MULTI-OBJECTIVE OPTIMIZATION OF PLANNING ELECTRICITY GENERATION AND CO 2 MITIGATION STRATEGIES INCLUDING ECONOMIC AND FINANCIAL RISK

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1 MULTI-OBJECTIVE OPTIMIZATION OF PLANNING ELECTRICITY GENERATION AND CO 2 MITIGATION STRATEGIES INCLUDING ECONOMIC AND FINANCIAL RISK Jee-Hoon Han and In-Beum Lee * Depatment of Chemical Engineeing POSTECH Pohang KOREA Abstact In this pape we pesent a mathematical pogamming model in planning electicity geneation and CO 2 mitigation (EGCM infastuctue including financial is management unde uncetainty. The objective of ou study is to detemine the optimal design of the EGCM infastuctue which is composed of available technologies to poduce electicity and teat CO 2 capable of fulfilling electicity demands and CO 2 mitigation standads. In addition the model pesented allows contolling the vaiation of the economic pefomance of the EGCM infastuctue in the space of uncetain paametes (i.e. CO 2 mitigation opeating costs cabon cedit pices and electicity pices etc.. This is accomplished by using the weighted-sum method that imposes a penalty fo is to the objective function. The capability of the poposed modeling famewo is illustated and applied to a eal case study based on Koea fo which valuable insights ae obtained. Keywods Electicity geneation CO 2 mitigation infastuctue uncetainty financial is management Intoduction Cuently a lage amount of electicity elies pimaily on fossil fuels combustion powe plants. These plants have emitted a geat deal of geenhouse gas (GHG which is nown as a pimay acceleating facto of global waming. Thee has been concen about whethe enegy supplies can meet inceasing electicity demands with the eduction of GHG emissions. Seveal eseach wos wee undetaen fo the planning of electicity geneation and CO 2 mitigation (EGCM stategies unde meeting the GHG mitigation standads. Seveal mathematical pogamming models have been poposed that addess the design of the EGCM infastuctue (Nasii and Huang 2008; Han and Lee 2011; Han and Lee These studies addess deteministic appoaches assuming that all poblem paametes ae invaiant ove a given planning hoizon. Uncetainties may exist in vaious impact factos such as GHG emission inventoy GHG eduction costs electicity pices and emission eduction cedits. Hence seveal eseach effots wee conducted fo dealing with vaious uncetainties in the EGCM infastuctue. Fo example inteval mathematical pogamming (IMP and stochastic mathematical pogamming (SMP was poposed to the design of the EGCM infastuctue unde uncetainties (Chen Li et al. 2010; Li Huang et al These appoaches allow assessing the pefomance of the poblem unde study in the space of uncetain paametes by optimizing the expected value of the objective function. * iblee@postech.ac.

2 Howeve this stategy does not allow contolling the vaiability of the objective function in the uncetain space. The intoduction of a financial is metic enable to contol the vaiability of the objective function in the space of uncetain paametes (Babao and Bagajewicz In the context of designing the EGCM infastuctue unde uncetainties few eseach wos have adopted financial is management techniques. Theefoe this study aims to addess the financial is management associated with the planning of the EGCM infastuctue unde uncetainty in pices (i.e. the electicity pice and cabon cedit pice and opeating costs (i.e. the cabon captue and sequestation cost. A multi-objective optimization poblem which consists of the expected total pofit of the infastuctue and a specific metic fo financial is is geneated to conside this poblem. Hence the weighted-sum method is also pesented to expedite the seach fo the Paeto solutions of the model. Finally the capability of the poposed model is illustated though its application to a eal case study based on Koea. Poblem statement The ey objective of this pape is to constuct a mathematical optimization model that detemines the configuation of the EGCM infastuctue with the goal of maximizing the expected total pofit and minimizing financial is. The supestuctue of the EGCM infastuctue in this wo is depicted in Figue 1. This infastuctue model includes thee main components such as an envionmental management system the powe plants themselves and an enegy management system. The decision-maing poblem of the EGCM infastuctue model is to detemine whee and how to geneate electicity and teat CO 2 unde the given conditions which include electicity demand CO 2 eduction taget capacity limitations of electicity geneation technologies and CO 2 mitigation technologies uncetain paametes (i.e. pices and opeating costs; in ode to simultaneously maximize the expected total pofit and minimize the associated financial is of the EGCM infastuctue. Figue 1. The supestuctue of the EGCM infastuctue. Mathematical model The model pesented is motivated by pevious fomulations (Han and Lee Specifically the model consides the uncetainty of the coefficients (e.g. pices and opeating costs of the objective function via a multiscenaio stochastic pogamming appoach. The EGCM system whose model has been descibed peviously must meet two taget equiements; a maximizing the expected total net pofit of the netwo b minimizing the total financial is of the netwo. Expected total net pofit The expected total net pofit is given by the mean value of the pofit distibution: E [ TNP ] = pob TNP (1 whee is the numbe of scenaios implemented to epesent the uncetain paametes space and pob is the pobability of occuence associated to each scenaio. The total net pofit (TNP in each paticula scenaio is calculated by the diffeence between total net benefit (TNB and total net cost (TNC : TNP = TNB TNC. (2 In Equation (2 the total net benefit (TNB in each paticula scenaio is the income fom selling electicity geneated by powe plants and the total net cost (TNC is the sum of emission tading cost and CCS facility cost: TNB = UNB G (3 e p f g p g epf g Cpice AEP i p f g TNC = p f g i ( CCSCCi CCSOCi + + (4 whee the capital cost (eg CCSCC i can be egaded as non-scenaio-dependent vaiables wheeas the pices and opeating costs (eg UNB pg Cpice and CCSOC i will in geneal depend on the specific scenaio ealization. The detailed explanations fo the fist objective and its constaints wee descibed by Han and Lee (Han and Lee Expected total financial is In the pevious wo (Babao and Bagajewicz 2004 the financial is associated with a design x and taget pofit Ω can be expessed as follows: Ris( Ω = P[ TNP( x < Ω ] = pob z ( Ω (5

