An Integrated Electric Power Supply Chain and Fuel Market Network ...

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An Integrated Electric Power Supply Chain and Fuel Market Network ...

Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsSource: http://www.nasa.gov


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsOutlineIntroductionLiterature reviewAn integrated electric power supply chain and fuel marketnetwork frameworkEmpirical case study and examplesConclusions.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsElectric Power Supply Chains and Fuel Suppliers


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsElectric Power Supply Chains (Cont’d)The U.S. electric power industry: Half a trillion dollars of netassets, $220 billion annual sales, 40% of domestic primaryenergy (Energy Information Administration (2000, 2005))DeregulationWholesale marketBilateral contractPower pool.Electric power supply chain networksVarious generation technologiesInsensitive demandsTransmission congestionIn 2007, the total transmission congestion cost in NewEngland was about $130 million (ISO New England AnnualMarket Report, 2007).


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsLoad Curve


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsA Simple Example of Transmission Congestion


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsA Simple Example of Transmission Congestion


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsA Simple Example of Transmission Congestion


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsA Simple Example of Transmission Congestion


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsA Simple Example of Transmission Congestion


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsSources of Electricity in the U.S. in 2007Source: http://www.eia.doe.gov


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsElectric Power Supply Chains and Fuel MarketsIn the U.S., electric power generation accounts for significantportions of fuel demands30% of the natural gas demand (over 50% in the summer)90% of the coal demandover 45% of the residual fuel oil demand.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsElectric Power Supply Chains and Fuel Markets (Cont’d)The interactions between electric power supply chains and fuelmarkets affect demands and prices of electric power and fuels.From December 1, 2005 to April 1, 2006, the wholesaleelectricity price in New England decreased by 38% mainlybecause the delivered natural gas price declined by 45%.In August, 2006, the natural gas price jumped 14% becausehot weather across the U.S. led to elevated demand forelectricity. This high electricity demand also caused the crudeoil price to rise by 1.6%.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsLiterature ReviewElectric power wholesale and retail marketsSmeers (1997), Hogan (1992), Chao and Peck (1996), Casazzaand Delea (2003), Hobbs and Pang (2003), Borenstein andHolland (2003), and Garcia, Campos, and Reitzes (2005), etc.Electric power markets and fuel marketsEmery and Liu (2001), Bessembinder and Lemmon (2002),Huntington and Schuler (1997), Brown and Yucel (2007), etc.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsLiterature Review (Cont’d)A. Nagurney and D. Matsypura, “A Supply Chain NetworkPerspective for Electric Power Generation, Supply,Transmission, and Consumption,” in Optimisation,Econometric and Financial Analysis, E. J. Kontoghiorghesand C. Gatu, Editors (2006) Springer, Berlin, Germany, pp3-27A. Nagurney, Z. Liu, M. G. Cojocaru, and P. Daniele,“Dynamic electric power supply chains and transportationnetworks: An evolutionary variational inequality formulation,”Transportation Research E 43 (2007), 624-646D. Matsypura, A. Nagurney, and Z. Liu, “Modeling of electricpower supply chain networks with fuel suppliers via variationalinequalities,” International Journal of Emerging Electric PowerSystems 8 (2007), 1, Article 5.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples Conclusions“An Integrated Electric Power Supply Chain and Fuel MarketNetwork Framework: Theoretical Modeling with Empirical Analysisfor New England”, Zugang Liu and Anna Nagurney, to appear inNaval Research Logistics.This paper can be downloaded at:http://supernet.som.umass.edu/dart.html.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsContributionsThe model captures both economic transactions and physicaltransmission constraints.The model considers the behaviors of all major decisionmakers including gencos, consumers and the independentsystem operator (ISO).The model considers multiple fuel markets, electricitywholesale markets, and operating reserve markets.The model is applied to the New England electric powersupply chain consisting of 6 states, 5 fuel types, 82 powergenerators, with a total of 573 generating units, and 10demand markets.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe Electric Power Supply Chain Network with FuelSupply Markets


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsEnergy Fuel Supply CurvesSource: Minerals Management Service, Gulf of Mexico Region


