of new energy output and distribution network flexibility using sub-bar opportunity constraints and embedding it into the main and distribution network coordinated scheduling model.
[0014] Optionally, in one embodiment of this application, the construction module includes: a determination unit, used to determine a deterministic dispatch model of the transmission network, wherein minimizing the total generation cost of the entire system is taken as the objective function, and multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the node power balance, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources; a first construction unit, used to construct the original power flow constraints of the distribution network using the linearized power flow equation, wherein the original power flow constraints include the power balance at the transmission and distribution network interface, the linearized distribution network power flow equation, the active and reactive power balance of the node, the voltage and phase angle at the distribution network balance node, the node voltage limit, and the branch active power transmission capacity limit; and a definition unit, used to define the operating range constraints of the distributed flexible resources in the distribution network and the precise model of the distribution network aggregation flexibility.
[0015] Optionally, in one embodiment of this application, the generation module includes: a boundary-finding unit, used to find the flexibility boundary whose probability of operation satisfies preset conditions based on the regularity of power grid operation; and a second construction unit, used to construct the flexibility aggregation model according to the flexibility boundary.
[0016] Optionally, in one embodiment of this application, the generation module further includes: an input unit for inputting the number of constraint pairs, shadow price samples, and flexibility parameter samples of the target; a calculation unit for calculating the optimization model for all samples, and based on the optimization model, identifying the constraint sets of the power-energy boundary model and the constraint sets of the energy change boundary model that are in effect; and a sorting unit for calculating the probability of all constraints being in effect, and sorting them to obtain a set of constraint pairs to obtain a price-guided flexibility model.
[0017] Optionally, in one embodiment of this application, the main and distribution network coordinated scheduling model is as follows:
[0018]
[0019] Where, Δ t Indicates the length of time period t; Let each represent a set of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; j∈i indicates that node j is connected to node i. A flexible distribution network connected to node i, consisting of a collection of traditional and renewable energy generating units; P ij,t ,P d,t ,P g,t ,P r,t These represent the active power of line ij, distribution network d, traditional generating unit g, and new energy generating unit r during time period t, respectively. This represents the fixed load of node i; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill gradient for conventional generator sets.
[0020] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to implement the centralized main distribution network collaborative distributed control optimization scheduling method as described in the above embodiments.
[0021] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described centralized main and distribution network collaborative distributed control optimization scheduling method.
[0022] Therefore, the embodiments of this application have the following beneficial effects:
[0023] The embodiments of this application construct a framework for a deterministic main grid-distribution network coordinated scheduling problem, including individual models of the main grid, distribution network, and flexible resources. Based on this framework, a distribution network flexibility aggregation model is generated. The uncertainty of renewable energy output and distribution network flexibility is modeled using distributed bar chance constraints and embedded into the main grid-distribution network coordinated scheduling model. This allows for a one-time solution to the optimization problem to obtain the scheduling strategy, eliminating the need for iterations and efficiently characterizing power flexibility at the main grid-distribution network interface. The number of constraints is small, and the accuracy is high. Furthermore, this application provides a decision-making scheme for flexible resources to participate in the economic scheduling or market clearing of the large power grid. It balances distribution network security constraints, the uncertainty of renewable energy output and demand-side resource flexibility in main grid scheduling, maximizing the utilization of demand-side resource flexibility and improving the economy and security of the entire network operation. This solves the problems of related technologies, such as the lack of an efficient demand-side flexibility aggregation model, the difficulty in constructing the probability distribution of flexibility parameters, the difficulty in calculating traditional chance constraints, and the difficulty in generalizing methods such as sampling averaging and scenario set optimization.
[0024] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description
[0025] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:
[0026] Figure 1 This is a flowchart of a centralized main distribution network collaborative distributed control system optimization scheduling method according to an embodiment of this application;
[0027] Figure 2 This is an example diagram of a centralized main and distribution network collaborative distributed control system optimized scheduling device according to an embodiment of this application;
[0028] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.
[0029] Figure labeling: Centralized main distribution network collaborative distributed control optimization scheduling method-10; Construction module-100, generation module-200, embedding module-300; Memory-301, processor-302, communication interface-303. Detailed Implementation
[0030] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.
