變電站電纜自動(dòng)化系統(tǒng)的有效計(jì)劃電氣工程及其自動(dòng)化專業(yè)畢業(yè)設(shè)計(jì)外文翻譯中英文對(duì)照

1、Efficient Planning of Substation AutomationSystem CablesThanikesavan Sivanthi and Jan PolandABB Switzerland Ltd, Corporate Research,Segelhofstrasse 1K, 5405, Baden-Dattwil, Aargau, SwitzerlandAbstract The manual selection and assignment of appropriate cables to the interconnections between the devic

2、es of a substation automation system is a major cost factor in substation automation system design. This paper discusses about the modeling of the substation automation system cable planning as an integer linear optimization problem to generate an efficient cable plan for substation automation syste

3、ms.1 IntroductionCabling between different devices of a substation automation system (SAS) is a major cost factor in the SAS design process. Usually computer aided design software is used to create the design templates of SAS devices and their interconnections. The design templates are then instanti

4、ated in a SAS project and the cables are manually assigned to the connections. The selection and assignment of cables to connections must follow certain engineering rules. This engineering process is usually time consuming and can cause engineering errors, thereby increasing the engineering cost. Ap

5、parently, the SAS cable planning is related to the well known bin packing problem. The SAS cable planning can be formulated as an integer 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. Th

6、is paper describes the formulation of SAS cable planning problem as an integer linear optimization problem and presents the results for 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 follow

7、s. Section 2 presents an overview of the SAS cable planning process. Section 3 expresses the SAS cable planning problem as an integer linear optimization problem. The results obtained by solving the optimization problem using some solvers is presented in Section 4. Section 5 draws some conclusions o

8、f this work.2 SAS Cable PlanningThe SAS cable planning begins after the system design phase of a SAS project.The SAS cable planning is at present done manually by computer aided designT. Achterberg and J.C. Beck (Eds.): CPAIOR 2011, LNCS 6697, pp. 210214, 2011.cSpringer-Verlag Berlin Heidelberg 2011

9、Efficient Planning of Substation Automation System Cables 211Fig. 1. Fields, devices and their interconnections(CAD) engineers. The different 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

10、 has fields which are logical groups of devices as shown in Figure 1. Moreover, a field corresponds to a physical assembly interface class 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 p

11、ath between exactly two pins and every connection carries a physical signal. A signal can traverse over one or more connections. Each connection 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

12、cable engineering rules can be classified into two types, namely the cable rules and the signal rules. The cable rules specify the allowed 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

13、 signal rules specify restrictions on allocation of connections which carry signals that should not be allocated to the same cable or preferably allocated to the same cable. The current practice is to manually select and assign cables to connections according to the cable engineering rules. This pro

14、cedure is time consuming and can cause engineering errors thereby increasing the engineering cost. In what follows is the formulation of 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 For

15、mulationThe SAS cable planning problem is divided into sub problems where each sub problem considers connections between distinct set of 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

16、and should not mix connections between two different source or destination physical assembly interface classes in one cable. This is ensured 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 t

17、otal number of connections, and K = 1, 2, 3, . . .,M212 T. Sivanthi and J. Polandrepresent the set of all cable types, where M is the total 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 con

18、nections in the cable instance as the leader and the other connections as the followers. This implies that all connections except the first 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

19、 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) / 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 th

20、e 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 connection 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 tru

21、e implies that the leader i is assigned to an instance of cable type j. (2)Table 1 illustrates all binary variables corresponding to the 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

22、an allowed cable type for connection C3. As mentioned before all connections except the first connection, which must be a leader, can either 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

23、cable. This is expressed by the following constraint. （4）An implicit constraint of the cable planning problem is the capacity constraintwhich implies that the number of connections assigned to a cable must be lessTable 1. Binary variables corresponding to Figure 1 exampleEfficient Planning of Substa

24、tion Automation System Cables 213 than the capacity requirement i.e. the total number of conductors in the cable minus the spare core requirement 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 capac

25、ity constraint. In this equation, if the connection I is a leader then the sum of all connections including the connectioni and its followers 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 fo

26、rmulation needs the following constraint to avoid indirect pairing of connections i and i which have the same leaderi but (i, i) is in X. （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

27、）Finally, the sub problem may include a set of preferred allocation rules which specify that all connections carrying certain signals should 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

28、 connections of any preferred allocation rule have the same leader or when there exists more than one leader among the connections within any preferred allocation rule. The constraints related to preferred allocation rules are not expressed due to space limitation. The objective of the cable plannin

