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1、Efficient Planning of Substation AutomationSystem CablesAbstract The manual selection and assignment of appropriate cables to the interconnections between the devices of a substation automation system is a major cost factor in substation automation system design. This paper discusses about the model

2、ing of the substation automation system cable planning as an integer linear optimization problem to generate an efficient cable plan for substation automation systems.1 IntroductionCabling between different devices of a substation automation system (SAS) is a major cost factor in the SAS design proc

3、ess. Usually computer aided design software is used to create the design templates of SAS devices and their interconnections. The design templates are then instantiated in a SAS project and the cables are manually assigned to the connections. The selection and assignment of cables to connections mus

4、t follow certain engineering rules. This engineering process is usually time consuming and can cause engineering errors, thereby increasing the engineering cost. Apparently, the SAS cable planning is related to the well known bin packing problem. The SAS cable planning can be formulated as an intege

5、r linear optimization problem with the cable engineering rules expressed as a set of linear constraints and a cost objective for minimizing the total cable cost. This paper describes the formulation of SAS cable planning problem as an integer linear optimization problem and presents the results for

6、some representative test cases. To the best of the authors knowledge the work is the first of the kind to study SAS cable planning. The paper is organized as follows. Section 2 presents an overview of the SAS cable planning process. Section 3 expresses the SAS cable planning problem as an integer li

7、near optimization problem. The results obtained by solving the optimization problem using some solvers is presented in Section 4. Section 5 draws some conclusions of this work.2 SAS Cable PlanningThe SAS cable planning begins after the system design phase of a SAS project.The SAS cable planning is a

8、t present done manually by computer aided designT. Achterberg and J.C. Beck (Eds.): CPAIOR 2011, LNCS 6697, pp. 210214, 2011.cSpringer-Verlag Berlin Heidelberg 2011Efficient Planning of Substation Automation System Cables 211Fig. 1. Fields, devices and their interconnections(CAD) engineers. The diff

9、erent design templates corresponding to the actual devices of a SAS are instantiated in one or more CAD jobs. Each job consists of one or more sheets and each sheet has fields which are logical groups of devices as shown in Figure 1. Moreover, a field corresponds to a physical assembly interface cla

10、ss e.g. Metering box, Protection cubicle etc. Each device has pins which are the physical interconnection interfaces of the device. A valid connection is a unique path between exactly two pins and every connection carries a physical signal. A signal can traverse over one or more connections. Each co

11、nnection is assigned to exactly one of the conductors of a cable. The type of cables to which the connections are assigned is based on cable engineering rules. The cable engineering rules can be classified into two types, namely the cable rules and the signal rules. The cable rules specify the allow

12、ed cable types for a set of connections. It can also specify the number of spare conductors which must be left free in each instance of the allowed cable types. The signal rules specify restrictions on allocation of connections which carry signals that should not be allocated to the same cable or pr

13、eferably allocated to the same cable. The current practice is to manually select and assign cables to connections according to the cable engineering rules. This procedure is time consuming and can cause engineering errors thereby increasing the engineering cost. In what follows is the formulation of

14、 the SAS system cable planning as an integer linear optimizationproblem with which a more efficient cable plan for SAS can be generated.3 Integer Linear Program FormulationThe SAS cable planning problem is divided into sub problems where each sub problem considers connections between distinct set of

15、 field pairs within a given set of CAD jobs. The rationale behind this decomposition is that the cable plan should consider the physical assembly interface classes and should not mix connections between two different source or destination physical assembly interface classes in one cable. This is ens

16、ured by deriving a cable plan for each distinct field pairs. Let C = 1, 2, 3, . . .,N represent the set of all connections between two field pairs, where N is the total number of connections, and K = 1, 2, 3, . . .,M212 T. Sivanthi and J. Polandrepresent the set of all cable types, where M is the to

17、tal number of cable types in a sub problem. In a cable instance, there can be one or more connections and we refer to the connection with lowest index among all connections in the cable instance as the leader and the other connections as the followers. This implies that all connections except the fi

