Johns Hopkins Stochastic Multi-stage Integrated Network Expansion (JHSMINE) Version 1

Transcription

1 Jons Hopkins Stocastic Muti-stage Integrated Network Expansion (JHSMINE) Version 1 Qingyu Xu, Benjamin F. Hos Juy Introduction In tis document, te asic JHSMINE formuation wi e sown. Tis woe formuation is a resut of mode deveopment across mutipe artices/reports. Tis is tus a comination of works of researcers from Hos group. Te origina formuation wit two-stage stocastic programming was from 1. Ten in 2, tis formuation was at te first time appied to WECC wit DC OPF mode enancement. Detais of a susequent appication tat incudes inearized unit commitment constraints 3 are in 4. 1, A. H. van der Weijde, B. F. Hos, Te economics of panning eectricity transmission to accommodate renewaes: Using two-stage optimisation to evauate fexiiity and te cost of disregarding uncertainty, Energy Economics, vo. 34, no. 6, pp , F. D. Munoz, B. F. Hos, J. L. Ho, S. Kasina, An Engineering-economic approac to transmission panning under market and reguatory uncertainties: WECC case study, IEEE Transactions on Power Systems, co. 29, no. 1, pp , S. Kasina, S. Wogrin and B. Hos, Approximations to unit comment in panning modes, INFORMS Annua Meeting, Minneapois, J. Ho, B. F. Hos, P. Donooo-Vaett, Q. Xu et a., Panning transmission for uncertainty: Appications and essons for te western interconnection, WECC, Sat Lake City, UT, Formuation 2.1 Set Root Set B: Bus set. Index:, i G: Generation type set. Index: g H: Mode stage set. Index: J: State set. Index: j L: Line set. Index: P : Period set. Index: t P at: Pat set. Index: u RP : REC trading pat set. Index: p S: Scenario set. Index: s 1

2 2.1.2 Suset B C : Conventiona u set B E : Existing use set B W : Renewae energy u set G D : Generation types to e dispatced G P : Generation types modeed as parameters G E : Existing generation types G I : Generation types to e invested G R : Renewae generation types L EXA : Existing AC Lines L EXD : Existing DC ines L CF B : First stage ackone reinforcement candidate ines L CSB : Second stage ackone reinforcement candidate ines L CBR : First stage renewae access candidate ines L CW R : Second stage renewae access candidate ines L EQ : Equivaent ines L H : Unidirectiona fictitious u ines, connecting conventiona us to te grid 2.2 Parameters Universa Parameters A, : Stage avaiaiity of candidate ine, for first-stage candidates, 1 for year 10 and 20; for second-stage candidates, 1 for ony year 20 ACPj : Aternate compiance payment (ACP) rate, Miion$/GW B : Susceptance of ine, GW CX : Capita cost of ine, Miion$ EM g : Emission rate, ton/mmbtu F : Line terma capacity, GW F OM g : Fixed O&M cost Miion$/(GW year) F OR g : Forced outage rate HW t : Hour-weigt of t HR g, : Heat rate of generation g on us, GW $/MMBTU IRP S j : Instate RPS requirement M : Large positive numer for AC candidate ine, GW P OR g : Paned Outage Rate P W,j : Popuation aocation weigt per us to eac state R u : Existing Pat rating, GW 2

3 RX : Expansion of pat rating wit candidate ine, non-zero for ackone reinforcement V : Numer of years for stage V OLL: Vaue of oad oss, Miion$/GW V OM g, : Variae O&M cost Miion$/GW W,g,t : Houry capacity factors for wind, soar and ydro, 1 for oter tecs Y,g 0 : Existing Capacity, GW Y Max,g : Maximum resource potentia at us under investment, GW Y R g : Cumuative forced retirement of generation capacity in stage δ: Discount Rate Φ, Eement of ine-node incidence matrix, 1 for to-us, -1 for from-us, oterwise 0 Ψ u, Eement of pat-ine incidence matrix, 1 for to-us, -1 for from-us, oterwise 0 Ω p,j : Eement of REC trading pat-state incidence matrix, inary Scenario Specific Parameters p s : Proaiity of scenario s CT ax s : Caron tax per scenario, $/ton CY,g,s : Capita cost of generation, Miion$/GW D,t,s : Forecasted demand, GW F P,g,s,t : Fue price of generation g on us, Miion $/MMBTU MC,g,s,t : Generation margina cost, Miion$/GW RP Sj,s : Renewae oigation of state j,% W RP S s : Region-wise RPS renewae oigation, % Cacuating MC g,s,t 2.3 Decision Variaes Investment Decision Variaes MC g,s,t = F P,g,s,tHR g, + CT ax s HR g, EM g + V OM g, (1) x CF B : Backone reinforcement first stage decision, inary, defined on L CF B x CSB,s : Backone reinforcement recourse decision, inary, defined on L CSB x CF R : Renewae access first stage investment decision, continuous 0-1, defined on L CF R x CSR,s : Renewae access investment recourse decision, continuous 0-1, defined on L CSR y,g : Generation expansion anticipation, GW, positive, defined on B C B W, G I y,g,s : Generation expansion recourse anticipation, GW, positive, defined on B C B W, G I 3

