Research ArticleReal-Time Multifault Rush Repairing Strategy Based onUtility Theory and Multiagent System in Distribution Networks

Zhao Hao1 Zhang Jing12 Lu Zhi-gang1 Yang Li-jun1 and Cheng Hui-lin3

1Key Laboratory of Power Electronics for Energy Conservation and Motor Drive of Hebei Province Yanshan UniversityHebei 066004 China2State Grid Jinzhou County Electric Power Supply Company Jinzhou Hebei 052200 China3State Grid Shijiazhuang Power Supply Company Shijiazhuang Hebei 050000 China

Correspondence should be addressed to Lu Zhi-gang zhgluysueducn

Received 11 May 2016 Accepted 6 September 2016

Academic Editor Guangming Xie

Copyright copy 2016 Zhao Hao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The problem of multifault rush repair in distribution networks (DNs) is a multiobjective dynamic combinatorial problem withtopology constraintsThe problem consists of archiving an optimal faultsrsquo allocation strategy to squads and an admissible multifaultrush repairing strategy with coordinating switch operations In this article the utility theory is introduced to solve the first problemand a new discrete bacterial colony chemotaxis (DBCC) algorithm is proposed for the second problem to determine the optimalsequence for each squad to repair faults and the corresponding switch operations The above solution is called the two-stageapproach Additionally a double mathematical optimization model based on the fault level is proposed in the second stage tominimize the outage loss and total repairing time The real-time adjustment multiagent system (RA-MAS) is proposed to providefacility to achieve onlinemultifault rush repairing strategy in DNs when there are emergencies after natural disastersThe two-stageapproach is illustrated with an example from a real urban distribution network and the simulation results show the effectiveness ofthe two-stage approach

1 Introduction

Distribution network (DN) as the end of the entire powersystem is connected with the users directly and the normaland economical operation of the DN is crucial [1] Snow-storms earthquakes and other natural disasters have broughtgreat damage to the distributed network in recent yearsThe power equipment failure tower collapsed substationdamaged and even partial paralysis of the grid have causedserious influence on the production and life of the damagedareas Huge losses of life and property of the people will becaused if the power supply can not be restored quickly Therepairing personnel and resource may be insufficient on therush repairing site due to the diversity of the outage loadCoupled with the emergencies the existing researches cannot fully meet the needs of the rush repair In order to dealwith the emergencies on repairing site tominimize the outageloss and total repairing time it is important to carry out

researches on rush repairing strategy with limited repairingpersonnel and resource

There has been many investigations on power systemrestoration and fault diagnosis while studies on multifaultrush repair in distribution systems are quite limited andexisting literatures are to develop the repairing strategiesahead of time based on the deterministic fault message [2ndash5] But in the actual rush repair the prestrategy is feasibleonlywhen the relevant forecast information is consistent withthe actual information However many unexpected eventsmay occur during an actual rush repair which will result inthe prestrategy becoming unreasonable or even unfeasibleTherefore this paper proposes to research on how to adjustthemultifault rush repairing strategy in real-time consideringthe uncertainty of the emergencies on rush repairing site

The real-time adjustment reflects the characteristics ofautomation and intelligence of the multifault rush repairAgent is an intelligent entity with a high degree of autonomy

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 3891595 12 pageshttpdxdoiorg10115520163891595

2 Mathematical Problems in Engineering

capability that keeps running in a dynamic environmentAccording to their own resources status capacity relevantknowledge and knowledge rules and the external environ-ment information acquired they can perceive the environ-ment accomplish specific tasks independently and achievethe intended target by planning reasoning and decision-making [6 7] MAS has become hot for more than 20 yearsIn the field of power systems there are many researches andapplications of multiagent technology and the agent compo-nent can be increased flexibly based on the actual demandwhich is consistentwith the functional requirements of powerdispatching automation system [8] A MAS is proposed tomanage the power dispatch inDNdynamically to balance thesupply and demand by considering the variability of DGs andloads through five types of autonomous agents in [9] A noveldistributed algorithm is presented for service restorationwithdistributed energy storage support following fault detectionlocation and isolation in [10] A MAS including communi-cation of agents is presented to restore a power system after afault in [11] Considering the excellent performance of MASthis paper introducesmultiagent theory to solve the real-timeadjustment problem of the multifault rush repairing strategyin distribution network

In the existing literatures on multifault rush repair ofdistribution network researches can be divided into twoparts the allocation of the fault tasks and the model ofmultifault rush repair in DN For the first part a multifaultrush repairing strategy optimization model with a singlesquad is established in [2] which can not be applied to theactual multisquad collaboration a multisquad cooperationmechanism is given in [5] which considers the allocationof resources and a repairing scheduling multiagent approachis proposed to archive an emergency repairing plan quicklyas well as a resource grouping scheme For the second partthe tie switch is taken as a virtual fault and a multifault rushrepairingmodel is built in [3 4] which assumes the repairingpersonnel and resource are enough and assigns fault tasks toeach squad randomly It seemingly simplifies the repairingmodel but it has some drawbacks (1) It increases the searchscope of the solution space greatly resulting in ldquocurse ofdimensionalityrdquo problem reducing the formulation speed ofthe repairing strategy and disobeying the characteristic ofurgency of the actual rush repair (2) It does not match withthe actual role of tie switches in DN (3) Only achievingrestoration of the load is the main content of fault recoverybut the rush repair needs to ensure all faults repaired

In response to these problems this paper first introducesutility theory to achieve an efficient allocation of fault tasksdivides fault level and develops repairing principle Then areal-time adjustment of repairing strategy multiagent system(RA-MAS) is established considering two cases when thereare no emergencies repairing squads complete the entireintelligent repair following the prestrategy when unexpectedevents occur it determines the real-time adjustment decisionultimately achieving the repairing target of restoring themaximum load power supply with minimum time cost

The remainder of the paper is organized as followsIn Section 2 a multisquad dynamic allocation of the faulttasks based on utility theory is discussed The distribution

network multifault repairing model and DBCC algorithmare introduced in Section 3 In Section 4 a multiagentsystem model for real-time adjustment of repairing strategyis presented Simulation results are analyzed to demonstratethe performance of the proposed approach in Section 5 Con-clusions and some possible paths for future researches arefinally drawn in Section 6

2 Multisquad Dynamic Allocation of the FaultTasks Based on Utility Theory

21 Goals of Allocation of the Fault Tasks It is assumed thatafter multiple faults occur in the DN the repairing taskscollection is 119879 = 1199051 1199052 119905119895 119905119899 where 119899 is the numberof faults the repairing squad collection is 119877 = 1199031 1199032 119903119894 119903119898 where 119898 (119898 lt 119899) is the number of repairingsquads which are equipped with the repairing personnel andresource 120588 is the task allocation solution set

The assignment of fault tasks needs to achieve the fol-lowing objectives A ensuring that a repairing squad hassufficient capacity to repair a fault B ensuring that eachsquadrsquosmission is broadly balancedC ensuring the repairingsquad with better expertise repairing their types of fault inpriority where ldquobetterrdquo means a relatively short period oftime to repair the same fault D ensuring that faults withhigh urgency are repaired in priority where the urgency isconsistent with the level of outage loadsE guaranteeing thatthe time of faults waiting to be repaired is as short as possibleF guaranteeing that faults assigned to the same squad arerepaired as continuous as possible in order to reduce thesquadrsquos waiting time

Targets AsimC can be realized by the utility model sothat a fault task allocation scheme can be quickly developeddynamically [12] TargetsDsimF need the automation of MASto achieve the adjustment of the rush repairing strategyactually according to the emergency

22 Utility Theory The utility theory is proposed byeconomists to characterize consumersrsquo consumption deci-sion and decision scheme and provide a mathematical toolto calculate the relative value of different indicators [13]Recently utility theory has been used by many researchers invarious fields to obtain the optimal decision [14 15] Utilityusually represents the userrsquos satisfaction to accept a serviceor resource The economic Cobb-Douglas utility function isoften used to describe the individual utility as it can betterreflect the tradeoffs among the model variables The typesof the utility function contain linear type conservative type(exponential type) adventure type and long type and theproper types need to be selected according to actual eventcharacteristics and the nature of the utility function [16]

In the multifault rush repair problem the early assign-ment of fault tasks can select the appropriate squad based onthe features of faultsrsquo demands and repairing squadsrsquo capa-bilities So the utility theory is introduced to characterize theheterogeneity of faultsrsquo demands and repairing squadsrsquo capa-bilities by constructing a utility function in this paper Utilityvalues reflect the competence for squad 119903119894 to repair fault 119905119895that is the satisfaction obtained by fault 119905119895 to be repaired

Mathematical Problems in Engineering 3

by squad 119903119894 resulting in a fault task allocation scheme withhigher satisfaction and overall utility Attribute vector isapplied to characterize the features of faultsrsquo demands andrepairing squadsrsquo capabilities in this paper

23 Attribute Vector

231 Repairing Squadrsquos Capability Vector

Definition 1 (repairing squad preference) Due to the lim-itations of squad location traffic conditions among faultsnatural conditions and different human factors repairingsquads have different wills to complete the repairing missionthat is repairing squadsrsquo preferences are different [17] Setthe level of preference of squad 119903119894 to repair fault 119905119895 as 120575119895119894(0 le 120575119895119894 le 1) and (120575119895119894 )min as the minimum level of preferencethen squad 119903119894may choose to repair fault 119905119895 when 120575119895119894 ge (120575119895119894 )minotherwise not

In order to quantify squadrsquos capability we classify it into119896 intuitive atomic capabilities 119888119894 and constitute the capabilityset 119862 = 1198881 1198882 119888119896 [18] Define the quantified descriptionof the squad capability vector119862119903119894 for the atomic capabilities ofsquad 119903119894 as follows

119862119903119894 = [12057211989411198881 12057211989421198882 120572119894119896119888119896]119879 (1)

where 120572119894119896 (120572119894119896 ge 0) is squadrsquos capability coefficient which is arelative value and dimensionless reflecting the relative degreeof squad 119903119894 to have atomic capability 119888119896 Squad 119903119894 does not havethe atomic capability 119888119896 when 120572119894119896 = 0Definition 2 (failure degree) After each fault has beenrepaired the squadrsquos resources will reduce and repairing effi-ciency will decline where the fault also has some ldquodamagerdquo tothe squad during the repair process Therefore the capabilitydrop of squad 119903119894 is defined as the failure degree 120583119903119894 (0 le 120583119903119894 le1) of its atomic capability to reflect the damage cost that thesquad suffered during the repairing process

Failure degree indicates that 120572119894119896 is not a constant but willshow a decreasing trend in the repairing process

232 Faultrsquos Demand Vector On the actual rush repairingsite each fault has a demand vector to quantify the degree ofits demand for different atomic capabilities and the demandvector 119862119905119895 of fault 119905119895 is as follows

119862119905119895 = [12057311989511198881 12057311989521198882 120573119895119896119888119896]119879 (2)

where 120573119895119896 (120573119895119896 ge 0) is faultrsquos demanding coefficient whichis a relative value and dimensionless reflecting the relativedemanddegree of fault 119905119895 for atomic capability 119888119896 Fault 119905119895 doesnot need the atomic capability 119888119896 when 120573119895119896 = 0

It is necessary to reduce the dimension of the repairingsquadrsquos capability vector and the faultrsquos demand vector tosimplify the utility function model and develop the faulttask allocation scheme quickly So the resources needed areprocessed into four groups according to the fault type trans-former failure resource group backup power failure resource

group cable failure resource group and overhead line failureresource group Squadsrsquo ability for these resources corre-sponds to squadsrsquo atomic capabilities 1198881sim1198884 in turn and thephysical meaning of 120572119894119896 is the comprehensive strength ofsquad 119903119894 to equip 119888119896