18、rst connection in C can either be a leader or follower. Moreover, based on the signal rules a set of connection pairs X can be derived where each (i,i) X represents the connections i andi that must not be assigned to the same cable. Let C be the set of connection pairs (i,i) where i,i C, i i, (i,i)

19、/ X. We introduce the following binary variable Xi,i, where (i,i) C, which when true implies that connection i is a follower of a leaderi. (1)Similarly, based on the cable rules a set of connection cable pairs Y can be derived where each (i, j) Y implies that cable type j is not allowed for connecti

20、on i.Let K be the set of connection cable pairs (i, j), where i C, j K, (i, j) / Y. We introduce the following binary variable Yi,j, where (i, j) K , which when true implies that the leader i is assigned to an instance of cable type j. (2)Table 1 illustrates all binary variables corresponding to the

21、 example shown in Figure 1 for the case with two cable types K1 and K2. It is assumed that connections C1 and C3 cannot be assigned to the same cable and K1 is not an allowed cable type for connection C3. As mentioned before all connections except the first connection, which must be a leader, can ei

22、ther be a leader or follower. This is ensured by the following constraint. （3）A connection which is a leader in a cable cannot be a follower of a leader in another cable. This is expressed by the following constraint. （4）An implicit constraint of the cable planning problem is the capacity constraint

23、which implies that the number of connections assigned to a cable must be lessTable 1. Binary variables corresponding to Figure 1 exampleEfficient Planning of Substation Automation System Cables 213 than the capacity requirement i.e. the total number of conductors in the cable minus the spare core re

24、quirement of the cable. Let Uj and Sj be the total number of conductors and the required spare core in cable type j, then the following equation expresses the capacity constraint. In this equation, if the connection I is a leader then the sum of all connections including the connectioni and its foll

25、owers is less than the capacity requirement of the cable type j to whichi is assigned, otherwise the equation is by default satisfied. （5）In addition the problem formulation needs the following constraint to avoid indirect pairing of connections i and i which have the same leaderi but (i, i) is in X

26、. （6）Similarly, the following constraint prohibits a follower to choose a leader whose selected cable type is not one of the allowed cable types of the follower. （7）Finally, the sub problem may include a set of preferred allocation rules which specify that all connections carrying certain signals sh

27、ould preferably be assigned to the same cable. This is achieved by introducing a penalty cost in the objective function. The penalty cost will increase when not all connections of any preferred allocation rule have the same leader or when there exists more than one leader among the connections withi

28、n any preferred allocation rule. The constraints related to preferred allocation rules are not expressed due to space limitation. The objective of the cable planning problem is then specified asminimize （8）where Mj is the cost of cable type j. The optimization of the above problem results in a SAS c

29、able plan with minimal total cable cost.4 ResultsIn order to conduct a meaningful experiment, due to the lack of sufficient real sub-problem instances, we generated random sub problem instances with nine cable types. The number of connections N in each sub problem instance is varied from 10 to 50. E

30、ach cable type has a cable cost which is discrete uniformly distributed between 1 and 2 and has a total number of conductors which is discrete uniformly distributed between 1 and 5. Each connection is allowed to be assigned to M out of the nine cable types, where M is discrete uniformly distributed

31、between 3 and 6. Furthermore, the number of connection pairs which214 T. Sivanthi and J. PolandFig. 2. Performance obtained with different solverscannot be assigned to the same cable is on average equal to (N 2)/3. It should be noted that the sub problem instances generated are harder than typical S

32、AS cable planning sub problems. The instances are solved using different solvers and the results obtained are shown in Figure 2. The left plot shows the median computation time to obtain the optimal solution with some non-commercial solvers SCIP-SOPLEX 2 3 4, CBC 5 and commercial solver CPLEX 6. The

33、 right plot shows the performance of the non-commercial solvers relative to CPLEX. It is observed that SCIP-CLP 2.0.1 which is on average 3.6 times slower than CPLEX scales well with increasing problem size unlike CBC-CLP 2.6.2 which scales poorly and is on average 13.9 times slower than CPLEX. The

