CN110556847A - Energy storage system planning operation joint optimization method and system in photovoltaic-containing power distribution network - Google Patents
Energy storage system planning operation joint optimization method and system in photovoltaic-containing power distribution network Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for AC mains or AC distribution networks
- H02J3/28—Arrangements for balancing of the load in a network by storage of energy
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- Y02B10/00—Integration of renewable energy sources in buildings
- Y02B10/10—Photovoltaic [PV]
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E70/00—Other energy conversion or management systems reducing GHG emissions
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Abstract
本公开提出了含光伏配电网中储能系统规划运行联合优化方法及系统,建立配电网储能系统规划三层鲁棒优化模型,包括规划主问题模型,安全校验子问题模型和经济运行最优子问题模型;通过对鲁棒优化模型的三层分解,同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,通过三层迭代求解获得最优解。充分考虑源荷不确定性,在保证配电网不出现电压越限问题的基础上,寻求最恶劣场景下的最优配置方案,但此问题因变量维数过多而变得复杂,于是通过分解理论将原问题分解为规划主问题,安全校验子问题以及经济运行最优子问题,方便快速有效的迭代求解。
This disclosure proposes a joint optimization method and system for energy storage system planning and operation in a photovoltaic distribution network, and establishes a three-layer robust optimization model for distribution network energy storage system planning, including a planning master problem model, a safety check sub-problem model and an economic Run the optimal sub-problem model; through the three-layer decomposition of the robust optimization model, while considering the worst scenarios of different situations under the safety analysis of voltage over-limit and economic optimal operation, the optimal solution is obtained through three-layer iterative solution. Fully consider the uncertainty of source load, on the basis of ensuring that the distribution network does not have the problem of voltage exceeding the limit, seek the optimal configuration scheme in the worst scenario, but this problem becomes complicated due to too many variable dimensions, so through Decomposition theory decomposes the original problem into the main planning problem, the safety verification sub-problem and the optimal sub-problem of economic operation, which is convenient for fast and effective iterative solution.
Description
技术领域technical field
本公开涉及配电网储能技术领域,特别是涉及含光伏配电网中储能系统规划运行联合优化方法及系统。The present disclosure relates to the technical field of distribution network energy storage, in particular to a joint optimization method and system for energy storage system planning and operation in a photovoltaic distribution network.
背景技术Background technique
随着高渗透率分布式光伏的大量接入,配电网的电压越限问题愈发严重。但近年来,储能的技术得以不断成熟,且成本不断下降,使得光储一体化系统得以推广,这不仅缓和了配电网的电压越限问题,而且运行商还可以通过储能系统的低储高发特性进行套利运作。但配电网中存在的源荷等多重不确定性给储能系统的规划和运行优化带来了巨大的挑战,使得储能系统无法更加充分的发挥自身的综合价值。因此,深入研究配电网中储能系统的规划方法对解决配电网电压越限问题具有重要意义。With the large-scale access of high-penetration distributed photovoltaics, the voltage limit problem of the distribution network is becoming more and more serious. However, in recent years, the energy storage technology has been continuously matured and the cost has been continuously reduced, which has enabled the promotion of the integrated solar storage system. Carry out arbitrage operations based on the characteristics of reserves and high issuance. However, multiple uncertainties such as source and load in the distribution network have brought huge challenges to the planning and operation optimization of the energy storage system, making it impossible for the energy storage system to fully exert its comprehensive value. Therefore, it is of great significance to deeply study the planning method of energy storage system in distribution network to solve the problem of distribution network voltage exceeding the limit.
目前,主流解决方案有以下:Currently, mainstream solutions include the following:
(1)通过增加网架结构及负荷转移消纳光伏,但是改造费用较大,很难有经济效益;(1) To absorb photovoltaics by increasing the grid structure and load transfer, but the cost of transformation is relatively high, and it is difficult to have economic benefits;
(2)光伏自身参与调节无功、甚至在关键时段剪切有功的方法解决过电压问题,但是该方案有可能会损害光伏投资者的经济利益,光伏如何公平公正积极的参与调节一直是需要解决的难题。(2) Photovoltaic itself participates in the regulation of reactive power, and even cuts active power in critical periods to solve the overvoltage problem, but this solution may damage the economic interests of photovoltaic investors. How to participate in the regulation fairly, justly and actively has always been a need to solve problem.
发明内容Contents of the invention
本发明的目的是提供含光伏配电网中储能系统规划运行联合优化方法,综合考虑源荷不确定性以及储能系统运行情况的储能系统规划问题,建立相应模型并求解,获得最优配置方案。The purpose of the present invention is to provide a joint optimization method for energy storage system planning and operation in a photovoltaic distribution network, which comprehensively considers the energy storage system planning problem of source load uncertainty and energy storage system operation, establishes a corresponding model and solves it, and obtains the optimal solution. Configuration.
为了实现上述目的,本说明书实施方式提供含光伏配电网中储能系统规划运行联合优化方法,通过以下技术方案实现:In order to achieve the above purpose, the implementation mode of this specification provides a joint optimization method for the planning and operation of the energy storage system in the photovoltaic distribution network, which is realized through the following technical solutions:
包括:include:
建立配电网储能系统规划三层鲁棒优化模型,包括规划主问题模型,安全校验子问题模型和经济运行最优子问题模型;Establish a three-layer robust optimization model for distribution network energy storage system planning, including the planning main problem model, the safety verification sub-problem model and the economic operation optimal sub-problem model;
规划主问题模型以配电网储能系统安装位置和安装容量为决策变量;The planning master problem model takes the distribution network energy storage system installation location and installation capacity as the decision variables;
安全校验子问题模型用来校验当前配电网储能系统配置在最恶劣情况下的电压越限问题,直至电压越限问题得以解决;The safety check sub-problem model is used to check the voltage limit problem of the current distribution network energy storage system configuration in the worst case until the voltage limit problem is solved;
经济最优子问题模型则是得到当前配电网储能系统配置在最恶劣情况下配电网的经济最优运行情况;The economic optimal sub-problem model is to obtain the economic optimal operation of the distribution network under the worst case of the current distribution network energy storage system configuration;
通过对鲁棒优化模型的三层分解,同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,通过三层迭代求解获得最优的配电网储能系统安装位置和安装容量。Through the three-layer decomposition of the robust optimization model, and considering the worst scenarios of different situations under the safety analysis of voltage violation and optimal economic operation, the optimal installation location of the energy storage system in the distribution network is obtained through three-layer iterative solution and installed capacity.
