CN105160490A - Cooperative game and DEA (Data Envelopment Analysis) based method for sharing fixed cost of power transmission system - Google Patents
Cooperative game and DEA (Data Envelopment Analysis) based method for sharing fixed cost of power transmission system Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及一种基于合作博弈与DEA的输电系统固定成本分摊方法,具体涉及一种传统发电情况下的固定成本分摊,属于成本分摊领域。The invention relates to a method for apportioning fixed costs of a power transmission system based on cooperative game and DEA, in particular to a method for apportioning fixed costs in the case of traditional power generation, and belongs to the field of cost apportionment.
背景技术Background technique
一般输电系统固定成本与单个负荷(或发电)电量之间存在映射关系称之为费用-电量映射。研究表明,费用-电量映射的拓扑结构复杂,呈现强非线性、不连续、高维和多时段特征。也就是说费用的使用或者获益与费用的支付之间的信息流是不确定的、复杂的。同时,对于不以赢利为目标的电网运营者而言,其固定成本必须合理公平完全的分摊给用户(固定成本的使用者,包括发电机和电力负荷)。There is a mapping relationship between the fixed cost of a general transmission system and a single load (or power generation) electricity, which is called cost-energy mapping. Research shows that the topological structure of cost-electricity mapping is complex, showing strong nonlinearity, discontinuity, high dimensionality and multi-period characteristics. That is to say, the information flow between the use of expenses or benefits and the payment of expenses is uncertain and complicated. At the same time, for grid operators who do not aim at profit, their fixed costs must be allocated reasonably, fairly and completely to users (users of fixed costs, including generators and power loads).
输电系统固定成本具有不可解耦的特性,即固定成本的产生与具体的负荷之间并不存在一一对应的关系。人们不可能明确指出,哪个负荷应当对哪部分固定成本负责。这主要是因为,电力网络是垄断经营的,全体负荷和发电机必须同时使用同一个电力网络,它们之间复杂的交互作用共同产生了固定成本,要区分实际的交互作用责任在现实中通常无法做到。因此,输电系统固定成本的分摊问题是一个必须解决的难点问题。The fixed cost of transmission system has the characteristic of non-decoupling, that is, there is no one-to-one correspondence between the generation of fixed cost and the specific load. It is impossible to pinpoint which load is responsible for which part of the fixed costs. This is mainly because the power network is a monopoly operation, and all loads and generators must use the same power network at the same time, and the complex interactions between them jointly generate fixed costs, and it is usually impossible to distinguish the actual interaction responsibility in reality. do it. Therefore, the allocation of the fixed cost of the transmission system is a difficult problem that must be solved.
目前,在世界各国的输电系统运营中,通常按照负荷大小的比例来分摊固定成本。然而,按比例分摊法的缺点非常明显,不但容易造成负荷之间的交叉补贴,违反经济公平的市场原则,而且更重要的是,它不能够提供正确的经济激励信号,促进负荷在全网的合理分布以达到减少固定成本、节约社会资源的优化目标。At present, in the operation of transmission systems in countries all over the world, fixed costs are usually apportioned according to the proportion of load. However, the disadvantages of the proportional apportionment method are very obvious. Not only is it easy to cause cross subsidies between loads, which violates the market principle of economic fairness, but more importantly, it cannot provide correct economic incentive signals to promote load distribution in the entire network. Reasonable distribution to achieve the optimization goal of reducing fixed costs and saving social resources.
输电系统开放将向发电市场和用户提供一个规范、公正的竞争环境,它使得电力交易能够在公平、无歧视的条件下使用输电资源或设备。为了保证输电系统开放正常有序的进行,如何制定输电定价系统就显得至关重要。The opening of the power transmission system will provide a standardized and fair competition environment for the power generation market and users, which enables power transactions to use power transmission resources or equipment under fair and non-discriminatory conditions. In order to ensure the normal and orderly opening of the transmission system, how to formulate a transmission pricing system is very important.
