a new method of network reconfiguration

8/12/2019 A new Method of Network Reconfiguration

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A.New Method of Network Reconfiguration for Service Restoration in Shipboard Power SystemsKaren,. L. Butler N.D.R. Sarrnal V. Rajendra PrasadMember, IEEE Member, IEEE

Power System Automation LaboratoryDepartment of Electrical EngineeringTexas A&M UniversityCollege Station, TX-77843-3 128,USA( On Sabbatical Leave flom CMC Limited, INDIA. )

Abstrack The electric power systems of ships supply energy tosophkticated systems for weapons, communications,navigation andoperaticm.Circuit breakers(CBs)and fuses are provided at differentlocations in order to remove faulted loads, generators or distributionsystems from unfaulted portions of the system. These faults could bedue to material causalities of individual loads or cables or due towidespread system fault due to battle damage. Because of the faultsand after isolating the fault, there are unfaulted sections which are leftwithout supply. It is required to quickly restore supply to theseunfaultcd sections of the shipboard power systems. This paper presentsa new method to reconfigure the network to restore service to unfaultedsections of the system. The problem is formulated as a modification ofthe fixed charge network flow problem. The proposed method isillustrated using different case studies.Keywords: Shlpborrrd Power Systems, Reconfiguration, ServiceRestoration, Network Flow Method.

L INTRODUCTIONShipboard Power Systems (SPS) consist of generators which areconnected in ring configuration through generator switchboards[1]. Elus tie circuit breakers interconnect the generatorswitchboards which allow for the transfer of power ffom oneswitchboard to another. Load centers and some loads aresupplied from generator switchboards. Load centers in turnsupply power to power panels to which different loads areconnected. Feeders supplying power to load centers, powerpanels, and loads are radial in nature. For vital loads, twosources of power (normal and alternate) are provided ffomseparate sources via automatic bus transfers (ABTs) or manualbus transfers (MBTs). Further, vital loads are isolated ffom non-vital loads to accommodate load shedding during an electricalsystem causality.

Department of Industrial EngineeringTexas A&M UniversityCollege Station, TX-77843-3 131, USA

Circuit breakers(CBs) and fises are provided at differentlocations in order to remove faulted loads, generators ordistribution systems from unfaulted portions of the system,These faults could be due to material causalities of individualloads or cables or due to widespread system fault due to battledamage. Because of the faults and after isolating the fault, thereare unfaulted sections which are left without supply. It isrequired to quickly restore supply to these unfaulted sections ofthe SPS. This is accomplished by changing the configuration ofthe system by opening andlor closing some switches(CBs/MBTs/ABTs) to restore supply to maximum load in theunfaulted section of SPS to continue the present mission.While reconfiguring the network for service restoration it is alsoimportant to maintain the radial nature of the system, for ease offault location and isolation and coordination of the protectivedevices. Another important factor to be considered whilereconfiguring the network is to ensure that the capacities of thegenerators, circuit breakers and cables are not violated.In the literature there are several papers [2-11] discussing thisproblem for utility systems. Most of the methods are based onheuristic search techniques. Some of the methods are based ongraph theory [9- 11]. However, SPS have differentconfigurations when compared to utility systems[ 1]. There areno papers publicly available in the literature which address theproblem of service restoration for SPS. In this paper a new andsimple method is proposed to solve this problem for SPS.Though the existing methods available for utility systems can beimplemented for SPS, in this paper, it is attempted to solve theproblem in a simpler way which is more suitable to SPS. Theproblem is formulated as a modification of Fixed ChargeNeWork Flow problem [12]. The proposed method does notrequire any load flow/power flow analysis to veri~ the currentcapacity and voltage constraints. It would directly suggest thereconfigured network which restores maximum load satisfyingthe constraints and also ensuring the radiality condition. Themethod is illustrated with various case studies. The paper isorganized as follows: Section 2 presents the mathematicalproblem formulation. This is illustrated using various casestudies in section 3. Conclusions are given in section 4.