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe Equilibrium Conditions for the Fuel Supply MarketsAssume that the following conservation of flow equations musthold for all fuel supply markets a = 1, . . . , A; m = 1, . . . , M:W∑G∑w=1 g=1 r 1 =1 u=1N R∑ ∑ gr1qgr am1 uw + ¯q am = h am .The (spatial price) equilibrium conditions (cf. Nagurney (1999))for suppliers at fuel supply market am; a = 1, ..., A; m = 1, ..., M,take the form: for each generating unit gr 1 u; g = 1, ..., G;r 1 = 1, ..., R; u = 1, ..., N gr1 , and at each demand level w:{π am (h ∗ ) + cgr am = ρam∗gr 1 uw, if qgr am∗1 uw > 0,1 uw≥ ρ am∗gr 1 uw, if qgr am∗1 uw = 0.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsPower Generator’s Maximization ProblemMultiple power plantsDual-fuel power plantsRevenueBilateral contractsPower poolOperating reserve markets.CostFuel costOperating costTransaction costCongestion cost.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsPower Generator’s Maximization Problem (Cont’d)−W∑w=1−+W∑w=1L wW∑w=1MaximizeL wr 1 =1 u=1W∑w=1r 1 =1 u=1 r 2 =1L wN R∑ ∑ gr1 R∑ K∑r 1 =1 u=1 r 2 =1 k=1N R∑ ∑ gr1 R∑ρ ∗ r 2 w y gr 1ur 2 w +−W∑A∑M∑w=1 a=1 m=1 r 1 =1 u=1N R∑ ∑ gr1W∑f gr1 uw (q gr1 uw ) −L w−r 1 =1 u=1 r 2 =1W∑w=1 r 1 =1 u=1N R∑ ∑ gr1ρ am∗gr 1 uw qgr am1 uww=1N R∑ ∑ gr1 R∑c gr 1ur 2 w (y gr 1ur 2 w ) −W∑w=1L wr 1 =1 u=1 r 2 =1 b=1L wρ gr 1u∗r 2 kw qgr 1ur 2 kwN R∑ ∑ gr1L w ϕ ∗ r 1 w z gr1 uwN R∑ ∑ gr1 R∑ K∑c gr 1ur 2 kw (qgr 1ur 2 kw )W∑w=1r 1 =1 u=1 r 2 =1 k=1L wN R∑ ∑ gr1c gr1 uw (z gr1 uw )r 1 =1 u=1N R∑ ∑ gr1 R∑ B∑K∑µ ∗ bw α r1 r 2 b[ q gr 1ur 2 kw + y gr 1ur 2 w ]k=1


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsPower Generator’s Maximization Problem (Cont’d)subject to:R∑K∑r 2 =1 k=1q gr 1ur 2 kw + R∑A∑a=1β gr1 uar 2 =1y gr 1ur 2 w = q gr1 uw , r 1 = 1, ..., R; u = 1, ..., N gr1 ; w = 1, ..., W ,M∑m=1q amgr 1 uw + L w β gr1 u0q gr1 uw = L w q gr1 uw , r 1 = 1, ..., R;u = 1, ..., N gr1 ; w = 1, ..., W ,q gr1 uw + z gr1 uw ≤ Cap gr1 u, r 1 = 1, ..., R; u = 1, ..., N gr1 ; w = 1, ..., W ,z gr1 uw ≤ OP gr1 u, r 1 = 1, ..., R; u = 1, ..., N gr1 ; w = 1, ..., W ,q gr 1ur 2 kw ≥ 0, r1 = 1, ..., R; u = 1, ..., Ngr 1; r 2 = 1, ..., R; k = 1, ..., K; w = 1, ..., W ,qgr am1 uw ≥ 0, a = 1, ..., A; m = 1, ..., M; r 1 = 1, ..., R; u = 1, ..., N gr1 ; w = 1, . . . , W ,y gr 1ur 2 w ≥ 0, r 1 = 1, ..., R; u = 1, ..., N gr1 ; r 2 = 1, ..., R; w = 1, .., W ,z gr1 uw ≥ 0,r 1 = 1, ..., R; u = N gr1 ; w = 1, ..., W