电力工业正在全世界范围内发生着显著的变化,世界上许多国家都在进行或将要进行电力工业的改革,即放松管制,打破垄断,重组结构,建设竞争的市场机制。电力工业改革的目标在于提高电力生产效率,使电价机制合理化,提供安全、高质量的电力产品,促进电力工业的良性发展,以取得更好的经济效益和社会效益。目前,智利、阿根廷、英国、美国、澳大利亚等国的电力市场改革已经为其电力工业注入了新的活力,并激励了世界其他各国的电力市场化发展。电力市场实质上就是电力的买方和卖方相互作用以决定其电价和电量的过程。具体的讲是采用经济手段,本着公平竞争、自愿互利的原则,对电力系统中发电、输电、配电、用户等各成员组织协调运行的管理机制和执行系统的总和。电力市场建设的总体目标是引入竞争机制,优化资源配置、提供优质服务、促使电价合理化、促进电力工业的可持续发展电力市场改革的一个最重要的方面是实行输电系统开放,输电系统开放随之带来的就是输电系统的定价问题。电力市场建立以前,电力系统的发电、输电、配电系统没有分开,输电系统的成本不需要向使用输电线路的发电厂或用户单独收取,但实际上每个使用电能的用户电费中都包含了这部分输电费用。电力市场建立以后,输电公司与发电公司分开核算,输电费用与发电费用也要分开核算,而此时使用输电系统的成员将包含很多发电厂和用户,它们通过一个错综复杂的电网联系,那么如何合理的计算与分摊输电费用就成为电力市场一个亟待解决的问题。The electric power industry is undergoing significant changes all over the world. Many countries in the world are carrying out or will carry out the reform of the electric power industry, that is, deregulation, breaking monopoly, restructuring, and building a competitive market mechanism. The goal of power industry reform is to improve power production efficiency, rationalize the electricity price mechanism, provide safe and high-quality power products, promote the healthy development of the power industry, and achieve better economic and social benefits. At present, the power market reforms in Chile, Argentina, the United Kingdom, the United States, Australia and other countries have injected new vitality into their power industries and stimulated the development of power markets in other countries around the world. The electricity market is essentially a process in which buyers and sellers of electricity interact to determine their electricity prices and quantities. Specifically speaking, it is the sum of the management mechanism and execution system that organizes the coordinated operation of power generation, transmission, distribution, and users in the power system by using economic means and in line with the principles of fair competition, voluntariness and mutual benefit. The overall goal of power market construction is to introduce a competitive mechanism, optimize resource allocation, provide high-quality services, promote the rationalization of electricity prices, and promote the sustainable development of the power industry. One of the most important aspects of power market reform is to implement the opening of the transmission system, and the opening of the transmission system What brings is the pricing problem of the transmission system. Before the establishment of the electricity market, the power generation, transmission, and distribution systems of the power system were not separated, and the cost of the transmission system did not need to be charged separately to the power plant or user using the transmission line, but in fact, each user who uses electric energy included it in the electricity fee This part of the transmission cost. After the establishment of the electricity market, the transmission company and the power generation company are accounted for separately, and the transmission fee and the power generation fee are also separately accounted for. At this time, the members who use the transmission system will include many power plants and users, and they are connected through an intricate grid. How reasonable? The calculation and allocation of transmission costs has become an urgent problem in the electricity market.