[0031] The following describes a centralized main and distribution network coordinated sub-Bluerg bar optimization scheduling method and apparatus according to embodiments of this application, with reference to the accompanying drawings. Addressing the problems mentioned in the background section, this application provides a centralized main and distribution network coordinated sub-Bluerg bar optimization scheduling method. This method establishes a framework for a deterministic main and distribution network coordinated scheduling problem, including individual models of the main network, distribution network, and flexible resources. Based on this framework, a distribution network flexibility aggregation model is generated. Sub-Bluerg bar opportunity constraints are used to model the uncertainty of renewable energy output and distribution network flexibility, embedding this model into the main and distribution network coordinated scheduling model. This allows for a one-time solution to the optimization problem to obtain the scheduling strategy, eliminating the need for iteration and efficiently characterizing power flexibility at the main and distribution network interface. The method also features fewer constraints and higher accuracy. Furthermore, this application provides decision-making solutions for flexible resources participating in the economic scheduling or market clearing of the large power grid, balancing distribution network security constraints, renewable energy output, and the uncertainty of demand-side resource flexibility in main grid scheduling. This maximizes the utilization of demand-side resource flexibility and improves the overall network's economic efficiency and security. This solves the problems of the lack of efficient demand-side flexibility aggregation models, the difficulty in constructing the probability distribution of flexibility parameters, the difficulty in calculating traditional opportunity constraints, and the difficulty in generalizing methods such as sampling average and scenario set optimization.
[0032] Specifically, Figure 1 The flowchart illustrates a centralized main and distribution network collaborative distributed control optimization scheduling method provided in this application embodiment.
[0033] like Figure 1 As shown, the centralized main and distribution network collaborative distributed optimization scheduling method includes the following steps:
[0034] In step S101, a framework for the deterministic primary and distribution network coordinated scheduling problem is established, which includes individual models of the primary network, distribution network, and flexible resources.
[0035] It should be noted that the embodiments of this application establish a framework for the deterministic main and distribution network coordinated scheduling problem by building a single model including the main network, distribution network and flexible resources. Thus, the scheduling result of the main network can be obtained by solving an optimization problem once, without the need for repeated iterative calculations of distributed optimization algorithms, which is more in line with the mainstream framework of current power system operation.
[0036] Optionally, in one embodiment of this application, a framework for the deterministic primary and distribution network coordinated scheduling problem is established, including: determining a deterministic scheduling model for the transmission network, wherein minimizing the total generation cost of the entire system is taken as the objective function, and multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the node power balance, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources; constructing the original power flow constraints of the distribution network using the linearized power flow equation, the original power flow constraints include the power balance at the transmission and distribution network interface, the linearized distribution network power flow equation, the active and reactive power balance of the node, the voltage and phase angle at the distribution network balance node, the node voltage limit, and the branch active power transmission capacity limit; and defining the operating range constraints of the distributed flexible resources in the distribution network and the precise model of the distribution network aggregation flexibility.
[0037] Specifically, firstly, in the embodiments of this application, the deterministic scheduling model of the power transmission network can be:
[0038]
[0039]
[0040]
[0041]
[0042]
[0043]
[0044]
[0045]
[0046]
[0047] Where t / T is the index / quantity of the time interval, [T] = {1, 2, ..., T} represents the set of all time intervals, Δ t Indicates the length of time interval t; C g (P g,t ) is the cost function of generator g; Let each represent a set of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; j∈i indicates that node j is connected to node i. A flexible distribution network connected to node i, consisting of a collection of traditional and renewable energy generating units; P ij,t ,P d,t ,P g,t ,P r,tThese represent the active power of line ij, distribution network d, traditional generating unit g, and new energy generating unit r during time period t, respectively. This represents the fixed load of node i; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill ramp rate of a conventional generator unit; P represents the maximum output of the new energy unit; d It is P d,t The constructed T×1 dimensional vector P represents d The feasible domain.
[0048] It should be noted that, in this application embodiment, minimizing the total power generation cost of the entire system can be used as the objective function, i.e., equation (1). Generally speaking, C g Usually P g,t The quadratic function is C, but embodiments of this application may use a common convex piecewise linear approximation to fit C. g As shown in the following formula:
[0049]
[0050] Wherein s / S g A represents the segment number / quantity of the unit's cost function segmentation. g,s P represents the cost coefficient for segment s. g,s,t This represents the power of segment s. This represents the maximum power of the s-th segment, thereby reducing computational complexity and facilitating subsequent handling of uncertainties.
[0051] It should be noted that constraint (2) is the DC power flow equation, constraint (3) defines the phase angle of the reference node as 0, constraint (4) represents the node power balance, equation (5) represents the active power limit of the line, constraints (6) and (7) represent the output limit of traditional generator sets and the ramp rate limit, respectively, constraint (8) is the output limit of new energy generator sets, and constraint (9) compactly represents the power feasible region of flexible resources, and the constraints in its feasible region have time coupling.
