Management of Complex Multi-reservoir Water Distribution Systems using Advanced Control Theoretic Tools and Techniques PDF
Preview Management of Complex Multi-reservoir Water Distribution Systems using Advanced Control Theoretic Tools and Techniques
SPRINGER BRIEFS IN APPLIED SCIENCES AND TECHNOLOGY COMPUTATIONAL INTELLIGENCE Wojciech Z. Chmielowski Management of Complex Multi- reservoir Water Distribution Systems Using Advanced Control Theoretic Tools and Techniques SpringerBriefs in Applied Sciences and Technology Computational Intelligence Series Editor Janusz Kacprzyk For furthervolumes: http://www.springer.com/series/10618 Wojciech Z. Chmielowski Management of Complex Multi-reservoir Water Distribution Systems Using Advanced Control Theoretic Tools and Techniques 123 Wojciech Z. Chmielowski Instituteof WaterEngineering andWater Management Krakow Universityof Technology Kraków Poland ISSN 2191-530X ISSN 2191-5318 (electronic) ISBN 978-3-319-00238-5 ISBN 978-3-319-00239-2 (eBook) DOI 10.1007/978-3-319-00239-2 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013939065 (cid:2)TheAuthor(s)2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Contents Part I Steady Boundary Conditions in the Trajectories of States for Optimal Management of Complex Multi-Reservoir Water Distribution System 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Steady Optimisation Time, ST . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Steady Optimisation Time, ST . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Quality Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 State Equation of Reservoirs . . . . . . . . . . . . . . . . . . . . 12 2.1.3 Solution for the Optimising Task . . . . . . . . . . . . . . . . . 13 2.1.4 Computer Simulations. . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.5 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Transient Optimisation Horizon. . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Transient Optimisation Horizon. . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Free Optimisation Time, FT . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.1 Quality Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 The System State Equation . . . . . . . . . . . . . . . . . . . . . 28 3.2.3 Solution for the Optimisation Task . . . . . . . . . . . . . . . . 30 3.2.4 For the Vector of Free Optimisation Start Times . . . . . . 31 3.2.5 Computer Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 v vi Contents Part II Related Boundary Conditions in the Trajectories of States for Optimal Management of Complex Multi-Reservoir Water Distribution System 4 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5 Free Optimisation Time, FT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.1 Free Optimisation Time, FT . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.1.1 Quality Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.1.2 State Equation for Reservoirs. . . . . . . . . . . . . . . . . . . . 52 5.1.3 Optimisation Task Solution . . . . . . . . . . . . . . . . . . . . . 54 6 Steady Optimisation Time, ST . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.1 Steady Optimisation Time, ST . . . . . . . . . . . . . . . . . . . . . . . . 69 6.2 Quality Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.3 The System State Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 6.4 Optimisation Task Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . 72 7 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Part I Steady Boundary Conditions in the Trajectories of States for Optimal Management of Complex Multi-Reservoir Water Distribution System Chapter 1 Introduction Thewaterdeficitoccurringonaneverlargerscalenecessitatesefficientuseofexist- ingwatersuppliesusinganetworkofartificialandnaturalwaterreservoirstosupply countries’ economic macro-regions with water. Many of these reservoirs are con- nectedbyrivers,canalsorpipelineswithwaterpumpingstations,alongwithusers consumingaparticularwaterresourcesinagivenhydrologicalareamakeeconomic watersystemscomplex.Asinglewaterreservoir,astheprimaryobjectofacomplex economic water system plays one of the most important roles in this area. Hence