输电定价系统包括输电费用的计算与分摊,其过程可以看作是在考虑了输电公司的收支平衡和适当的盈利情况下,输电费用在使用输电线路的发电厂或用户之间的分配问题。电力系统的输电费用一般由两部分构成:一部分是反映输电系统的运行费用,也称为可变成本,主要包括电能的损耗成本、阻塞成本与基于合作博弈核仁解的输电固定费用分摊成本;另一部分是反映输电线路的投资建设费用,又称为固定成本,包括修建输电线路、购买设备的费用、运行管理和维护费、折旧费以及投资成本的回报率等,由于输电系统的固定成本在输电费用中占有很大比重,并且输电固定成本的分摊方法同样适用于输电系统可变成本(网损、阻塞费用)的分摊,本发明中仅以输电固定成本为例,探讨费用的分摊方法。The transmission pricing system includes the calculation and apportionment of transmission costs. The process can be regarded as the allocation of transmission costs among power plants or users using transmission lines, taking into account the balance of payments and appropriate profitability of the transmission company. The transmission cost of the power system is generally composed of two parts: one part reflects the operating cost of the power transmission system, also known as variable cost, which mainly includes the loss cost of electric energy, the congestion cost and the fixed cost sharing cost of power transmission based on the cooperative game kernel solution The other part is to reflect the investment and construction costs of transmission lines, also known as fixed costs, including the construction of transmission lines, the cost of purchasing equipment, operation management and maintenance costs, depreciation costs, and the rate of return on investment costs, etc., due to the fixed costs of the transmission system Occupy a large proportion in power transmission costs, and the apportionment method of the fixed cost of power transmission is also applicable to the apportionment of variable costs (network losses, congestion costs) of the power transmission system. In the present invention, only the fixed cost of power transmission is taken as an example to discuss the apportionment of expenses method.
输电费用具体的分配方式由电力法和电力市场运营的规约确定,在不同的场合或为达到不同的运行目的,可以实行不同的定价模式,相应的,在不同的定价模式下也可以采用不同的分配形式。如成本结算时需要满足输电系统投资费用的完全回收问题,可以采用综合成本分摊法;若为了给用户和发电厂提供明确的系统运行状态信息,促进网络资源良性发展,可以采用边际成本法。但无论采用哪种方法都需要尽可能地保证输电公司的年收支平衡,能为用户和发电厂提供长期或短期的经济信息,并对复杂的输电网和交易网具有可行性和透明性。The specific allocation method of transmission costs is determined by the Electricity Law and the regulations on the operation of the electricity market. Different pricing models can be implemented on different occasions or to achieve different operational purposes. Correspondingly, different pricing models can also be adopted under different pricing models. distribution form. If the cost settlement needs to meet the problem of complete recovery of the investment cost of the transmission system, the comprehensive cost allocation method can be used; if in order to provide users and power plants with clear system operation status information and promote the healthy development of network resources, the marginal cost method can be used. However, no matter which method is adopted, it is necessary to ensure the annual balance of the transmission company's income and expenditure as much as possible, to provide long-term or short-term economic information for users and power plants, and to be feasible and transparent to the complex transmission network and trading network.
国内外研究输电费用计算与分摊的方法很多,从总体上看,各种方法由于都不能在兼顾完全回收输电成本和提供经济信号的同时,公平的将输电固定成本分摊到各个使用输电网的发电厂或用户,故至今为止尚未对输电定价系统形成公认的成熟理论,各国的做法相差甚远,理论与实践之间仍然存在较大差距。There are many methods for calculating and apportioning transmission costs at home and abroad. On the whole, all methods cannot fairly allocate the fixed costs of transmission to each power generation that uses the transmission network while taking into account the complete recovery of transmission costs and the provision of economic signals. Therefore, no mature theory has been formed on the transmission pricing system. The practices of various countries are far from each other, and there is still a large gap between theory and practice.
发明内容Contents of the invention
本发明所要解决的技术问题是:提供一种基于合作博弈与DEA的输电系统固定成本分摊方法,满足有效性、加法性、非负性和规模不变性公理,是一种比较合理的固定成本分摊方法。The technical problem to be solved by the present invention is to provide a fixed cost allocation method for power transmission system based on cooperative game and DEA, which satisfies the axioms of validity, additiveness, non-negativity and scale invariance, and is a relatively reasonable fixed cost allocation method method.