The squadrsquos repairing efficiency is corresponding toatomic capability 1198885 and its physical meaning is the efficiencyof different squads to repair the same fault when the resourceis consistent

24 Utility Model

241 Utility Function Model

Definition 3 (capability condition matrix119881119898times119899) It is a matrixthat reflects whether squad 119903119894 has the capability to repair fault119905119895 alone Thus the expression of element V119894119895 is given in theform of Boolean variables

V119894119895 = 1 if 120575119895119894 ge (120575119895119894 )min forall119886 120572119894119886 ge 1205731198951198860 others

(3)

Considering both the repairing squadrsquos preference andcapability vector we can find that only when V119894119895 = 1 doessquad 119903119894 have the capability to repair fault 119905119895 alone and fault119905119895 can not be assigned to squad 119903119894 when V119894119895 = 0 Then it willavoid the infeasible allocation of faults and greatly reduce thesearch space dimension of the fault allocation scheme

Set the utility function 119906119895(119894) = 0when V119894119895 = 0 yet we needto quantify the competent degree of squad 119903119894 for fault 119905119895 to getthe optimal-utility fault allocation scheme set when V119894119895 = 1thus getting higher satisfaction of fault 119905119895 Faultsrsquo demandsand squadsrsquo capabilities will change with the repairing envi-ronment changes and the repairing process performancesand the competent degree is also changed accordingly Thus119906119895(119894) is a function of the squadrsquos capability and faultrsquos de-mand

119906119895 (119894) = 119880119895 (119862119903119894 119862119905119895) V119894119895 = 10 V119894119895 = 0

119880119895 (119862119903119894 119862119905119895) = 119896sum119901=1

120596119901 sdot 119891119901 (120572119894119901 120573119895119901) (119896 = 5) (4)

where 120596119901 is the utility weight of a faultrsquos atomic demands andsum119896119901=1 120596119901 = 1 Its value is determined through a method (cha-racteristic value method) that is a combination of subject andobject119891119901(sdot) = 120573119895119901120572119894119901 is the utility function of the squadrsquos pthatomic capability to the faultrsquos pth atomic demand reflectingthat the closer a squadrsquos capability to a faultrsquos demand is thehigher the overall utility of faults task allocation is under thepremise of meeting fault demands

4 Mathematical Problems in Engineering

Set 119906119894119895 = 119906119895(119894) and get the utility function matrix

119880 = [1198801 1198802 sdot sdot sdot 119880119899] =[[[[[[[[[[

11990611199062119906119898

]]]]]]]]]]

=[[[[[[[[[[

11990611 11990612 sdot sdot sdot 119906111989911990621 11990622 sdot sdot sdot 1199062119899 d

1199061198981 1199061198982 sdot sdot sdot 119906119898119899

]]]]]]]]]]

(5)

Under the current state for the same fault the greater thevalue of the utility function is the higher the satisfaction ofits acceptance of the squadrsquos repair is that is the stronger thesquadrsquos capability to repair the fault is the more competentthe squad for the fault is

Finally based on the above utility function matrix 119880 theRoulette Wheel Selection method [19] is applied to allocatethe fault mission and 120588 will be archived

242 Squad Collaboration The cooperationmust be consid-ered when every squad can not repair a fault alone That istwo or more squads will repair a fault together

If fault 119905119895 needs to be repaired together by squads 119903119894 and119903119897 the repairing process is as follows(1) Combine capability vectors 119862119903119894 and 119862119903119897 as 119862119903119894+119897 The

capability vector 119862119903119894+119897 of the combined squad 119903119894+119897 is119862119903119894+119897

= [(1205721198941 + 1205721198971) 1198881 (1205721198942 + 1205721198972) 1198882 (120572119894119896 + 120572119897119896) 119888119896]119879 (6)

(2) Redevelop a capability conditionmatrix together withfaultrsquos demand vector 119862119905119895 The capability condition ofthe combined squad 119903119894+119897 to complete fault 119905119895 is as fol-lows V(119894+119897)119895 = 1 only when 120575119895119894 ge (120575119895119894 )min 120575119895119897 ge (120575119895

119897)minforall119886 120572119894119886 + 120572119897119886 ge 120573119895119886

(3) Establish a new utility function model and a newutility function matrix 1198801015840

3 Distribution Network MultifaultRepairing Model

31 Classification of Fault Levels andDevelopment of RepairingPrinciples The structure of DN is radial and the repairingpersonnel and resource are limited So it is particularlyimportant to determine the repairing priority of faults torestore important load when multifaults occur in DN

According to the three load levels divided in load reliabil-ity the urgency of the need to restore the power supply is also

divided into three levels loads of the first level the secondlevel and the third level are corresponding to loads of thehighest urgency the medium urgency and the low urgencyseparately

Faults are divided into two levels and the minimum faultset 119879min is defined Faults with the highest urgency are thefirst level faults and other faults are the second level faultsThe first level faults are included in 119879min where 119879min =1199051 1199052 119905119902 (119902 le 119899) With the premise of contact switchoperation all loads with the highest urgency can be restoredas long as 119902 faults in 119879min are repaired

Thus the actual rush repair should follow the followingrepairing principles repair the first level fault in priority andthen the second level fault after all loads with the highesturgency have been restored faults in the same level needto optimize the repairing order according to their objectivevalues

32 Objective Function The multifault rush repair shouldachieve the following four objectives each squad A repairsthe nearest fault to reduce the delay on power restorationcaused by drive B completes the repairing plan in advancerather than postponing itC restores loads of highest urgencyin priority to reduce the outage loss D ensures that therepairing process is affected as little as possible when emer-gencies occur for example the repairing route is damaged ora new fault occurs

According to repairing principles faults in119879min should berepaired prior to restore loads of highest urgency as quicklyas possible Thus the repairing order of the first level loadsshould be repaired with the shortest time Meanwhile inorder to ensure the maximum satisfaction of all faults therepairing efficiency is considered in the repairing time Thetotal repairing time of the first step can be expressed asfollows

min1198911 (1198832) = max 1198631 1198632 119863119898 (7)

where1198832 is the repairing sequence of faults119863119898 is the time ofsquad119898 to complete its repairing task the time of squad 119894 torepair fault 119909119895 is 119879119894(119909119895) + 119879119861(119909119895)1205721198945 119879119894(119909119895) is the driving timeand 119879119861(119909119895) is the expected repairing time of fault 119909119895

The objective of the repairing order of other faults is tominimize comprehensive outage loss and the total outageloss in the second step can be described as follows

min1198912 (1198832)

= 119898sum119894=1

119899minus119902sum119895=1

(119879119894(119909119895) + 119879119861 (119909119895)1205721198945 ) sdot 3sum119889119895=2

120573119889119895 (119909119895) 119871119889119895 (119909119895) (8)

where 120573119889119895(119909119895) is the level coefficient of outage load and119871119889119895(119909119895) is active power of outage load caused by fault 119909119895

Mathematical Problems in Engineering 5

Constraints in the model are introduced as follows

119892119896 isin 119866119877 (9)10038161003816100381610038161198751198961003816100381610038161003816 le 119875119896max (10)

119880119886min le 119880119886 le 119880119886max (11)

119877119904 le 119877 (12)

The constraints listed above include radial network topol-ogy constraint (9) branch current capacity constraint (10)node voltage constraint (11) and repair resources constraint(12)

In the above constraints 119892119896 is network topology of thearea which has been restored and 119866119877 is the set of radialnetwork structure under consideration If 119894th fault has beenrepaired the connection status between both sides of thefault will be changed by switch operation Constraint (9) is toprevent ring network operating 119875119896 is the power flow throughbranch 119896which is calculated by backforward sweep method119875119896max is the maximum power flow capacity limit of branch119896 Ua is node voltage in the repairing process 119880119886min is thelower limit of the node voltage 119880119886max is the upper limit ofthe node voltage 119877119904 is the required resources when multiplefaults occur and 119877 is resources available

For these two objectives the double-level mathematicaloptimization model of distribution network multifault rushrepair is establishedTheoptimal faults allocation scheme andrepairing order from 120588will be archived through the improvedDBCC algorithm

33 The Improved Discrete Mechanism of BCC AlgorithmBCC algorithm is an intelligent optimization algorithm forcontinuous variables and has been widely used in the con-tinuous problem field [20 21] However the control variablesin the multifault rush repairing order optimization is asequence of discrete variables and its value represents onlythe code of the fault rather than the position of bacteria in thesolution space Existing BCC algorithm is only applicable tooptimization problems with continuous variables Thus thefollowing method is applied to discretize the BCC algorithm

The bacteria dimension is taken to be 119899 since there are119899 faults in DN Represent the 119899 faults by random numbers1198861 1198862 119886119899 with values taken within 0sim1 and calculate theinitial position of bacteria by unitary processing as follows

119909119894 = 119886119894sum119899119894=1 119886119894 (119894 = 1 2 119899) (13)

Now sort 1199091 1199092 119909119899 in descending order and the orderof 119909119894 represents the sequence of fault repairing4 Multiagent System Model for Real-Time

Adjustment of Repairing Strategy

41 Architecture of the RA-MAS The RA-MAS is made upby such three types of agents as coordination agent (CA)assist agent (AA) and execution agent (EA) Figure 1 showsa simple structure diagram charactering RA-MASrsquos operating

EA1EA2

AA2AA1

CAEA3 AA3

Figure 1 A simplified structure of RA-MAS

characteristics It can be seen that CA can share informationsimultaneously with EA and AA AA can only exchangeinformation with CA and its assisting role for EA can beonly achieved through CA parts of EA can also exchangeinformation between each other

Multifault rush repair is actually the service of squads forfaults thus this article presents the concept of unit-task andservice entity to facilitate characterization

Unit-task is the basic unit of the fault task and its demandfor the resource is more than one type It is necessary tospecify such attributes as the maximum expected time tocomplete the repair process the resource needed and soforth The number of the unit-tasks will be reduced as a faultis repaired and increased as a new fault occurs suddenly

Service entity is the basic unit of the repairing squadsand its capability is more than one type It is necessary tospecify such attributes as the repairing efficiency the resourceneeded and so forth The number of the service entities willbe reduced as a squad needs a rest and increased as a squadreturn to the repairing process

The multifault rush repair in DN in this paper includesfault tasks allocation fault recovery and repairing sequenceoptimization and information coordination which are imple-mented by CA AA and EA The working processes of CAAA and EA are described as follows

(1) Coordination Agent (CA) CA consists of the controlcenter agent (CCA) the background data processing (BDP)platform and the blackboardTheir communication is shownin Figure 2 The BDP platform is mainly responsible for thetwo tasks fault tasks allocation and emergency informationprocessing thus it consists of the utility model unit (UMU)and the emergency processing unit (EPU)

When faults occurred in DN after a disaster CCA willanalyze the information obtained from the informationacquisition system Then CCA writes the information into

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

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Mathematical Problems in Engineering

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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2 Mathematical Problems in Engineering

capability that keeps running in a dynamic environmentAccording to their own resources status capacity relevantknowledge and knowledge rules and the external environ-ment information acquired they can perceive the environ-ment accomplish specific tasks independently and achievethe intended target by planning reasoning and decision-making [6 7] MAS has become hot for more than 20 yearsIn the field of power systems there are many researches andapplications of multiagent technology and the agent compo-nent can be increased flexibly based on the actual demandwhich is consistentwith the functional requirements of powerdispatching automation system [8] A MAS is proposed tomanage the power dispatch inDNdynamically to balance thesupply and demand by considering the variability of DGs andloads through five types of autonomous agents in [9] A noveldistributed algorithm is presented for service restorationwithdistributed energy storage support following fault detectionlocation and isolation in [10] A MAS including communi-cation of agents is presented to restore a power system after afault in [11] Considering the excellent performance of MASthis paper introducesmultiagent theory to solve the real-timeadjustment problem of the multifault rush repairing strategyin distribution network