29、g 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 cable 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

30、 random sub problem instances with nine cable types. The number of connections N in each sub problem instance is varied from 10 to 50. Each 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

31、 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 between 3 and 6. Furthermore, the number of connection pairs which214 T. Sivanthi and J. PolandFig. 2. Performance obtained with different solverscannot be assigned

32、 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 SAS 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 comp

33、utation time to obtain the optimal solution with some non-commercial solvers SCIP-SOPLEX 2 3 4, CBC 5 and commercial solver CPLEX 6. The 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 CPLE

34、X 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 salient result of our experiment is that even the harder than typical instances are fairly easily solved, therefore the integer linear optimization formulation clea

35、rly offers time and cost efficient solution for SAS cable planning.5 ConclusionThis paper presented the modeling of substation automation system cable planning as an integer optimization problem to generate a more efficient cable plan for substation automation systems. The results obtained for typic

36、al test cases show that the integer linear optimization formulation clearly offers time and cost efficient solution for the substation automation system cable planning.References1. Brand, K.-P., et al.: Substation Automation Handbook. Utility Automation Consulting(2003)2. Achterberg, T.: SCIP: Solvi

37、ng Constraint Integer Programs. J. Math. Prog.Comp. 1(1), 141 (2009)3. Achterberg, T.: Constraint Integer Programming, Technische Universitat Berlin(2007)4. SCIP Mixed Integer Programming Solver, 5. CLP Linear Programming Solver, 6. CPLEX Optimizer, cplex-optimizer11 / 11文檔可自由編輯打印變電站電纜自動(dòng)化系統(tǒng)的有效計(jì)劃Than

38、ikesavan Sivanthi and Jan PolandABB Switzerland Ltd, Corporate Research,Segelhofstrasse 1K, 5405, Baden-D attwil, Aargau, Switzerland摘要：手動(dòng)選擇和適當(dāng)?shù)姆峙潆娎|，在變電站自動(dòng)化系統(tǒng)的設(shè)計(jì)時(shí)，對(duì)變電站自動(dòng)化系統(tǒng)之間的聯(lián)系的是一個(gè)主要成本因素。本文論述了變電站自動(dòng)化系統(tǒng)電纜計(jì)劃的建模作為一個(gè)整數(shù)線性優(yōu)化問題來生成一個(gè)高效的變電站電纜自動(dòng)化系統(tǒng)的計(jì)劃。1簡(jiǎn)介在變電站自動(dòng)化系統(tǒng)設(shè)計(jì)(SAS)過程中，不同設(shè)備之間的接線是變電站自動(dòng)化系統(tǒng)的一個(gè)主要成本因素。通常計(jì)算機(jī)輔助

39、設(shè)計(jì)軟件是用來創(chuàng)建變電站自動(dòng)化系統(tǒng)設(shè)計(jì)模板的和設(shè)備之間的聯(lián)系。然后手動(dòng)分配連接變電站自動(dòng)化系統(tǒng)設(shè)計(jì)模板項(xiàng)目和電纜。選擇和分配電纜連接必須遵循一定的工程規(guī)則。這個(gè)過程通常是耗費(fèi)時(shí)間,并可導(dǎo)致工程錯(cuò)誤增加工程的成本的工程。顯然，SAS電纜規(guī)劃是眾所周知的裝箱問題。SAS公司的電纜計(jì)劃可以制定為一個(gè)整數(shù)線性優(yōu)化問題，與電纜工程規(guī)則表示為一組線性約束和成本目標(biāo)的總成本最小化電纜。本文描述了SAS電纜規(guī)劃問題作為一個(gè)整數(shù)線性優(yōu)化問題,提出了具有代表性的測(cè)試用例的結(jié)果方案。對(duì)作者的來說最大的收獲是學(xué)習(xí)SAS電纜規(guī)劃。本文組要內(nèi)容如下。第二節(jié)介紹SAS電纜規(guī)劃過程。第三節(jié)表述了SAS電纜規(guī)劃問題作為一個(gè)整數(shù)