进一步的技术方案,通过三层迭代求解可以找到最优解的过程为:As a further technical solution, the process of finding the optimal solution through three-layer iterative solution is as follows:
规划主问题模型的初始化储能系统配置方案带入安全校验子问题模型,该子问题模型首先进行安全性校验,判断规划主问题模型的决策变量是否能满足在最恶劣场景下的电压不越限要求,若不能满足则返回可行割,对规划主问题模型配置方案进行调整,直到满足所有的约束条件为止;The initial energy storage system configuration scheme of the planning main problem model is brought into the safety verification sub-problem model. If the requirement beyond the limit is not satisfied, return to feasible cut, and adjust the configuration scheme of the planning master problem model until all the constraints are met;
若规划主问题模型的决策变量能够满足安全性校验子问题模型,再进入经济最优子问题模型,进一步进行经济优化计算,向规划主问题模型返回可行割或最优割,直到找到最优解。If the decision variables of the planning main problem model can satisfy the safety check sub-problem model, then enter the economic optimal sub-problem model, further perform economic optimization calculations, and return the feasible cut or optimal cut to the planning main problem model until the optimal untie.
进一步的技术方案,所述规划主问题模型的目标函数以投资成本及典型日天数的经济最优子问题模型的目标函数值之和最小为目标。In a further technical solution, the objective function of the planning main problem model is to minimize the sum of the objective function values of the economic optimal sub-problem models of investment cost and typical number of days.
进一步的技术方案,所述规划主问题模型约束条件包括规划投资约束,安全性检验可行割集,以及经济最优可行割集或经济最优割集。In a further technical solution, the constrained conditions of the planning master problem model include planning investment constraints, safety test feasible cut sets, and economically optimal feasible cut sets or economically optimal cut sets.
进一步的技术方案,所述规划主问题模型的决策变量约束条件为:储能的额定功率和额定容量均大于等于零;经济最优子问题模型的目标函数值大于等于设定的极小值。In a further technical solution, the decision variable constraints of the planning main problem model are: the rated power and rated capacity of the energy storage are both greater than or equal to zero; the objective function value of the economic optimal sub-problem model is greater than or equal to a set minimum value.
进一步的技术方案,所述安全校验子问题模型为使所述规划主问题模型的配置方案可行,而引入松弛变量,目标函数为所引入的松弛变量的最大值为目标。In a further technical solution, the security verification sub-problem model introduces slack variables to make the configuration scheme of the planning main problem model feasible, and the objective function is the maximum value of the introduced slack variables as the target.
进一步的技术方案,所述安全校验子问题模型目标函数的约束包括:电压上下限约束、支路潮流约束、储能系统运行约束。In a further technical solution, the constraints of the objective function of the safety syndrome problem model include: voltage upper and lower limit constraints, branch power flow constraints, and energy storage system operation constraints.
进一步的技术方案,所述经济最优子问题模型以配电网的运行费用最低为目标,约束包括:电压上下限约束、支路潮流约束、储能系统运行约束。In a further technical solution, the economic optimal sub-problem model aims at the lowest operating cost of the distribution network, and the constraints include: voltage upper and lower limit constraints, branch power flow constraints, and energy storage system operation constraints.
本说明书实施方式提供含光伏配电网中储能系统规划运行联合优化系统,通过以下技术方案实现:The implementation mode of this manual provides a joint optimization system for the planning and operation of the energy storage system in the photovoltaic distribution network, which is realized through the following technical solutions:
包括:include:
三层鲁棒优化模型建立模块,被配置为:建立配电网储能系统规划三层鲁棒优化模型,包括规划主问题模型,安全校验子问题模型和经济运行最优子问题模型;The three-layer robust optimization model building module is configured to: establish a three-layer robust optimization model for distribution network energy storage system planning, including a planning master problem model, a safety check sub-problem model and an economic operation optimal sub-problem model;
规划主问题模型以配电网储能系统安装位置和安装容量为决策变量;The planning master problem model takes the installation location and installation capacity of the distribution network energy storage system as decision variables;
安全校验子问题模型用来校验当前配电网储能系统配置在最恶劣情况下的电压越限问题,直至电压越限问题得以解决;The safety check sub-problem model is used to check the voltage limit problem of the current distribution network energy storage system configuration in the worst case until the voltage limit problem is solved;
经济最优子问题模型则是得到当前配电网储能系统配置在最恶劣情况下配电网的经济最优运行情况;The economic optimal sub-problem model is to obtain the economic optimal operation of the distribution network under the worst case of the current distribution network energy storage system configuration;
三层鲁棒优化模型求解模块,被配置为:通过对鲁棒优化模型的三层分解,同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,通过三层迭代求解获得最优解。The three-layer robust optimization model solving module is configured to: through the three-layer decomposition of the robust optimization model, while considering the worst scenarios of different situations under the safety analysis of voltage over-limit safety and economic optimal operation, through three-layer iteration Solve for the optimal solution.
与现有技术相比,本公开的有益效果是:Compared with the prior art, the beneficial effects of the present disclosure are:
本公开提出一种全新的min-max-min配电网储能系统规划三层鲁棒优化模型,充分考虑源荷不确定性,采用不确定集的形式将源荷不确定性引入规划模型中,通过配置储能系统的容量,光伏输出过多的时候储存能量,负荷较重的时候释放能量,从而在保证配电网不出现电压越限问题的基础上,寻求最恶劣场景下的储能系统最优配置方案,但此问题因变量维数过多而变得复杂,于是通过分解理论将原问题分解为规划主问题模型,安全校验子问题模型以及经济运行最优子问题模型,方便快速有效的迭代求解,从而得到最优储能系统配置方案。This disclosure proposes a brand-new three-layer robust optimization model for min-max-min distribution network energy storage system planning, fully considers source-load uncertainty, and introduces source-load uncertainty into the planning model in the form of an uncertain set , by configuring the capacity of the energy storage system, the energy is stored when the photovoltaic output is too much, and the energy is released when the load is heavy, so as to ensure that the distribution network does not have voltage over-limit problems, and seek energy storage in the worst scenario The optimal configuration scheme of the system, but this problem becomes complicated due to too many variable dimensions, so the original problem is decomposed into the planning main problem model, the safety verification sub-problem model and the economic operation optimal sub-problem model through the decomposition theory, which is convenient Fast and effective iterative solution to obtain the optimal energy storage system configuration scheme.