In the existing literatures on multifault rush repair ofdistribution network researches can be divided into twoparts the allocation of the fault tasks and the model ofmultifault rush repair in DN For the first part a multifaultrush repairing strategy optimization model with a singlesquad is established in [2] which can not be applied to theactual multisquad collaboration a multisquad cooperationmechanism is given in [5] which considers the allocationof resources and a repairing scheduling multiagent approachis proposed to archive an emergency repairing plan quicklyas well as a resource grouping scheme For the second partthe tie switch is taken as a virtual fault and a multifault rushrepairingmodel is built in [3 4] which assumes the repairingpersonnel and resource are enough and assigns fault tasks toeach squad randomly It seemingly simplifies the repairingmodel but it has some drawbacks (1) It increases the searchscope of the solution space greatly resulting in ldquocurse ofdimensionalityrdquo problem reducing the formulation speed ofthe repairing strategy and disobeying the characteristic ofurgency of the actual rush repair (2) It does not match withthe actual role of tie switches in DN (3) Only achievingrestoration of the load is the main content of fault recoverybut the rush repair needs to ensure all faults repaired

In response to these problems this paper first introducesutility theory to achieve an efficient allocation of fault tasksdivides fault level and develops repairing principle Then areal-time adjustment of repairing strategy multiagent system(RA-MAS) is established considering two cases when thereare no emergencies repairing squads complete the entireintelligent repair following the prestrategy when unexpectedevents occur it determines the real-time adjustment decisionultimately achieving the repairing target of restoring themaximum load power supply with minimum time cost

The remainder of the paper is organized as followsIn Section 2 a multisquad dynamic allocation of the faulttasks based on utility theory is discussed The distribution

network multifault repairing model and DBCC algorithmare introduced in Section 3 In Section 4 a multiagentsystem model for real-time adjustment of repairing strategyis presented Simulation results are analyzed to demonstratethe performance of the proposed approach in Section 5 Con-clusions and some possible paths for future researches arefinally drawn in Section 6

2 Multisquad Dynamic Allocation of the FaultTasks Based on Utility Theory

21 Goals of Allocation of the Fault Tasks It is assumed thatafter multiple faults occur in the DN the repairing taskscollection is 119879 = 1199051 1199052 119905119895 119905119899 where 119899 is the numberof faults the repairing squad collection is 119877 = 1199031 1199032 119903119894 119903119898 where 119898 (119898 lt 119899) is the number of repairingsquads which are equipped with the repairing personnel andresource 120588 is the task allocation solution set

The assignment of fault tasks needs to achieve the fol-lowing objectives A ensuring that a repairing squad hassufficient capacity to repair a fault B ensuring that eachsquadrsquosmission is broadly balancedC ensuring the repairingsquad with better expertise repairing their types of fault inpriority where ldquobetterrdquo means a relatively short period oftime to repair the same fault D ensuring that faults withhigh urgency are repaired in priority where the urgency isconsistent with the level of outage loadsE guaranteeing thatthe time of faults waiting to be repaired is as short as possibleF guaranteeing that faults assigned to the same squad arerepaired as continuous as possible in order to reduce thesquadrsquos waiting time

Targets AsimC can be realized by the utility model sothat a fault task allocation scheme can be quickly developeddynamically [12] TargetsDsimF need the automation of MASto achieve the adjustment of the rush repairing strategyactually according to the emergency

22 Utility Theory The utility theory is proposed byeconomists to characterize consumersrsquo consumption deci-sion and decision scheme and provide a mathematical toolto calculate the relative value of different indicators [13]Recently utility theory has been used by many researchers invarious fields to obtain the optimal decision [14 15] Utilityusually represents the userrsquos satisfaction to accept a serviceor resource The economic Cobb-Douglas utility function isoften used to describe the individual utility as it can betterreflect the tradeoffs among the model variables The typesof the utility function contain linear type conservative type(exponential type) adventure type and long type and theproper types need to be selected according to actual eventcharacteristics and the nature of the utility function [16]

In the multifault rush repair problem the early assign-ment of fault tasks can select the appropriate squad based onthe features of faultsrsquo demands and repairing squadsrsquo capa-bilities So the utility theory is introduced to characterize theheterogeneity of faultsrsquo demands and repairing squadsrsquo capa-bilities by constructing a utility function in this paper Utilityvalues reflect the competence for squad 119903119894 to repair fault 119905119895that is the satisfaction obtained by fault 119905119895 to be repaired

Mathematical Problems in Engineering 3

by squad 119903119894 resulting in a fault task allocation scheme withhigher satisfaction and overall utility Attribute vector isapplied to characterize the features of faultsrsquo demands andrepairing squadsrsquo capabilities in this paper

23 Attribute Vector

231 Repairing Squadrsquos Capability Vector

Definition 1 (repairing squad preference) Due to the lim-itations of squad location traffic conditions among faultsnatural conditions and different human factors repairingsquads have different wills to complete the repairing missionthat is repairing squadsrsquo preferences are different [17] Setthe level of preference of squad 119903119894 to repair fault 119905119895 as 120575119895119894(0 le 120575119895119894 le 1) and (120575119895119894 )min as the minimum level of preferencethen squad 119903119894may choose to repair fault 119905119895 when 120575119895119894 ge (120575119895119894 )minotherwise not

In order to quantify squadrsquos capability we classify it into119896 intuitive atomic capabilities 119888119894 and constitute the capabilityset 119862 = 1198881 1198882 119888119896 [18] Define the quantified descriptionof the squad capability vector119862119903119894 for the atomic capabilities ofsquad 119903119894 as follows

119862119903119894 = [12057211989411198881 12057211989421198882 120572119894119896119888119896]119879 (1)

where 120572119894119896 (120572119894119896 ge 0) is squadrsquos capability coefficient which is arelative value and dimensionless reflecting the relative degreeof squad 119903119894 to have atomic capability 119888119896 Squad 119903119894 does not havethe atomic capability 119888119896 when 120572119894119896 = 0Definition 2 (failure degree) After each fault has beenrepaired the squadrsquos resources will reduce and repairing effi-ciency will decline where the fault also has some ldquodamagerdquo tothe squad during the repair process Therefore the capabilitydrop of squad 119903119894 is defined as the failure degree 120583119903119894 (0 le 120583119903119894 le1) of its atomic capability to reflect the damage cost that thesquad suffered during the repairing process

Failure degree indicates that 120572119894119896 is not a constant but willshow a decreasing trend in the repairing process

232 Faultrsquos Demand Vector On the actual rush repairingsite each fault has a demand vector to quantify the degree ofits demand for different atomic capabilities and the demandvector 119862119905119895 of fault 119905119895 is as follows

119862119905119895 = [12057311989511198881 12057311989521198882 120573119895119896119888119896]119879 (2)

where 120573119895119896 (120573119895119896 ge 0) is faultrsquos demanding coefficient whichis a relative value and dimensionless reflecting the relativedemanddegree of fault 119905119895 for atomic capability 119888119896 Fault 119905119895 doesnot need the atomic capability 119888119896 when 120573119895119896 = 0

It is necessary to reduce the dimension of the repairingsquadrsquos capability vector and the faultrsquos demand vector tosimplify the utility function model and develop the faulttask allocation scheme quickly So the resources needed areprocessed into four groups according to the fault type trans-former failure resource group backup power failure resource

group cable failure resource group and overhead line failureresource group Squadsrsquo ability for these resources corre-sponds to squadsrsquo atomic capabilities 1198881sim1198884 in turn and thephysical meaning of 120572119894119896 is the comprehensive strength ofsquad 119903119894 to equip 119888119896

The squadrsquos repairing efficiency is corresponding toatomic capability 1198885 and its physical meaning is the efficiencyof different squads to repair the same fault when the resourceis consistent

24 Utility Model

241 Utility Function Model

Definition 3 (capability condition matrix119881119898times119899) It is a matrixthat reflects whether squad 119903119894 has the capability to repair fault119905119895 alone Thus the expression of element V119894119895 is given in theform of Boolean variables

V119894119895 = 1 if 120575119895119894 ge (120575119895119894 )min forall119886 120572119894119886 ge 1205731198951198860 others

(3)

Considering both the repairing squadrsquos preference andcapability vector we can find that only when V119894119895 = 1 doessquad 119903119894 have the capability to repair fault 119905119895 alone and fault119905119895 can not be assigned to squad 119903119894 when V119894119895 = 0 Then it willavoid the infeasible allocation of faults and greatly reduce thesearch space dimension of the fault allocation scheme

Set the utility function 119906119895(119894) = 0when V119894119895 = 0 yet we needto quantify the competent degree of squad 119903119894 for fault 119905119895 to getthe optimal-utility fault allocation scheme set when V119894119895 = 1thus getting higher satisfaction of fault 119905119895 Faultsrsquo demandsand squadsrsquo capabilities will change with the repairing envi-ronment changes and the repairing process performancesand the competent degree is also changed accordingly Thus119906119895(119894) is a function of the squadrsquos capability and faultrsquos de-mand

119906119895 (119894) = 119880119895 (119862119903119894 119862119905119895) V119894119895 = 10 V119894119895 = 0

119880119895 (119862119903119894 119862119905119895) = 119896sum119901=1

120596119901 sdot 119891119901 (120572119894119901 120573119895119901) (119896 = 5) (4)

where 120596119901 is the utility weight of a faultrsquos atomic demands andsum119896119901=1 120596119901 = 1 Its value is determined through a method (cha-racteristic value method) that is a combination of subject andobject119891119901(sdot) = 120573119895119901120572119894119901 is the utility function of the squadrsquos pthatomic capability to the faultrsquos pth atomic demand reflectingthat the closer a squadrsquos capability to a faultrsquos demand is thehigher the overall utility of faults task allocation is under thepremise of meeting fault demands

4 Mathematical Problems in Engineering

Set 119906119894119895 = 119906119895(119894) and get the utility function matrix

119880 = [1198801 1198802 sdot sdot sdot 119880119899] =[[[[[[[[[[

11990611199062119906119898

]]]]]]]]]]

=[[[[[[[[[[

11990611 11990612 sdot sdot sdot 119906111989911990621 11990622 sdot sdot sdot 1199062119899 d

1199061198981 1199061198982 sdot sdot sdot 119906119898119899

]]]]]]]]]]

(5)

Under the current state for the same fault the greater thevalue of the utility function is the higher the satisfaction ofits acceptance of the squadrsquos repair is that is the stronger thesquadrsquos capability to repair the fault is the more competentthe squad for the fault is

Finally based on the above utility function matrix 119880 theRoulette Wheel Selection method [19] is applied to allocatethe fault mission and 120588 will be archived

242 Squad Collaboration The cooperationmust be consid-ered when every squad can not repair a fault alone That istwo or more squads will repair a fault together

If fault 119905119895 needs to be repaired together by squads 119903119894 and119903119897 the repairing process is as follows(1) Combine capability vectors 119862119903119894 and 119862119903119897 as 119862119903119894+119897 The

capability vector 119862119903119894+119897 of the combined squad 119903119894+119897 is119862119903119894+119897

= [(1205721198941 + 1205721198971) 1198881 (1205721198942 + 1205721198972) 1198882 (120572119894119896 + 120572119897119896) 119888119896]119879 (6)

(2) Redevelop a capability conditionmatrix together withfaultrsquos demand vector 119862119905119895 The capability condition ofthe combined squad 119903119894+119897 to complete fault 119905119895 is as fol-lows V(119894+119897)119895 = 1 only when 120575119895119894 ge (120575119895119894 )min 120575119895119897 ge (120575119895