theneedforaplannedandsafeexecutionoftasks,basedontherelevantdecisions concerningtheregulationoftheoutflowofwaterfromthereservoirandtheproper useofitsusablecapacity.Controllingacomplexsystemofreservoirscanbedivided accordingtothetypeofdecisionsandtimehorizontowhichtheyrelate.Thedivision identifiesthreemainlayers: (cid:129) planninglong-termretentionsystemofreservoirs, (cid:129) planningshort-termretentionsystemofreservoirs, (cid:129) operationalcontrol(ongoing). In each layer, different rules apply for determining the retention system of the reservoirs.Forplanninglong-termretention,thedominantroleisplayedbymethods based on the analysis of hydrological data and outflows over the longest possible periodoftime.Analyzinghistoricalhydrologicaldatainthecatchmentofreservoirs andwaterdistributiondata,withaspecificapproximationanargumentcanbemade forlong-termretentionofthekeyelementsidentifiedbythefollowingparameters: (cid:129) statesofthefillingsystemforreservoirsinspecificdivisionsoftime, (cid:129) aguaranteetomeettheneedsofusersdownstreamofthereservoirintheintervals, (cid:129) maintainingovertimetheappropriateretentionoffloodpreventioninthesystem. Theshort-termretentionplanisdependentondecisionsresultingfromtheimple- mentationofdifferenttypesoftrainingsimulation,basedoncomputeralgorithms. Thepurposeofthealgorithmsistoallowobservationoftheeffectsofcertaindecision rules on the process of controlling the reservoir system (reservoir outflow vector), andthusmaketherightdecisionsinagivensituation.Itisnecessarytodistinguish W.Z.Chmielowski,ManagementofComplexMulti-reservoirWaterDistributionSystems 3 UsingAdvancedControlTheoreticToolsandTechniques,SpringerBriefsinComputational Intelligence,DOI:10.1007/978-3-319-00239-2_1,©TheAuthor(s)2013 4 1 Introduction clearly between short-term retention planning in normal operating conditions and regardingfloodsanddroughts. Notwithstanding the foregoing division, especially at the short-term retention planning layer, computer algorithms often contain computational modules using advancedoptimizationtechniques.Atthisstageofformulation,solutionandanalysis of the results is certainly one of the essential building blocks for limiting the set of possible decisions concerning the hypothetical outflow from the reservoir. The decisionmakingprocessregardingtheoutflowfromthereservoirsystem,including solutions for specifically defined and conditioned optimization problems, can be usedtotakeintoaccounttheobtainedsolutionsasoneofthebuildingblocksfora dispatcher’sfinaldecisionwhensettingshort-termretentionstrategyplanning. Theoperationalcontrollayerisanareaofoperationswhich,inaccordancewiththe guidelinesandinstructionsofthepreviouslydescribedanalysesandtheassessment ofthecurrenthydrometeorologicalstateofthecatchmentsysteminthereservoirs, thefinalselectiondecisioncanbemadeonthecontrollingtheoutflowvector.Inthis case, the distinction between normal operation mode and operation in emergency situations (floods and drought) is of paramount importance. Control of the current outflowsfromreservoirsduringflooding(floodwavecontrol)isverydifferentasthe specificworkingconditions,i.e.thevdramaticallyshortperiodoftimefortakingand implementing decisions, dominate in determining the rules of procedure. Current control of a reservoir (system of reservoirs) during normal operation is to select a decisionfromthesetofhypotheticaldecisionrulesinthislayerandforthiskindof operation.Oftenintheoperationalcontrollayer,theselectionofadecisionisbased onfindingacompromisesolutiononthebasisofoptimizationofthegroupofmulti- criteriatasks.Followingthedecision,thistimeregardlessofthemodeofoperation ofthereservoirsystem,appropriatedevices(controllers,actuators,positioners,etc.) willperformtheclosingoropeningofthereservoirdrainageequipment,thusturn- ingthedispatcher’s(person,groupofpeople)decisionsintospecificactivity(vector outflowsfromreservoirs),fromwhichirreversibleconsequencesfollow,bothatthe time of implementation, as well as in subsequent time periods. The consequences ofbaddecisionsareoftencatastrophic.Inadequatepreparationespeciallyofasin- glereservoir(earliermethodically justifiedloweringofthereservoirinthefaceof anapproachingfloodsurge)isthereforelikelytocauseuncontrolledfloodsituation