本公开同时考虑储能系统的规划配置与运行控制,提出储能系统的规划-运行联合优化方法,由于电压越限安全性分析和经济性分析所得到的恶劣场景是不同的,传统两层分解仅考虑不确定性对运行成本的影响,不能同时考虑不确定性对配电网电压的影响,故本公开所提三层求解框架方便同时考虑安全性分析和经济性分析两种不同情况下的不确定性问题。This disclosure considers the planning configuration and operation control of the energy storage system at the same time, and proposes a planning-operation joint optimization method for the energy storage system. Due to the different harsh scenarios obtained from the safety analysis and economic analysis of the voltage exceeding the limit, the traditional two-layer decomposition Only considering the impact of uncertainty on operating costs, the impact of uncertainty on the distribution network voltage cannot be considered at the same time, so the three-layer solution framework proposed in this disclosure is convenient for considering both security analysis and economic analysis in two different situations Uncertainty problem.
本公开鉴于不同的不确定集区间,在储能系统规划问题的求解基础上,对储能系统规划问题的风险与收益进行代价分析,有利决策者更好的决策,降低鲁棒优化的保守性。In view of different uncertainty set intervals, this disclosure analyzes the risks and benefits of the energy storage system planning problem based on the solution of the energy storage system planning problem, which is beneficial for decision makers to make better decisions and reduces the conservatism of robust optimization .
本公开综合考虑了源荷不确定性,并提出三层鲁棒规划-运行优化模型,针对储能规划-运行联合优化问题,寻求最恶劣场景下的储能系统配置方案。利用Benders分解一方面在优化问题中添加安全性约束,另一方面计及经济最优,使问题更加合理且能够快速求解。而传统的规划方法未能充分地考虑源荷不确定性,并不能更好的应对源荷不确定性对配电网产生的电压越限问题。This disclosure comprehensively considers the uncertainty of source load, and proposes a three-layer robust planning-operation optimization model, aiming at the energy storage planning-operation joint optimization problem, and seeks an energy storage system configuration scheme in the worst scenario. On the one hand, Benders decomposition is used to add security constraints to the optimization problem, and on the other hand, the economic optimization is taken into account, so that the problem is more reasonable and can be solved quickly. However, the traditional planning method fails to fully consider the source-load uncertainty, and cannot better deal with the voltage limit problem caused by the source-load uncertainty on the distribution network.
附图说明Description of drawings
构成本公开的一部分的说明书附图用来提供对本公开的进一步理解,本公开的示意性实施例及其说明用于解释本公开,并不构成对本公开的不当限定。The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure, and the exemplary embodiments and descriptions of the present disclosure are used to explain the present disclosure, and do not constitute improper limitations to the present disclosure.
图1为本公开实施例子提供的规划-运行联合优化详细流程图;Fig. 1 is a detailed flowchart of planning-operation joint optimization provided by the implementation example of the present disclosure;
图2为本公开实施例子规划方法下的四季典型日光伏出力鲁棒优化结果;Fig. 2 is the results of robust optimization of photovoltaic output in typical four seasons under the planning method of the implementation example of the present disclosure;
图3为本公开实施例子规划方法下的四季典型日负荷功率鲁棒优化结果;Fig. 3 is the results of robust optimization of typical daily load power in four seasons under the planning method of the implementation example of the present disclosure;
图4为本公开实施例子规划方法下的节点电压情况;Fig. 4 is the node voltage situation under the planning method of the implementation example of the present disclosure;
图5为本公开实施例子规划方法下的储能系统SOC情况;Fig. 5 shows the SOC of the energy storage system under the planning method of the implementation example of the present disclosure;
图6为本公开实施例子规划方法下的储能系统充放电功率情况;Fig. 6 shows the charging and discharging power of the energy storage system under the planning method of the implementation example of the present disclosure;
图7为本公开实施例子规划方法下的储能系统配置方案。Fig. 7 is an energy storage system configuration scheme under the planning method of the implementation example of the present disclosure.
具体实施方式Detailed ways
应该指出,以下详细说明都是例示性的,旨在对本公开提供进一步的说明。除非另有指明,本文使用的所有技术和科学术语具有与本公开所属技术领域的普通技术人员通常理解的相同含义。It should be noted that the following detailed description is exemplary and intended to provide further explanation of the present disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
需要注意的是,这里所使用的术语仅是为了描述具体实施方式,而非意图限制根据本公开的示例性实施方式。如在这里所使用的,除非上下文另外明确指出,否则单数形式也意图包括复数形式,此外,还应当理解的是,当在本说明书中使用术语“包含”和/或“包括”时,其指明存在特征、步骤、操作、器件、组件和/或它们的组合。It should be noted that the terminology used herein is only for describing specific embodiments, and is not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural, and it should also be understood that when the terms "comprising" and/or "comprising" are used in this specification, they mean There are features, steps, operations, means, components and/or combinations thereof.
实施例子一Implementation example one
该实施例公开了含光伏配电网中储能系统规划运行联合优化方法,现有技术中未能充分考虑源荷不确定性,且传统方法难于处理,为了解决如上的技术问题,本申请提出了基于三层分解的综合考虑源荷不确定性的储能规划-运行联合优化方法。This embodiment discloses a joint optimization method for the planning and operation of energy storage systems in photovoltaic distribution networks. The uncertainty of source and load is not fully considered in the prior art, and the traditional method is difficult to deal with. In order to solve the above technical problems, this application proposes A joint energy storage planning-operation optimization method based on a three-level decomposition that comprehensively considers source-load uncertainty is proposed.
