Modeling and Optimization of Interdependent Energy Infrastructures PDF
Preview Modeling and Optimization of Interdependent Energy Infrastructures
Wei Wei · Jianhui Wang Modeling and Optimization of Interdependent Energy Infrastructures Modeling and Optimization of Interdependent Energy Infrastructures Wei Wei • Jianhui Wang Modeling and Optimization of Interdependent Energy Infrastructures 123 WeiWei JianhuiWang StateKeyLaboratoryofPowerSystems DepartmentofElectricalandComputer DepartmentofElectricalEngineering Engineering Beijing,China SouthernMethodistUniversity Dallas,TX,USA ISBN978-3-030-25957-0 ISBN978-3-030-25958-7 (eBook) https://doi.org/10.1007/978-3-030-25958-7 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Preface MotivationofThisBook The everlasting consumption of fossil fuels with limited reserves amid climate change and environmental pollution arises public awareness of sustainable devel- opment, which calls for technology innovations as well as policy reformations to encourage energy saving, enhance system efficiency, and harness green resources. Nowadays, our energy supply infrastructures are experiencing rapid changes in two aspects. First, renewable energies are utilized at various levels of our energy systems. This initiative alleviates the dependence on traditional fossil fuels and remarkably reduces carbon emissions. However, their volatility could impose significant challenges on real-time power balancing of the electric power grid and mayevenwrecksystemsecurity.Second,systemintegrationhasbecomeaprevalent issue so as to unleash synergetic potentials across multiple energy carriers. The scalablestorageofheatmakesitanattractivemediumforrenewableenergystorage; the relatively low carbon impact of natural gas, its large reserve in shale rocks, the fast-response capability of gas-fired power generation units, and the growing maturity of power-to-gas technology will underpin a nexus of renewables, natural gas,andelectricityinthecomingdecades.Moreover,thebidirectionalinformation and energy flows allow electric vehicles to play an increasingly influential role in future power grids. The complementary natures of different energy resources precipitate the integration of traditionally independent energy systems, such as the power system, natural gas system, heating system, and even the transportation system,creatingenergyflowinterdependenceacrossinvolvedphysicalsystems. Thetransitiontoacleanerandmoresustainableenergyindustryisaffectingthe currentstructureofenergysystemsrangingfromthenational,state,andcityscales down to the distribution, residential, and building levels. However, this ambitious plannecessitatesbrand-newregulatoryframeworks,strategiceconomicincentives, innovative business models, and active participation of consumers as responsive demands. vii viii Preface Withtheprogressofenergysystemintegration,decision-makingproblemsforall involvedstakeholdersarebecomingmorechallenging,complicated,andinteractive. Weperceivethenecessityofdisseminatingfundamentalmethodsinenergysystem modeling as well as advanced theory and methodology in mathematical program- ming which could address these problems faced by the broad energy research community. OrganizationofThis Book Thisbookwillcoversomepromisingandactiveresearchtopicsandwillcomprehen- sively address the modeling and optimization issues in the analysis, management, and operation of interdependent energy systems from technical, economic, and regulatory perspectives. Based on thorough mathematical methodologies, we can makebestuseofpotentialsynergeticeffectsandachievedesiredgoals.Thisbookis organizedasfollows: Chapter 1 provides an overview on the functionality of several representative physical systems which will be discussed in this book, including the electric powergrid,naturalgasnetwork,districtheatingnetwork,andurbantransportation network.Thecomplementarynaturalandsynergeticeffectsamongdifferentenergy resources are revealed. The advantages, benefits, and challenges lying ahead, brought by energy system integration, are introduced. The remaining chapters are dedicatedtospecialformsofintegratedenergysystems. Chapter 2 discusses the power system with renewable power integration. The mainpurposeofthischapteristotacklethenon-convexityofpowerflowequations as well as uncertainties brought by renewable integration. In view of the funda- mental role of power flow in power system analysis, we give a thorough tutorial on various power flow models in Sect.2.2, including AC power flow, DC power flow, branch flow, and its linear approximation. Then, we proceed to the optimal power flow problem and its variations, which actually come down to optimize a specific objective function subject to power flow constraints. Convex relaxation methods are employed to cope with the intrinsic non-convexity. We propose a sequentialconvexoptimizationmethodtorecoverahigh-qualitysolutionwhenthe convex relaxation is inexact, which usually happens in the maximum loadability problem and the multi-objective optimal power flow problem. Next, we commit effortstocopewithuncertaintiesresultingfromrenewableintegration.Depending on the available