本发明为解决上述技术问题采用以下技术方案:The present invention adopts the following technical solutions for solving the problems of the technologies described above:
一种基于合作博弈与DEA的输电系统固定成本分摊方法,包括如下步骤:A transmission system fixed cost allocation method based on cooperative game and DEA, comprising the following steps:
步骤1,获取输电系统中各用户的基本情况,包括:负荷季节、工作制度、峰谷电价时段划分、峰谷平电价比、电能质量及用电量;Step 1. Obtain the basic situation of each user in the transmission system, including: load season, working system, peak-valley power price period division, peak-valley average power price ratio, power quality and power consumption;
步骤2,对各用户的基本情况进行归一化处理,得到各用户的标准化指标;Step 2, normalize the basic situation of each user to obtain the standardized index of each user;
步骤3,将步骤2得到的各用户的标准化指标数据,在有保证区域约束下,利用DEA联盟博弈法核仁解计算各用户的分摊比例;Step 3, use the standardized index data of each user obtained in step 2, under the constraints of the guaranteed area, use the kernel solution of the DEA alliance game method to calculate the apportionment ratio of each user;
步骤4,将步骤3得到各用户的分摊比例乘以固定成本,得到各用户应分摊的成本。Step 4: Multiply the apportionment ratio of each user obtained in Step 3 by the fixed cost to obtain the cost to be apportioned by each user.
优选的,步骤2所述标准化指标包括:直购电量指标、电能质量指标以及分时电价指标。Preferably, the standardized indicators in step 2 include: direct power purchase indicators, power quality indicators, and time-of-use electricity price indicators.
优选的,所述分时电价指标的计算公式为:j=1,…,n,其中,Dj为第j个用户的分时电价指标,n为用户总数,l为针对各用户划分的典型日数,Ta为典型日a对应的天数,αa:1:βa为典型日a的峰、平、谷电价比,tja,f、tja,p、tja,g分别为用户j在典型日a的峰、平、谷利用小时数。Preferably, the calculation formula of the time-of-use electricity price index is: j=1,...,n, where D j is the time-of-use electricity price index of the jth user, n is the total number of users, l is the number of typical days divided for each user, T a is the number of days corresponding to the typical day a, α a :1:β a is the peak, average, and valley electricity price ratio of a typical day a, t ja,f , t ja,p , and t ja,g are the peak, average, and valley utilization hours of user j on a typical day a, respectively.
优选的,步骤3所述DEA联盟博弈法核仁解的计算公式为:Tj/ΣTj-yj,其中,Tj=Djω1+Qjω2+qjω3,Dj、Qj、qj分别为用户j的分时电价指标、电能质量指标、直购电量指标,ω1、ω2、ω3分别为分时电价指标、电能质量指标、直购电量指标对应的权重值,yj为用户j参加联盟后能够减少分摊的固定成本比例。Preferably, the formula for calculating the kernel solution of the DEA alliance game method in step 3 is: T j /ΣT j -y j , wherein, T j =D j ω 1 +Q j ω 2 +q j ω 3 , D j , Q j , and q j are the time-of-use electricity price index, power quality index, and direct purchase electricity index of user j respectively, and ω 1 , ω 2 , and ω 3 are the time-of-use electricity price index, power quality index, and direct purchase electricity index respectively. Weight value, y j is the fixed cost ratio that user j can reduce after joining the alliance.
优选的,所述yj的计算方法为核仁分摊法。Preferably, the calculation method of y j is the kernel allocation method.
优选的,所述ω1、ω2、ω3的计算公式为:Preferably, the calculation formulas of ω 1 , ω 2 , ω 3 are:
其中,(i=1,…,m,j=1,…,n),S为用户集合N=(1,…,n)的任一子集构成的联盟,c(S)为联盟S的最小联盟分摊成本,Xij为联盟S中第j个用户的第i个标准化指标的值,m为所有标准化指标的个数,n为所有用户的个数,m=3。in, (i=1,...,m,j=1,...,n), S is the alliance formed by any subset of the user set N=(1,...,n), c(S) is the smallest alliance S Cost sharing, Xij is the value of the i-th standardized indicator of the j-th user in the alliance S, m is the number of all standardized indicators, n is the number of all users, m=3.