[0052] Secondly, embodiments of this application can use linearized power flow equations to construct the original power flow constraints of the distribution network (since each distribution network uses the same model, the subscript d of the distribution network is omitted), as shown in the following equation:
[0053]
[0054]
[0055]
[0056]
[0057]
[0058]
[0059] v 0,t =1 (16)
[0060] θ 0,t =0 (17)
[0061]
[0062]
[0063] The lowercase letters have the same meaning as the uppercase letters in (1)-(9), only representing the variables and parameters of the distribution network; L and I represent the set of lines and nodes of the distribution network, respectively. + H represents the set of nodes after removing the balancing node, and H represents the set of all distributed flexible resources in the distribution network. i p represents a flexible set of resources connected to distribution network node i; h,t q represents the active power of flexible resource h during time period t; ij,t ,q h,t , Represents the reactive power of line ij, flexible resource h, and fixed load at node i; v i,t This represents the voltage at node i. Indicates the upper / lower limit of the voltage.
[0064] Equation (11) represents the power balance at the transmission and distribution network interface, formulas (12) and (13) represent the linearized power flow equations of the distribution network, constraints (14) and (15) represent the active and reactive power balance of the nodes, constraints (16) and (17) give the voltage and phase angle at the distribution network balance node, constraint (18) represents the node voltage limit, and formula (19) represents the branch active power transmission capacity limit.
[0065] Furthermore, embodiments of this application may also define operational scope constraints for distributed flexible resources in the distribution network.
[0066] Specifically, the operating range of distributed flexible resources, including electric vehicles, distributed photovoltaics, distributed energy storage, and thermal control loads, can be represented by the following power-energy boundary model:
[0067]
[0068]
[0069]
[0070] q h,t =p h,t tanγ h (twenty two)
[0071] in, and γ represents the upper / lower bounds of the active power and the upper / lower bounds of the accumulated power consumption of flexible resource h in time period t, respectively. h This represents the power factor angle. Since the model includes both power and energy constraints, these constraints are time-coupled.
[0072] In addition, embodiments of this application also need to define an accurate model for the flexibility of distribution network aggregation.
[0073] In the embodiments of this application, according to the feasible region projection theory, the power flow constraints of the distribution network modeled according to (11)-(19) above and the operating range (20)-(22) of all flexible resources are projected onto the variable P of the main distribution network interface. d,t At that point, P d,t The constraints that need to be satisfied can be precisely expressed as:
[0074]
[0075] Among them, parameters and It can be calculated using an optimization model with constraints (11)-(22).
[0076] It should be noted that the physical meaning of the above aggregation model is: the total power P of the distribution network. d,t The integral over every non-empty subset of the entire time window [T] is constrained. Therefore, it is a highly time-coupled model with a total number of constraints of 2(2). T -1). In practical scheduling applications, T is usually 24 or 96, which makes the number of constraints too large. Therefore, it is necessary to design an approximate model to reduce its complexity, namely the price-guided flexibility model proposed later. The embodiments of this application will describe the model in detail later, and will not be repeated here.
[0077] Therefore, the embodiments of this application propose a centralized main and distribution network collaborative scheduling framework that considers the distribution network security constraints and the feasible domain projection of the flexibility range of flexible resources in the distribution network at the main and distribution network interfaces in the main network scheduling model, thereby enabling the scheduling strategy to be obtained by solving the optimization problem in one go without iteration.
[0078] In step S102, a distribution network flexibility aggregation model is generated based on the framework of the deterministic primary and distribution network coordinated scheduling problem.
[0079] After establishing the framework of the deterministic primary and distribution network coordinated scheduling problem, the embodiments of this application can further generate a distribution network flexibility aggregation model based on the framework of the deterministic primary and distribution network coordinated scheduling problem, thereby efficiently characterizing the power flexibility at the primary and distribution network interface.
[0080] Optionally, in one embodiment of this application, designing a distribution network flexibility aggregation model includes: identifying the flexibility boundary whose probability of operation satisfies preset conditions based on the regularity of power grid operation; and constructing a flexibility aggregation model based on the flexibility boundary.
[0081] It should be noted that, in the embodiments of this application, the high-efficiency distribution network flexibility aggregation model is a price-guided flexibility model. It can identify flexibility boundaries with a high probability of activation by utilizing the regularity of power grid operation, and construct the flexibility model using constraints with a high probability of activation. Specifically, it includes the following steps:
[0082] 1. Define the basic approximation model:
[0083] In the embodiments of this application, two basic approximation models can be defined as follows:
[0084] (1) Power-Energy Boundary Model:
[0085]
[0086]
[0087] Since the case at t=1 has already been included in equation (24), constraint (25) starts from t=2.