information on the uncertainty, we apply two kinds of robust optimization approaches to the hourly ahead energy and reserve dispatch problem andtheday-aheadunitcommitmentproblem,aimingatimprovingsystemreliability attheminimumcost.Weproposetheconceptofdispatchableregion,whichexactly characterizes how much uncertainty can be dealt with in real-time operation with a fixed energy and reserve dispatch strategy and propose an integer programming approach to generate the boundaries of the dispatchable region. This concept inspiresmanyinterestingapplications.Forexample,controlandoptimizationofthe Preface ix dispatchableregion,aswellasdata-drivenreliabilityassessmentwithoutprobability distribution,areelaboratedinthischapter. Chapter 3 is devoted to the integrated gas-power system. Such integration is usuallyseenattheinter-areatransmissionlevel.InSect.3.2,weprovidethemathe- maticalmodelofanaturalgaspipelinenetworkandsummarizetwoapproximations forthegasflowpropagation equation,whichisapartialdifferentialequation.The steady-state approximation is known as the Weymouth equation, and the quasi steady-state approximation is usually referred to as the line pack model. Both of them render algebraic equations. In the rest of this chapter, convex optimization methodsforgas-powerflow,equilibriaofcoupledgas-powermarkets,andresilient operationofgas-powersystemsarediscussed. Chapter 4 is devoted to the integrated heat-power system. Such integration is usually seen at the distribution level, as long-distance delivery of heat is not economically efficient. In Sect.4.2, we introduce the mathematic model of a districtheatingpipelinenetwork,calledthehydraulic-thermalmodel.Werevealthe decompositionstructureoftheoptimalhydraulic-thermalflowproblemandpropose amethodtodeterminethenearoptimalhydraulicconditionsinthesystem,suchthat thethermalstateoptimizationgivesrisetoaconvexprogramwithlinearconstraints. In the rest of this chapter, market-based decentralized operation schemes for the heat-power system, equilibria of coupled heat-power markets, strategic behaviors ofenergyhubsinelectricityandheatingmarkets,andcapacityplanningofenergy hubsarepresented. Chapter 5 is devoted to the city-sized transportation network and power distri- bution network which are coupled by electric vehicles and on-road fast-charging stations. In Sect.5.2, we present the mathematical descriptions of two traffic user equilibrium models, which determine the steady-state vehicular flow distributions inthetransportationnetwork.Differentfromotherenergyflowproblems,inwhich the system is controlled by a central authority, the equilibrium in a transportation networkisaspontaneousoutcomeofindividualrationalitiesoftravelers.Apractical algorithm is introduced to solve large-scale instances by dynamically generating active paths. In the rest of this chapter, important issues covering the topics in network flow equilibria and optimization, system operation with uncertain traffic demands,vulnerabilityanalysis,andcapacityexpansionplanningarestudied. Given the interdependence across multiple energy systems, a central issue encountered in energy markets is the transaction policy. Imitating the pool-based powermarket,wegeneralizethemarginalcost-basedenergypricingschemetothe companionenergysystemsinChaps.3–5andproposeabilateraltradingframework for the integrated energy systems. Because the energy price should be retrieved from the dual variables from the corresponding market clearing problems, the analysisofstrategicbehaviorsofmarketparticipantsandcalculationofequilibrium points can be challenging. We establish fundamental computation tools for such interactivedecision-makingproblemsbasedonsophisticatedoptimizationtheories andmethodologies. Theformalcontentsofthisbookcenteronengineeringoptimizationproblemsof the interdependent energy systems. Due to their complexity, it is usually difficult x Preface to clearly describe both the specific problem formulation and the mathematical substance simultaneously, although we have tried our best to do so. In this book, engineering problems in practice are set up in the main body, namely, Chaps.2– 5. Four advanced optimization techniques which are frequently used throughout the main body are comprehensively tutored in the appendices, where optimization problems are cast as compact matrix form in order to highlight the mathemat- ical substance. The majority of materials in this part are concentrated from the operationalresearchliteratureandpresentedinamoresystematicandapplication- oriented manner after our filtering and refinement. Particular tricks discovered in ourownresearchcanbequiteusefulforcertainproblems.Comprehensivesurveys on the state-of-the-art development in respective fields are provided at the end of each chapter. As such, we hope the readers can get clear landscape and concise summariesofthesemethodswithoutbeingtrappedintedioussymbolsandnotations forspecificapplicationsorabstrusemathematicaltheory.Theminimalbackground knowledge required to understand these contents is tantamount to the level of an introductorycourseonmathematicalprogrammingoroperationalresearch. AppendixAreviewsbasicconceptsinconvexoptimization.Themostattractive