本发明采用以上技术方案与现有技术相比,具有以下技术效果:Compared with the prior art, the present invention adopts the above technical scheme and has the following technical effects:
1、本发明采用基于DEA联盟博弈的方法,使得在满足各用户利益最大化的基础上,通过对DEA联盟博弈中加入AR(保证区域)限制,在限定的权重范围内计算出取得最优的、合理的权重,使各方得到满意的分摊结果。1. The present invention adopts a method based on the DEA alliance game, so that on the basis of satisfying the maximization of the interests of each user, by adding AR (guaranteed area) restrictions to the DEA alliance game, the optimal weight is calculated within the limited weight range. , Reasonable weight, so that all parties can get a satisfactory apportionment result.
2、本发明所有用户(即固定成本的使用者)共同使用了整个电网,电网固定成本是所有用户共同作用产生的,它们之间复杂的交互作用共同产生了固定成本,要区分实际的交互作用责任在现实中通常很难做到。但从合作博弈的角度,用户之间构成了事实上的合作关系。采用基于DEA联盟博弈的方法发明输电系统固定成本分摊问题,具有公理优势。2. All users of the present invention (i.e. users with fixed costs) use the entire power grid together, and the fixed costs of the power grid are generated by the joint action of all users, and the complex interactions between them jointly produce fixed costs, so it is necessary to distinguish the actual interaction Responsibility is often difficult to achieve in reality. But from the perspective of cooperative game, users constitute a de facto cooperative relationship. Using the method based on the DEA alliance game to invent the fixed cost allocation problem of the transmission system has the advantage of axiom.
3、本发明以核仁解作为多人合作博弈的分配方法,具有其他方法所不具备的优点,并能保证联盟稳定。3. The present invention uses the kernel solution as the distribution method of multi-person cooperative game, which has advantages that other methods do not have, and can ensure the stability of the alliance.
附图说明Description of drawings
图1是本发明基于合作博弈与DEA的输电系统固定成本分摊方法的整体流程图。FIG. 1 is an overall flow chart of the method for allocating fixed costs of a power transmission system based on cooperative game and DEA in the present invention.
图2是无AR约束下核仁法计算出的输电系统固定成本的分摊比例图。Figure 2 is a graph of the allocation ratio of the fixed cost of the transmission system calculated by the Kernel method without AR constraints.
图3是本发明有AR约束下核仁法计算出的输电系统固定成本的分摊比例图。Fig. 3 is a distribution ratio diagram of the fixed cost of the power transmission system calculated by the Kernel method under AR constraints in the present invention.
图4是各用户对4种方法(邮票法、Shapely值、无约束核仁法、有约束核仁法)固定成本分摊比例的对比图。Figure 4 is a comparison chart of the fixed cost allocation ratio of each user for the four methods (stamp method, Shapely value, unconstrained kernel method, and constrained kernel method).
具体实施方式Detailed ways
下面详细描述本发明的实施方式,所述实施方式的示例在附图中示出,其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施方式是示例性的,仅用于解释本发明,而不能解释为对本发明的限制。Embodiments of the present invention are described in detail below, examples of which are shown in the 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 by referring to the figures are exemplary only for explaining the present invention and should not be construed as limiting the present invention.
合作博弈论是微观经济学的一个重要分支。经济学理论已经证明,基于合作博弈论的固定成本分摊方法满足有效性、加法性、非负性和规模不变性公理,是一种比较合理的固定成本分摊方法。事实上,经济学家已经在公用事业网络费用分摊问题上成功地运用了这种分摊方法,如供水系统费用的分摊和电信网络运营费用的分摊等等,取得了良好的分摊效果。核仁法是求解合作博弈问题的方法之一,主要用在同时使用某项设施产生的共同费用在合作各方之间的分配。Cooperative game theory is an important branch of microeconomics. Economic theory has proved that the fixed cost allocation method based on cooperative game theory satisfies the axioms of effectiveness, additiveness, non-negativity and scale invariance, and is a relatively reasonable fixed cost allocation method. In fact, economists have successfully applied this apportionment method on public utility network cost apportionment, such as water supply system cost apportionment and telecommunication network operating cost apportionment, etc., and achieved good apportionment results. The kernel method is one of the methods for solving cooperative game problems, and it is mainly used in the distribution of the common costs generated by the simultaneous use of a certain facility among the cooperative parties.