downstreamofthereservoir,theeffectsofwhichmaybedifficulttopredict.Anunjus- tifiedreductionofthewaterinthereservoirbasedonunreliableestimatesofinflow, incombinationwiththedispatcher’sinsufficientexperiencemistakenlyassessingthe hydrometeorologicalsituation,inthecaseoflowinflowtothereservoirintheimme- diatefuturethefirststepistoproduceanemergencysituationassociatedwithalack ofadequatewatersuppliesusuallystoredinreservoirsystem.Thisshowshowgreat theresponsibilityrestswiththeemployeewithanimpactoncontrollingtheoutflow of water from the reservoir system. Therefore, it is very risky to leave dispatcher alonewiththeproblemoftakingadecisionbasedsolelyonexperience,intuition,or routine,hopingthatitwillbeadequate,andtheresultspositive.Ontheotherhand,the conceptof“autopilot”,i.e.completelyreplacingthedispatcherwitheventhemost specialisedcomputationalalgorithms,iscompletelyunacceptable..Thatiswhyover 1 Introduction 5 theyears some automated decision-making in each of theselayers of control have continuallybeenproposedandintroduced,whichinvolvestheadaptationofdifferent supportalgorithms,leavingthepossibilityofinputbythedispatcherinspecificsitu- ationsfromhispointofview.Takingtherightdecisionattherighttimeisbecoming oneofthemostimportanttasks.Posingthequestionofdecision-makingsupportfor theoutflowofasystemofreservoirsisstronglyconditionedbyitslocationinoneof thethreeaforementionedlayers.Thistaskisfarmorecomplicatedwithincreasing thedimensionalityoftheproblem.Wearethentalkingaboutoutflowvectorsfrom reservoirs, structurally and task related within a complex system of water supply and management. The structure of the system takes into account all the possible connectionsbetweenthereservoirsandwatercustomers.Whatisusuallyanalysed arevariationsofuseofthewatersourcesinthereservoirsduringtheoperationand takingintoaccounttheeffectsofprospectivemanagementofthereservoirscaused bythecurrentcontrolsystem,accordingtoadecisionbythedispatcherrecognised asthemostappropriateinagivensituation.Thedispatcher’sdecisionsdetermining control system of outflows from the reservoirs contain elements of such issues as multi-criteria,randomness,dynamics,non-linearityandthescaleofcomplexitycom- plementingthefactorsdirectlylinkedtothedispatcher(includingattitudestorisk). Theissuerelatedtodecision-makinginwatermanagementsystemsischaracterised byitsinterdisciplinarynature,andthequalitycontrolofthesysteminthisregardcan onlybeachievedbyacomparativeanalysisofthesystem’shistoricalhydrological data in the long term. Therefore, the need to eliminate bad dispatcher decisions is beyondquestionby: (cid:129) continuous,multidirectionaldevelopmentofmethodologiesanddecisionsupport algorithmsforplanningforalllayersofreservoirretention,leadingtotheappli- cationofthelatestachievementsinscienceandtechnologyinthisarea, (cid:129) Theselectionofdispatcherswiththerelevantexperienceandrelevantmentaland physicalcharacteristicswhichintimesofcrisismaybeanecessaryprecondition andguaranteeofaproperconduct. Thisstudydiscussesissuesofoptimalwatermanagementinadistributionsystem. Themainelementsofthecomplexwater-managementsystemunderconsideration are retention reservoirs, among which water transfers are possible, and a network ofconnectionsbetweenthesereservoirsandwatertreatmentplants(WTPs).System operation optimisation involves determining the proper water transport routes and their flow volumes from the retention reservoirs to the WTPs, and the volumes of possibletransfersamongthereservoirs,takingintoaccounttransport-relateddelays forinflows,outflowsandwatertransfersinthesystem.Totalsystemoperationcosts defined by an assumed quality coefficient should be minimal. An analytical solu- tion of the optimisation task so formulated has been obtained as a result of using Pontriagin’smaximumprinciplewithreferencetothequalitycoefficientassumed. Stablestartandendconditionsinreservoirstatetrajectorieshavebeenassumed.The researchershavetakenintoaccountcasesofsteady(Chap.2)andtransient(Chap.3) optimisationduration.Thesolutionsobtainedhaveenabledthecreationofcomputer models simulating system operation. In future, an analysis of the results obtained
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