[0088] (2) Energy change boundary model:
[0089]
[0090] parameter as well as All from The definitions are as follows:
[0091] 1) express time
[0092] 2) express time
[0093] 3) express time
[0094] It is understandable that, since the two models mentioned above only include the constraints of Equation (23), they are both external approximations of Equation (23). The power-energy boundary model is a simple extension of the flexible resource unit model, which restricts the total power of the distribution network and the accumulated power consumption, with a total number of constraints of 4T-2. The energy change boundary model restricts the energy change between every two time periods, and it contains T(T+1) constraints. The number of constraints in the power-energy boundary model is linearly related to T, which is very beneficial for scaling and subsequent consideration of uncertainties, but its accuracy is low.
[0095] Furthermore, although the energy change boundary model has higher accuracy, its number of constraints is only 2(2) times that of the exact model. T The number of constraints has been greatly reduced by -1), however, the number of constraints is still proportional to the number of time periods, meaning the number of constraints is still too large.
[0096] 2. Construct a flexible price-guided model:
[0097] It should be noted that the embodiments of this application propose a price-guided flexibility model, aiming to find an efficient flexibility model between the power energy boundary model and the energy change boundary model, making its constraint number linearly related to T, while significantly improving its accuracy compared to the power energy boundary model. Furthermore, the regularity of the power system's operating state proves its feasibility, and the shadow price can characterize the power system's operating state. In the dispatch environment, the shadow price of the node power balance equation corresponds to the node electricity price in the market environment. Existing methods can generate predicted node electricity prices, and these methods can also be used to predict shadow prices in the dispatch environment. In other words, the goal is to minimize the distribution network operating cost, i.e., the predicted shadow price multiplied by the power, using the energy change boundary model as a constraint for optimization. The probability of each constraint taking effect is statistically analyzed, and those constraints with higher probabilities of action are selected to construct the flexibility model, hence the term "price-guided flexibility model."
[0098] It is important to note that the price-guided flexibility model should include all constraints from the power-energy boundary model to satisfy the basic feasibility of power and energy. Furthermore, since the constraints in both the exact model and the two approximate models mentioned above appear in the form of upper and lower bound pairs, the constraints in the price-guided flexibility model should also be paired to define the support set when considering uncertainties later. That is, the upper bound parameter in the flexibility model must always remain greater than or equal to the lower bound parameter.
[0099] Optionally, in one embodiment of this application, a flexibility aggregation model is constructed based on the flexibility boundary, including: inputting the number of constraint pairs of the target, shadow price samples, and flexibility parameter samples; calculating an optimization model for all samples, and based on the optimization model, identifying the constraint sets of the power energy boundary model and the constraint sets of the energy change boundary model that are in effect; calculating the probability of all constraints being in effect, and sorting them to obtain a set of constraint pairs, so as to obtain a price-guided flexibility model.
[0100] Specifically, the price-guided flexibility model in this application embodiment can be constructed as follows:
[0101] 1) The number of constraint pairs N for the input objective C (N C ≥2T-1), shadow price sample And flexibility parameter samples Where K1 and K2 are the number of samples. The constraint set of the power-energy boundary model is denoted as... The constraint set of the energy change boundary model is denoted as
[0102] 2) Calculate the optimization model for all k1, 1 ≤ k1 ≤ K1, and k2, 1 ≤ k2 ≤ K2:
[0103]
[0104] Where (·)′ denotes finding the transpose of a vector;
[0105] 3) The calculated Find (Right now and The constraint pairs that are active in the difference set (the active constraint pair is defined as any one of the constraints in it being active);
[0106] 4) Calculation The probability that all constraints take effect;
[0107] 5) For all Sort the constraints in the table according to their probability of activation from high to low, and find the top N. C -2T+1 constraints
[0108] To construct a collection
[0109] 6) Output As a flexible model guided by price.
[0110] Therefore, in the above process, the constraint of the objective affects the quantity N. CIt can be arbitrarily specified between 2T-1 and T(T+1) / 2, therefore, it can be set to be linearly related to T. In actual implementation, those skilled in the art can also set N. C =4T, thus allowing for further improvement in accuracy with only a small increase in complexity.