119897)minforall119886 120572119894119886 + 120572119897119886 ge 120573119895119886

(3) Establish a new utility function model and a newutility function matrix 1198801015840

3 Distribution Network MultifaultRepairing Model

31 Classification of Fault Levels andDevelopment of RepairingPrinciples The structure of DN is radial and the repairingpersonnel and resource are limited So it is particularlyimportant to determine the repairing priority of faults torestore important load when multifaults occur in DN

According to the three load levels divided in load reliabil-ity the urgency of the need to restore the power supply is also

divided into three levels loads of the first level the secondlevel and the third level are corresponding to loads of thehighest urgency the medium urgency and the low urgencyseparately

Faults are divided into two levels and the minimum faultset 119879min is defined Faults with the highest urgency are thefirst level faults and other faults are the second level faultsThe first level faults are included in 119879min where 119879min =1199051 1199052 119905119902 (119902 le 119899) With the premise of contact switchoperation all loads with the highest urgency can be restoredas long as 119902 faults in 119879min are repaired

Thus the actual rush repair should follow the followingrepairing principles repair the first level fault in priority andthen the second level fault after all loads with the highesturgency have been restored faults in the same level needto optimize the repairing order according to their objectivevalues

32 Objective Function The multifault rush repair shouldachieve the following four objectives each squad A repairsthe nearest fault to reduce the delay on power restorationcaused by drive B completes the repairing plan in advancerather than postponing itC restores loads of highest urgencyin priority to reduce the outage loss D ensures that therepairing process is affected as little as possible when emer-gencies occur for example the repairing route is damaged ora new fault occurs

According to repairing principles faults in119879min should berepaired prior to restore loads of highest urgency as quicklyas possible Thus the repairing order of the first level loadsshould be repaired with the shortest time Meanwhile inorder to ensure the maximum satisfaction of all faults therepairing efficiency is considered in the repairing time Thetotal repairing time of the first step can be expressed asfollows

min1198911 (1198832) = max 1198631 1198632 119863119898 (7)

where1198832 is the repairing sequence of faults119863119898 is the time ofsquad119898 to complete its repairing task the time of squad 119894 torepair fault 119909119895 is 119879119894(119909119895) + 119879119861(119909119895)1205721198945 119879119894(119909119895) is the driving timeand 119879119861(119909119895) is the expected repairing time of fault 119909119895

The objective of the repairing order of other faults is tominimize comprehensive outage loss and the total outageloss in the second step can be described as follows

min1198912 (1198832)

= 119898sum119894=1

119899minus119902sum119895=1

(119879119894(119909119895) + 119879119861 (119909119895)1205721198945 ) sdot 3sum119889119895=2

120573119889119895 (119909119895) 119871119889119895 (119909119895) (8)

where 120573119889119895(119909119895) is the level coefficient of outage load and119871119889119895(119909119895) is active power of outage load caused by fault 119909119895

Mathematical Problems in Engineering 5

Constraints in the model are introduced as follows

119892119896 isin 119866119877 (9)10038161003816100381610038161198751198961003816100381610038161003816 le 119875119896max (10)

119880119886min le 119880119886 le 119880119886max (11)

119877119904 le 119877 (12)

The constraints listed above include radial network topol-ogy constraint (9) branch current capacity constraint (10)node voltage constraint (11) and repair resources constraint(12)

In the above constraints 119892119896 is network topology of thearea which has been restored and 119866119877 is the set of radialnetwork structure under consideration If 119894th fault has beenrepaired the connection status between both sides of thefault will be changed by switch operation Constraint (9) is toprevent ring network operating 119875119896 is the power flow throughbranch 119896which is calculated by backforward sweep method119875119896max is the maximum power flow capacity limit of branch119896 Ua is node voltage in the repairing process 119880119886min is thelower limit of the node voltage 119880119886max is the upper limit ofthe node voltage 119877119904 is the required resources when multiplefaults occur and 119877 is resources available

For these two objectives the double-level mathematicaloptimization model of distribution network multifault rushrepair is establishedTheoptimal faults allocation scheme andrepairing order from 120588will be archived through the improvedDBCC algorithm

33 The Improved Discrete Mechanism of BCC AlgorithmBCC algorithm is an intelligent optimization algorithm forcontinuous variables and has been widely used in the con-tinuous problem field [20 21] However the control variablesin the multifault rush repairing order optimization is asequence of discrete variables and its value represents onlythe code of the fault rather than the position of bacteria in thesolution space Existing BCC algorithm is only applicable tooptimization problems with continuous variables Thus thefollowing method is applied to discretize the BCC algorithm

The bacteria dimension is taken to be 119899 since there are119899 faults in DN Represent the 119899 faults by random numbers1198861 1198862 119886119899 with values taken within 0sim1 and calculate theinitial position of bacteria by unitary processing as follows

119909119894 = 119886119894sum119899119894=1 119886119894 (119894 = 1 2 119899) (13)

Now sort 1199091 1199092 119909119899 in descending order and the orderof 119909119894 represents the sequence of fault repairing4 Multiagent System Model for Real-Time

Adjustment of Repairing Strategy

41 Architecture of the RA-MAS The RA-MAS is made upby such three types of agents as coordination agent (CA)assist agent (AA) and execution agent (EA) Figure 1 showsa simple structure diagram charactering RA-MASrsquos operating

EA1EA2

AA2AA1

CAEA3 AA3

Figure 1 A simplified structure of RA-MAS

characteristics It can be seen that CA can share informationsimultaneously with EA and AA AA can only exchangeinformation with CA and its assisting role for EA can beonly achieved through CA parts of EA can also exchangeinformation between each other

Multifault rush repair is actually the service of squads forfaults thus this article presents the concept of unit-task andservice entity to facilitate characterization

Unit-task is the basic unit of the fault task and its demandfor the resource is more than one type It is necessary tospecify such attributes as the maximum expected time tocomplete the repair process the resource needed and soforth The number of the unit-tasks will be reduced as a faultis repaired and increased as a new fault occurs suddenly

Service entity is the basic unit of the repairing squadsand its capability is more than one type It is necessary tospecify such attributes as the repairing efficiency the resourceneeded and so forth The number of the service entities willbe reduced as a squad needs a rest and increased as a squadreturn to the repairing process

The multifault rush repair in DN in this paper includesfault tasks allocation fault recovery and repairing sequenceoptimization and information coordination which are imple-mented by CA AA and EA The working processes of CAAA and EA are described as follows

(1) Coordination Agent (CA) CA consists of the controlcenter agent (CCA) the background data processing (BDP)platform and the blackboardTheir communication is shownin Figure 2 The BDP platform is mainly responsible for thetwo tasks fault tasks allocation and emergency informationprocessing thus it consists of the utility model unit (UMU)and the emergency processing unit (EPU)

When faults occurred in DN after a disaster CCA willanalyze the information obtained from the informationacquisition system Then CCA writes the information into

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

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Mathematical Problems in Engineering

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Mathematical Problems in Engineering 3

by squad 119903119894 resulting in a fault task allocation scheme withhigher satisfaction and overall utility Attribute vector isapplied to characterize the features of faultsrsquo demands andrepairing squadsrsquo capabilities in this paper

23 Attribute Vector

231 Repairing Squadrsquos Capability Vector

Definition 1 (repairing squad preference) Due to the lim-itations of squad location traffic conditions among faultsnatural conditions and different human factors repairingsquads have different wills to complete the repairing missionthat is repairing squadsrsquo preferences are different [17] Setthe level of preference of squad 119903119894 to repair fault 119905119895 as 120575119895119894(0 le 120575119895119894 le 1) and (120575119895119894 )min as the minimum level of preferencethen squad 119903119894may choose to repair fault 119905119895 when 120575119895119894 ge (120575119895119894 )minotherwise not

In order to quantify squadrsquos capability we classify it into119896 intuitive atomic capabilities 119888119894 and constitute the capabilityset 119862 = 1198881 1198882 119888119896 [18] Define the quantified descriptionof the squad capability vector119862119903119894 for the atomic capabilities ofsquad 119903119894 as follows

119862119903119894 = [12057211989411198881 12057211989421198882 120572119894119896119888119896]119879 (1)

where 120572119894119896 (120572119894119896 ge 0) is squadrsquos capability coefficient which is arelative value and dimensionless reflecting the relative degreeof squad 119903119894 to have atomic capability 119888119896 Squad 119903119894 does not havethe atomic capability 119888119896 when 120572119894119896 = 0Definition 2 (failure degree) After each fault has beenrepaired the squadrsquos resources will reduce and repairing effi-ciency will decline where the fault also has some ldquodamagerdquo tothe squad during the repair process Therefore the capabilitydrop of squad 119903119894 is defined as the failure degree 120583119903119894 (0 le 120583119903119894 le1) of its atomic capability to reflect the damage cost that thesquad suffered during the repairing process

Failure degree indicates that 120572119894119896 is not a constant but willshow a decreasing trend in the repairing process

232 Faultrsquos Demand Vector On the actual rush repairingsite each fault has a demand vector to quantify the degree ofits demand for different atomic capabilities and the demandvector 119862119905119895 of fault 119905119895 is as follows

119862119905119895 = [12057311989511198881 12057311989521198882 120573119895119896119888119896]119879 (2)

where 120573119895119896 (120573119895119896 ge 0) is faultrsquos demanding coefficient whichis a relative value and dimensionless reflecting the relativedemanddegree of fault 119905119895 for atomic capability 119888119896 Fault 119905119895 doesnot need the atomic capability 119888119896 when 120573119895119896 = 0

It is necessary to reduce the dimension of the repairingsquadrsquos capability vector and the faultrsquos demand vector tosimplify the utility function model and develop the faulttask allocation scheme quickly So the resources needed areprocessed into four groups according to the fault type trans-former failure resource group backup power failure resource

group cable failure resource group and overhead line failureresource group Squadsrsquo ability for these resources corre-sponds to squadsrsquo atomic capabilities 1198881sim1198884 in turn and thephysical meaning of 120572119894119896 is the comprehensive strength ofsquad 119903119894 to equip 119888119896

The squadrsquos repairing efficiency is corresponding toatomic capability 1198885 and its physical meaning is the efficiencyof different squads to repair the same fault when the resourceis consistent

24 Utility Model

241 Utility Function Model

Definition 3 (capability condition matrix119881119898times119899) It is a matrixthat reflects whether squad 119903119894 has the capability to repair fault119905119895 alone Thus the expression of element V119894119895 is given in theform of Boolean variables

V119894119895 = 1 if 120575119895119894 ge (120575119895119894 )min forall119886 120572119894119886 ge 1205731198951198860 others

(3)

Considering both the repairing squadrsquos preference andcapability vector we can find that only when V119894119895 = 1 doessquad 119903119894 have the capability to repair fault 119905119895 alone and fault119905119895 can not be assigned to squad 119903119894 when V119894119895 = 0 Then it willavoid the infeasible allocation of faults and greatly reduce thesearch space dimension of the fault allocation scheme

Set the utility function 119906119895(119894) = 0when V119894119895 = 0 yet we needto quantify the competent degree of squad 119903119894 for fault 119905119895 to getthe optimal-utility fault allocation scheme set when V119894119895 = 1thus getting higher satisfaction of fault 119905119895 Faultsrsquo demandsand squadsrsquo capabilities will change with the repairing envi-ronment changes and the repairing process performancesand the competent degree is also changed accordingly Thus119906119895(119894) is a function of the squadrsquos capability and faultrsquos de-mand