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe ISO’s RoleManages the power pool.Schedules transmission.Manages congestion.Ensures system reliability.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe ISO’s RoleThe ISO ensures that the regional electricity markets r = 1, . . . , R clear at eachdemand level w = 1, . . . , W , that is,G∑N R∑ ∑ gr1g=1 r 1 =1 u=1y gr 1u∗rw{= ∑ R∑ Kr 2 =1 k=1 y r r∗2 kw , if ρ ∗ rw > 0,≥ ∑ R∑ Kr 2 =1 k=1 y r r∗2 kw , if ρ ∗ rw = 0.The ISO also ensures that the regional operating reserve markets; hence,r 1 = 1, . . . , R clear at each demand level w = 1, . . . , W , that is,N G∑ ∑ gr1g=1 u=1z ∗ gr 1 uw{ = OPRr1 w , if ϕ ∗ r 1 w > 0,≥ OPR r1 w , if ϕ ∗ r 1 w = 0.The following conditions must hold for each interface b and at each demandlevel w, where b = 1, . . . , B; w = 1, . . . , W :N R∑ R∑ G∑ ∑ gr1 K∑G N[ q gr 1u∗r 2 kw + ∑ ∑ gr1y gr 1u∗r 2 w +r 1 =1 r 2 =1 g=1 u=1 k=1g=1 u=1K∑k=1y r 1∗r 2 kw ]α r 1 r 2 b{ = TCapb , if µ ∗ bw > 0,≤ TCap b , if µ ∗ bw = 0.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe Equilibrium Conditions for the Demand MarketsWe assume that all demand markets have fixed and known demands. and thefollowing conservation of flow equations, hence, must hold for all demandmarkets k = 1, . . . , K r2 , all regions r 2 = 1, . . . , R, and at all demand levelsw = 1, . . . , W :G∑N R∑ ∑ gr1g=1 r 1 =1 u=1q gr 1u∗r 2 kw+ R∑r 1 =1y r 1∗r 2 kw = (1 + κr 2w )d r2 kw .The equilibrium conditions for consumers at demand market k in region r 2 takethe form: for each power plant u; u = 1, ..., U r1 g ; each generator g = 1, ..., G;each region r 1 = 1, ..., R, and each demand level w; w = 1, . . . , W :andρ ∗ r 1 w +ρ gr 1u∗r 2 kwB∑b=1{ + ĉgr 1u = ρ∗r 2 kw (Q2∗ w )r2 kw , if q gr 1u∗r 2 kw > 0,≥ ρ ∗ r 2 kw , if q gr 1u∗r 2 kw = 0;{µ ∗ bw α r1 r 2 b + ĉ r 1 2∗ = ρ∗r 2 kw(Yw )r2 kw , if y r 1∗r 2 kw > 0,≥ ρ ∗ r 2 kw , if y r 1∗r 2 kw = 0.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsLemmas 1 and 2Lemma 1In equilibrium, if the u th generating unit of genco g in region r 1supplies electricity to the power pool in region r 2 at demand levelw, the marginal supply cost of the generating unit, ψ gr 1u∗r 2 w , is lessthan or equal to the clearing price at the power pool, ρ ∗ r 2 w .Lemma 2In equilibrium, if at the power pool in region r 2 at demand level w,the u th generating unit of genco g in region r 1 has availablecapacity, the marginal supply cost of the generating unit, ψ gr 1u∗r 2 wgreater than or equal to the market clearing price at the powerpool, ρ ∗ r 2 w ., is