数据包络分析(DEA)是一种数学规划方法,也是一种广泛认可的效率评价方法。它运用多目标规划理论和基于投入产出相对绩效的非参数方法,量化评价了多投入—多产出模式下部门的相对有效性。数据包络分析方法一般被用来评价一组多个决策单元(DecisionMakingUnit,DMU)之间的相对效率。决策单元可以理解为在社会、经济和管理领域中投入一定要素以产生一定产品的实体。在该系统中,具有相同目标、相同外部环境和相同投入产出指标的同类型决策单元可以构成一个决策单元集合。以决策单元的投入产出指标数据作为评价依据,可以对各决策单元的相对效率进行排序,并指出非有效决策单元。其中,投入指标用来代表决策单元在相关经济活动中耗用的资源量;产出指标表示决策单元在投入要素的前提下获得的经济产出。Data envelopment analysis (DEA) is a mathematical programming method and a widely recognized efficiency evaluation method. It uses multi-objective programming theory and non-parametric methods based on the relative performance of input and output to quantitatively evaluate the relative effectiveness of departments under the multi-input-multi-output model. The data envelopment analysis method is generally used to evaluate the relative efficiency among a group of multiple decision-making units (DecisionMakingUnit, DMU). A decision-making unit can be understood as an entity that invests certain elements in the social, economic and management fields to produce certain products. In this system, the same type of decision-making units with the same goal, the same external environment and the same input-output indicators can form a set of decision-making units. Using the input-output index data of decision-making units as the evaluation basis, the relative efficiency of each decision-making unit can be sorted, and ineffective decision-making units can be pointed out. Among them, the input index is used to represent the amount of resources consumed by the decision-making unit in related economic activities; the output index represents the economic output obtained by the decision-making unit on the premise of input factors.
对输电系统固定成本分摊,目前有嵌入成本法(又称综合成本法)和边际成本法,其中嵌入成本法主要包括邮票法(postagestampmethod)、合同路径法(contractpathmethod)、边界潮流法(boundaryflowmethod)、MW-km法;边际成本法又有短期和长期边际成本法之分。For the fixed cost allocation of the transmission system, there are currently embedded cost methods (also known as comprehensive cost methods) and marginal cost methods. The embedded cost methods mainly include postage stamp method, contract path method, boundary flow method, MW-km method; marginal cost method is divided into short-term and long-term marginal cost method.
针对我国电网运行特点,提出了一种综合考虑分时电价、电能质量和购电量的多因素大用户转运费用固定成本的综合分摊方法,即修正的邮票法,较好地解决了这个问题。但是由于其权重的确定由电网和用户交互确定,增加了交易的难度。Aiming at the operation characteristics of my country's power grid, a comprehensive allocation method for the fixed cost of multi-factor large user transshipment costs, which considers time-of-use electricity price, power quality and purchased electricity, is proposed, that is, the modified stamp method, which solves this problem better. However, since the determination of its weight is determined by the interaction between the power grid and users, it increases the difficulty of transactions.
基于DEA联盟博弈的方法是DEA研究的一个新方向,用于处理固定成本分摊问题,有良好的效果。本发明使用DEA联盟博弈的方法,使得在满足各用户利益最大化的基础上,通过对DEA联盟博弈中加入保证区域(AR)限制,在限定的权重范围内计算出取得最优的、合理的权重,使各方得到满意的分摊结果。The method based on DEA coalition game is a new direction of DEA research, which is used to deal with the problem of fixed cost allocation and has good results. The present invention uses the DEA alliance game method, so that on the basis of maximizing the interests of each user, by adding the guarantee area (AR) restriction to the DEA alliance game, the optimal and reasonable weight is calculated within the limited weight range. Weights, so that all parties can get a satisfactory apportionment result.