119906119895 (119894) = 119880119895 (119862119903119894 119862119905119895) V119894119895 = 10 V119894119895 = 0

119880119895 (119862119903119894 119862119905119895) = 119896sum119901=1

120596119901 sdot 119891119901 (120572119894119901 120573119895119901) (119896 = 5) (4)

where 120596119901 is the utility weight of a faultrsquos atomic demands andsum119896119901=1 120596119901 = 1 Its value is determined through a method (cha-racteristic value method) that is a combination of subject andobject119891119901(sdot) = 120573119895119901120572119894119901 is the utility function of the squadrsquos pthatomic capability to the faultrsquos pth atomic demand reflectingthat the closer a squadrsquos capability to a faultrsquos demand is thehigher the overall utility of faults task allocation is under thepremise of meeting fault demands

4 Mathematical Problems in Engineering

Set 119906119894119895 = 119906119895(119894) and get the utility function matrix

119880 = [1198801 1198802 sdot sdot sdot 119880119899] =[[[[[[[[[[

11990611199062119906119898

]]]]]]]]]]

=[[[[[[[[[[

11990611 11990612 sdot sdot sdot 119906111989911990621 11990622 sdot sdot sdot 1199062119899 d

1199061198981 1199061198982 sdot sdot sdot 119906119898119899

]]]]]]]]]]

(5)

Under the current state for the same fault the greater thevalue of the utility function is the higher the satisfaction ofits acceptance of the squadrsquos repair is that is the stronger thesquadrsquos capability to repair the fault is the more competentthe squad for the fault is

Finally based on the above utility function matrix 119880 theRoulette Wheel Selection method [19] is applied to allocatethe fault mission and 120588 will be archived

242 Squad Collaboration The cooperationmust be consid-ered when every squad can not repair a fault alone That istwo or more squads will repair a fault together

If fault 119905119895 needs to be repaired together by squads 119903119894 and119903119897 the repairing process is as follows(1) Combine capability vectors 119862119903119894 and 119862119903119897 as 119862119903119894+119897 The

capability vector 119862119903119894+119897 of the combined squad 119903119894+119897 is119862119903119894+119897

= [(1205721198941 + 1205721198971) 1198881 (1205721198942 + 1205721198972) 1198882 (120572119894119896 + 120572119897119896) 119888119896]119879 (6)

(2) Redevelop a capability conditionmatrix together withfaultrsquos demand vector 119862119905119895 The capability condition ofthe combined squad 119903119894+119897 to complete fault 119905119895 is as fol-lows V(119894+119897)119895 = 1 only when 120575119895119894 ge (120575119895119894 )min 120575119895119897 ge (120575119895

119897)minforall119886 120572119894119886 + 120572119897119886 ge 120573119895119886

(3) Establish a new utility function model and a newutility function matrix 1198801015840

3 Distribution Network MultifaultRepairing Model

31 Classification of Fault Levels andDevelopment of RepairingPrinciples The structure of DN is radial and the repairingpersonnel and resource are limited So it is particularlyimportant to determine the repairing priority of faults torestore important load when multifaults occur in DN

According to the three load levels divided in load reliabil-ity the urgency of the need to restore the power supply is also

divided into three levels loads of the first level the secondlevel and the third level are corresponding to loads of thehighest urgency the medium urgency and the low urgencyseparately

Faults are divided into two levels and the minimum faultset 119879min is defined Faults with the highest urgency are thefirst level faults and other faults are the second level faultsThe first level faults are included in 119879min where 119879min =1199051 1199052 119905119902 (119902 le 119899) With the premise of contact switchoperation all loads with the highest urgency can be restoredas long as 119902 faults in 119879min are repaired

Thus the actual rush repair should follow the followingrepairing principles repair the first level fault in priority andthen the second level fault after all loads with the highesturgency have been restored faults in the same level needto optimize the repairing order according to their objectivevalues

32 Objective Function The multifault rush repair shouldachieve the following four objectives each squad A repairsthe nearest fault to reduce the delay on power restorationcaused by drive B completes the repairing plan in advancerather than postponing itC restores loads of highest urgencyin priority to reduce the outage loss D ensures that therepairing process is affected as little as possible when emer-gencies occur for example the repairing route is damaged ora new fault occurs

According to repairing principles faults in119879min should berepaired prior to restore loads of highest urgency as quicklyas possible Thus the repairing order of the first level loadsshould be repaired with the shortest time Meanwhile inorder to ensure the maximum satisfaction of all faults therepairing efficiency is considered in the repairing time Thetotal repairing time of the first step can be expressed asfollows

min1198911 (1198832) = max 1198631 1198632 119863119898 (7)

where1198832 is the repairing sequence of faults119863119898 is the time ofsquad119898 to complete its repairing task the time of squad 119894 torepair fault 119909119895 is 119879119894(119909119895) + 119879119861(119909119895)1205721198945 119879119894(119909119895) is the driving timeand 119879119861(119909119895) is the expected repairing time of fault 119909119895

The objective of the repairing order of other faults is tominimize comprehensive outage loss and the total outageloss in the second step can be described as follows

min1198912 (1198832)

= 119898sum119894=1

119899minus119902sum119895=1

(119879119894(119909119895) + 119879119861 (119909119895)1205721198945 ) sdot 3sum119889119895=2

120573119889119895 (119909119895) 119871119889119895 (119909119895) (8)

where 120573119889119895(119909119895) is the level coefficient of outage load and119871119889119895(119909119895) is active power of outage load caused by fault 119909119895

Mathematical Problems in Engineering 5

Constraints in the model are introduced as follows

119892119896 isin 119866119877 (9)10038161003816100381610038161198751198961003816100381610038161003816 le 119875119896max (10)

119880119886min le 119880119886 le 119880119886max (11)

119877119904 le 119877 (12)

The constraints listed above include radial network topol-ogy constraint (9) branch current capacity constraint (10)node voltage constraint (11) and repair resources constraint(12)

In the above constraints 119892119896 is network topology of thearea which has been restored and 119866119877 is the set of radialnetwork structure under consideration If 119894th fault has beenrepaired the connection status between both sides of thefault will be changed by switch operation Constraint (9) is toprevent ring network operating 119875119896 is the power flow throughbranch 119896which is calculated by backforward sweep method119875119896max is the maximum power flow capacity limit of branch119896 Ua is node voltage in the repairing process 119880119886min is thelower limit of the node voltage 119880119886max is the upper limit ofthe node voltage 119877119904 is the required resources when multiplefaults occur and 119877 is resources available

For these two objectives the double-level mathematicaloptimization model of distribution network multifault rushrepair is establishedTheoptimal faults allocation scheme andrepairing order from 120588will be archived through the improvedDBCC algorithm

33 The Improved Discrete Mechanism of BCC AlgorithmBCC algorithm is an intelligent optimization algorithm forcontinuous variables and has been widely used in the con-tinuous problem field [20 21] However the control variablesin the multifault rush repairing order optimization is asequence of discrete variables and its value represents onlythe code of the fault rather than the position of bacteria in thesolution space Existing BCC algorithm is only applicable tooptimization problems with continuous variables Thus thefollowing method is applied to discretize the BCC algorithm

The bacteria dimension is taken to be 119899 since there are119899 faults in DN Represent the 119899 faults by random numbers1198861 1198862 119886119899 with values taken within 0sim1 and calculate theinitial position of bacteria by unitary processing as follows

119909119894 = 119886119894sum119899119894=1 119886119894 (119894 = 1 2 119899) (13)

Now sort 1199091 1199092 119909119899 in descending order and the orderof 119909119894 represents the sequence of fault repairing4 Multiagent System Model for Real-Time

Adjustment of Repairing Strategy

41 Architecture of the RA-MAS The RA-MAS is made upby such three types of agents as coordination agent (CA)assist agent (AA) and execution agent (EA) Figure 1 showsa simple structure diagram charactering RA-MASrsquos operating

EA1EA2

AA2AA1

CAEA3 AA3

Figure 1 A simplified structure of RA-MAS

characteristics It can be seen that CA can share informationsimultaneously with EA and AA AA can only exchangeinformation with CA and its assisting role for EA can beonly achieved through CA parts of EA can also exchangeinformation between each other

Multifault rush repair is actually the service of squads forfaults thus this article presents the concept of unit-task andservice entity to facilitate characterization

Unit-task is the basic unit of the fault task and its demandfor the resource is more than one type It is necessary tospecify such attributes as the maximum expected time tocomplete the repair process the resource needed and soforth The number of the unit-tasks will be reduced as a faultis repaired and increased as a new fault occurs suddenly

Service entity is the basic unit of the repairing squadsand its capability is more than one type It is necessary tospecify such attributes as the repairing efficiency the resourceneeded and so forth The number of the service entities willbe reduced as a squad needs a rest and increased as a squadreturn to the repairing process

The multifault rush repair in DN in this paper includesfault tasks allocation fault recovery and repairing sequenceoptimization and information coordination which are imple-mented by CA AA and EA The working processes of CAAA and EA are described as follows

(1) Coordination Agent (CA) CA consists of the controlcenter agent (CCA) the background data processing (BDP)platform and the blackboardTheir communication is shownin Figure 2 The BDP platform is mainly responsible for thetwo tasks fault tasks allocation and emergency informationprocessing thus it consists of the utility model unit (UMU)and the emergency processing unit (EPU)

When faults occurred in DN after a disaster CCA willanalyze the information obtained from the informationacquisition system Then CCA writes the information into

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Set 119906119894119895 = 119906119895(119894) and get the utility function matrix

119880 = [1198801 1198802 sdot sdot sdot 119880119899] =[[[[[[[[[[

11990611199062119906119898

]]]]]]]]]]

=[[[[[[[[[[

11990611 11990612 sdot sdot sdot 119906111989911990621 11990622 sdot sdot sdot 1199062119899 d

1199061198981 1199061198982 sdot sdot sdot 119906119898119899

]]]]]]]]]]

(5)

Under the current state for the same fault the greater thevalue of the utility function is the higher the satisfaction ofits acceptance of the squadrsquos repair is that is the stronger thesquadrsquos capability to repair the fault is the more competentthe squad for the fault is

Finally based on the above utility function matrix 119880 theRoulette Wheel Selection method [19] is applied to allocatethe fault mission and 120588 will be archived

242 Squad Collaboration The cooperationmust be consid-ered when every squad can not repair a fault alone That istwo or more squads will repair a fault together

If fault 119905119895 needs to be repaired together by squads 119903119894 and119903119897 the repairing process is as follows(1) Combine capability vectors 119862119903119894 and 119862119903119897 as 119862119903119894+119897 The

capability vector 119862119903119894+119897 of the combined squad 119903119894+119897 is119862119903119894+119897

= [(1205721198941 + 1205721198971) 1198881 (1205721198942 + 1205721198972) 1198882 (120572119894119896 + 120572119897119896) 119888119896]119879 (6)

(2) Redevelop a capability conditionmatrix together withfaultrsquos demand vector 119862119905119895 The capability condition ofthe combined squad 119903119894+119897 to complete fault 119905119895 is as fol-lows V(119894+119897)119895 = 1 only when 120575119895119894 ge (120575119895119894 )min 120575119895119897 ge (120575119895

119897)minforall119886 120572119894119886 + 120572119897119886 ge 120573119895119886

(3) Establish a new utility function model and a newutility function matrix 1198801015840

3 Distribution Network MultifaultRepairing Model

31 Classification of Fault Levels andDevelopment of RepairingPrinciples The structure of DN is radial and the repairingpersonnel and resource are limited So it is particularlyimportant to determine the repairing priority of faults torestore important load when multifaults occur in DN

According to the three load levels divided in load reliabil-ity the urgency of the need to restore the power supply is also

divided into three levels loads of the first level the secondlevel and the third level are corresponding to loads of thehighest urgency the medium urgency and the low urgencyseparately