34、salient result of our experiment is that even the harder than typical instances are fairly easily solved, therefore the integer linear optimization formulation clearly offers time and cost efficient solution for SAS cable planning.5 ConclusionThis paper presented the modeling of substation automatio

35、n system cable planning as an integer optimization problem to generate a more efficient cable plan for substation automation systems. The results obtained for typical test cases show that the integer linear optimization formulation clearly offers time and cost efficient solution for the substation a

36、utomation system cable planning.References1. Brand, K.-P., et al.: Substation Automation Handbook. Utility Automation Consulting(2003)2. Achterberg, T.: SCIP: Solving Constraint Integer Programs. J. Math. Prog.Comp. 1(1), 141 (2009)3. Achterberg, T.: Constraint Integer Programming, Technische Univer

37、sitat Berlin(2007)4. SCIP Mixed Integer Programming Solver, http:/zibopt.zib.de5. CLP Linear Programming Solver, https:/projects.coin-or.org/Clp6. CPLEX Optimizer, cplex-optimizer变电站电缆自动化系统的有效计划Thanikesavan Sivanthi and Jan PolandABB Switzerland Ltd, Corporate Research,Segelhofstrasse 1K, 5405, Bade

38、n-D attwil, Aargau, Switzerland摘要：手动选择和适当的分配电缆，在变电站自动化系统的设计时，对变电站自动化系统之间的联系的是一个主要成本因素。本文论述了变电站自动化系统电缆计划的建模作为一个整数线性优化问题来生成一个高效的变电站电缆自动化系统的计划。1简介在变电站自动化系统设计(SAS)过程中，不同设备之间的接线是变电站自动化系统的一个主要成本因素。通常计算机辅助设计软件是用来创建变电站自动化系统设计模板的和设备之间的联系。然后手动分配连接变电站自动化系统设计模板项目和电缆。选择和分配电缆连接必须遵循一定的工程规则。这个过程通常是耗费时间,并可导致工程错误增加工程

39、的成本的工程。显然，SAS电缆规划是众所周知的装箱问题。SAS公司的电缆计划可以制定为一个整数线性优化问题，与电缆工程规则表示为一组线性约束和成本目标的总成本最小化电缆。本文描述了SAS电缆规划问题作为一个整数线性优化问题,提出了具有代表性的测试用例的结果方案。对作者的来说最大的收获是学习SAS电缆规划。本文组要内容如下。第二节介绍SAS电缆规划过程。第三节表述了SAS电缆规划问题作为一个整数线性优化问题。第四节通过求解该优化问题获得的结果，提出了一些解决方案。第五节得出结论这样的工作。2 SAS电缆计划SAS电缆计划从系统设计阶段的情景应用程序项目开始。SAS电缆规划是目前由计算机（CAD）

40、辅助设计工程师手工完成的。图1 各设备之间的联系不同的设计模板对于实际设备情景应用程序是在实例化一个或多个CAD工作。每个任务由一个或多个表,每个表的字段是逻辑组设备如图1所示。此外，一个字段对应于一个物理装配接口测量框、保护隔间等。每个设备都有物理连接的接口装置。一个有效的连接是一个独特的通道，并且每个连接携带一个物理信号。一个信号可以遍历一个或多个连接。每个连接被指定到唯一的一个导体的线缆。这个类型的电缆的连接分配是基于电缆工程规则。电缆工程规则可以分为两种类型，即电缆规则和信号规则。电缆规则指定了允许的电缆类型的一组连接，它还可以指定备用导体的数量和每个实例允许的电缆类型。信号规则指定配