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsDefinition: Electric Power Supply Chain NetworkEquilibriumThe equilibrium state of the electric power supply chain networkwith fuel supply markets is one where the fuel flows and electricpower flows and prices satisfy the equilibrium conditions for thefuel markets, the optimality conditions for the power generators,the equilibrium conditions for the demand markets, and theequilibrium conditions for the ISO.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsTheorem: Variational Inequality Formulation of theElectric Power Supply Chain Network EquilibriumThe equilibrium conditions governing the electric power supply chain network coincide with the solution of thevariational inequality given by: determine (Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ , η ∗ , λ ∗ , µ ∗ , ρ ∗ 3 , ϕ∗ ) ∈ K 1 satisfyingW∑ A∑ M∑ G∑ R∑w=1 a=1 m=1 g=1 r 1 =1Ngr ∑1[u=1π am(Q 1∗ ) + c amgr 1 uw]× [q amgr 1 uw − qam∗ gr 1 uw ]W∑ G Ngr [∑ R∑ ∑1∂fgr1 uw (qgr ∗ + L 1 uw ) ]w+ η ∗ grw=1 g=1 r 1 =1 u=1 ∂q 1 uw × [q gr1 uw − q ∗ gr 1 uw ]gr1 uw⎡W∑ G Ngr∑ R∑ ∑1R∑ K∑+ L ww=1 g=1 r 1 =1 u=1 r 2 =1 k=1W∑ G Ngr∑ R∑ ∑1+ L ww=1 g=1 r 1 =1 u=1⎣ ∂cgr 1 ur 2 kw (qgr 1 u∗r 2 kw )⎡R∑r 2 =1∂q gr 1 ur 2 kw⎣ ∂cgr 1r u2 w (y gr 1r u∗2 w )∂y gr 1 ur 2 w+B∑b=1⎤µ ∗ bw α r 1 r 2 b + ĉ gr 1 ur 2 kw (Q2∗ w ) ⎦ × [q gr 1 ur 2 kw − qgr 1 u∗r 2 kw ]⎤B∑+ µ ∗ bw α r 1 r 2 b − ρ ∗ r 2 wb=1⎦ × [y gr 1 ur 2 w − y gr 1 u∗r 2 w ]W∑ G Ngr [∑ R∑ ∑1∂cgr1 uw (zgr ∗ + L 1 uw )]w+ λ ∗ grw=1 g=1 r 1 =1 u=1 ∂z 1 uw + η∗ gr 1 uw − ϕ∗ r 1 w × [z gr1 uw − z ∗ gr 1 uw ]gr1 uw⎡⎤W∑ ∑ R R∑ K∑+ L w⎣ρ ∗ r 1 w + ĉr 1 2∗r2(Ykw w ) + ∑ B µ ∗ bw α ⎦r 1 r 2 b × [y r 1r2 kw − y r 1 ∗r 2 kw ]w=1 r 1 =1 r 2 =1 k=1b=1


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsTheorem: Variational Inequality Formulation of theElectric Power Supply Chain Network Equilibrium (Cont’d)W∑ G Ngr∑ R∑ ∑1[+ L ww=1 g=1 r 1 =1 u=1W∑ G Ngr∑ R∑ ∑1[+ L ww=1 g=1 r 1 =1 u=1Cap gr1 u − q ∗ gr 1 uw − z∗ gr 1 uwOP gr1 u − z ∗ gr 1 uw]× [η gr1 uw − η ∗ gr 1 uw ]]× [λ gr1 uw − λ ∗ gr 1 uw ]W∑ B Ngr∑R∑ R∑ G∑ ∑1K∑+ L w [TCap b − [q gr 1 u∗ G Ngrr 2 kw + ∑ ∑1K∑y gr 1 u∗r 2 w + y r 1 ∗r 2 kw ]α r 1 r 2 b] × [µ bw − µ ∗ bw ]w=1 b=1r 1 =1 r 2 =1 g=1 u=1 k=1g=1 u=1k=1W∑ ∑ R G∑ R∑+ L w [w=1 r=1 g=1 r 1 =1Ngr 1 ∑u=1y gr 1 u∗rwR∑ K∑−r 2 =1 k=1y r∗r 2 kw ] × [ρrw − ρ∗ rw ]W∑ R Ngr∑ G∑ ∑1+ L w [ z ∗ gr 1 uw − OPRr 1 ] × [ϕr 1 w − ϕ∗ r 1 w ] ≥ 0,w=1 r 1 =1 g=1 u=1∀(Q 1 , q, Q 2 , Y 1 , Y 2 , Z, η, λ, µ, ρ 3 , ϕ) ∈ K 1 , (1)where K 1 ≡ {(Q 1 , q, Q 2 , Y 1 , Y 2 , Z, η, λ, µ, ρ 3 , ϕ)|(Q 1 , q, Q 2 , Y 1 , Y 2 , Z, η, λ, µ, ρ 3 , ϕ)∈ R AMNW +NRKW +NRW +4NW +R2 KW +BW +2RW+ and the conservation of flow equations hold}.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsTheorem: ExistenceIf (Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ , η ∗ , λ ∗ , µ ∗ , ρ ∗ 3 , ϕ∗ ) satisfies variational inequality (1) then(Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ ) is a solution to the variational inequality problem: determine(Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ ) ∈ K 2 satisfyingW∑ A∑ M∑ G∑ R∑w=1 a=1 m=1 g=1 r 1 =1Ngr ∑1[u=1π am(Q 1∗ ) + c amgr 1 uw]× [q amgr 1 uw − qam∗ gr 1 uw ]W∑ G Ngr [∑ R∑ ∑1∂fgr1 uw (qgr ∗ + L 1 uw ) ]w× [q gr1 uw − q ∗ grw=1 g=1 r 1 =1 u=1 ∂q 1 uw ]gr1 uw⎡W∑ G Ngr∑ R∑ ∑1R∑ K∑+ L ww=1 g=1 r 1 =1 u=1 r 2 =1 k=1W∑ G Ngr∑ R∑ ∑1+ L ww=1 g=1 r 1 =1 u=1⎣ ∂cgr 1 ur 2 kw (qgr 1 u∗r 2 kw )R∑r 2 =1∂q gr 1 ur 2 kw∂c gr 1 ur 2 w (y gr 1 u∗r 2 w )∂y gr 1 ur 2 w⎤+ ĉ gr 1 ur 2 kw (Q2∗ w ) ⎦ × [q gr 1 ur 2 kw − qgr 1 u∗r 2 kw ]× [y gr 1 ur 2 w − y gr 1 u∗r 2 w ]W∑ G Ngr∑ R∑ ∑1∂c gr1 uw (zgr ∗ + L 1 uw )w× [z gr1 uw − z ∗ grw=1 g=1 r 1 =1 u=1 ∂z 1 uw ]gr1 uwW∑ ∑ R R∑ K∑+ L wĉ r 1 2∗r2(Ykw w ) × [y r 1r2 kw − y r 1 ∗r 2 kw ] ≥ 0, ∀(Q1 , q, Q 2 , Y 1 , Y 2 , Z) ∈ K 2 , (2)w=1 r 1 =1 r 2 =1 k=1