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II. MATHEMATICAL PROBLEM FORMULATIONConsider a small shipboard power system (SPS) as shown inFig. 1. This system consists of two generators each supplying aload center. Some loads are connected to the load center directlyand some via ABTM13Ts. The loads connected via ABT/MBThave an alternate supply. Graphical representation of thissystem is shown in Fig, 2. In Fig. 2, ABT/MBT is representedwith two switches as shown in Fig. 3. Since supply should befrom only one source (in radial systems), only one of theseswitches is in a closed position at a given time. The edges indotted line indicate alternate paths. The switches in open andclose position are depicted as J and + respectively.Whenever there is a fault on any of the edges, and after it isisolated, there would be no supply to the loads on the path whichare beyond the faulted edge. Supply has to be restored to most ofthese affected loads, by closing some of the switches which areopen. This has to be done while satis@g the capacity andvoltage constraint and ensuring the radiality condition. Voltageconstraints are not handled in the present work.For example, if there is a fault on cable (edge 15) connectingload 1A (at node 17) and after it is isolate~ there would be nopower to the load L4 at node 17 (as can be seen from in Fig. 1).Power has to be restored to this load without any capacityviolations. Also the radiality configuration has to be maintained.Also it is possible that there are several simultaneous faultsaffecting several loads. In such cases supply has to be restored tomaximum load satis~ing the constraints.The mathematical formulation of this problem is explained inthe following section.A. Problem formulation:

The problem is now formulated as a modification of the fwedcharge Network Flow Problem [2].Let Vrepresent the set of nodes and E represent set of edges inthe network. Let C=represent the capaci~ of the edge a. LetD = {D,,D2,...,D~}represent the set of load nodes in the network.The set {KE} represents the network under consideration. Let Ecrepresent the set of edges which are in closed position.Therefore, the set E.= E - E=) represents the set of open edgesin the network. After the fault there are some edges which arefaulty and some which are not faulty. Let Ep~ represent the set ofedges which are not faulty. Now the set of edges which areavailable for the restoration of power to all load points given inD is given by A = - u E - Ec) and the network would berepresented by the set {W}.

Q=.Load terJ> 4 : GAltmlat. ; 7 ~ ~tia b : MBT18 : LiLOadi i:L4 17 t ;3 20z - NormalLoadL3 Tgbadinter >10 21Generator >9 Bus-tieswik mard

6breakerG

Fig, 1.ExampleSystem1

m

20

m10

EIl L4 s. . . . . .14Fig. 2. GraphicalrepresentationofExampleSystem 1 (Fig. 1)

Load LoadFig. 3. Modeling of ABTM4BTAt a node i, let Ii represent the set of edges, through whichcurrents flows into the node, and Oi the set of edges withcurrent flowing out of the node. Let Li represent the load currentat node i.

Zi ={(r, i)e A\re V}; (1)where (r, i ) represents the directed edge from node r to i

Similarly, @Oi ={(i, r)e Alre V}; (2) iwhere (i, r) represents the directed edge fi-omnode i to r

LetX_,be the flow in edge a. Let Y.be defined as follows:

Y,= 1, if current flows through edge a= O, otherwise.To restore service through reconfiguration, some of the edges ofEOhave to be closed.

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Now, tlhemathematical formulation of the problem is as follows:Obiective Function :

kMinimize x Li 3i=l

kIt maybe noted that ~ Li is the total load supplied at loadi=1nodes D,, Dz, ....DConstraints:.1.

2.

3.

4.

At any source node i, the sum of the flows going out of thesource node should be less than the total capacity of therespective source node Ci : Ci 4)aCOi

At any node i, (except source node) sum of flows into thenode should be equal to sum of the flows coming out of thenode:2.1

2.2

At a load node Di

tiGZi ZiEOiAt any other intermediate node i5)

6a= Ii aGOi

The flow in an edge should be less than or equal to thecapacity of the edge:x,< ~ci fori~ A 7)The system should be radial: This implies that at any node ithere should be only one edge feeding that node.

z Ya=l (8)a~IiIf this problem [presented in Equations (3)-(8)] is solved, it willensure that the restored network would restore supply power toas much load as possible and also all the capacity constraints aresatisfied. Further, this would also ensure radlality condition.This is illustrated in the following section.