[0111] It is understood that the price-guided flexibility model proposed in this application is an efficient method for characterizing the flexibility of flexible resource aggregation in the distribution network. It can efficiently characterize the power flexibility at the main distribution network interface, describe the flexibility range of inter-time coupling, and has fewer constraints, lower complexity, and higher accuracy. It is very suitable for large-scale transmission and distribution coordination scheduling scenarios and modeling after embedding uncertainty.
[0112] In step S103, the uncertainty of new energy output and distribution network flexibility is modeled using distributed bar chance constraints and embedded into the main distribution network coordinated scheduling model.
[0113] After generating a distribution network flexibility aggregation model based on the framework of the deterministic main and distribution network coordinated scheduling problem, the embodiments of this application can further use distributed bar chance constraints to model the uncertainty of renewable energy output and distribution network flexibility, and embed it into the main and distribution network coordinated scheduling model. This allows for the consideration of distribution network security constraints, renewable energy output and the uncertainty of demand-side resource flexibility in the main network scheduling, maximizing the utilization of demand-side resource flexibility and improving the economy and security of the entire network operation.
[0114] Specifically, in the embodiments of this application, the uncertainty of new energy output and distribution network flexibility in the above-mentioned distributed rod opportunity constraint modeling specifically includes:
[0115] 1. Define the Bruker chance constraint using Wasserstein distance.
[0116] In the model of coordinated dispatching of primary and distribution networks, uncertain variables include the maximum output of new energy sources and the upper and lower bound parameters in the flexibility model. For all If the T-dimensional column vector is formed, then the right half of constraint (8) can be expressed as follows:
[0117]
[0118] All constraints in the price-guided flexibility model are written in the following form:
[0119]
[0120] Among them, M d For N C The coefficient matrix of ×T, and For N C A vector consisting of boundary parameters of size ×1.
[0121] consider and Given the uncertainty, the above two equations can be expressed in the form of a joint opportunity constraint, as shown in the following equation:
[0122]
[0123]
[0124] Where, ε r ,ε d ∈(0,1) represent the tolerable risk levels of transmission network operators for new energy and flexible distribution networks, respectively. Constraint (30) is a joint chance constraint for each r, indicating that the probability that all inequalities in the set of inequalities within the parentheses are simultaneously true is greater than 1-ε. r Furthermore, the interpretation of constraint (31) is similar, and will not be repeated here.
[0125] It should be noted that since the probability constraint of the split bar applies to both (30) and (31), for the convenience of research and analysis, the embodiments of this application can represent (30) and (31) as follows:
[0126]
[0127] in, Indicates the number of the opportunity constraint; constraint (30) for new energy power generation corresponds to:
[0128]
[0129] The constraint (31) of the flexible distribution network corresponds to:
[0130]
[0131] It should be noted that, due to physical limitations, the uncertain variable ξ w It will be subject to the constraints of the support set, that is Specifically, although the output of new energy sources is random, it should always be no less than 0, corresponding to H. r =-I,h r =0; Although the upper and lower bound parameters for distribution network flexibility are random, they should always satisfy that the upper bound is greater than or equal to the lower bound, i.e., H d =[I,-I],h d =0, this information is crucial to the feasibility of the split-bar chance constraint.
[0132] Power transmission network operators cannot know the true distribution information. However, it can be constructed through certain means. The fuzzy set Π in which the distribution resides requires that the joint chance constraint (32) holds for all distributions in the fuzzy set Π, that is:
[0133]
[0134] 2. The conversion probability constraint is presented in a form that is easy to calculate:
[0135] For ease of description of the following process, embodiments of this application may omit the subscript w of the random variable and define the fuzzy set Π using a Wasserstein sphere, denoted as... Let W be the i-th sample of a random variable, and let W(·,·) represent the Wasserstein distance between two random distributions. Then the Wasserstein sphere is defined as follows:
[0136]
[0137] Where Γ(Ξ) represents all distributions on the support set Ξ. It represents a discrete uniform distribution on the random variable sample, where ρ is the pre-given radius of the Wasserstein sphere, which can be used to control the conservatism of the model.