合作博弈是指系统中若干个参与者相互结合成联盟体(coalition),共同协作获得联盟体内的最大利益,然后再将所得共同利益在联盟系统内部进行分配。合作博弈分配解的概念主要包括核心(core)、夏普利值(Shapley)、核仁(nucleolus)等,本发明中主要采用核仁法来解决输电系统固定成本分摊问题。Cooperative game means that several participants in the system combine with each other to form a coalition, and work together to obtain the maximum benefit in the coalition, and then distribute the common benefits in the coalition system. The concepts of cooperative game allocation solution mainly include core, Shapley value, nucleolus, etc. In the present invention, the nucleolus method is mainly used to solve the fixed cost allocation problem of the transmission system.
本发明基于合作博弈与DEA的输电系统固定成本分摊方法的流程如图1所示,基于该流程图的实施例采用的数据如表1所示。为了简化起见,该实施例直接给出了5个电能质量等级:A、B、C、D、E,对应的电能质量指标为5、4、3、2、1。首先,我们要对数据进行无量纲归一化,得到表2。The process flow of the transmission system fixed cost allocation method based on cooperative game and DEA in the present invention is shown in FIG. 1 , and the data used in the embodiment based on the flow chart is shown in Table 1. For the sake of simplicity, this embodiment directly provides five power quality grades: A, B, C, D, and E, and the corresponding power quality indexes are 5, 4, 3, 2, and 1. First, we need to perform dimensionless normalization on the data to obtain Table 2.
表1各用户基本情况Table 1 Basic information of each user
表2各用户的标准化指标Table 2 Standardized indicators for each user
数据包络分析:设输电系统中各用户的集合N=(1,…,n)的任一子集S构成一个联盟。例如{1,2},{1,2,4}等。定义联盟S的值为:Data envelopment analysis: Let any subset S of user sets N=(1,...,n) in the power transmission system form an alliance. For example {1,2}, {1,2,4} etc. Define the value of alliance S as:
其中,Xij为联盟S中第j个用户的第i个标准化指标的值,m为所有标准化指标的个数,n为所有用户的个数,本发明中n取4,m取3。Wherein, X ij is the value of the i-th standardized indicator of the j-th user in the alliance S, m is the number of all standardized indicators, and n is the number of all users. In the present invention, n is 4, and m is 3.
组成联盟S的目的是获得最小的联盟分配成本c(S),可以通过解以下线性规划:The purpose of forming an alliance S is to obtain the minimum alliance allocation cost c(S), which can be solved by solving the following linear programming:
其中,ωi为xi(S)对应的权重值。Wherein, ω i is the weight value corresponding to x i (S).
根据下式计算各用户的综合指标:Tj=Djω1+Qjω2+qjω3,其中,Dj、Qj、qj分别为分时电价指标、电能质量指标、直购电量指标。Calculate the comprehensive index of each user according to the following formula: T j = D j ω 1 + Q j ω 2 + q j ω 3 , where D j , Q j , q j are time-of-use electricity price index, power quality index, direct Power purchase index.
根据成本分摊公式可以得到每个用户的分摊成本:C′j=C×Tj/ΣTj。The apportioned cost of each user can be obtained according to the cost apportionment formula: C′ j =C×T j /ΣT j .
核仁法:定义联盟收益函数如下:其中c(S)为联盟特征函数。Kernel method: define the alliance revenue function as follows: where c(S) is the coalition feature function.