参见附图1所示,基于三层分解的高渗透率光伏配电网储能系统规划-运行联合优化方法,包括:As shown in Figure 1, the planning-operating joint optimization method for high-permeability photovoltaic distribution network energy storage system based on three-layer decomposition includes:
(1)建立储能系统规划模型,其主要可分为储能系统规划投资模型,配电网安全校验运行模型和配电网最优经济运行模型,为使上下文连贯,故用规划主问题模型,安全校验子问题模型和经济运行最优子问题模型分别表示,再通过三层分解算法进行迭代求解;(1) Establish the energy storage system planning model, which can be mainly divided into energy storage system planning investment model, distribution network safety verification operation model and distribution network optimal economic operation model. In order to make the context coherent, the planning main problem is used model, the safety check sub-problem model and the optimal sub-problem model of economic operation are represented separately, and then solved iteratively through a three-layer decomposition algorithm;
(2)规划主问题模型是以储能系统安装位置和安装容量为决策变量的储能系统规划问题,基于下层子问题模型所产生的约束,得到一个当前的最优储能系统配置方案,但该方案未必是全局最优;(2) The planning master problem model is an energy storage system planning problem in which the energy storage system installation location and installation capacity are decision variables. Based on the constraints generated by the lower sub-problem model, a current optimal energy storage system configuration scheme is obtained, but This scheme may not be the global optimal;
(3)安全校验子问题模型用来校验主问题模型传递过来的最优储能系统配置方案在最恶劣情况下的电压越限问题,并产生安全运行割约束传递至主问题模型,直至电压越限问题得以解决;(3) The safety verification sub-problem model is used to verify the voltage limit problem of the optimal energy storage system configuration scheme transferred from the main problem model in the worst case, and generates a safe operation cut constraint and passes it to the main problem model until The voltage limit problem is solved;
(4)经济最优子问题模型则是得到基于安全校验子问题模型传递过来的最优储能系统配置方案在最恶劣情况下配电网的经济最优运行情况,从而验证该方案是否全局最优;(4) The economic optimal sub-problem model is to obtain the optimal economic operation of the distribution network in the worst case of the optimal energy storage system configuration scheme transferred from the security check sub-problem model, so as to verify whether the scheme is global optimal;
通过三层分解,可以同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,通过三层迭代求解可以找到最优解。Through the three-layer decomposition, the worst scenarios of different situations under the safety analysis of voltage violation and the optimal economic operation can be considered at the same time, and the optimal solution can be found through the three-layer iterative solution.
进一步地,将子问题模型产生的割约束带入主问题模型,依次迭代直至问题最优,具体为:Furthermore, the cut constraint generated by the sub-problem model is brought into the main problem model, and iterated successively until the problem is optimal, specifically:
主问题模型初始化储能系统配置方案,并带入子问题模型,子问题模型首先进行安全性校验,判断主问题模型的决策变量是否能满足在最恶劣场景下的电压不越限要求。若不能满足则返回可行割,对主问题模型配置方案进行调整,直到满足所有的约束条件为止。若主问题模型的决策变量能够满足安全性校验子问题模型的要求,再进入经济最优子问题模型,进一步进行经济优化计算,向主问题模型返回可行割或最优割,直到找到最优解。The main problem model initializes the configuration scheme of the energy storage system and brings it into the sub-problem model. The sub-problem model first conducts safety verification to judge whether the decision variables of the main problem model can meet the voltage limit requirement in the worst scenario. If it cannot be satisfied, return to feasible cut, and adjust the configuration scheme of the main problem model until all constraints are satisfied. If the decision variables of the main problem model can meet the requirements of the safety check sub-problem model, then enter the economic optimal sub-problem model, further perform economic optimization calculations, and return the feasible cut or optimal cut to the main problem model until the optimal untie.
第一层规划主问题模型的约束条件包括规划投资约束,安全性检验可行割集,经济最优可行割集以及经济最优割集,可以构建为如下形式:The constraints of the first-level planning master problem model include planning investment constraints, safety test feasible cut sets, economic optimal feasible cut sets and economic optimal cut sets, which can be constructed as follows:
(1)目标函数:(1) Objective function:
其中,in,
式中,CIN表示主问题模型投资成本,由储能安装功率和安装容量决定;CP和CE分别表示单位储能功率和容量的单价;Pi和Ei表示第i个储能的额定功率和额定容量;n表示储能安装的数量;Zj为引入的辅助变量,与第j个经济最优子问题模型的目标函数值有关;Day表示选取的典型日天数。In the formula, C IN represents the investment cost of the main problem model, which is determined by the installed power and installed capacity of energy storage; C P and C E represent the unit price of unit energy storage power and capacity respectively; P i and E i represent the cost of the i-th energy storage Rated power and rated capacity; n represents the number of energy storage installations; Z j is the introduced auxiliary variable, which is related to the objective function value of the jth economic optimal sub-problem model; Day represents the number of typical days selected.
(2)决策变量约束:(2) Decision variable constraints:
Pi≥0 (3)P i ≥ 0 (3)
Ei≥0 (4)E i ≥ 0 (4)
Zj≥φ,φ为一个极小的值(5)Z j ≥ φ, φ is a very small value (5)
(3)第二层安全校验子问题模型提供的安全性可行割:(3) The security feasibility provided by the second layer security syndrome problem model:
式中,表示第二层子问题模型中的松弛变量之和,松弛变量即为解决强电压约束下可能出现的不可解情况而引入的辅助变量,将电压上下限约束放宽以使问题可解,具体如式(10)和式(11);表示由第二层子问题模型返回的对偶变量,对偶变量即对偶线性规划问题中引入的辅助变量,具体可参考运筹学相关书籍;X(k)和X(k-1)分别表示第k次迭代和第k-1次迭代的规划主问题模型生成的储能系统配置方案;G为引入的系数矩阵,后续具体介绍。In the formula, Indicates the sum of the slack variables in the second-layer sub-problem model. The slack variables are the auxiliary variables introduced to solve the unsolvable situation that may occur under the strong voltage constraint. The upper and lower limits of the voltage are relaxed to make the problem solvable, as shown in the formula ( 10) and formula (11); Indicates the dual variable returned by the second-level sub-problem model. The dual variable is the auxiliary variable introduced in the dual linear programming problem. For details, please refer to related books on operations research; X (k) and X (k-1) represent the k-th time The energy storage system configuration scheme generated by the planning master problem model of iteration and k-1 iteration; G is the coefficient matrix introduced, which will be introduced in detail later.