[0138] Thus far, the split-bar joint chance constraint remains an NP-hard problem. Therefore, the embodiments of this application need to simplify it to make it solvable. The feasible region determined by the split-bar joint chance constraint (33) is:
[0139]
[0140] Suppose the joint opportunity constraint consists of K constraints, then A and b can be expressed in decomposition form as follows:
[0141] A = [a1,...,a] K ]′,b(x)=[b1(P),...,b K (P)]′
[0142] Therefore, the original Bruker joint chance constraint (33) is equivalent to
[0143]
[0144] Define a risk level ε for each constraint in the parentheses above. k ,satisfy (In actual implementation, ε can generally be taken) k =ε / K), then define a feasible region Ψ Bonf for:
[0145]
[0146] According to Bonferroni's inequality, we have Therefore, the joint opportunity constraint is decomposed into individual opportunity constraints, which can be conservatively estimated using conditional value at risk (CVaR):
[0147] satisfy Therefore, Ψ Bonf-CVaR It is Ψ Bonf A conservative approximation. Based on rigorous mathematical derivation, Ψ Bonf-CVaR It can be equivalently transformed into the following expression:
[0148]
[0149] Where, s, ζ, β, γ ik These are all auxiliary variables generated during the transformation process. `dim(·)` calculates the dimension of the vector. ||·|| * Let ||·|| be the dual norm of the norm ||·||. In practical applications, let ||·|| be the l1 norm, then its dual norm is l. ∞ Norm, therefore, Ψ Bonf-CVaR All expressions in the expression are linear.
[0150] 3. Embed the distributed opportunity constraints into the centralized main and distribution network collaborative scheduling model.
[0151] Therefore, the distributed robust chance constraint of this application embodiment is a data-driven method that can be calculated without probability distribution information, and has higher reliability than traditional sampling average and scenario optimization, while avoiding the disadvantage of traditional robust optimization being too conservative.
[0152] Optionally, in one embodiment of this application, the main and distribution network coordinated scheduling model is as follows:
[0153]
[0154] Where, Δ t Indicates the length of time period t; Let each represent a set of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; j∈i indicates that node j is connected to node i. A flexible distribution network connected to node i, consisting of a collection of traditional and renewable energy generating units; P ij,t ,P d,t ,P g,t ,P r,t These represent the active power of line ij, distribution network d, traditional generating unit g, and new energy generating unit r during time period t, respectively. This represents the fixed load of node i; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill gradient for a conventional generator set.
[0155] It should be noted that, after the above transformation, the distributed bar opportunity constraint (35) is finally transformed into a set of linear constraints, which are then embedded in the scheduling model. The final result is the centralized distributed bar scheduling model for main and distribution network coordination:
[0156]
[0157] It is understood that the embodiments of this application use data-driven sub-Brooker chance constraints to simultaneously characterize the uncertainties of renewable energy output and demand-side flexibility. These sub-Brooker chance constraints can be transformed into a set of linear constraints through a series of mathematical transformations and can be efficiently solved using commercial solvers. The model considers the support set of random variables, making the results more reliable. The embodiments of this application provide a decision-making scheme for flexible resources participating in the economic dispatch or market clearing of the large power grid. This scheme can balance distribution network security constraints, the uncertainties of renewable energy output and demand-side resource flexibility in the main grid dispatch, maximizing the utilization of demand-side resource flexibility and improving the economy and security of the entire grid operation.
[0158] The centralized main and distribution network coordinated sub-Bluerge bar optimization scheduling method proposed in this application establishes a framework for a deterministic main and distribution network coordinated scheduling problem, including individual models of the main network, distribution network, and flexible resources. Based on this framework, a distribution network flexibility aggregation model is generated. Sub-Bluerge bar opportunity constraints are used to model the uncertainty of renewable energy output and distribution network flexibility, which is then embedded into the main and distribution network coordinated scheduling model. This allows for a one-time solution to the optimization problem to obtain the scheduling strategy without iteration, and can efficiently characterize the power flexibility at the main and distribution network interface with fewer constraints and higher accuracy. Furthermore, this application provides a decision-making scheme for flexible resources to participate in the economic scheduling or market clearing of the large power grid, taking into account the uncertainty of distribution network security constraints, renewable energy output, and demand-side resource flexibility in the main grid scheduling, maximizing the utilization of demand-side resource flexibility, and improving the economy and security of the entire network operation.
[0159] Next, referring to the accompanying drawings, we describe the centralized main and distribution network collaborative distributed control system optimized scheduling device proposed according to the embodiments of this application.
[0160] Figure 2 This is a block diagram of a centralized main and distribution network collaborative distributed control system optimized scheduling device according to an embodiment of this application.
[0161] like Figure 2As shown, the centralized main distribution network collaborative distribution network optimization scheduling device 10 includes: a construction module 100, a generation module 200, and an embedding module 300.
[0162] Among them, module 100 is used to build a framework for the deterministic main network and distribution network coordinated scheduling problem. The framework includes individual models of the main network, distribution network, and flexible resources.
[0163] The generation module 200 is used to generate a distribution network flexibility aggregation model based on the framework of the deterministic primary and distribution network collaborative scheduling problem.
