Integrated planning of biomass inventory and energy production Marco Chiarandini 1 Niels Kjeldsen 1 , 2 Napoleão Nepomuceno 3 1 Department of Mathematics and Computer Science, University of Southern Denmark 2 Model development, DONG Energy Thermal Power A/S 3 Universidade de Fortaleza, Programa de Pós-Graduação em Informática Aplicada, Fortaleza, Brazil July 5th, 2012
Investment evaluation Mathematical model Benders decomposition Outline Results 1. Production planning and investment evaluation Changing fuel: From coal to wood pellets 2. Mathematical model Mixed integer linear programming model 3. Benders decomposition Benders optimality cuts Handling multiple scenarios 4. Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 2
Investment evaluation Mathematical model Benders decomposition Outline Results 1. Production planning and investment evaluation Changing fuel: From coal to wood pellets 2. Mathematical model Mixed integer linear programming model 3. Benders decomposition Benders optimality cuts Handling multiple scenarios 4. Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 3
Investment evaluation Mathematical model Benders decomposition Danish energy system Results (source Energinet.dk) M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 4
Investment evaluation Mathematical model Benders decomposition Danish energy system Results Weekly demand profile Demand Remaining Wind 5000 MW 3000 1000 0 200 250 300 Hours (source Energinet.dk) M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 4
Investment evaluation Mathematical model Benders decomposition Energy production Results ◮ Uncontrollable: ◮ Wind power ◮ Solar power ◮ Controllable ◮ Thermal units: Providing heat to the local heating area ◮ Connections to neighboring countries ◮ Other sources: ◮ SmartGrid ◮ Electric cars M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 5
Investment evaluation Mathematical model Benders decomposition Overview of Avedøre power plant Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 7
Investment evaluation Mathematical model Benders decomposition Wood pellet storage at Avedøre Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 8
Investment evaluation Mathematical model Fuel delivery processes Benders decomposition Results Logistics differences Coal logistics Wood pellets logistics M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 9
Investment evaluation Mathematical model Benders decomposition Biomass contracts Results Uniform contract 0 730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 hours Seasonal contract 0 730 1460 2190 2920 3650 4380 5110 5840 6570 7300 8030 8760 hours M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 10
Investment evaluation Mathematical model Benders decomposition Two stage stochastic approach Results ◮ Biomass contracts must be decided a year ahead. ◮ But future demand, prices and exact delivery times are unknown � uncertainty. Two stage stochastic approach (look-ahead policy): ◮ First stage : long term decisions on biomass contracts might yield: ◮ Running out of fuel (underflow) ◮ Running out of storage space (overflow) ◮ Second stage : optimize when uncertainty is revealed ◮ Production of electricity and heat. ◮ Foreign trade (only electricity). ◮ Using an alternative (fossil) fuel ◮ Redirection of deliveries. M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 11
Investment evaluation Mathematical model Benders decomposition Outline Results 1. Production planning and investment evaluation Changing fuel: From coal to wood pellets 2. Mathematical model Mixed integer linear programming model 3. Benders decomposition Benders optimality cuts Handling multiple scenarios 4. Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 12
Investment evaluation Mathematical model Benders decomposition Mixed integer linear programming model Results Several scenarios for future uncertainty Objective function (minimize): ◮ Cost of biomass contracts ◮ Use of fossil fuel ◮ Foreign trade ◮ Over/under production (slack/surplus demand) Constraints: ◮ Electricity and heat demand ◮ Power plant production (including trade with neighboring countries) ◮ Biomass fuel levels and redirection of deliveries M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 14
Investment evaluation Mathematical model Constraints Benders decomposition Results Electricity and heat balance Electricity Heat q k , i , t − 1 , s q k , i , t , s p k , i , t − 1 , s p k , i , t , s p e p e q a q a q a n , t − 1 , s n , t − 1 , s h , t − 2 , s h , t − 1 , s h , t , s t − 1 t t − 1 t q h , t − 1 , s q h , t , s p t − 1 , s p t , s q h , t − 1 , s h , t , s q p t − 1 , s t , s p D q D q h , t − 1 , s h , t , s D p D p t − 1 , s t , s M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 15
Investment evaluation Mathematical model Constraints Benders decomposition Results Biomass fuel level constraints capacity fuel level f 2 ,t,s = f 2 ,t − 1 ,s − τ · u 2 ,i,t,s + j ∈ J A j,t,s · x j,i,t,s � time M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 16
Investment evaluation Mathematical model Constraints Benders decomposition Results Modeling power plant production Cogeneration power plant p p = ρ max − ς v q ρ max p = ρ min − ς v q p = ς b q ρ min q M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 17
Investment evaluation Mathematical model Benders decomposition The full model Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 18
Investment evaluation Mathematical model Benders decomposition Outline Results 1. Production planning and investment evaluation Changing fuel: From coal to wood pellets 2. Mathematical model Mixed integer linear programming model 3. Benders decomposition Benders optimality cuts Handling multiple scenarios 4. Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 19
Investment evaluation Mathematical model Benders decomposition Benders Decomposition Results We consider the MILP with complicating y -variables, which are the biomass contracts: z = c T x + f T y min x , y Ax + By ≥ b y ∈ Y x ≥ 0 M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 20
Investment evaluation Mathematical model Benders decomposition Benders Decomposition Results We consider the MILP with complicating y -variables, which are the biomass contracts: z = c T x + f T y min x , y Ax + By ≥ b y ∈ Y x ≥ 0 or emphasizing the two stage approach: � �� f T y + min c T x | Ax ≥ b − By � min y ∈ Y x ≥ 0 M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 20
Investment evaluation Mathematical model Benders decomposition Benders optimality cuts Results Given a specific set of biomass contracts y the dual of the inner problem is: f T y + ( b − By ) T u max u A T u ≤ c u ≥ 0 The solution u to the dual problem gives a lower bound to the original problem. The lower bound is valid for all biomass contracts y and the generalization gives: Benders optimality cut z ≥ f T y + ( b − By ) T u . M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 22
Investment evaluation Mathematical model Benders decomposition Handling multiple scenarios Results Benders optimality cuts for multiple Block angular structure scenarios Variables One year f T y + 1 � min z s scenarios | S | y ∈ Y s ∈ S Biomass contracts s.t. z s ≥ ( b s − B s y ) T u s Constraints k ∀ s ∈ S , k = 1 . . . K M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 24
Investment evaluation Mathematical model Benders decomposition Outline Results 1. Production planning and investment evaluation Changing fuel: From coal to wood pellets 2. Mathematical model Mixed integer linear programming model 3. Benders decomposition Benders optimality cuts Handling multiple scenarios 4. Results M. Chiarandini, N. Kjeldsen, N. Nepomuceno .::. Integrated planning of biomass inventory and energy production 25
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