(4)第三层经济运行最优子问题模型提供的经济性可行割或经济性最优割:(4) Economically feasible cut or economically optimal cut provided by the optimal sub-problem model of the third layer of economic operation:
Zj≥Λj+Πo,j*G*(X(k)-X(k-1)) (8)Z j ≥Λ j +Π o,j *G*(X (k) -X (k-1) ) (8)
式中,表示第三层子问题模型中引入的松弛变量之和;Λj表示第三层子问题模型的目标函数值;Πf2,j和Πo,j表示由第三层子问题模型返回的对偶变量。对偶变量是在优化进程中自动生成的辅助变量。In the formula, Indicates the sum of slack variables introduced in the third-level sub-problem model; Λ j represents the objective function value of the third-level sub-problem model; Πf2 ,j and Πo ,j represent the dual variables returned by the third-level sub-problem model . Dual variables are auxiliary variables that are automatically generated during the optimization process.
第二层安全校验子问题模型为了使第一层规划主问题模型得到的配置方案可行,而引入松弛变量,构建问题如下:In order to make the configuration scheme obtained by the first-level planning main problem model feasible, the second-level security verification sub-problem model introduces slack variables, and the construction problem is as follows:
(1)目标函数:(1) Objective function:
式中,S1,i(t)和S2,i(t)分别为第二层子问题模型约束中引入的松弛变量,以应对第二层子问题模型不可解的情况。In the formula, S 1,i (t) and S 2,i (t) are the slack variables introduced in the constraints of the second-level sub-problem model to deal with the unsolvable situation of the second-level sub-problem model.
(2)电压上下限约束:(2) Voltage upper and lower limit constraints:
Vi(t)+S1,i(t)≥Vmin (10)V i (t)+S 1,i (t)≥V min (10)
Vi(t)-S2,i(t)≤Vmax (11)V i (t)-S 2,i (t)≤V max (11)
式中,Vmin和Vmax分别表示电压的上下限约束;Vi(t)表示第i的节点在第t时的电压值。In the formula, V min and V max represent the upper and lower limit constraints of the voltage respectively; V i (t) represents the voltage value of the i-th node at the t-th time.
(3)支路潮流约束:(3) Branch flow constraints:
V1(t)=1 (13)V 1 (t)=1 (13)
Qi+1(t)-Qi(t)=-qi(t) (15)Q i+1 (t)-Q i (t)=-q i (t) (15)
式中,ri和xi分别表示支路i的电阻和电抗;Pi(t)和Qi(t)分别表示t时刻支路i的有功功率和无功功率;V0表示电压的基准值;表示t时刻第i个光伏的有功出力;表示t时刻第i个储能系统的放电功率;表示t时刻第i个储能系统的充电功率;pi(t)和qi(t)表示t时刻节点i上的负载有功功率和无功功率。In the formula, r i and x i represent the resistance and reactance of branch i respectively; P i (t) and Q i (t) represent the active power and reactive power of branch i at time t respectively; V 0 represents the voltage reference value; Indicates the active output of the i-th photovoltaic at time t; Indicates the discharge power of the i-th energy storage system at time t; Represents the charging power of the i-th energy storage system at time t; p i (t) and q i (t) represent the active power and reactive power of the load on node i at time t.
(4)储能系统运行约束:(4) Energy storage system operating constraints:
式中,Ci(t)表示t时刻储能系统i的电量;ηch和ηdis分别表示储能系统充放电的效率;SSOCmax和SSOCmin表示储能系统荷电状态的上下限;表示储能系统i的额定容量,Pi N表示储能系统i的额定功率。In the formula, C i (t) represents the electric quantity of the energy storage system i at time t; η ch and η dis represent the charging and discharging efficiency of the energy storage system respectively; S SOCmax and S SOCmin represent the upper and lower limits of the state of charge of the energy storage system; Indicates the rated capacity of the energy storage system i, and P i N indicates the rated power of the energy storage system i.
(5)其他约束:(5) Other constraints:
S1,i(t)≥0 (23)S 1,i (t)≥0 (23)
S2,i(t)≥0 (24)S 2,i (t)≥0 (24)
式中,S1,i(t)和S2,i(t)分别表示第二层子问题模型引入的松弛变量。In the formula, S 1,i (t) and S 2,i (t) respectively represent the slack variables introduced by the second-level sub-problem model.
第三层经济运行最优子问题模型是在第二层子问题模型的目标值为0时,进而求解经济运行问题最优解,构建问题如下:The third-level economic operation optimal sub-problem model is to solve the optimal solution of the economic operation problem when the target value of the second-level sub-problem model is 0. The construction problem is as follows:
(1)目标函数:(1) Objective function:
其中,in,
式中,COP表示配电网的运行费用;price(t)表示t时刻首节点的购售电价格,P1(t)表示t时刻首节点的流入或流出的功率值,UL和UPV表示负荷功率不确定集和光伏出力不确定集。In the formula, C OP represents the operating cost of the distribution network; price(t) represents the purchase and sale price of the first node at time t, P 1 (t) represents the inflow or outflow power value of the first node at time t, U L and U PV represents an uncertain set of load power and an uncertain set of photovoltaic output.
