Pedro M. Castro Iiro Harjunkoski Ignacio E. Grossmann. Lisbon, Portugal Ladenburg, Germany Pittsburgh, USA

Transcription

1 Pedro M. Casro Iro Harjunkosk Ignaco E. Grossmann Lsbon Porugal Ladenburg Germany Psburgh USA 1

2 Process operaons are ofen subjec o energy consrans Heang and coolng ules elecrcal power Avalably Prce Challengng aspec of plan schedulng Curren pracce heursc rules for feasbly Due o complexy choces are far from opmal No connuous me formulaon for me dependen uly profles Proposed approach general for connuous plans Focus on cemen ndusry Grndng process major consumer of elecrcy Augus

3 Mulproduc sngle sage plan Inensve use of elecrcy When and where o produce a ceran grade? How much o keep n sorage? Mee produc demands (mulple due daes for each produc) Mnmze oal energy cos Respec power avalably consrans Augus

4 Conracs beween elecrcy suppler and plans Energy cos [ /kwh] Vares up o facor of 5 durng he day Maxmum power consumpon [MW] Harsh cos penales f levels are exceeded Opmal schedulng can have 20% mpac on elecrcy bll Produce n low cos perods Augus

5 From flowshee o Resource Task Nework Conver problem daa Augus

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7 Slo1 Slo 2 Slo 3 Slo T-2 Slo T-1 δ T-2 T-1 1 T Elegan and compac formulaon Dscree evens handled naurally Tme nervals of 1 hour () for 1 week horzon Mnor lmaons Can lead o slghly subopmal soluons Wh oo many changeovers Augus

8 Slo 1 Slo 2 Slo T-2 Slo T T-2 T-1 1 T General and accurae formulaon Dffcul o accoun for dscree evens Locaon of even pons unknown a pror Elecrcy prcng & avalably Produc due daes Locaon of even pons A demand pons A some energy prcng/avalably levels Augus

9 Slo1 Slo 2 Slo 3 Slo T-2 Slo T T-2 T-2 T-1 T-1 1 T Looks n beween consecuve demand pons Merges perods wh same energy prcng/power level Low cos energy level Medum cos Hgh cos Demand pon Demand pon Power avalably (MW) Low cos Medum cos Hgh cos Demand pon Demand pon Power avalably (MW) Only vald for sngle sage plans Augus

10 Can be vew as a plannng approach No concerned wh acual mng of evens Connuous me whn a me nerval whou even pons Resource balances for equpmens and ules replaced by wo ses of consrans Tme nerval duraon greaer han sum of processng mes Energy balances (sof consrans due o slacks S r ) Augus max T T R r TC I r c ) ( max T T R r S UT I r r n r c

11 Calls combned aggregae/connuous me model Augus

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13 Case (PMS) Power Model T DV SV EQ RMIP MIP [ ] CPUs Gap (%) EX5 (322) U DT AG RH CT EX5a (322) R DT AG RH CT EX6 (323) U DT AG RH CT Inf EX7 (334) U DT AG RH CT no sol EX8 (335) R DT AG RH EX9 (434) U DT AG RH EX10 (534) U DT AG RH DT dffcul o close opmaly CT lmed o small problems RH generaes full schedule relavely fas M M M S S S (on) P1 P P3 P4 S P Tme (h) S P1 P2 400 P3 200 P4 P Tme (h) S P1 400 P2 P3 200 P4 (on) (on) P Tme (h) S P1 400 P2 P3 200 P4 (on) P Tme (h) S P1 P2 400 P3 200 P4 P Tme (h) Augus

14 Problems wh unlmed power avalably Aggregae model s rgorous and very powerful Lower degree of degeneracy 1/10 problem sze 4 orders magnude reducon CPUs vs. DT Rollng horzon algorhm fnds praccal global opmal soluons effcenly Consders he whole remanng problem smulaneously EX10 Day T LB (k ) OBJ (k ) MO TU WE TH FR SA SU Augus

15 Problems wh resrced power Dscree me formulaon s he bes Fnds very good soluons (<0.8 %) rapdly (5 mn) Aggregae model s a relaxaon (underesmaes cos) Rollng horzon may generae subopmal soluons Augus

16 Dscree and connuous me models IECR Aggregae model and rollng horzon approach To be submed o CACE Specal Issue PSE09 Acknowledgmens Fnancal suppor from CAPD Cener a Carnege Mellon Unversy Fundação para a Cênca e Tecnologa Fundação Calouse Gulbenkan Augus

17 Upgrade from Casro e al. (2004) Bnary varables N ask execued a nerval Y pe me perod p of level e acve durng nerval Y d ou even pon s demand pon d New consrans Tasks sarng me greaer han energy level lower bound Mus end before me nerval T and energy level upper bound Ts r Ts r RTC 1 T max c ee ptp I lb e Y e p p e r Ts ube py p e H ( 1 r N ) r e max c c I e ptpe I e Y +1d ou =1 fx d Absolue me of a demand pon equal o a due dae dtd fx d Y ou d T dtd fx d Y ou d H ( 1 Y ou d dtd ) Augus