Faults are divided into two levels and the minimum faultset 119879min is defined Faults with the highest urgency are thefirst level faults and other faults are the second level faultsThe first level faults are included in 119879min where 119879min =1199051 1199052 119905119902 (119902 le 119899) With the premise of contact switchoperation all loads with the highest urgency can be restoredas long as 119902 faults in 119879min are repaired

Thus the actual rush repair should follow the followingrepairing principles repair the first level fault in priority andthen the second level fault after all loads with the highesturgency have been restored faults in the same level needto optimize the repairing order according to their objectivevalues

32 Objective Function The multifault rush repair shouldachieve the following four objectives each squad A repairsthe nearest fault to reduce the delay on power restorationcaused by drive B completes the repairing plan in advancerather than postponing itC restores loads of highest urgencyin priority to reduce the outage loss D ensures that therepairing process is affected as little as possible when emer-gencies occur for example the repairing route is damaged ora new fault occurs

According to repairing principles faults in119879min should berepaired prior to restore loads of highest urgency as quicklyas possible Thus the repairing order of the first level loadsshould be repaired with the shortest time Meanwhile inorder to ensure the maximum satisfaction of all faults therepairing efficiency is considered in the repairing time Thetotal repairing time of the first step can be expressed asfollows

min1198911 (1198832) = max 1198631 1198632 119863119898 (7)

where1198832 is the repairing sequence of faults119863119898 is the time ofsquad119898 to complete its repairing task the time of squad 119894 torepair fault 119909119895 is 119879119894(119909119895) + 119879119861(119909119895)1205721198945 119879119894(119909119895) is the driving timeand 119879119861(119909119895) is the expected repairing time of fault 119909119895

The objective of the repairing order of other faults is tominimize comprehensive outage loss and the total outageloss in the second step can be described as follows

min1198912 (1198832)

= 119898sum119894=1

119899minus119902sum119895=1

(119879119894(119909119895) + 119879119861 (119909119895)1205721198945 ) sdot 3sum119889119895=2

120573119889119895 (119909119895) 119871119889119895 (119909119895) (8)

where 120573119889119895(119909119895) is the level coefficient of outage load and119871119889119895(119909119895) is active power of outage load caused by fault 119909119895

Mathematical Problems in Engineering 5

Constraints in the model are introduced as follows

119892119896 isin 119866119877 (9)10038161003816100381610038161198751198961003816100381610038161003816 le 119875119896max (10)

119880119886min le 119880119886 le 119880119886max (11)

119877119904 le 119877 (12)

The constraints listed above include radial network topol-ogy constraint (9) branch current capacity constraint (10)node voltage constraint (11) and repair resources constraint(12)

In the above constraints 119892119896 is network topology of thearea which has been restored and 119866119877 is the set of radialnetwork structure under consideration If 119894th fault has beenrepaired the connection status between both sides of thefault will be changed by switch operation Constraint (9) is toprevent ring network operating 119875119896 is the power flow throughbranch 119896which is calculated by backforward sweep method119875119896max is the maximum power flow capacity limit of branch119896 Ua is node voltage in the repairing process 119880119886min is thelower limit of the node voltage 119880119886max is the upper limit ofthe node voltage 119877119904 is the required resources when multiplefaults occur and 119877 is resources available

For these two objectives the double-level mathematicaloptimization model of distribution network multifault rushrepair is establishedTheoptimal faults allocation scheme andrepairing order from 120588will be archived through the improvedDBCC algorithm

33 The Improved Discrete Mechanism of BCC AlgorithmBCC algorithm is an intelligent optimization algorithm forcontinuous variables and has been widely used in the con-tinuous problem field [20 21] However the control variablesin the multifault rush repairing order optimization is asequence of discrete variables and its value represents onlythe code of the fault rather than the position of bacteria in thesolution space Existing BCC algorithm is only applicable tooptimization problems with continuous variables Thus thefollowing method is applied to discretize the BCC algorithm

The bacteria dimension is taken to be 119899 since there are119899 faults in DN Represent the 119899 faults by random numbers1198861 1198862 119886119899 with values taken within 0sim1 and calculate theinitial position of bacteria by unitary processing as follows

119909119894 = 119886119894sum119899119894=1 119886119894 (119894 = 1 2 119899) (13)

Now sort 1199091 1199092 119909119899 in descending order and the orderof 119909119894 represents the sequence of fault repairing4 Multiagent System Model for Real-Time

Adjustment of Repairing Strategy

41 Architecture of the RA-MAS The RA-MAS is made upby such three types of agents as coordination agent (CA)assist agent (AA) and execution agent (EA) Figure 1 showsa simple structure diagram charactering RA-MASrsquos operating

EA1EA2

AA2AA1

CAEA3 AA3

Figure 1 A simplified structure of RA-MAS

characteristics It can be seen that CA can share informationsimultaneously with EA and AA AA can only exchangeinformation with CA and its assisting role for EA can beonly achieved through CA parts of EA can also exchangeinformation between each other

Multifault rush repair is actually the service of squads forfaults thus this article presents the concept of unit-task andservice entity to facilitate characterization

Unit-task is the basic unit of the fault task and its demandfor the resource is more than one type It is necessary tospecify such attributes as the maximum expected time tocomplete the repair process the resource needed and soforth The number of the unit-tasks will be reduced as a faultis repaired and increased as a new fault occurs suddenly

Service entity is the basic unit of the repairing squadsand its capability is more than one type It is necessary tospecify such attributes as the repairing efficiency the resourceneeded and so forth The number of the service entities willbe reduced as a squad needs a rest and increased as a squadreturn to the repairing process

The multifault rush repair in DN in this paper includesfault tasks allocation fault recovery and repairing sequenceoptimization and information coordination which are imple-mented by CA AA and EA The working processes of CAAA and EA are described as follows

(1) Coordination Agent (CA) CA consists of the controlcenter agent (CCA) the background data processing (BDP)platform and the blackboardTheir communication is shownin Figure 2 The BDP platform is mainly responsible for thetwo tasks fault tasks allocation and emergency informationprocessing thus it consists of the utility model unit (UMU)and the emergency processing unit (EPU)

When faults occurred in DN after a disaster CCA willanalyze the information obtained from the informationacquisition system Then CCA writes the information into

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

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Mathematical Problems in Engineering

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering 5

Constraints in the model are introduced as follows

119892119896 isin 119866119877 (9)10038161003816100381610038161198751198961003816100381610038161003816 le 119875119896max (10)

119880119886min le 119880119886 le 119880119886max (11)

119877119904 le 119877 (12)

The constraints listed above include radial network topol-ogy constraint (9) branch current capacity constraint (10)node voltage constraint (11) and repair resources constraint(12)

In the above constraints 119892119896 is network topology of thearea which has been restored and 119866119877 is the set of radialnetwork structure under consideration If 119894th fault has beenrepaired the connection status between both sides of thefault will be changed by switch operation Constraint (9) is toprevent ring network operating 119875119896 is the power flow throughbranch 119896which is calculated by backforward sweep method119875119896max is the maximum power flow capacity limit of branch119896 Ua is node voltage in the repairing process 119880119886min is thelower limit of the node voltage 119880119886max is the upper limit ofthe node voltage 119877119904 is the required resources when multiplefaults occur and 119877 is resources available

For these two objectives the double-level mathematicaloptimization model of distribution network multifault rushrepair is establishedTheoptimal faults allocation scheme andrepairing order from 120588will be archived through the improvedDBCC algorithm

33 The Improved Discrete Mechanism of BCC AlgorithmBCC algorithm is an intelligent optimization algorithm forcontinuous variables and has been widely used in the con-tinuous problem field [20 21] However the control variablesin the multifault rush repairing order optimization is asequence of discrete variables and its value represents onlythe code of the fault rather than the position of bacteria in thesolution space Existing BCC algorithm is only applicable tooptimization problems with continuous variables Thus thefollowing method is applied to discretize the BCC algorithm

The bacteria dimension is taken to be 119899 since there are119899 faults in DN Represent the 119899 faults by random numbers1198861 1198862 119886119899 with values taken within 0sim1 and calculate theinitial position of bacteria by unitary processing as follows

119909119894 = 119886119894sum119899119894=1 119886119894 (119894 = 1 2 119899) (13)

Now sort 1199091 1199092 119909119899 in descending order and the orderof 119909119894 represents the sequence of fault repairing4 Multiagent System Model for Real-Time

Adjustment of Repairing Strategy

41 Architecture of the RA-MAS The RA-MAS is made upby such three types of agents as coordination agent (CA)assist agent (AA) and execution agent (EA) Figure 1 showsa simple structure diagram charactering RA-MASrsquos operating

EA1EA2

AA2AA1

CAEA3 AA3

Figure 1 A simplified structure of RA-MAS

characteristics It can be seen that CA can share informationsimultaneously with EA and AA AA can only exchangeinformation with CA and its assisting role for EA can beonly achieved through CA parts of EA can also exchangeinformation between each other

Multifault rush repair is actually the service of squads forfaults thus this article presents the concept of unit-task andservice entity to facilitate characterization

Unit-task is the basic unit of the fault task and its demandfor the resource is more than one type It is necessary tospecify such attributes as the maximum expected time tocomplete the repair process the resource needed and soforth The number of the unit-tasks will be reduced as a faultis repaired and increased as a new fault occurs suddenly

Service entity is the basic unit of the repairing squadsand its capability is more than one type It is necessary tospecify such attributes as the repairing efficiency the resourceneeded and so forth The number of the service entities willbe reduced as a squad needs a rest and increased as a squadreturn to the repairing process

The multifault rush repair in DN in this paper includesfault tasks allocation fault recovery and repairing sequenceoptimization and information coordination which are imple-mented by CA AA and EA The working processes of CAAA and EA are described as follows

(1) Coordination Agent (CA) CA consists of the controlcenter agent (CCA) the background data processing (BDP)platform and the blackboardTheir communication is shownin Figure 2 The BDP platform is mainly responsible for thetwo tasks fault tasks allocation and emergency informationprocessing thus it consists of the utility model unit (UMU)and the emergency processing unit (EPU)

When faults occurred in DN after a disaster CCA willanalyze the information obtained from the informationacquisition system Then CCA writes the information into

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

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Mathematical Problems in Engineering

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

BDP platform

UMU

EPU

CCA

Blackboard

Figure 2 A simplified structure of CA

the blackboard for other agents to read and transmits it tothe BDPplatformThe information includes theDN topologyinformation geographical information of the outage zonethe load information the repairing squad information thefault information the DG and emergent power-vehicle infor-mation and the possible unexpected event information

CCA analyzes and processes the geographical informa-tion of the outage zone the repairing squadsrsquo informationand the faultsrsquo information and then predicts the driving time119865119861 and the fault repairing time 119879119861 At last CCA transmitsthem to the DP platform and the blackboard

UMU of the BDP platform integrates the DN topologyinformation the repairing squadsrsquo information and thefaultsrsquo information Then it will provide attribute vectors 119862119903119894and 119862119905119895 the utility model and the utility function matrix Atlast it will obtain the task allocation solution set 120588 via theroulette wheel selection method and write it into the black-board

When the BDP platform gets any information aboutemergencies EPU processes the emergency information andreports it to CCA CCA reanalyzes and reprocesses largeamounts of information and then transmits it to the BDPplatform and blackboard

(2) Assist Agent (AA) AA is comprised of the distribu-tion generator agent (DGA) the emergent power-vehicleagent (EPA) and the switch control agent (SCA) They canexchange information with each other directly and cooperatetogether to repair the faults

DGA is in the charge of CCA and in charge of controllingconnection states of all DGs in the outage zone to supplypower to its maximum ability for the microgrid it belongsto When the fault is repaired DG continues to operate ingrid-connected state Meanwhile DGA monitors and storesDG information and then writes it into the blackboard DGinformation includes the amount type rated power utiliza-tion rate of fuel electricity price and connection state of thedevice

