Felipe Beltrán Rodríguez 1, Eng., Master Student Prof. Erlon Cristian Finardi 1, D. Eng., Advisor Welington de Oliveira 2, D.Sc.

Transcrição

1 Felipe Beltrán Rodríguez 1, Eng., Master Student Prof. Erlon Cristian Finardi 1, D. Eng., Advisor Welington de Oliveira 2, D.Sc., Co-Advisor 1-UFSC 2-IMPA

2 (Dec. 2013) N NE 90 Demand of Electricity (GW) Hydro Plants Storage Capacity Run of River 86.7 GW Installed SE S Thermal Units Nuclear Coal Natural Gas Diesel Biomass 39.7 GW Installed approx. 100,000 km Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 2

3 future more uncertainties and modeling approximations present Long-Term Short-Term Daily Schedule less uncertainties and more modeling details 5 years monthly stages 2 months weekly stages 1 week ½ hour steps NEWAVE DECOMP DESSEM Official Software Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 3

4 Represented by means of a two-stage linear stochastic problem Planning horizon: 2 months Inflows scenario tree: first month with a single weekly inflows realization and the second month with several realizations R$ Long-term Policy (water values) Energy Storage Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 4

5 Multistage setting: possibility for improvement in the representation of the stochastic process The price: high dimensionality of the scenario tree. Hence, high computational burden Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 5

6 Scenario reduction techniques can handle with the high dimensionality The aim is to find a reduced tree which supplies similar decisions but with less effort (CPU time) Reduction Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 6

7 Nested Distance metric [G. Pflug and A. Pichler, 2012]is used to measure distances in multistage scenario trees consists in solving a mass transportation problem between each pair of nodes (tree branches) Generalization of the Wasserstein metric [Dupacova,Gröwe-Kuska, W. Römisch 2003], [Gröwe-Kuska, H. Heitsch, W. Römisch 2003], [Oliveira, Sagastizábal et al 2010] Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 7

8 Nested Distance Solves a mass transportation problem (LP) between each pair of nodes (tree branches) Probabilities and scenarios are updated in an iterative manner Reduced tree is not a subset of the given original tree Wasserstein Distance (Two-stage setting) Solves only one mass transportation problem between trees (the mass transportation problem is a MILP, but solved via heuristics) Updates only probabilities Reduced tree is a subset of the given original tree Wasserstein Distance (Multistage setting) Solves many mass transportation problem between trees (MILP+heuristics) Only probabilities are updated (and scenarios if distance between Filtrations are considered) The reduced tree is not a subset of the original tree Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 8

9 Out of all the possible reduced trees, try to find the one with the smallest nested distance. Nested Distance (Original-Phase 2) < The Nested Distance (Original-Phase 1) Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 9

10 Step 1: Merge Stage 2: Merge Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 10

11 Step3: Merge Step4: Merge Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 11

12 Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 12

13 Thermal Plants Data Load Hydroelectric Data Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 13

14 Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 14

15 Quantity Stage Original Tree: AO3 / Stages: 4 / Scenarios: 1000 ReducedTree: AR31 / Stages: 4 / Scenarios: 8 Cost [$R] MCO [$R/MWmonth] q [m3/seg] s [m3/seg] Pthermal [MWmonth] Pdeficit [MWmonth] μ σ μ σ ,0 0, ,0 0, , , , , , , , , , , , , ,5 0,0 493,9 0, ,4 6,1 497,7 1, ,0 20,4 496,1 25, ,3 90,9 479,3 88, ,7 0, ,0 0, ,7 231, ,5 211, ,7 540, ,2 565, ,3 915, ,3 927, ,1 0,0 3021,1 0, ,4 247,1 2323,1 319, ,0 690,1 2496,3 856, ,4 1461,3 2750,0 1384, ,0 0,0 1275,0 0, ,0 0,0 1275,0 0, ,0 0,7 1274,9 4, ,9 17,5 1272,0 17,0 1 0,0 0,0 0,0 0,0 2 60,6 85,8 44,98 77, ,2 234,1 569,9 245, ,2 404,5 625,1 411,3 Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 15

16 The results indicate that the Nested Distance can reduce the computational burden without compromising the expected operational cost The size of the scenario trees that can be reduced and the operative policies obtained from the reduced tree are still being studied Apply the methodology in the context of the Brazilian Short-term Hydrothermal Scheduling problem Laboratório de Planejamento de Sistemas de Energia Elétrica- LabPlan 16

17 Thank You Takk Obrigado