(2)约束条件:(2) Constraints:
与第二层安全校验子问题模型约束相同,即(10)-(22),只是(10)和(11)中不含松弛变量,形式如下:The model constraints are the same as those of the second-level safety check subproblem, that is, (10)-(22), except that (10) and (11) do not contain slack variables, and the form is as follows:
Vi(t)≥Vmin (27)V i (t)≥V min (27)
Vi(t)≤Vmax (28)V i (t)≤V max (28)
为更好的介绍本发明提出的三层分解方法机理,下文采用三层分解问题的紧凑形式进行讲解,具体如下:In order to better introduce the mechanism of the three-layer decomposition method proposed by the present invention, the following uses the compact form of the three-layer decomposition problem to explain, as follows:
本发明所提出的储能系统规划-运行联合优化模型可写成如下的min-max-min优化问题,为优化问题的原问题形式:The energy storage system planning-operation joint optimization model proposed by the present invention can be written as the following min-max-min optimization problem, which is the original problem form of the optimization problem:
式中,X和Y分别表示规划问题决策变量和运行问题决策变量;A和B分别表示决策变量的系数矩阵;D、E、F、G、K、M、f、g、h、pPV、pL分别为关于Y的等式、不等式约束所对应的系数矩阵;Φ表示规划问题决策变量的约束集合;Ω表示运行问题决策变量的约束集合;R为实数集;UPV和UL分别表示源荷不确定集。In the formula, X and Y represent the decision variables of the planning problem and the decision variables of the operation problem respectively; A and B represent the coefficient matrix of the decision variables respectively; D, E, F, G, K, M, f, g, h, p PV , p L is the coefficient matrix corresponding to the equality and inequality constraints on Y, respectively; Φ represents the constraint set of decision variables in planning problems; Ω represents the constraint set of decision variables in operation problems; R is a set of real numbers; Uncertain set of source charges.
以上问题是一个三层非线性非凸的问题,且由于问题变量维数过多,求解困难,故本发明将原问题分解为三层问题,通过迭代高效求解。由于考虑多重不确定性,但安全校验子问题模型和经济最优子问题模型考虑的不确定性最恶劣场景不同,为方便考虑,本文采用Benders分解理论将原问题分解为投资规划主问题模型,安全校验子问题模型,经济运行最优子问题模型。主问题模型是以储能系统安装位置和安装容量为决策变量的储能系统规划问题;安全校验子问题模型用来校验当前配置在最恶劣情况下的电压越限问题,直至电压越限问题得以解决;经济运行最优子问题模型则是得到当前配置在最恶劣情况下配电网的经济最优运行情况。通过三层分解,可以同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,但传统的两层分解不易实现,通过三层迭代求解可以找到最优解。The above problem is a three-layer non-linear and non-convex problem, and it is difficult to solve due to too many dimensions of the problem variables. Therefore, the present invention decomposes the original problem into three-layer problems and solves it efficiently through iteration. Due to the consideration of multiple uncertainties, the safety check sub-problem model and the economic optimal sub-problem model consider different worst scenarios of uncertainty. For convenience, this paper uses Benders decomposition theory to decompose the original problem into the main problem model of investment planning , the safety check sub-problem model, and the optimal sub-problem model of economic operation. The main problem model is an energy storage system planning problem with the energy storage system installation location and installation capacity as decision variables; the safety check sub-problem model is used to verify the voltage limit problem of the current configuration in the worst case, until the voltage limit is exceeded The problem is solved; the optimal sub-problem model of economic operation is to obtain the optimal economic operation of the current configuration of the distribution network in the worst case. Through the three-level decomposition, the worst scenarios of different situations under the safety analysis of voltage violation and the optimal economic operation can be considered at the same time. However, the traditional two-level decomposition is not easy to achieve, and the optimal solution can be found through the three-level iterative solution.
为了实现上述过程,需进一步进行如下分解:In order to realize the above process, the following decomposition needs to be further carried out:
(1)第一层规划主问题模型(1) The main problem model of the first level planning
第一层规划主问题模型获得储能系统的最优配置方案,考虑的约束条件有规划层决策变量约束以及第二层安全校验子问题模型提供的可行割和第三层经济运行最优子问题模型提供的最优割。第一层规划主问题模型以规划期内储能系统的投资运行成本之和最小为目标,式子(30)为第一层主问题模型的目标函数,式子(31)和(32)是规划层决策变量约束,式子(33)表示安全性可行割,式子(34)和(35)表示经济性可行割和经济性最优割,每次迭代子问题模型只产生式子(33)、(34)和(35)中的一个,并添加到主问题模型的约束中,初次迭代无Benders割约束。The first-level planning master problem model obtains the optimal configuration scheme of the energy storage system, and the constraints considered include the planning-level decision variable constraints, the second-level safety check sub-problem model provided by the feasible cut and the third-level economic operation optimal sub-problem The optimal cut provided by the problem model. The first-level planning master problem model aims to minimize the sum of investment and operation costs of the energy storage system during the planning period. Equation (30) is the objective function of the first-level master problem model. Equations (31) and (32) are The decision variable constraints of the planning layer, the formula (33) represents the security feasible cut, the formulas (34) and (35) represent the economically feasible cut and the economic optimal cut, each iteration sub-problem model only generates the formula (33 ), (34) and (35), and added to the constraints of the main problem model, there is no Benders cut constraint in the first iteration.
1)规划层决策变量约束1) Planning layer decision variable constraints
X≥0 (31)X≥0 (31)
Zj≥φ,φ为一个极小的值 (32)Z j ≥ φ, φ is a very small value (32)
2)第二层安全校验子问题模型提供的安全性可行割2) The security feasibility provided by the second layer security syndrome problem model
3)第三层经济运行最优子问题模型提供的经济性可行割或经济性最优割3) The economically feasible or economically optimal cut provided by the optimal sub-problem model of the third layer of economic operation
Zj≥Λj+Πo,j*G*(X(k)-X(k-1)) (35)Z j ≥Λ j +Π o,j *G*(X (k) -X (k-1) ) (35)
其中,和分别是第二层安全校验子问题模型和第三层经济运行最优子问题模型中的所有约束松弛量之和,即为优化问题的目标函数值;Zj作为新的变量引入主问题模型的目标函数中,代表运行费用;Λj代表上一次迭代经济运行最优子问题模型得到的目标函数值;和Πo分别为从第二层安全校验子问题模型和第三层经济运行最优子问题模型中得到的对偶变量。in, and are respectively the sum of all constraint slacks in the second-level security verification sub-problem model and the third-level economic operation optimal sub-problem model, which is the objective function value of the optimization problem; Z j is introduced into the main problem model as a new variable In the objective function of , it represents the operating cost; Λ j represents the objective function value obtained from the optimal sub-problem model of the last iterative economic operation; and Π o are the dual variables obtained from the second-level safety syndrome sub-problem model and the third-level economic operation optimal sub-problem model respectively.