EPA is in the charge of CCA and in charge of controllingconnection states and power supply positions of the emergentpower-vehicles which supply power temporarily for the firstlevel loads as a priority When the fault is repaired the emer-gent power-vehicles go on working as the principle of theshortest path and the maximum reduced economic loss

AASCA

DGAEPA

CCA

DP platform

RAA

RSA1

RSA2RSAm

Blackboard

⋱

Figure 3 The architecture diagram of RA-MAS

Meanwhile EPA monitors and stores the emergent power-vehicle information and then writes it into the black-boardThe emergent power-vehicle information includes theamount capacity connection state current position and util-ization rate of fuel of the device

SCA is in the charge of CCA and in charge of controllingon-or-off state of the tie breaking switch and the sectionswitch to optimize the cooperative operation strategy for theobject of the fault recovery The improved DBCC algorithmis used in the process Meanwhile SCA monitors and storesthe switch information and then writes it into the blackboardSwitch information includes the amount capacity and on-or-off state of the switch

(3) Execute Agent (EA) EA includes the real-time adjust agent(RAA) and repairing squad agent (RSA) and RSA is for theservice entity

At first RAA reads 120588 andAArsquos information from the black-board Then it optimizes each scheme in phase according tothe load level via the improved DBCC algorithm It reportsthe best scheme and repairing order directly to CCA at last

RSA is the real service entity and in charge of repairingunit-tasks and writing the repairing process and local infor-mation into the blackboard in the time

The architecture of RA-MAS is shown in Figure 3

42Workflow of the RA-MAS Theproposed RA-MAS in thispaper is based on the premise of normal communicationThewidespread outage after a disaster causes its communicationinterrupt so the system will be the first to be repairedFaults in DN will be repaired after RA-MAS has recovered itscommunication ability RA-MAS is a system in the essencethat the service entity processes the unit-task in intelligenceIts intelligence mainly embodies developing the prestrategyin advance and adjusting the prestrategy in real-time whenemergencies occur The specific work process is as followsand Figure 4 shows the simplified operation flowchart of RA-MAS

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

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Mathematical PhysicsAdvances in

Complex AnalysisJournal of

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OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Faults occur in the DN

CCA obtains information

Analyze information

Estimate FB and TB

BDP platform

Blackboard

Emergency

UMUEEU

AA

RSA

Report information i = n

i = i minus 1

Repair

Empty faultcollection

EndYes

Yes

No

No

RAA

Figure 4 The simplified operation flowchart of RA-MAS

(1) CCAmonitors the current state of DN obtains infor-mation from the information collection system gives119879119861 and 119865119861 via the information integrationanalysismodule and updates the BDP platform and theblackboard

(2) After UMU of the BDP platform has integrated andanalyzed the above information the repairing squadsrsquocapability vector and the faultsrsquo demand vector areobtained The utility model building module estab-lishes the capability condition judgment matrixaccording to the attribute vector builds the utilitymodel and calculates the utility function matrix Thefault task allocation module starts the roulette wheelselection method to complete the effective allocationof all unit-tasks generating 120588 which is written intothe blackboard by the information output unit If theinformation repository unit obtains any informationabout emergencies turn to step (3) otherwise go tostep (4)

(3) EPU processes emergency information and reports itto CCA CCA reanalyzes and reprocesses the infor-mation

(a) When a new fault occurs suddenly it willbe added into the queue where the faults are

waiting for repairing and the faultsrsquo demandinformation will be modified and then return tostep (2)

(b) When a squad needs a rest its information willbe removed and the repairing squadsrsquo capabilityinformation will be modified and then return tostep (2)

(c) When the actual time is inconsistent with theexpected time either the repairing time or thedriving time either in advance or afterwardsthe current time will be taken as the startingtime and then return to step (2)

(4) AA finishes the following work

(a) DGA cooperates with the repairing work bycontrolling connection states of all DGs in theoutage zone When loads in the microgrid thatthe DG belongs to lose power due to faultsDG is isolated island operation and suppliespower independently of its internal loads Afterfaults have been repaired and the grid recoversnormal power supply DG gets back into thegrid-connected state

(b) EPA cooperates with the repairing work by con-trolling connection states and power supplypositions of the emergent power-vehicles Thepower-vehicle is dispatched to the capacity-matching and the nearest first level load tosupply power and the power supply time isrecorded When the fault is repaired and theload recovers normal power supply it will besent to the next capacity-matching and the near-est first level load till its fuel is depleted or allfaults are repaired

(c) SCA cooperates with the repairing work bycontrolling the on-or-off state of the tie breakingswitch and the section switch giving the on-or-off command to turn to supply with the max-imum loads and ensuring the least operationtimes After all faults are repaired the switcheswill be restored to the initial state

(5) RAA reads 120588 and AArsquos information from the black-board and stores them into the information repos-itory At first the rush repairing model buildingmodule establishes the double-level mathematicaloptimizationmodel according to the faultsrsquo hierarchyThen the repairing sequence optimization moduleoptimizes the repairing order of each service entity bythe improvedDBCCalgorithm giving the best repair-ing route and the specific actions of AA RAA reportsthe best scheme and repairing order to CCA finally

(6) RSA applies for unit-tasks from CCA and repairsfaults in turn After each RSA has finished its unit-tasks the mission ending information is reported toCCA directly

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

Table 1 Detail of load level

Load level Load number

The first level 101 105 107 109 110 115 119 128 132 135 137 138 140 144 145 148 150 153 154 155 156 161 169 170 172 177 183184 192 193 195

The second level 102 103 106 108 111 113 114 116 118 120 121 122 125 126 130 131 133 134 139 142 146 147 151 152 158 159 162 163164 166 167 168 171 174 176 179 180 181 185 186 187 188 189 190 191 194 197 198

The third level 104 112 117 123 124 127 129 136 141 143 149 157 160 165 173 175 178 182 196

Table 2 Preference information of squads

Squad Fault43 44 45 46 47 48 49 50 51 52 53

a 08 094 06 085 09 07 088 08 08 076 085b 078 09 055 085 095 077 092 08 081 075 09c 088 077 05 072 078 068 08 091 09 086 087

Table 3 Repairing squadsrsquo capability vector

Squad Atomic capacity1 2 3 4 5

a 185 197 177 173 193b 184 189 178 163 198c 183 177 185 172 194

(7) When the fault task set is null CCA receives allmission ending information from RSA and shuts offRA-MAS

5 Simulation Results and Discussion

51 Parameter Initialization In order to verify the perfor-mance of the proposed RA-MAS method a computationalstudy is presented in this section The distribution networkof H county [22] is operated and three DGs and elevenfaults are randomly added into the system which is shownin Figure 5 The system contains five distribution lines fivenormally open contact switches and fifteen normally closedsection switches Assuming the power company has threerepairing squads and two emergent power-vehicles for send-ing respectively a b c and EP1 EP2 Set bacterial population119873 = 100 iterations119870 = 50 (120575119895119894 )min = 05120583119903119894 = 0005119871 three =2MW and 119871 two = 1MW and the experiment is simulat-ed viaMATLAB71Thedetail of load level is shown inTable 1

According to the working characteristic of RA-MASCCA first gets the repairing capability information of threesquads the demanding information of the 11 faults andother information on repairing site When the estimatedrepairing information is consistent with the actual one UMUbuilds the utility function matrix model and provides theutility value and the fault task allocation scheme set 120588 ThenRAA establishes the faultsrsquo repairing optimization modeland provides repairing order with the cooperation of DGthe emergent power-vehicles and switches Finally CCA

Table 4 Faultsrsquo demanding vector

Atomicdemand

Fault43 44 45 46 47 48 49 50 51 52 53

1 0 0 0 0 0 0 0 0 0 0 183

2 0 0 0 168 0 0 0 190 0 0 0

3 155 135 0 0 168 0 175 0 0 156 0

4 0 0 157 0 0 163 0 0 166 0 0

5 190 184 109 172 182 139 174 194 171 169 186

controls each agent to complete the repairing work restoringloads with power supply

52 Analysis of UMU The preference values of squads torepair each fault are shown in Table 2 As long as the pre-ference value is more than the minimum preference of squad119903119894 to repair fault 119905119895 (120575119895119894 )min = 05 119903119894 would like to choose torepair fault 119905119895

Though each squad is willing to repair each fault itspreference to repair fault 45 is small Because the outage loads123 and 124 caused by fault 45 are not the first level load andtheir urge to recover power supply is not high

Each atomic capability coefficient of repairing squads andeach faultrsquos demanding coefficient is presented in Tables 3 and4 respectively

After the capability condition judgment to complete therepairing mission according to Tables 2sim4 it is found thatsquad b does not have the ability to repair fault 51 and allsquads do not have the ability to repair fault 50 which needsthe squadsrsquo collaboration Then the utility function matrix119880 and the new one 1198801015840 are obtained which characterize theutility value of each squad to repair each fault alone and theutility value of each of the two combined squads to repair fault50 respectively Finally considering the effect of 120583119903119894 faultsare allocated to each squad reasonably before repairing viathe roulette wheel selection method Table 5 shows the taskallocation scheme set 120588 with 8 dimensions

It is found that in the above 8 fault task allocationschemes fault 51 is never assigned to squad b since its fourthatomic demand for the overhead line failure resource group is166 which is higher than the fourth atomic capacity of squadb Besides fault 50 needs squadsrsquo collaboration as its fifthatomic demand for squadrsquos repairing efficiency is relativelythe highest as 194 However it is located on the main lineand near the power source so it needs to be repaired as soonas possible to reduce outage economic losses It is assigned

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

23

114

27

116 118 121

30 31

3

2

124

126 128

4

5

112

130 131

6 9

132 135

10

292528

142 144

26

24

136137

139

141

147

151

21 822

153 154 158

20 17 13

164

166167

175172

11

170168

12

18

159

161

19

179

177

182

14

15

184 188 194191

38 404139

37

113 115 117 119 120 122

123

125 127 129

1111

42

110

109

32

101 103

34

105 106

35

102 104

3336

107 108

133 134

138

140

143 145 146

148

149150

152 155 157156

160

162

163165 167 169 171 173 174 176

178

180

181

183 185 186 187 190189 192 193 196195 197 198

43

44

46

45

47

48

49

50

51

52

53

54Squad a

Squad c

Squad b

55

56

Faults

Emergency

Contact switch

Section switch

SquadLoad

Figure 5 The distribution network with DG of H county

Table 5 Task allocation solution set 120588Scheme a b c1 44 45 48 49 50 46 52 53 43 47 50 512 44 45 49 50 51 43 46 47 48 50 52 533 43 47 50 51 44 45 48 49 46 50 52 534 44 45 50 51 53 47 49 52 43 46 48 505 43 45 48 50 51 44 47 52 46 49 50 536 47 50 51 53 43 44 46 48 45 49 50 527 45 46 49 50 51 43 47 53 44 48 50 528 43 45 50 51 52 44 47 48 46 49 50 53

to squads a and c which is corresponding to the maximumutility value in 1198801015840

The proposed fault task allocation method based on theoptimal utility in this paper has realized the reasonablefaultsrsquo distribution in DN according to the information ofthe grid topology faults and the repairing squadsrsquo capabilityMeanwhile it is suitable for the situation where the squadsrsquocollaboration is needed and provides reference for power

decision-makers It also has achieved the rapid developmentof the task allocation schemes for that it has effectivelyreduced the searching space of the schemes