featuresofconvexoptimizationproblemsaretheirpolynomial-timesolvabilityand zero duality gap under mild conditions. The linear programming and its duality theoryareextendedtoconiclinearprogramminginthischapter.Thiscomparative description helps readers who are not familiar with convex optimization develop intuitiveunderstandingandnecessaryskillsforapplyingconiclinearprogramming anddualitytechniquesintheirproblems,suchasthesemidefiniteprogrammingand second-orderconeprogrammingencounteredintheoptimalpowerflowstudies.We pay special attention to the most general quadratic programs which include non- convex functions in constraints or the objective function or both. Such a problem frequentlyarisesinpower flowoptimization,robustoptimization,andequilibrium problems.Particularly,itisshownthatwhentheconstraintsarelinear,aquadratic programwithanon-convexobjectivefunctioncanbeequivalentlyformulatedviaa mixed-integerlinearprogramwithoutexploitingapproximation. Appendix B summarizes linearization techniques in mixed-integer linear pro- grams.Itiscommonknowledgethatreal-worldoptimizationproblemsareusually non-convex and a non-convex program is generally NP-hard to solve globally. Nevertheless, the progress in state-of-the-art solvers makes it possible for solving a large-scale mixed-integer linear program in reasonable time, although it is also NP-hard in the worst case. More importantly, many non-convex programs can be approximatedviamixed-integerlinearprograms,whichcanbesolvedinreasonable time. In this chapter, we summarize various formulation tricks which can convert non-convex terms into linear expressions with integer variables, offering a viable option to approximately solve particular classes of hard optimization problems (globally) via mixed-integer linear programs. These techniques are particularly useful for dealing with univariate nonlinear functions, bilinear terms, and logical (disjunctive)constraints. Appendix C illuminates the basics of robust optimization approaches, catego- rizedbythedescriptionsofuncertainty(whetherdistributionalinformationistaken Preface xi into account) and the way of mitigating uncertainty (whether a recourse action is allowed). It is demonstrated that for a fairly broad class of uncertain set, a robustoptimizationproblemadmitsatractablecounterpart,whichcanbeefficiently solved. In other cases, the problem can be solved in a decomposition fashion, and thedifficultyrestsinrobustfeasibilitycheckorthedeterminationoftheworst-case scenarioforagivenstrategy,whichcanbeformulatedasamax-minproblem.The developmentofrobustoptimizationtheoryandmethodologyhasalreadyputitinto applicationonrealengineeringproblems,whichisdesiredbytheelectricitysector due to the volatility of ubiquitous renewable generation. This method is attracting researchattentionatanunprecedentedlevel. AppendixDshedslightsonequilibriumproblems.Forsingle-levelequilibrium problems, we discuss the standard Nash game and the generalized Nash game. We show how these problems that entail simultaneous decision-making can be solved in a distributed manner via a best response iteration algorithm. As special cases of the standard Nash game, matrix game and potential game are also elucidated with more dedicated treatments. For bilevel equilibrium problems, we elaborate bilevel program (single-leader-single-follower Stackelberg game), mathematical program with equilibrium constraints (single-leader-multi-follower Stackelberg game), and equilibrium program with equilibrium constraints (multi- leader-multi-follower Stackelberg game). We set forth solution methodologies for these challenging problems mainly based on mixed-integer linear programming techniques. Specifically, the linear complementarity problem is discussed which servesasthebasisfortheequivalentreformulationofbilevelgames.Inaddition,we discuss several useful market models abstracted from our own research which are generalenoughtoencompassawidespectrumofpracticalenergymarketproblems. Webelievethesemodelshelppractitionersunderstandthemathematicalsubstance behindcomplexequationsandapplyrelatedtheorymoreconveniently. Althoughalotofmathematicaltheoremsareinvolvedintheappendicesofthis book, we avoid mathematical formality and do not focus on proofs of theoretical results. Instead, we give their implications on algorithm development and still maintain sufficient mathematical rigor for readers to understand the elegance of optimization. Fromtheapplicationperspective,mathematicaltricksperformedinlinearization, convexification,androbustification,amongotherreformulationtechniquesthathelp solveacomplicateddecision-makingproblem,areratherscrappyandfragmentary. The recent upsurge of research on robust and distributionally robust optimization makesitdifficultforbeginnerstoquicklygrasptheessenceofrobustoptimization. We feel the necessity of something like a dictionary which encapsulates all useful knowledgealongeachdirectioninaunifiedandconcisearchitecture.Thismotivates the appendix part, and we believe it will make the book widely accessible and helpfulforpractitionersintheirresearch.
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