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsTheorem: Existence (Cont’d)where K 2 ≡ {(Q 1 , q, Q 2 , Y 1 , Y 2 , Z)|(Q 1 , q, Q 2 , Y 1 , Y 2 , Z) ∈ R AMNW +NRKW +NRW +2NW +R2 KW+and the conservation of flow equations and∑ G R∑L wg=1 r 1 =1Ngr 1 ∑u=1y gr 1 urw ≥ L w R ∑K∑r 2 =1 k=1y r r 2 kw , ∀r; ∀w,are satisfied}.R Ngr∑ R∑ G∑ ∑1K∑and L w [q gr 1 u G Ngrr 2 kw +∑ ∑1r 1 =1 r 2 =1 g=1 u=1 k=1g=1 u=1G Ngr∑ ∑1L w z gr1 uw ≥ L w OPR r1 w , ∀r 1 ; ∀w,g=1 u=1y gr 1 ur 2 w+ K ∑k=1y r 1r2 kw ]α r 1 r 2 b ≤ L w TCap b , ∀b; ∀wA solution to (2) is guaranteed to exist provided that K 2 is nonempty. Moreover, if(Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ ) is a solution to (2), there exist (η ∗ , λ ∗ , µ ∗ , ρ ∗ 3 , ϕ∗ 2NW +BW +2RW) ∈ R+ with(Q 1∗ , q ∗ , Q 2∗ , Y 1∗ , Y 2∗ , Z ∗ , η ∗ , λ ∗ , µ ∗ , ρ ∗ 3 , ϕ∗ ) being a solution to variational inequality (1).


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsTheorem: MonotonicitySuppose that all cost functions in the model are continuouslydifferentiable and convex; all unit cost functions are monotonicallyincreasing, and the inverse price functions at the fuel supplymarkets are monotonically increasing. Then the vector F thatenters the variational inequality (1) is monotone, that is,〈(F (X ′ ) − F (X ′′ )) T , X ′ − X ′′〉 ≥ 0, ∀X ′ , X ′′ ∈ K, X ′ ≠ X ′′ .


