Towards Optimal Production of Industrial Gases with Uncertain Energy Prices Natalia P. Basán, Carlos A. Méndez. National University of Litoral / CICET Ignacio Grossmann. Carnegie Mellon University Ajit Gopalakrishnan, Irene Lotero, Brian Besancon. Air Liquide March 8 9 th, 2016 1
Motivation How to optimize participation in electricity markets under uncertainty in the operation of power intensive i air separation processes. Day ahead markets (forecasts are available) Spot/Imbalance markets (hard to predict) Efficiently adjust production operation according to time dependent electricity pricing. Consider explicit modeling of feasible plant operational transitions. Propose a systematic way of representing transition states. Develop a systematic discrete time, deterministic MILP model to optimal production planning of continuous power intensive air separation processes. Propose an efficient predictive and reactive solution strategy for real world industrial scale problems. 2
Problem Definition Major Problem Features 1. Min/max production rates based on the plant state 2. Power consumption for the different operating modes 3. Power consumption follows linear correlation: PW = a + b*production Surface-treatment operations of heavy aircraft-parts are 4. Min/max storage capacity in the plant characterized by a higher complexity than typical flow-shop 5. Minimum final tank levels at the end of the scheduling horizon 6. Expected daily demand and hourly scheduling electricity cost. problems. This particular process in-volves a series of chemical stages s=0,1,2,...,li, disposed in a single production line, in which an automated material-handling tool is in charge of all transfer movements. State Graph of the Plant in Netherlands 3
PSTN - Process State Transition Network Plant states with minimum duration: 3 hours STAND BY Decomposition in 3sub states: states: 1 hour each RDCAP1 SB1 SB2 SBn RDCAP2 1 2 n RDCB RUCB 1 2 n RACAP2 Initial sequential transition states (4) Intermediate transition states (8) RUCAP1 Critical transition states (3) 4
Proposed MILP Model Indexes Time periods (168) States (15) Days (7) Sets Energy Parameters prices for the week of January 15 2015 Min Tank Level Min production per hour in each state Max production per hour in each state Minimum final tank levels at the end of the day Hourly expected Demand Fixed Power Consumption Continuous Variables Initial sequential states Intermediate transition states Critical transition states Next to transition states Last intermediate and critical state Variable Power Consumption Hourly energy prices for the week Min Tank Level Max Tank Level Binary Variables Production at time t for state s Indicates whether plant operates in state s Power consumption at time t during time period t Inventory available at tthe end of time period t Objective function (total energy cost) 5
Proposed MILP Model Plant State Min/Max Storage Capacity Sequential Transition States Tank Level Constraints Critical Transition States Power Consumption Min/Max Production Objective Function 6
Computational Results SOLUTI BASED FLAT ENERGY COST RU RD SB GANTT CHART SCHEDULE 15 10 5 0 Final status of solution: OPTIMAL CPU time: 5.242 sec. TOTAL COST = 40131.82 POWER CSUMPTI 0 50 100 150 SOLUTI BASED TIME OF DAY PRICES RU RD GANTT CHART SCHEDULE 15 Final status of solution: OPTIMAL CPU time: 0.093 sec. TOTAL COST = 35524.16 POWER CSUMPTI SB 10 5 0 7
Computational Results PREDICTIVE MODEL ENERGY PRICE FORECAST (FEBRUARY 15, 2015) HOUR Monday Tuesday Wednesday Thursday Friday Saturday Sunday 1 39.99 40.88 41.87 40.22 42.88 44.48 45 2 36.3 36.97 39.3 37 40.02 43.32 41.35 3 34.48 36.2 39.8 36.82 40.11 42.03 39.27 4 30.38 34.19 36.67 35.38 37.7 39.6 34.95 5 29.21 32.29 34.33 33.38 35.14 37.1 30.35 6 29.49 36.03 37.32 35.51 37.06 39.41 28.49 7 30.15 44.85 42.39 41.06 43.6 45.8 31.92 8 32.18 55.1 53.56 53.06 54.21 55.36 34.68 9 34.48 58.37 58.5 57.57 58.35 58.9 35.66 10 38.37 60.33 60.05 60.1 59.53 58.85 41.52 11 39.61 59.35 59.17 57.71 57.31 55.35 44.22 12 42.67 58.77 53.31 51.82 51.17 51.5 47.34 13 43.93 55.5 50.07 48 47.36 48.88 43.24 14 40.03 53.26 47.57 44.98 44.65 48.13 39.92 15 35.08 49.65 44.6 41.91 41.9 46.45 36.41 16 33.93 46.59 43.54 41.25 41.55 44.39 33.31 17 34.17 45.95 44.52 41.85 42.74 43.73 30.89 18 44.36 52.91 50.84 50.07 49.96 49.49 40.44 19 54.91 78.61 64.05 62.11 63.66 55.88 50.07 20 56.27 72.84 58.17 59.81 60.85 55.89 43.74 21 51.94 57.81 50.29 52.09 52.72 48.77 40.96 22 44.76 51.51 42.85 45.64 46.37 45.22 36.46 23 44.79 49.13 43.97 46.49 47.39 46.18 39.8 24 44.51 47.01 43.44 43.94 46.65 43.26 40.46 CPU time: 0.093 sec. EXPECTED TOTAL COST = 35524.16 REAL TOTAL COST = 41214.65 GANTT CHART SCHEDULE RU RD SB POWER CSUMPTI 15 10 5 0 2145 100 1950 90 1755 80 1560 70 1365 60 1170 50 975 780 40 585 30 390 20 195 10 0 0 INVENTORY Qmin Qmax MDTL PRODUCTI 8
Computational Results PREDICTIVE MODEL RU EXPECTEDTOTAL TOTAL COST = 35524.16 RD Binary Variables: 2541 SB Continuous Variables: 2858 Equations: 7730 CPU time: 0.093 sec. REAL TOTAL COST = 41214.65 14.35 % RU RD SB ROLLING HORIZ MODEL Schedule Changes EXPECTED TOTAL COST = 40623.78 Binary Variables: 2541 Continuous Variables: 2858 Equations: 7730 CPU time: 0.109 sec. REAL TOTAL COST = 41326.93 9
Remarks Very efficient and robust predictive MILP based scheduling approach Modest computational effort considering a one hour time grid and oneweek time horizon Model able to consider all problem features and easy to adapt to reactive scheduling (rolling horizon) Promising INDUSTRIAL solution scheduling APPLICATI for real world Air EXAMPLE Liquide industrial plants Future Work Evaluate daily and hourly reactive decisions based on energy price changes (day ahead market and imbalance market). Test model with other Air Liquide plant configurations. Identify additional features to be included in the model. Evaluate model with uncertain demands. 10