[0164] Embedded module 300 is used to model the uncertainty of new energy output and distribution network flexibility using distributed bar chance constraints, and is embedded into the main distribution network coordinated scheduling model.
[0165] Optionally, in one embodiment of this application, the building module includes: a determining unit, a first building unit, and a defining unit.
[0166] Among them, the deterministic unit is used to determine the deterministic scheduling model of the transmission network. The objective function is to minimize the total generation cost of the entire system. Multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the node power balance, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources.
[0167] The first building unit is used to construct the original power flow constraints of the distribution network using the linearized power flow equations. The original power flow constraints include power balance at the transmission and distribution network interface, linearized distribution network power flow equations, active and reactive power balance at nodes, voltage and phase angle at the distribution network balance nodes, node voltage limits, and branch active power transmission capacity limits.
[0168] Define the unit, which is used to define the precise model of the operating range constraints of distributed flexible resources in the distribution network and the aggregation flexibility of the distribution network.
[0169] Optionally, in one embodiment of this application, the generation module includes: a boundary-finding unit and a second construction unit.
[0170] Among them, the boundary-finding unit is used to find the flexibility boundary whose probability of functioning satisfies preset conditions based on the regularity of power grid operation.
[0171] The second building block is used to construct a flexibility aggregation model based on the flexibility boundary.
[0172] Optionally, in one embodiment of this application, the generation module further includes an input unit, a calculation unit, and a sorting unit.
[0173] The input unit is used to input the quantity of constraint pairs, shadow price samples, and flexibility parameter samples of the target.
[0174] The computational unit is used to compute the optimization model for all samples, and based on the optimization model, to find the constraint sets that are in effect in the constraint sets of the power-energy boundary model and the energy change boundary model.
[0175] The sorting unit is used to calculate the probability that all constraints take effect and sort them to obtain a set of constraint pairs, thus obtaining a price-guided flexibility model.
[0176] Optionally, in one embodiment of this application, the main and distribution network coordinated scheduling model is as follows:
[0177]
[0178] Where, Δ t Indicates the length of time period t; Let each represent a set of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; j∈i indicates that node j is connected to node i. A flexible distribution network connected to node i, consisting of a collection of traditional and renewable energy generating units; P ij,t ,P d,t ,P g,t ,P r,t These represent the active power of line ij, distribution network d, traditional generating unit g, and new energy generating unit r during time period t, respectively. This represents the fixed load of node i; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill gradient for conventional generator sets.
[0179] It should be noted that the foregoing explanation of the centralized main and distribution network collaborative sub-branch optimization scheduling method embodiment also applies to the centralized main and distribution network collaborative sub-branch optimization scheduling device of this embodiment, and will not be repeated here.
[0180] The centralized main and distribution network coordinated sub-Bluerg bar optimization scheduling device proposed in this application establishes a framework for a deterministic main and distribution network coordinated scheduling problem, including individual models of the main network, distribution network, and flexible resources. Based on this framework, a distribution network flexibility aggregation model is generated. Sub-Bluerg bar opportunity constraints are used to model the uncertainty of renewable energy output and distribution network flexibility, embedding this model into the main and distribution network coordinated scheduling model. This allows for a one-time solution to the optimization problem to obtain the scheduling strategy without iteration, and can efficiently characterize the power flexibility at the main and distribution network interface with fewer constraints and higher accuracy. Furthermore, this application provides a decision-making scheme for flexible resources to participate in the economic scheduling or market clearing of the large power grid, balancing distribution network security constraints, renewable energy output, and the uncertainty of demand-side resource flexibility in main grid scheduling, maximizing the utilization of demand-side resource flexibility, and improving the economy and security of the entire network operation.
[0181] Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:
[0182] The memory 301, the processor 302, and the computer program stored on the memory 301 and capable of running on the processor 302.
[0183] When the processor 302 executes the program, it implements the centralized main and distribution network collaborative distributed bar optimization scheduling method provided in the above embodiments.
[0184] Furthermore, electronic devices also include:
[0185] Communication interface 303 is used for communication between memory 301 and processor 302.
[0186] The memory 301 is used to store computer programs that can run on the processor 302.
[0187] The memory 301 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.
[0188] If the memory 301, processor 302, and communication interface 303 are implemented independently, then the communication interface 303, memory 301, and processor 302 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 3 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.
[0189] Optionally, in a specific implementation, if the memory 301, processor 302, and communication interface 303 are integrated on a single chip, then the memory 301, processor 302, and communication interface 303 can communicate with each other through an internal interface.