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsModified Projection MethodStep 0: InitializationSet X 0 ∈ K. Let T = 1 and let α be a scalar such that 0 < α ≤ 1 , where L isLthe Lipschitz continuity constant.Step 1: ComputationCompute ¯X T by solving the variational inequality subproblem:〈 ¯X T + αF (X T −1 ) − X T −1 , X − ¯X T 〉 ≥ 0, ∀X ∈ K.Step 2: AdaptationCompute X T by solving the variational inequality subproblem:〈X T + αF ( ¯X T ) − X T −1 , X − X T 〉 ≥ 0, ∀X ∈ K.Step 3: Convergence VerificationIf max |XlT − X T −1l| ≤ ɛ, for all l, with ɛ > 0, a prespecified tolerance, thenstop; else, set T =: T + 1, and go to Step 1.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsModified Projection Method (Cont’d)The method converges to a solution of the model provided thatF (X ) is monotone and Lipschitz continuous, and a solution exists.In Steps 1 and 2 of the modified projection method, due to thespecial structure of the underlying feasible set, the subproblems arecompletely separable and can be solved as W transportationnetwork problems with the prices in each subproblem solvable inclosed form.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsEmpirical Case Study and ExamplesNew England electric power market and fuel markets82 generators who own and operate 573 power plants5 types of fuels: natural gas, residual fuel oil, distillate fuel oil, jet fuel,and coalTen regions (R=10): 1. Maine, 2. New Hampshire, 3. Vermont, 4.Connecticut(excluding Southwestern Connecticut), 5. SouthwesternConnecticut(excluding Norwalk-Stamford area), 6. Norwalk-Stamfordarea, 7. Rhode Island, 8. Southeastern Massachusetts, 9. Western andCentral Massachusetts, 10. Boston/Northeastern MassachusettsHourly demand/price data of July 2006 (24 × 31 = 744 scenarios)6 blocks (L 1 = 94 hours, and L w = 130 hours; w = 2, ..., 6).


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThe New England Electric Power Supply Chain Networkwith Fuel Supply Markets


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsEmpirical Case Study and ExamplesExample 1: Simulation of the regional electric power pricesExample 2: Sensitivity analysis for electricity prices undernatural gas and oil price variationsExample 3: The impact of the oil price on the natural gasprice through electric power marketsExample 4: The impact of changes in the electricity demandsfor electricity on the electric power and fuel supply markets.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 1: Simulation of the Regional Electric PowerPricesAverage Regional Demands for Each Demand Level (Mwh)Region Block 1 Block 2 Block 3 Block 4 Block 5 Block 61 1512 1425 1384 1292 1051 8892 1981 1868 1678 1481 1193 10053 774 760 717 654 560 5004 2524 2199 2125 1976 1706 14325 2029 1798 1636 1485 1257 10656 1067 931 838 740 605 5097 1473 1305 1223 1112 952 8018 2787 2478 2315 2090 1736 13979 2672 2457 2364 2262 2448 218610 4383 4020 3684 3260 2744 2384Total 21201 19241 17963 16350 14252 12168


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 1: Simulation of the Regional Electric PowerPricesActual Regional Prices ($/Mwh)Region Block 1 Block 2 Block 3 Block 4 Block 5 Block 6ME 96.83 72.81 59.78 52.54 45.79 36.70NH 102.16 77.17 63.07 56.31 48.20 38.35VT 105.84 80.69 65.32 58.39 49.71 39.24CT 133.17 112.25 86.85 65.97 50.92 39.97RI 101.32 75.66 61.84 56.06 47.55 37.94SE MA 101.07 75.78 62.09 56.27 47.54 38.05WC MA 104.15 79.19 64.49 58.41 49.25 39.53NE MA 109.29 83.96 63.93 63.02 48.11 38.22


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 1: Simulation of the Regional Electric PowerPricesSimulated Regional Prices ($/Mwh)Region Block 1 Block 2 Block 3 Block 4 Block 5 Block 6ME 97.07 82.66 62.40 53.49 51.00 51.00NH 97.39 82.66 62.40 53.49 51.00 51.00VT 97.39 82.66 62.40 53.49 51.00 51.00CT 127.48 114.96 67.62 62.61 51.00 51.00RI 97.39 82.66 62.40 56.65 51.00 51.00SE MA 97.39 82.66 62.40 56.65 51.00 51.00WC MA 97.39 82.66 62.40 56.65 51.00 51.00NE MA 99.90 78.43 62.40 56.65 51.00 51.00


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsActual Prices vs. Simulated Prices ($/Mwh)


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsNatural gas units and oil units generate 38% and 24% ofelectric power in New England, respectively.Generating units that burn gas or oil set electric power marketprice 85% of the time.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsAverage Electricity Prices at Peak Demand Level under Fuel Price VariationsElectricity PriceResidual Fuel Oil Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 5.46 6.18 6.42 8.51 9.667.00 6.27 6.70 6.91 8.62 9.66Natural Gas 9.00 7.72 7.95 8.01 9.01 9.84($/MMBtu) 11.00 9.04 9.38 9.53 10.24 10.5313.00 10.29 10.75 11.02 11.43 11.58