53 Analysis of RA-MAS According to the working charac-teristic of AA when multifaults occur in a DN

(1) SCA controls section switches to isolate faults in thefirst place and opens the 17 section switches andpower sources 7 22 23 and 36 then the tie switchtransfers to on state to supply outage loads as muchas possible and restores the initial open state after thefaults were repaired

(2) DGA controls DG10 and DG29 supply power for itsinternal loads respectively and operate again in thegrid-connecting mode until the corresponding faultsare repaired that is DG10 connects to the grid whensection switch 9 is charged and DG29 connects to thegrid when section switches 26 and 28 are charged

(3) EPA controls EP1 and EP2 moving to loads of thehighest urgency immediately cooperating with therepair of the first level faults and ensuring restorationof power to the first level loads in the shortest time

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

Table 6 The repairing order of three schemes

Squad Repairing order1 2 3

a 47 51 52 49 47 46 52 49 49 51 52 43b 46 53 50 45 53 44 50 45 53 44 50 45c 44 43 50 48 43 51 50 48 47 46 50 48

The repairing order of the eight schemes mentioned inTable 5 will be optimized and archived according to theproposed double-levelmathematicalmodel ofmultifault rushrepair and three optimal schemeswill be chosen as well as thecorresponding repairing orders which are shown in Table 6Table 7 shows the cooperating operation actions of the sectionswitches and the tie breaking switches after each fault hasbeen repaired

It is found that the actions of tie breaking switches 111 and 14 are to transfer to on state to supply outage loadstemporarily The switchesrsquo actions are open to isolate thefaults at first and to restore the original state after a fault isrepaired In addition the open of section switches 9 and 28has the role of cooperating with DGrsquos island operation

Table 8 shows the objectives of the three schemes men-tioned in Table 7 1198911(119883) is the time to repair the first levelfaults and 1198912(119883) is the comprehensive outage loss caused bythe second level fault

According to the optimized principle of the proposedmultifault repair double-level mathematical model wherethe minimum 1198911(119883) is considered at first scheme 1 is thebest since only for 3425 hours power supply of all the firstlevel loads can be recovered And from the perspective of1198912(119883) in scheme 1 the comprehensive outage loss causedby the second level fault 12 501 000 kWh is not the largestTherefore scheme 1 should be implemented and at this pointEP1 and EP2 are respectively sent to the first level loads 107and 161 to supply power until the corresponding faults arerepaired or their fuel is insufficient

Without loss of generality it is assumed that the powercompany has carried out the repair as scheme 1 randomlySquad a has repaired fault 51 with 06 hours ahead When therepair is at the fifth hour a new fault 54 occurs which is afirst level fault The first level loads 101 105 109 and 110 willstill be outage loads even though fault 43 has been repairedEPU processes the emergency information that informs RA-MAS to adjust the rush repairing strategy immediately At thesame time from the informationwritten to the blackboard byRSA it is known that faults 44 46 and 47 have been repairedsquads a and b are on the way to faults 52 and 53 respectivelyand squad c is repairing fault 43 At the same time UMUshows that the current ability of squad b is not enough tocomplete repairing fault 54 alone and the fault task demandvector needs to be modified

Table 9 shows the new fault task allocation scheme forfaults 45 48 49 50 51 52 53 and 54 which are waiting forrepair when new fault 54 appears suddenly as well as thecorresponding repairing order Faults having been repairedare shown in brackets

If the repairing strategy is not updated let squad c whichfinished the original repairing task first repair the new fault54The results of the strategy are shown inTable 10 comparingwith results of the repairing strategy in Table 9 It can beseen from Table 10 that the repairing time and outage lossof the strategy which is not updated are bigger than these ofthe strategy which is updated In the former strategy fault54 is repaired after the other faults by squad c so the firstlevel loads 101 105 109 and 110 will be outage loads until thelast And it is useless to complete fault 43 as some loads areoutage loads because of fault 54 which result in bigger outageloss It can be seen that the RA-MAS will work well whensome emergencies occur and the updated strategy can reducerepairing time and outage loss efficiently

6 Conclusion

In this article the utility model and real-time adjustmentmultiagent system are proposed to generate real-time emer-gency adjustment of multifault rush repairing strategy Thismethod can solve the dynamic allocation of faults and dealwith the emergencies on repairing siteThe salient features ofthis work are as follows

(1) The proposed method deals with problems causedby the random assignment of faults and the squadcooperation introducing utility theory to the multi-fault task allocation problem in DN Attribute vectorhas realized to quantify and dynamically updaterepairing information Utility function matrix modelhas achieved the dynamic allocation of faults and therapid development of allocation schemes

(2) The article divides faults into two levels and developsfaultsrsquo repairing principles The double-level mathe-matical optimization model of multifault rush repairhas been established and DBCC algorithm is usedto find the optimal strategy which has reduced theoutage time of the first level loads as well as thecomprehensive outage losses

(3) Simulation results show that the proposed RA-MAScan not only develop the faultsrsquo task allocation schemequickly but also effectively cope with on-site emer-gencies by adjusting repairing strategies in real-timewhich can restore power supply quickly and reducethe comprehensive outage losses at the same time

The future work on this research will focus on uncer-tain factors in the multifault rush repair process such asrepairing time the resources needed and power of renewableenergyThe rush repairingwork combinedwith power systemrestoration will also be further researched in the futureAlso the impact of communication ability of the real-timeadjustment multiagent system on the repairing model will beinvestigated

Competing Interests

The authors declare that they have no competing interests

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

Table 7 Switchesrsquo operation action

Fault Scheme1 2 3

43 Close 33 35 42 Close 33 35 42 Close 35 open 144 Close 30 Close 30 Close 3045 Close 31 Close 31 Close 3146 Close 26 28 Close 26 28 Close 26 2847 Close 20 Close 20 Close 16 20 open 1448 Close 18 Close 18 Close 1849 Close 12 16 open 11 Close 12 16 open 11 Close 12 1450 Close 11 55 Close 1155 Close 5551 mdash mdash mdash52 Close 9 56 Close 9 56 Close 1 9 33 42 5653 Close 15 38 40 Close 15 38 40 Close 15 38 40

Table 8 Objective value of each scheme

Objective Scheme1 2 31198911(119883)h 3425 3845 37651198912(119883)kWh 12 501 000 11 443 000 13 092 000

Table 9 The updated repairing strategy

Squad The updated allocationscheme

The updated fault repairingorder

a (47) 49 51 54 (47) 51 54 49b 45 (46) 50 53 (46) 53 50 45c 43 (44) 48 52 (44) 43 52 48

Table 10 Comparison results of two strategies

Objective Update No update1198911(119883)h 3505 42351198912(119883)kWh 13 921 000 16 756 000

Acknowledgments

The authors thank the anonymous reviewers for their valu-able comments which greatly helped them to improve thecontents of this paperThiswork is supported by PostgraduateInnovative Fund project of Hebei (no 00302-6370010) Nat-ural Science Foundation of Hebei Province Beijing TianjinHebei Cooperation project (F2016203507) National NaturalScience Foundation of China (no 61374098 no 61071201)and the Specialized Research Fund for the Doctoral Programof Higher Education (no 20131333110017)

References

[1] I S Baxevanos and D P Labridis ldquoImplementing multiagentsystems technology for power distribution network control andprotection managementrdquo IEEE Transactions on Power Deliveryvol 22 no 1 pp 433ndash443 2007

[2] J Zhang L Zhang and X Huang ldquoA multi-fault rush repairstrategy for distribution network based on genetic-topologyalgorithmrdquo Automation of Electric Power Systems vol 32 no22 pp 32ndash35 2008

[3] Z Lu B Sun Z Liu and L Yang ldquoA rush repair strategyfor distribution networks based on improved discrete multi-objective BCC algorithm after discretizationrdquo Automation ofElectric Power Systems vol 35 no 11 pp 55ndash59 2011

[4] X Li Z Lu Z Liu and T Feng ldquoMulti-agent strategy of distri-bution networks multi-faults rush-repair with distributed gen-eratorsrdquo Transactions of China Electrotechnical Society vol 28no 8 pp 48ndash55 2013

[5] Z Lu and K Wang ldquoMulti-agent based rush repair schedulingfor distribution networksrdquo Power System Technology vol 37 no1 pp 137ndash143 2013

[6] L Moreau ldquoStability of multiagent systems with time-depend-ent communication linksrdquo IEEE Transactions on AutomaticControl vol 50 no 2 pp 169ndash182 2005

[7] W Ren and R W Beard ldquoConsensus seeking in multiagentsystems under dynamically changing interaction topologiesrdquoIEEE Transactions on Automatic Control vol 50 no 5 pp 655ndash661 2005

[8] R Olfati-Saber ldquoFlocking for multi-agent dynamic systemsalgorithms and theoryrdquo IEEE Transactions on Automatic Con-trol vol 51 no 3 pp 401ndash420 2006

[9] F RenM Zhang andD Sutanto ldquoAmulti-agent solution to dis-tribution system management by considering distributed gen-eratorsrdquo IEEE Transactions on Power Systems vol 28 no 2 pp1442ndash1451 2013

[10] C P Nguyen and A J Flueck ldquoAgent based restoration withdistributed energy storage support in smart gridsrdquo IEEE Trans-actions on Smart Grid vol 3 no 2 pp 1029ndash1038 2012

[11] J M Solanki S Khushalani and N N Schulz ldquoA multi-agentsolution to distribution systems restorationrdquo IEEE Transactionson Power Systems vol 22 no 3 pp 1026ndash1034 2007

[12] A C Chapman R A Micillo R Kota and N R JenningsldquoDecentralized dynamic task allocation using overlappingpotential gamesrdquoComputer Journal vol 53 no 9 pp 1462ndash14772010

[13] L Zhang D Zhou P Zhu and H Li ldquoComparison analysisof MAUT expressed in terms of choquet integral and utilityaxiomsrdquo in Proceedings of the 1st International Symposium on

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

Systems and Control in Aerospace and Astronautics pp 85ndash89January 2006

[14] F Drews L Welch D Juedes et al ldquoUtility-function basedresource allocation for adaptable applications in dynamic dis-tributed real-time systemsrdquo in Proceedings of the 18th Interna-tional Parallel and Distributed Processing Symposium (IPDPSrsquo04) pp 1725ndash1732 April 2004

[15] G Zhang M Duan and J Zhang ldquoPower system risk assess-ment based on the evidence theory and utility theoryrdquo Automa-tion of Electric Power Systems vol 33 pp 1ndash4 2009

[16] Z JianDecisionAnalysis andManagementTheArchitecture andMethod of Comprehensive Decision-Making Quality AscensionTsinghua University Press Beijing China 2007

[17] M Hoogendoorn andM Gini ldquoPreferences of agents in decen-tralized task allocationrdquo AI Communications vol 22 no 3 pp143ndash152 2009

[18] J Vancza and A Markus ldquoAn agent model for incentive-basedproduction schedulingrdquo Computers in Industry vol 43 no 2pp 173ndash187 2000

[19] NGupta R Shekhar and P K Kalra ldquoCongestionmanagementbased roulette wheel simulation for optimal capacity selectionprobabilistic transmission expansion planningrdquo InternationalJournal of Electrical Power and Energy Systems vol 43 no 1 pp1259ndash1266 2012

[20] S D Muller J Marchetto S Airaghi and P KoumoutsakosldquoOptimization based on bacterial chemotaxisrdquo IEEE Transac-tions on Evolutionary Computation vol 6 no 1 pp 16ndash29 2002

[21] Z Lu H Zhao and H Xiao ldquoAn improvedmulti-objective bac-teria colony chemotaxis algorithmand convergence analysisrdquoApplied Soft Computing vol 21 pp 274ndash292 2015

[22] J Liu P Bi and H Dong Simplified Analysis and Optimizationof Complex Distribution Network China Electric Power PressBeijing China 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of