[0190] Processor 302 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.
[0191] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described centralized main and distribution network collaborative distributed control optimization scheduling method.
[0192] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0193] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.
[0194] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.
[0195] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.
[0196] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.
[0197] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.
[0198] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.
[0199] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.
Claims
1. A centralized main and distribution network collaborative distributed control optimization scheduling method, characterized in that, Includes the following steps: A framework is established for the deterministic main network and distribution network coordinated scheduling problem, the framework including individual models of the main network, distribution network, and flexible resources; Based on the framework of the deterministic primary and distribution network coordinated scheduling problem, a distribution network flexibility aggregation model is generated; and The uncertainty of new energy output and distribution network flexibility is modeled using distributed bar opportunity constraints and embedded into the main distribution network coordinated scheduling model; The framework for establishing a deterministic primary and secondary network coordinated scheduling problem includes: A deterministic dispatch model for the power transmission network is determined, in which the total generation cost of the entire system is minimized as the objective function, and multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the power balance of the node, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources. The original power flow constraints of the distribution network are constructed using linearized power flow equations. These original power flow constraints include power balance at the transmission and distribution network interface, linearized distribution network power flow equations, active and reactive power balance at nodes, voltage and phase angle at distribution network balance nodes, node voltage limits, and branch active power transmission capacity limits. Define an accurate model for the operational scope constraints of distributed flexible resources in the distribution network and the aggregation flexibility of the distribution network; The generated distribution network flexibility aggregation model includes: Based on the regularity of power grid operation, identify the flexibility boundary where the probability of operation meets preset conditions; The flexibility aggregation model is constructed based on the flexibility boundary.
2. The method according to claim 1, characterized in that, The construction of the flexibility aggregation model based on the flexibility boundary includes: The constraints on the input target are quantity, shadow price sample, and flexibility parameter sample; Calculate the optimization model for all samples, and based on the optimization model, identify the constraint sets that are in effect for the power-energy boundary model and the constraint pairs that are in effect for the energy change boundary model. Calculate the probability that all constraints take effect and sort them to obtain a set of constraint pairs, thus obtaining a price-guided flexibility model.
3. The method according to any one of claims 1-2, characterized in that, The main and distribution network coordinated scheduling model is as follows: , in, Indicates time period t Length; These respectively represent the collections of nodes, lines, flexible distribution networks, traditional generating units, and new energy generating units in the power transmission system; Represents a node j With nodes i Connected; Connect to node i A flexible power distribution network that combines traditional and new energy generating units; They represent the lines respectively. ij Distribution network d Traditional units g and new energy units r During the period t The active power; Represents a node i Fixed load; This indicates the upper and lower limits of the output of traditional generator units. This indicates the maximum uphill / downhill gradient for conventional generator sets.
4. A centralized main and distribution network collaborative distributed control system optimized scheduling device, characterized in that, include: A framework is built to address the deterministic main network and distribution network collaborative scheduling problem. The framework includes individual models of the main network, distribution network, and flexible resources. The generation module is used to generate a distribution network flexibility aggregation model based on the framework of the deterministic primary and distribution network coordinated scheduling problem. as well as An embedded module is used to model the uncertainty of new energy output and distribution network flexibility using distributed bar opportunity constraints, and is embedded into the main distribution network coordinated scheduling model; The construction module includes: The deterministic unit is used to determine the deterministic dispatch model of the transmission network. The objective function is to minimize the total generation cost of the entire system. Multiple constraints are obtained based on the DC power flow equation, the phase angle of the reference node, the node power balance, the active power limit of the line, the output limit of the generator unit and the ramp rate limit, the output limit of the new energy unit, and the power feasible region of the flexible resources. The first construction unit is used to construct the original power flow constraints of the distribution network using the linearized power flow equations. The original power flow constraints include power balance at the transmission and distribution network interface, linearized distribution network power flow equations, active and reactive power balance at nodes, voltage and phase angle at the distribution network balance nodes, node voltage limits, and branch active power transmission capacity limits. Define the unit, which is used to define the precise model of the operating range constraints of distributed flexible resources in the distribution network and the aggregation flexibility of the distribution network; The generation module includes: Boundary-finding units are used to find flexible boundaries whose probability of functioning satisfies preset conditions based on the regularity of power grid operation. The second building unit is used to build the flexibility aggregation model based on the flexibility boundary.
5. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the centralized main distribution network collaborative distributed control optimization scheduling method as described in any one of claims 1-3.
6. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the centralized main distribution network collaborative distributed control system optimized scheduling method as described in any one of claims 1-3.
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