(2)第二层安全校验子问题模型(2) The second layer security check sub-problem model
将第一层规划主问题模型得到的最优配置方案X(第k-1次迭代)带入第二层安全校验子问题模型中,第二层子问题模型的目标函数是为了满足在最劣场景下所有的约束条件引入的松弛量之和最小,式子(36)为第二层子问题模型的目标函数及约束条件。Bring the optimal configuration plan X (iteration k-1) obtained from the main problem model of the first layer planning into the second layer security check sub-problem model, the objective function of the second layer sub-problem model is to satisfy the In the bad scenario, the sum of the slack introduced by all constraints is the smallest, and Equation (36) is the objective function and constraints of the second-level sub-problem model.
其中,表示第二层子问题模型的决策变量集合,为将规划主问题模型得到的配置方案代入第二层子问题模型后的松弛变量之和。可见第二层子问题模型是一个max-min优化问题,不易进行求解,故本文通过对偶理论将原问题变为易求解的max问题。为方便变形,首先将原问题变为可对偶的严格形式,变形如下:in, Represents the decision variable set of the second-level sub-problem model, is the sum of the slack variables after substituting the configuration scheme obtained from the planning main problem model into the second-level sub-problem model. It can be seen that the second-level sub-problem model is a max-min optimization problem, which is not easy to solve. Therefore, this paper uses the dual theory to transform the original problem into a max problem that is easy to solve. In order to facilitate the transformation, the original problem is first transformed into a strict dual form, and the transformation is as follows:
由于原问题中Pi和Qi的符号未定,不满足对偶要求,故作一些变形,令Pi=Pi'-Pi”,Qi=Qi'-Qi”,其中Pi'≥0,Pi”≥0,Qi'≥0,Qi”≥0,则第二层子问题模型决策变量变为且Y1'≥0,再进行对偶处理可以得到如下形式:Since the signs of P i and Q i in the original problem are undecided and do not meet the requirements of duality, some deformations are pretended, so that P i =P i '-P i ", Q i =Q i '-Q i ", where P i ' ≥0, P i ”≥0, Q i '≥0, Q i ”≥0, then the decision variable of the second layer sub-problem model becomes And Y 1 '≥0, then the dual treatment can get the following form:
s.t.s.t.
a1≥0,a2≥0,a3≥0,a4≥0,a5≥0,a6≥0,a7≥0,a8≥0 (39)a 1 ≥ 0, a 2 ≥ 0, a 3 ≥ 0, a 4 ≥ 0, a 5 ≥ 0, a 6 ≥ 0, a 7 ≥ 0, a 8 ≥ 0 (39)
-DTa1+ΕTa2-ETa3-FTa4+KTa5-KTa6+MTa7-MTa8=B (40)-D T a 1 +Ε T a 2 -E T a 3 -F T a 4 +K T a 5 -K T a 6 +M T a 7 -M T a 8 =B (40)
其中,为对偶问题得到的对偶变量数组,由对偶问题的目标函数可知,存在对偶变量与不确定集中0-1变量的乘积,双线性形式的使得第二层子问题模型为较难求解的非线性优化问题,利用大M法将对偶问题(38)-(40)转化为线性问题。in, The dual variable array obtained for the dual problem can be known from the objective function of the dual problem, there is a product of the dual variable and the 0-1 variable in the uncertain set, and the bilinear form The second-layer sub-problem model is a nonlinear optimization problem that is difficult to solve, and the dual problems (38)-(40) are transformed into linear problems by using the big M method.
即可得,can be obtained,
s.t.s.t.
a1≥0,a2≥0,a3≥0,a4≥0,a5≥0,a6≥0,a7≥0,a8≥0 (47)a 1 ≥0,a 2 ≥0,a 3 ≥0,a 4 ≥0,a 5 ≥0,a 6 ≥0,a 7 ≥0,a 8 ≥0 (47)
-DTa1+ETa2-ETa3-FTa4+KTa5-KTa6+MTa7-MTa8=B (48)-D T a 1 +E T a 2 -E T a 3 -F T a 4 +K T a 5 -K T a 6 +M T a 7 -M T a 8 =B (48)
上述公式(46)-(50)即为将式子(41)-(45)带入式子(38)-(40)转化后的线性问题,式中,M为一取值足够大的常数。The above formulas (46)-(50) are the linear problems after bringing the formulas (41)-(45) into the formulas (38)-(40). In the formula, M is a constant with a large enough value .
(3)第三层经济运行最优子问题模型(3) Optimal sub-problem model of the third-level economic operation
第三层经济最优子问题模型是在满足了安全校验子问题模型的基础下,寻求经济最优解,该问题的目标函数为最大不确定性下的运行经济最优,每次只往规划主问题模型添加一次Benders割(可行割或最优割),其中,可行割在经济运行最优子问题模型不可行时产生;当经济运行最优子问题模型可行时,便可产生最优割。The third-level economic optimal sub-problem model is to seek the economic optimal solution on the basis of satisfying the safety check sub-problem model. Add a Benders cut (feasible cut or optimal cut) to the planning main problem model, where the feasible cut is generated when the optimal sub-problem model of economic operation is not feasible; when the optimal sub-problem model of economic operation is feasible, the optimal sub-problem model can be generated. cut.
经济运行最优子问题模型是在储能配置满足安全性校验后的对经济最优进行优化,从而得到最劣场景下的运行费用,判断是否收敛,否则向规划主问题模型返回最优割。式子(51)为经济运行最优子问题模型的目标函数及其约束条件,形式如下:The optimal sub-problem model of economic operation is to optimize the economic optimum after the energy storage configuration meets the safety check, so as to obtain the operating cost in the worst scenario, and judge whether it is converged, otherwise return the optimal cut to the planning main problem model . Equation (51) is the objective function and its constraints of the optimal sub-problem model of economic operation, in the following form:
其中,表示第三层子问题模型的决策变量集合,Λj为将规划主问题模型得到的配置方案代入第三层子问题模型后的运行成本。in, Indicates the decision variable set of the third-level sub-problem model, and Λ j is the operating cost after substituting the configuration scheme obtained from the planning main problem model into the third-level sub-problem model.