41、置的连接限制携带的信号,不应该被分配给相同的电缆或最好是分配给相同的电缆。当前实践是手动选择和分配电缆连接称工程规则。这个过程是费时并可能导致工程错误从而增加成本的工程。接下来的是把制订SAS系统电缆计划作为一个整数线性优化问题,这一个更高效的电缆计划。3 整数线性规划制定SAS电缆规划问题划分为子问题,其中每个子问题考虑到在不同的领域之间的连接，再给出一组正确的CAD工作。这种分解背后的基本原理是,电缆计划应该考虑物理装配接口类,不应该混之间的联系两个不同的源或目标物理装配接口类在一份电报。这是确保的派生一个有线电视计划对每个不同的领域。让代表的所有连接两个区域之间的双,其中N是总数量的连接

42、,并且代表的所有电缆类型，在是累计有线数字类型的子问题。在一份实例中，可以有一个或多个连接,我们将该连接与最低指数在所有连接的电缆实例作为领导者和其他连接的追随者。这意味着所有连接除了第一个连接在C可以是一个领导者或是跟随者。显然，基于信号规则一组连接双可以派生每个代表了和联系,一定不能被分配到相同的电缆。让是组连接双在那里，。我们引入下列二进制变量，在,当它真的意味着连接是追随者领导的一个。 （1）表1说明了所有二进制变量对应于图1所示的例子为案例和两个电缆类型和。假设连接和不能被分配到相同的有线电视和不是一个允许型号的电缆连接。正如前面提到过的所有连接的第一个连接除外,它必须是一个领导者，

43、可以是一个领导者或是跟随者。这是确保的下面的约束。 （2）同样,基于电缆规则一组连接电缆双可以派生每个意味着电缆类型是不允许我为连接。 （3）这种关联是一个领导人在一份电报中不能被一个追随者领袖的另一份电报。这是表现出下列约束。 （4）隐式约束的规划问题是电缆容量约束意味着数量的连接分配到一个电缆必须小于能力需求即导体的总数在电缆减去多余的核心要求的电缆表1 二进制变量对应于图1例让和总的数量的导体和所需的多余的核心在电缆类型，然后下面的方程式表达了容量约束。在这个方程式中,如果连接是一个领导者那么整体的所有连接包括连接和它的追随者小于电缆的能力需求,型分配,否则方程在缺省情况下是满意的。 （

44、5）此外,需要以下问题公式化的约束,避免间接配对的连接和有相同的领袖但是在。 （6）类似地,下面的约束禁止一个跟随者选择一个领袖,他的选择电缆类型不是一个允许的电缆类型的跟随者。 （7）最后,该子问题可能包括一组优先分配规则中指定了所有连接携带某些信号应该更好地分配给相同的电缆。这是通过引入一个点球成本在目标函数中。惩罚成本就会增加时,并不是所有的网络连接的任何优先分配规则有相同的领袖或当存在超过一个领袖。在任何首选内的连接分配规则。相关的约束优先分配规则没有被表达由于空间限制。电缆的目标规划问题会被指定为： （8）在的价钱是线缆。优化结果的上述问题在SAS电缆计划以最小成本总电缆。4结果为了

45、进行有意义的实验中，由于缺乏足够的真正的子问题的实例,我们生成的随机子问题实例与九电缆类型。连接数的在每个子问题实例从10到50多种多样。每束电缆类型有一个互不相连的光缆花费1和2之间均匀分布和总数量的导体是离散均匀分布的1-5。每一个连接都可以被分配到九个电缆类型，是离散均匀分布式3-6。此外,许多连接对不能被分配到相同的电缆平均等于。应该注意,生成的子，题实例都比典型的SAS电缆规划子问题。实例使用不同的解决者和解决获得的结果如图2所示。表2 不同性能得到不同求解方法左边的图显示,中值计算时间获得最优解与某些非商业的解决者。正确的图显示,非商业性的性能相对于动态的解决。据观察,SCIP-CLP 2.0.1那里平均3.6倍慢于动态可以很好地提高CBC-CLP问题大小不同这是管理不善,3.5.5的鳞片平均低于13.9倍动态。突出的实验结果是,甚至比典型的实例都相当容易解决,因此整数线性优化配方显然别人时间和成本高效的解决方案规划SAS电缆。5结论本文分析了变电站自动化系统的建模电缆