11[.ILLUSTRATION OF THE PROPOSED METHODThe proposed method is illustrated with the example systemshown in Fig. 1.Fig 2. represents the graphical representation ofFig. 1. It can be seen that all generators are connected in ring

configuration. When all the generators are in operation, fault onany of the components in ring may not affect supply to any load.All components below the generator switchboards are operatedin radial configuration and fault on any of these componentswould interrupt power supply to some loads. Hence for thepurpose of service restoration problem, faults on the componentsin ring configuration need not be studied. Hence the network canbe modified by merging all the generator switchboards and bus-tie breakers.Thus the example system shown in Fig. 2 will be modified asshown in Fig. 4 by merging the nodes corresponding to thegenerator switchboards connected in ring. In Fig. 4, node 21represents the new node after merging all the generatorswitchboards and bus-tie-breakers ( nodes 2,19,20,11). Node 22represents the new source node whose capacity is equal to thesum of the capacities of generators 1 and 2 (nodes 1 and 10).Accordingly, the capacity of edge 22 is equal to the capacity ofsource node 22. This system will be studied for the purpose ofreconfiguration for service restoration. It is assumed that someof the loads(L1, Lz and LJ can be varied ftom zero amps to 20amps. Such loads represent lump loads consisting of severalindividual loads. Load LJ is assumed to be a f~ed load of 20amps which represents loads like motors. This assumption helpsto demonstrate the effectiveness of the proposed model whichwill restore as much load as possible for a given fault condition.In case of load Lg,if it is supplied it will take 20 amps. Whereasthe other loads can be varied from Oto 20 amps. In order tofacilitate modeling of the loads as discussed above, a O-1 integervariable (zi) is associated with each load and loads are expressedas follows in the problem formulation:

L1-z1*20


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Also it is assumed that values of impedance of all the edges is0.01 except those representing switches which is assumed to beequal to zero. Also it is assumed that the capacity of each edge is80 amps.Various case studies are presented below to illustrate theeffectiveness of the proposed method.CASE 1: Initially, the system without any faults is studied.Based on the explanation given earlier the system is modeled asfollows:Objective Function :

Maximize L1+L2+L3+L4;Subject to :

Source node constraint;X22 -100 so;Load details;1.1- 21*2O


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and all[ the loads can be fed satistjing current and voltageconstraints.Case 3: Consider a case wherein there is fault on a componentwhich would affect a load which has no alternate path. In such acase service cannot be restored to that affected load until thefault is repaired. In shipboard power systems such loads are non-vital loads. This case is illustrated as follows.Assume that there is fault on CB (edge 3) supplying load L2 (atnode 4) and on the cable (edge 6) connecting the load L1 (atnode 8). Fault on component 3 would affect the load L2 (at node4) which has no alternate paths. Fault on component 6 wouldaffect IIoadL1 (at node 8) which has alternate paths. Faults oncomponents are modeled as explained in the previous case.When the faults are modeled as explained earlier and aftersolving the optimization problem, it could be seen that theoptimal value of yl 3 =1 indicating that switches 13 has to beclosed to restore supply to load L4 and load L2 cannot berestored since there isno alternate path for it.Various cases have been studied on this system with proposedmethoci and all results obtained were as expected.

IV. CONCLUSIONSA new and simple method of reconfiguration for servicerestoration in shipboard power systems is presented. Theproblem is formulated as the Fixed charge Network flowproblem. The proposed method restores as much as loadpossible satis~ing the capacity constraints directly. The faults inthe network can easily modeled. The proposed method does notrequire any load flow/power flow analysis to verify the currentconstraints. It would directly suggest the reconfigured networkwhich satisfies the capacity constraints. Different case studiespresented illustrate the effectiveness of the proposed method.Voltage constraints are being included in fiture work.

V. ACKNOWLEDMENTSThe authors acknowledge the OffIce of Naval Research for thesupport of this project through grant NOOO14-96-1-0523.

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[2]

[3]

VI. REFERENCESK;uenL Butler,NDRSarm~CliffWhltecomb,HyderDoCarmoandHaibo Zhrmg, Shipboard Systems Deploy Automated Protection, IEEE

Cc mputer Applications in Power Vol 11,No. 2, 1998,pp 31-36.S. Curcic, C.S. Ozveren, L. Crowe and P.K.L. Lo, Electric powerdistribution network restoration : A survey of papers and a review of therestoration problem, Electric Power Systems Research Vol. 35, 1996pp73 86.K AokI, H. Kuwabar T. Satoh, M.Kanezashi, Outage State OptimalLc,ad Allocation by Automatic Sectionalizing Switches Operation in

[4]

[5],

[6]

[7]

[8]

[9]