3 whee z is a binay vaiable defined fo each scenaio and pob is pobability of occuence of scenaio s. Multiobjective poblem The EGCM infastuctue design in this study is mathematically fomulated as follows: Maximize E[ TNP]( ; Minimize Ris( Ω Subject to : (6 h( = 0{ Oveall mass balance} g( 0{ Capacity limitations} x Ν R. whee x and y denote the intege and continuous vaiables of the poblem espectively. The afoementioned multi-objective poblem can be solved by the weighted-sum method (Ehgott and Gandibleux 2000 as pesented next. Maximize E[ TAP]( pob ρ 1 z R K ( Subject to : h( = 0 { Oveall mass balance} g( 0{ Capacity limitations} (7 x Ν R pobtnp Ω + U ( 1 z = 1 NK = 1 NR pobtnp Ω U z = 1 NK = 1 NR. whee ρ is goal pogamming weight fo financial is fomations. lage vaiability in the cabon cedit pice and petoleum pice has on the EGCM infastuctue design. Figue 2. Paeto optimal solution cuve Figue 2 pesents the Paeto fontie of the multiobjective poblem. The esults obtained show that in ode to minimize the financial is the model esolves to educe a petoleum-fied geneation. This is because the petoleum pice shows highe vaiability than the coal and natual gas. Let us note that electicity geneation plants utilize CCS o CET fo educing the GHG emissions (Figue 3 and 4. The minimum financial is solution which coesponds to point A of Figue 2 and to esults depicted in Figue 3 and 4 entails that CCS is utilized and CET is educed oveall in the entie powe system. This is because the pice vaiability of cabon cedit had diect effect on the configuation of CO 2 mitigation. Results and Discussion To veify the poposed model it is applied to the case study in pape (Han and Lee 2011 adopted as a benchma. The model contains 16 egions epesenting the self-govening communities of Koea whose electicity demand fulfilled (EDF by combustion powe plants is supposed to cove 58% of the total demand. Electicity can be obtained fom thee diffeent geneation technologies including gas-fied petoleum-fied and coal-fied electicity geneation. Also the CO 2 eduction taget is assumed to 30% of total CO 2 emissions. CO 2 can be disposed fom two diffeent mitigation technologies such as cabon captue and stoage (CCS and cabon emission tading (CET. The uncetainty is epesented by fifty scenaios geneated using Monte Calo sampling on a set of nomal distibutions that chaacteize the uncetain pices and opeating costs. Specifically in this paticula example we aim to analyze the impact that the Figue 3. CO 2 teated by CCS facilities in each plant type associated with the exteme solutions.

4 Acnowledgements This pape was suppoted by the Koea Reseach Foundation Gant funded by the Koea Govenment (MOEHRD Basic Reseach Pomotion Fund (KRF D Figue 4. Cabon emission cedit taded in each plant type associated with the exteme solutions. Figue 5 illustates a hypothetical example with thee is cuves esponding to these diffeent is attitudes. The figue eveals that fo high taget pofits (highe than $ the solution shows a level of is lowe than the one fo low taget pofits. Notation Indices e Poduct fom of electicity f Facility name fo electicity geneation g Geogaphical egion i Physical fom of CO 2 p Type of powe plant Scenaios Sets Feasibility set fo fist-stage decision vaiables y Feasibility set fo second-stage decision vaiables in scenaio Set of pofit tagets Paametes pob Pobability of occuence of scenaio UNB pg Unit net benefit of selling electicity geneated fom type of powe plant p into egion g in scenaio Cpice Pice of cabon emission cedits in scenaio Ω Taget pofit ρ Goal pogamming weight fo financial is fomations Figue 5. Diffeent inds of financial is cuves. A is-avese decision mae will pefe to lowe the taget pofit wheeas a is tae will pefe to highe the taget pofit. The tade-off lies in between these exteme solutions which eflect diffeent possible attitudes towads. Conclusions This wo has intoduced a mathematical model fo is management in the stategic design and planning of the EGCM infastuctue unde uncetainty in pices and opeating costs. The poblem has been consideed as a multi-objective stochastic MILP that simultaneously accounts fo the maximization of the expected total pofit and minimization of the financial is. The weighed-sum method has also been employed in ode to expedite the solution of such model. Simulation esults have shown that the petoleum-fied electicity geneation should be eplaced by coal-fied one to educe the vaiability of the pofit distibution. We can popose the optimal opeation of each powe plant unde uncetainty. Vaiables E[TNP] Expected total net pofit TNP Total net pofit in scenaio TNB Total net benefit in scenaio TNC Total net cost in scenaio CCSCC i Capital cost of CCS facilities fo CO 2 CCSOC i Opeating cost of CCS facilities fo CO 2 in scenaio G epfg Amount of electicity geneated by electicity facility f of plant type p in egion g AEP ipfg CO 2 emission pemit eallocated to electicity facility f of plant type p in egion g Ris(Ω Financial is of solution x at a pofit taget Ω Z Binay vaiable equal 1 if the pofit of scenaio is smalle than the pofit taget Ω Refeences Babao A. and M. J. Bagajewicz (2004. "Managing Financial Ris in Planning unde Uncetainty." AIChE Jounal 50(5: Chen W. T. Y. P. Li et al. (2010. "A two-stage inexactstochastic pogamming model fo planning cabon

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