4 2.3.2 Operation Decision Variaes f,t,s : Power fow, GW, unrestricted k,g,t,s : Generation, GW, positive n j,s : Noncompiance of renewae target, GW, positive q s,p: Renewae energy credit trading, GW, positive r,t,s : Load curtaiment, positive θ,t,s : Pase ange, unrestricted φ,t,s : Load upift, GW 2.4 Ojection Function V OPs = v=1 Is 0 = CX x + CY 0 L CF B L CF R g G I Is 1 = CX x,s + CY 1 L CSB L CSR g G I V OCs ( 1 ) v = v=1 t P g G,g,sy,g (2),g,sy,g,s (3) MCg,s,tHW t k,g,t,s (4) ( 1 ) v V OLLHW t (r,t,s + φ,t,s) + ACPj,sn j,s B j J OM 1 s =,g OM 2 s =,g F OM g Y 0,g Y R 1,g + y,g F OM g Y 0,g Y R 2,g + y,g + y,g,s (5) (6) (7) min I 0 + s S Os = OCs + OPs + OMs (8) ( 1 ) V1(I 1 p s s + Os) 1 + ( 1 ) V1+V 2O 2 s (9) 2.5 Constraints RPS Constraint Region-wise RPS: 8760HW t P W,j k,g,t,s + n j,s j J g G R,t, State-wise RPS: W RP S s 8760HW t P W,j D,t,s r,t,s + φ o,,t,s Ωp,j qs,p + n j,s j J s, (10) g G R,t, 8760HW t P W,j k,g,t,s p In-State RPS: g G R,t, 8760HW t P W,j k,g,t,s p RP S j,s Ω >0 p,j q s,p + n j,s RP S j,sirp S j 8760HW t P W,j D,t,s r,t,s + φ o,,t,s 8760HW t P W,j D,t,s r,t,s + φ o,,t,s s,, j (11) s,, j (12) 4

5 2.5.2 Transmission Constraint: KCL Component Kircoff s Current Law: k,g,t,s + r,t,s + Φ, f,t,s φ o,,t,s D,t,s = 0 g, t, s, (13) Pat Ratings: Ψ u, f,t,s R u + A, RX (x + x,s ) s,, u, t (14) Load Curtaiment Limits: r,t,s D,t,s, t, s, (15) Terma Limits for Existing AC & DC ines: f,t,s F L EXA L EXD, t, s, (16) Terma Limits for Candidate Lines: f,t,s F A, (x + x,s ), t, s, (17) Hu Line Fow Non-negativity: f,t,s 0 L H, t, s, (18) Equivaent Line Terma Capacity (For Pipe and Bue formuation): f,t,s π 6 B L EQ (19) Transmission Constraint: KVL Component Swing Bus: θ 1,t,s = 0 t, s, (20) Kircoff s Votage Law for Existing AC ines and Equivaent ines: B 1Φ, θ,t,s = f,t,s L EXA L EQ (21) Kircoff s Votage Law for First Stage Backone Candidates: B 1Φ, θ,t,s f,t,s M (1 x ) L CF B, t, s, (22) Kircoff s Votage Law for Second Stage Backone Candidates: B 1Φ, θ,t,s 2 f,t,s 2 M (1 x,s ) L CSB, t, s (23) Pase Ange Difference Limit: Φ, θ,t,s π L EQ, t, s, (24) Generation Constraints Generation Investment Potentia: Invested Generation Limit Year 10: Invested Generation Limit Year 20: Existing Parameterized Generation: Existing Dispatcae Generation: y,g + y,g,s Y MAX,g, g, s (25) k 1,g,t,s (1 P OR g )(1 F OR g )W,g,t y,g B W B C, g G I, t, s (26) k 2,g,t,s (1 P OR g )(1 F OR g )W,g,t ( y,g + y,g,s ) B W B C, g G I, t, s (27) k,g,t,s = (1 P OR g )(1 F OR g )W,g,t (Y 0,g Y R,g), g G P, t, s, (28) k,g,t,s (1 P OR g )(1 F OR g )W,g,t (Y 0,g Y R,g), g G D G E, t, s, (29) 5