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsAverage Electricity Prices at Intermediate Demand Level under Fuel PriceVariationsElectricity PriceResidual Fuel Oil Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 4.59 5.12 5.57 5.62 7.107.00 5.39 5.63 5.73 6.64 7.51Natural Gas 9.00 6.85 6.85 6.85 7.46 7.46($/MMBtu) 11.00 8.30 8.30 8.30 8.30 8.3013.00 9.76 9.76 9.76 9.76 9.76


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsAverage Electricity Prices at Low Demand Level under Fuel Price VariationsElectricity PriceResidual Fuel Oil Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 4.07 4.15 4.15 4.15 4.427.00 5.29 5.39 5.39 5.39 5.56Natural Gas 9.00 5.92 6.38 6.55 6.85 6.85($/MMBtu) 11.00 6.33 7.00 7.00 8.19 8.3013.00 7.58 7.62 7.62 9.18 9.63


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariations


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsThe spark spread of a power plant is the gross income of the power plant undercertain market conditions, and is defined as follows:Spark Spread = Electricity Price − Heat Rate of the Power Plant ∗ Fuel PriceThe spark spread has been widely utilized to evaluate the profitability and valueof power plants as well as to manage financial risks.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsSpark Spread at Peak Demand Level under Fuel Price VariationsElectricity PriceRFO Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 1.71 2.43 2.67 4.67 5.917.00 1.02 1.45 1.66 3.37 4.41Natural Gas 9.00 0.97 1.20 1.26 2.26 3.09($/MMBtu) 11.00 0.79 1.13 1.28 1.99 2.2813.00 0.54 1.00 1.24 1.68 1.83


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsSpark Spread at Intermediate Demand Level under Fuel Price VariationsElectricity PriceResidual Fuel Oil Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 0.84 1.37 1.82 1.87 3.357.00 0.14 0.38 0.48 1.39 2.26Natural Gas 9.00 0.10 0.10 0.10 0.71 1.21($/MMBtu) 11.00 0.05 0.05 0.05 0.17 0.6313.00 0.01 0.01 0.01 0.01 0.01


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 2: Electric Power Prices under Fuel PriceVariationsSpark Spread at Low Demand Level under Fuel Price VariationsElectricity PriceResidual Fuel Oil Prices ($/MMBtu)(cents/kwh) 4.00 5.00 6.00 7.00 8.005.00 0.32 0.40 0.40 0.40 0.677.00 0.04 0.14 0.14 0.14 0.31Natural Gas 9.00 -0.83 -0.37 -0.20 0.10 0.10($/MMBtu) 11.00 -1.92 -1.25 -1.25 -0.06 0.0513.00 -2.17 -2.17 -2.13 -0.57 -0.12


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 3: The Interactions Among Electric Power,Natural Gas and Oil MarketsBased on Wiser, Bolinger, and St. Clair (2005) and historicaldata, we assume that the natural gas price function (unit:$/MMBtu) takes the form:π GASm (h) = 7.5∑ 6∑ 6∑ Gw=1 m=1 g=1∑ R∑ Ngr1r 1 =1 u=1 qGASm61.149gr 1 uw + 30.811.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 3: The Interactions Among Electric Power,Natural Gas and Oil MarketsThe Price Changes of Natural Gas and Electric Power Under Residual Fuel OilPrice Variation (with switch)RFO Price 2.00 4.00 6.00 8.00 10.00 12.00 14.00NG Demand 21.94 24.40 35.17 39.86 44.51 45.06 45.06NG Price 6.47 6.77 8.09 8.67 9.24 9.31 9.31EP (Peak) 7.23 7.50 9.13 10.57 11.46 12.37 12.73EP (Intermediate) 4.96 5.29 6.76 8.38 9.37 9.51 9.62EP (Low) 4.81 5.12 6.22 6.87 7.31 7.39 7.39NG=Natural Gas, RFO=Residual Fuel Oil, EP=Average Electricity Price