40、線性優(yōu)化問題。第四節(jié)通過求解該優(yōu)化問題獲得的結(jié)果，提出了一些解決方案。第五節(jié)得出結(jié)論這樣的工作。2 SAS電纜計(jì)劃SAS電纜計(jì)劃從系統(tǒng)設(shè)計(jì)階段的情景應(yīng)用程序項(xiàng)目開始。SAS電纜規(guī)劃是目前由計(jì)算機(jī)（CAD）輔助設(shè)計(jì)工程師手工完成的。圖1 各設(shè)備之間的聯(lián)系不同的設(shè)計(jì)模板對(duì)于實(shí)際設(shè)備情景應(yīng)用程序是在實(shí)例化一個(gè)或多個(gè)CAD工作。每個(gè)任務(wù)由一個(gè)或多個(gè)表,每個(gè)表的字段是邏輯組設(shè)備如圖1所示。此外，一個(gè)字段對(duì)應(yīng)于一個(gè)物理裝配接口測(cè)量框、保護(hù)隔間等。每個(gè)設(shè)備都有物理連接的接口裝置。一個(gè)有效的連接是一個(gè)獨(dú)特的通道，并且每個(gè)連接攜帶一個(gè)物理信號(hào)。一個(gè)信號(hào)可以遍歷一個(gè)或多個(gè)連接。每個(gè)連接被指定到唯一的一個(gè)導(dǎo)體的線纜

41、。這個(gè)類型的電纜的連接分配是基于電纜工程規(guī)則。電纜工程規(guī)則可以分為兩種類型，即電纜規(guī)則和信號(hào)規(guī)則。電纜規(guī)則指定了允許的電纜類型的一組連接，它還可以指定備用導(dǎo)體的數(shù)量和每個(gè)實(shí)例允許的電纜類型。信號(hào)規(guī)則指定配置的連接限制攜帶的信號(hào),不應(yīng)該被分配給相同的電纜或最好是分配給相同的電纜。當(dāng)前實(shí)踐是手動(dòng)選擇和分配電纜連接稱工程規(guī)則。這個(gè)過程是費(fèi)時(shí)并可能導(dǎo)致工程錯(cuò)誤從而增加成本的工程。接下來的是把制訂SAS系統(tǒng)電纜計(jì)劃作為一個(gè)整數(shù)線性優(yōu)化問題,這一個(gè)更高效的電纜計(jì)劃。3 整數(shù)線性規(guī)劃制定SAS電纜規(guī)劃問題劃分為子問題,其中每個(gè)子問題考慮到在不同的領(lǐng)域之間的連接，再給出一組正確的CAD工作。這種分解背后的基本

42、原理是,電纜計(jì)劃應(yīng)該考慮物理裝配接口類,不應(yīng)該混之間的聯(lián)系兩個(gè)不同的源或目標(biāo)物理裝配接口類在一份電報(bào)。這是確保的派生一個(gè)有線電視計(jì)劃對(duì)每個(gè)不同的領(lǐng)域。讓代表的所有連接兩個(gè)區(qū)域之間的雙,其中N是總數(shù)量的連接,并且代表的所有電纜類型，在是累計(jì)有線數(shù)字類型的子問題。在一份實(shí)例中，可以有一個(gè)或多個(gè)連接,我們將該連接與最低指數(shù)在所有連接的電纜實(shí)例作為領(lǐng)導(dǎo)者和其他連接的追隨者。這意味著所有連接除了第一個(gè)連接在C可以是一個(gè)領(lǐng)導(dǎo)者或是跟隨者。顯然，基于信號(hào)規(guī)則一組連接雙可以派生每個(gè)代表了和聯(lián)系,一定不能被分配到相同的電纜。讓是組連接雙在那里，。我們引入下列二進(jìn)制變量，在,當(dāng)它真的意味著連接是追隨者領(lǐng)導(dǎo)的一個(gè)。 （1）表1說明了所有二進(jìn)制變量對(duì)應(yīng)于圖1所示的例子為案例和兩個(gè)電纜類型和。假設(shè)連接和不能被分配到相同的有線電視和不是一個(gè)允許型號(hào)的電纜連接。正如前面提到過的所有連接的第一個(gè)連接除外,它必須是一個(gè)領(lǐng)導(dǎo)者，可以是一個(gè)領(lǐng)導(dǎo)者或是跟隨者。這是確保的下面的約束。 （2）同樣,基于電纜規(guī)則一組連接電纜雙可以派生每個(gè)意味著電纜類型是不允許我為連接。 （3）這種關(guān)聯(lián)是一個(gè)領(lǐng)導(dǎo)人在一份電報(bào)中不能被一個(gè)追隨者領(lǐng)袖的另一份電報(bào)。這是表現(xiàn)出