Distribution System, IEEE Trans. on Power Delivery Vol. PWRD-2,No.4, Ott 1987,pp 1177-1185.Chen-Chhg LIU; Seung Jae Lee, S.S. Venkat~ An Expert SystemOperation Ald for Restorat ion and Loss Reduct ion of Distr ibut ionSystems, IEEE Trans. on Power Systems Vol. 3, No.2, May 1988, pp619-626.Tim Taylor, David Lubkeman, Implementation of Heuristic SearchStrategies for Distribution Feeder Reconfiguration, IEEE Trans. onPower Delivery Vol. 5 No. 1,Jan 1990,pp 239-246.S, Curcic, C.S. Ozveren, K.L. Lo, Computer-based Strategy for theRestoration Problem in Electric Power Distribution Systems, ZEE Proc.on Generation Transmission and Distribution Vol. 144, No. 5, Sept.1997,pp 389-398.Karen Nan MhI, Hsiao-Dong Chiang, Bentao Yuan, Gary Darling, FastService Restoration for Large-Scale Distribution Systems with PriorityCustomers and Constraints, Proceedings of the 2@h Internationalconference of Power Industry Applications 1997 pp 3-9.Qin Zhou, Dariush Shirmohammadi W. -H. Edwin Liu, DistributionFeeder Reconfiguration for Service Restoration and Load Balancing,IEEE Trans. on Power Systems Vol. 12,No.2, May 1997, pp 724-729.A.M. Stsnkovic, M.S. Calovic, Graph-Oriented Algorithm for the SteadyState Security Enhancement in Dis~lbution Netwo~ks, IEEE Trans. onPower Delivery VOI.4 No. 1,Jan 1989 pp 539 544.[10]. E.N. Dialynas, D.G. Mlchos, Interactive Modelling of Supply RestorationProcedures in Dktribution System Operation, IEEE Trans. on PowerDelivery Vol. 4 No. 3 July 1989,pp 1847-1854.[11]. N.D.R. rrn~ V.C.Prasad, K.S. Prakasa Rae, V. Sankar, A NewNetwork Reconfiguration Technique for Service Restoration inDistribution Networks, IEEE Trans. on Power Delivery Vol. 9, No. 4,Ott 1994.[12] George L Nemhauser and Laurence A. Wolsey, Integer and CombinatorialOptimization Wiley IntersciencePublications,1988,p.8, pp 495-513.

Karen L. Butler is an assistant professor in the department of electricalengineering at Texas A&M Universi ty. She received the B.S. degree fromSouthern University -- Baton Rouge in 1985, the M.S. degree from theUniversi ty of Texas at Austin in 1987, and the Ph.D. degree horn HowardUniversity in 1994,all in electrical engineering. In 1988-1989, Dr. Butler was aMember of Technical Staff at Hughes Akcratl Co. in Culver City, California.Her research focuses on the areas of computer and intelligent systemsappl icat ions in power, power dist ribution automation, and modeling andsimulation of vehicles and power systems. Dr. Butler is a member of IEEE,IEEE Power Engineering Society (PES), and the Louisiana EngineeringSocieiy. She is a registered professional engineer in the State of LouisianTexas, andMksissippi.N.D.R. Sarma obtained his B.Tech (Electrical) and M.Tech (Power Systems)degrees from Regional Engineering College, Warangal, India in 1983 and 1986respectively and Ph.D. from Indkm Institute of Technology, Delhi, India in1995.From 1992to September 1997he was with the R&D Dkision of CMCLimited, Hyderabad, India. Since October, 1997 he is on Sabbatical leave fromCMC and is presently workkig as a Post Doctoral Research Associate at TexasA&M Universi~, College Station, Texas, USA. Hk areas of interest includeLoad Dispatch andDk.tribution Automation Systems for power utilities. He is amember of IEEE andIEEE Power Engineering Society.V. Rajendra Prasad received B.S (Mathematics) and M.S (Statistics) fromAndhra University, Waltair, India in 1974 and 1977 respectively and Ph.D fromIndian Statistical Institute (1S1),Calcutt~ India in 1985. He served as tenuredfaculty of SQC and OR Division of 1S1during 1986-96.Since 1996he has beenworking as Visiting Scientist in the Department of Industrisd Engineering atTexas A&M University, Col lege Stat ion. Dr. Prasad provides consult ingservices to manufacturing industries on mathematical modeling of probIems inengineering process control and system design. His research interest are systemreliability optimization, stochastic modeIs and mathematical programming. Heis a member of INFORMS and life member of Operations Research Society ofIndia andNational Institute for Quality and Reliability (India).

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a new method of network reconfiguration

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