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 3: The Interactions Among Electric Power,Natural Gas and Oil MarketsThe Price Changes of Natural Gas and Electric Power Under Residual Fuel OilPrice Variation (without switch)RFO Price 2.00 4.00 6.00 8.00 10.00 12.00 14.00NG Demand 21.29 25.78 34.88 38.87 40.03 40.03 40.03NG Price 6.39 6.94 8.06 8.55 8.69 8.69 8.69EP (Peak ) 7.32 8.14 9.78 10.42 11.70 13.28 15.40EP (Intermediate ) 4.91 5.51 6.74 8.27 9.20 9.47 9.60EP (Low ) 4.70 5.14 6.38 6.78 6.89 6.89 6.89NG=Natural Gas, RFO=Residual Fuel Oil, EP=Average Electricity Price


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 3: The Interactions Among Electric Power,Natural Gas and Oil Markets


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 4: The Impact of Electricity Demand Changes onthe Electric Power and the Natural Gas MarketsWhen electricity demands increase (or decrease), the electricpower prices will increase (or decrease) due to two mainreasons:Power plants with higher generating costs (e.g. heat rates)have to operate more (or less) frequently.The demands for various fuels will also rise which may result inhigher (or lower) fuel prices/costs.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 4: The Impact of Electricity Demand Changes onthe Electric Power and the Natural Gas MarketsIn August, 2006, the natural gas price soared by 14% becausehot weather across the U.S. led to high electricity demand.In July 2007, the natural gas future price for September 2007increased by 4.7% mainly because of the forecasted highelectricity demands in Northeastern and Mid-western citiesdue to rising temperatures.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 4: The Impact of Electricity Demand Changes onthe Electric Power and the Natural Gas MarketsPrices Before the Demand Increase ($/Mwh)Region Block 1 Block 2 Block 3 Block 4 Block 5 Block 6ME 105.28 105.28 101.00 81.19 69.90 66.63NH 109.15 105.39 101.00 81.19 70.83 66.63VT 109.15 105.39 101.00 81.19 70.83 66.63CT 137.13 133.34 101.07 84.51 70.83 66.63RI 109.15 105.39 101.00 81.19 70.83 66.63SE MA 109.15 105.39 101.00 81.19 70.83 66.63WC MA 109.15 105.39 101.00 81.19 70.83 66.63NE MA 122.52 105.39 101.00 81.19 70.83 66.63NG Demand40.03 Billion MMBtuNG Price8.69 $/MMBtu


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 4: The Impact of Electricity Demand Changes onthe Electric Power and the Natural Gas MarketsPrices after the Demand Increase ($/Mwh)Region Block 1 Block 2 Block 3 Block 4 Block 5 Block 6ME 105.28 105.28 105.28 100.62 74.64 68.34NH 113.35 105.28 105.28 100.62 74.64 68.34VT 113.35 105.28 105.28 100.62 74.64 68.34CT 140.57 134.71 132.61 100.77 74.64 68.34RI 113.35 105.28 105.28 100.62 74.64 68.34SE MA 113.35 105.28 105.28 100.62 74.64 68.34WC MA 113.35 105.28 105.28 100.62 74.64 68.34NE MA 122.52 112.34 105.28 100.62 74.64 68.34NG Demand43.62 Billion MMBtuNG Price8.97 $/MMBtu


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsExample 4: Electric Power Prices Before and After theIncrease of Demands (Connecticut and Boston)


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsConclusionsWe developed a new variational inequality model of electric power supplychain networks with fuel markets, which considered both economictransactions and physical transmission networks.We provided some qualitative properties of the model as well as acomputational method.We then conducted a case study where our theoretical model was appliedto the New England electric power network and fuel supply markets.We also conducted sensitivity analysis in order to investigate the electricpower prices under fuel price variations.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsConclusions (Cont’d)We showed that not only the responsiveness of dual-fuel plants, but alsothe electric power market responsiveness, were crucial to theunderstanding and determination of the impact of the residual fuel oilprice on the natural gas price.We applied our model to quantitatively demonstrate how changes in thedemand for electricity influenced the electric power and fuel markets.The model and results presented in this paper are useful in determiningand quantifying the interactions between electric power flows and pricesand the various fuel supply markets.Such information is important to policy-makers who need to ensuresystem reliability as well as for the energy asset owners and investors whoneed to manage risk and evaluate their assets.


Introduction Literature Review Integrated Electric Power Supply Chains Empirical Examples ConclusionsThank You!

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