对于本问题出现的max-min形式依然需要通过对偶理论处理,变为max问题,跟安全检验子问题模型的处理方式相同,在此也不再赘述。The max-min form of this problem still needs to be dealt with by dual theory, and becomes a max problem, which is the same as the processing method of the safety check sub-problem model, so it will not be repeated here.
在此推导一下Benders割的构造形式,以最优割为例,形式如下:Here we deduce the construction form of Benders cut, taking the optimal cut as an example, the form is as follows:
假设在第k-1次迭代时,X=X(k-1),经济运行最优子问题模型的优化结果为Λj,令ΔX=X-X(k-1),则式子(52)可转化为:Assuming that at the k-1th iteration, X=X (k-1) , the optimization result of the optimal sub-problem model of economic operation is Λ j , let ΔX=XX (k-1) , then the formula (52) can be transform into:
同理可得安全性校验子问题模型和经济性可行性校验子问题模型返回的可行割为如下形式:In the same way, the feasible cuts returned by the security syndrome problem model and the economic feasibility syndrome problem model are as follows:
具体实施例子中,四季典型日光伏出力鲁棒优化结果参见附图2所示;四季典型日负荷功率鲁棒优化结果参见附图3所示;节点电压情况参见附图4所示,可见电压越限问题已合理解决;本公开规划方法下的储能系统SOC情况参见附图5所示;本发明规划方法下的储能系统充放电功率情况参见附图6所示;本发明规划方法下的储能系统配置方案参见附图7所示,基于不同不确定性的调节下,储能系统的优化配置也会有所改变。In the specific implementation example, the results of robust optimization of photovoltaic output in four seasons typical day are shown in Figure 2; the results of robust optimization of typical daily load power in four seasons are shown in Figure 3; The limit problem has been reasonably solved; the SOC of the energy storage system under the planning method of the present disclosure is shown in Figure 5; the charge and discharge power of the energy storage system under the planning method of the present invention is shown in Figure 6; the planning method of the present invention is shown in Figure 6. The configuration scheme of the energy storage system is shown in Figure 7. Under the adjustment of different uncertainties, the optimal configuration of the energy storage system will also change.
实施例子二Implementation Example 2
本说明书实施方式提供含光伏配电网中储能系统规划运行联合优化系统,通过以下技术方案实现:The implementation mode of this manual provides a joint optimization system for the planning and operation of the energy storage system in the photovoltaic distribution network, which is realized through the following technical solutions:
包括:include:
三层鲁棒优化模型建立模块,被配置为:建立配电网储能系统规划三层鲁棒优化模型,包括规划主问题模型,安全校验子问题模型和经济运行最优子问题模型;The three-layer robust optimization model building module is configured to: establish a three-layer robust optimization model for distribution network energy storage system planning, including a planning master problem model, a safety verification sub-problem model and an economic operation optimal sub-problem model;
规划主问题模型以配电网储能系统安装位置和安装容量为决策变量;The planning master problem model takes the distribution network energy storage system installation location and installation capacity as the decision variables;
安全校验子问题模型用来校验当前配电网储能系统配置在最恶劣情况下的电压越限问题,直至电压越限问题得以解决;The safety check sub-problem model is used to check the voltage limit problem of the current distribution network energy storage system configuration in the worst case until the voltage limit problem is solved;
经济运行最优子问题模型则是得到当前配电网储能系统配置在最恶劣情况下配电网的经济最优运行情况;The economical operation optimal sub-problem model is to obtain the economical optimal operation of the distribution network under the worst case of the current distribution network energy storage system configuration;
三层鲁棒优化模型求解模块,被配置为:通过对鲁棒优化模型的三层分解,同时考虑在电压越限安全性分析和经济最优运行下不同情况的最恶劣场景,通过三层迭代求解获得最优解。The three-layer robust optimization model solving module is configured to: through the three-layer decomposition of the robust optimization model, while considering the worst scenarios of different situations under the safety analysis of voltage over-limit safety and economic optimal operation, through three-layer iteration Solve for the optimal solution.
该实施例子中模块的具体实现过程可参见实施例子一中的具体公式表达,此处不再进行详细的描述。For the specific implementation process of the modules in this embodiment example, refer to the specific formula expression in Embodiment 1, and no detailed description is given here.
实施例子三Implementation example three
本说明书实施方式提供一种计算机设备,包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序,其特征在于,所述处理器执行所述程序时实现实施例子一中的含光伏配电网中储能系统规划运行联合优化方法的步骤。The implementation mode of this specification provides a computer device, including a memory, a processor, and a computer program stored on the memory and operable on the processor. It is characterized in that, when the processor executes the program, it implements the The steps of the joint optimization method for the planning and operation of the energy storage system in the photovoltaic distribution network are included.
实施例子四Implementation Example 4
本说明书实施方式提供一种计算机可读存储介质,其上存储有计算机程序,其特征在于,该程序被处理器执行时实现实施例子一中的含光伏配电网中储能系统规划运行联合优化方法的步骤。The implementation mode of this specification provides a computer-readable storage medium on which a computer program is stored, which is characterized in that, when the program is executed by a processor, the joint optimization of the planning and operation of the energy storage system in the photovoltaic power distribution network in the first implementation example is realized method steps.
可以理解的是,在本说明书的描述中,参考术语“一实施例”、“另一实施例”、“其他实施例”、或“第一实施例~第N实施例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不一定指的是相同的实施例或示例。而且,描述的具体特征、结构、材料的特点可以在任何的一个或多个实施例或示例中以合适的方式结合。It can be understood that, in the description of this specification, references to the terms "an embodiment", "another embodiment", "other embodiments", or "the first embodiment to the Nth embodiment" mean that A specific feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the described specific features, structures, and characteristics of materials may be combined in any suitable manner in any one or more embodiments or examples.
以上所述仅为本公开的优选实施例而已,并不用于限制本公开,对于本领域的技术人员来说,本公开可以有各种更改和变化。凡在本公开的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本公开的保护范围之内。The above descriptions are only preferred embodiments of the present disclosure, and are not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present disclosure shall be included within the protection scope of the present disclosure.
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