minz=y5 minz=y 5
s.ty1+y2+y3+y4+y5=1s.ty 1 +y 2 +y 3 +y 4 +y 5 =1
y1+y2+y5≥c(A,B)y 1 +y 2 +y 5 ≥c(A,B)
y1+y3+y5≥c(A,C)y 1 +y 3 +y 5 ≥c(A,C)
y1+y4+y5≥c(A,D)y 1 +y 4 +y 5 ≥c(A,D)
y2+y3+y5≥c(B,C)y 2 +y 3 +y 5 ≥c(B,C)
y2+y4+y5≥c(B,D)y 2 +y 4 +y 5 ≥c(B,D)
y3+y4+y5≥c(C,D)y 3 +y 4 +y 5 ≥c(C,D)
y1+y2+y3+y5≥c(A,B,C)y 1 +y 2 +y 3 +y 5 ≥c(A,B,C)
y1+y2+y4+y5≥c(A,B,D)y 1 +y 2 +y 4 +y 5 ≥c(A,B,D)
y1+y3+y4+y5≥c(A,C,D)y 1 +y 3 +y 4 +y 5 ≥c(A,C,D)
y2+y3+y4+y5≥c(B,C,D)y 2 +y 3 +y 4 +y 5 ≥c(B,C,D)
y1+y5≥c(A)y 1 +y 5 ≥c(A)
y2+y5≥c(B)y 2 +y 5 ≥c(B)
y3+y5≥c(C)y 3 +y 5 ≥c(C)
y4+y5≥c(D)y 4 +y 5 ≥c(D)
利用matlab求解y1、y2、y3、y4出的值,它们分别代表各用户参加联盟后能够减少分摊的固定成本比例,式中联盟的值均采用有AR约束下的联盟值。可得出联盟后各用户可以减少承担的固定成本为:Use matlab to solve the values of y 1 , y 2 , y 3 , and y 4 , which respectively represent the fixed cost ratio that each user can reduce after joining the alliance. The values of the alliance in the formula all adopt the alliance value under the AR constraint. It can be concluded that the fixed cost that each user can reduce after the alliance is:
y′j=yj×Cy′ j =y j ×C
因此,各用户需要分摊的固定成本为: Therefore, the fixed cost that each user needs to share is:
根据核仁分摊法,采用表3和表5中的数据进行计算,分别是无AR约束和有AR约束,可知根据表3的信息,核存在的个体理性、合作理性、整体理性不一定能满足,所以在无AR约束下的联盟博弈中核不存在,见表4。有AR约束下的联盟博弈中核是存在的。核仁分摊法得到的在有AR约束下的联盟博弈的结果见表6。表4和表6分别对应图2和图3。According to the nucleolus apportionment method, the data in Table 3 and Table 5 are used for calculation, which are without AR constraints and AR constraints respectively. It can be seen that according to the information in Table 3, individual rationality, cooperative rationality, and overall rationality in the kernel may not be able to satisfy , so the kernel does not exist in the coalition game without AR constraints, see Table 4. The core exists in the coalition game with AR constraints. See Table 6 for the results of the coalition game under AR constraints obtained by the kernel apportionment method. Table 4 and Table 6 correspond to Figure 2 and Figure 3, respectively.
表3无AR约束条件下各联盟特征函数Table 3 The characteristic functions of each alliance under the condition of no AR constraint
表4无AR约束下核仁分摊法的值Table 4 Values of nucleolus apportionment method without AR constraints
表5有AR约束条件下各联盟特征函数Table 5 has the characteristic functions of each alliance under AR constraints
表6有AR约束下核仁分摊法的值Table 6 has the value of nucleolus apportionment method under AR constraints
如图4所示,为各用户对4种方法(邮票法、Shapely值、无约束核仁法、有约束核仁法)固定成本分摊比例的对比图。通过对四种方法的比较,更进一步的说明了采用AR-DEA联盟博弈核仁法的合理性。As shown in Figure 4, it is a comparison chart of the fixed cost allocation ratio of each user for the four methods (stamp method, Shapely value, unconstrained kernel method, and constrained kernel method). Through the comparison of the four methods, the rationality of using the AR-DEA alliance game kernel method is further illustrated.
以上实施例仅为说明本发明的技术思想,不能以此限定本发明的保护范围,凡是按照本发明提出的技术思想,在技术方案基础上所做的任何改动,均落入本发明保护范围之内。The above embodiments are only to illustrate the technical ideas of the present invention, and cannot limit the protection scope of the present invention with this. All technical ideas proposed according to the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. Inside.
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