Stochastic Market Clearing: Advances in Computation and Economic Impacts

Transcription

1 Engineering Conferences International ECI Digital Archives Modeling, Simulation, And Optimization for the 21st Century Electric Power Grid Proceedings Fall Stochastic Market Clearing: Advances in Computation and Economic Impacts Victor Zavala Argonne National Laboratory Follow this and additional works at: Part of the Electrical and Computer Engineering Commons Recommended Citation Victor Zavala, "Stochastic Market Clearing: Advances in Computation and Economic Impacts" in "Modeling, Simulation, And Optimization for the 21st Century Electric Power Grid", M. Petri, Argonne National Laboratory; P. Myrda, Electric Power Research Institute Eds, ECI Symposium Series, (2013). This Conference Proceeding is brought to you for free and open access by the Proceedings at ECI Digital Archives. It has been accepted for inclusion in Modeling, Simulation, And Optimization for the 21st Century Electric Power Grid by an authorized administrator of ECI Digital Archives. For more information, please contact

2 Stochastic Market Clearing: Advances in Computation and Economic Implications Victor M. Zavala Assistant Computational Mathematician Mathematics and Computer Science Division Argonne National Laboratory Fellow Computation Institute University of Chicago With: John Birge (UChicago), Mihai Anitescu Contributors: Miles Lubin, Cosmin Petra, J Hall (Edinburgh) October, 2012

3 Deterministic Market Clearing Zavala, Constantinescu, Wang, and Botterud,

4 Prices at Illinois Hub, 2009 Market Volatility

5 Constraint Anticipation Effect of Foresight on Economic Dispatch Performance

6 Deterministic Clearing Formulation Classical Two-Stage Stochastic Formulation 5

7 Illinois System Constantinescu, Zavala, Anitescu 2011, Lubin, Petra, Anitescu, Zavala Buses 261 Generators 24 Hours 6

8 Simplex 7

9 Parallel Simplex Implementation Non-Trivial : Numerical Stability, Communication, Load Balancing 8

10 PIPS-S (Lubin, Hall, Petra, Anitescu, 2012) Distributed Memory (MPI), C++ Primal and Dual Simplex Algorithms Specialized Block-LU Decomposition and Dantzig s Product-Form Updates Use CoinFactorization for Scenario LU Factorizations Basis Bootstrapping (Warm-Start Using Small Number of Scenarios) Rounding Heuristics for MILP Experiments: Compare with CLP (Open-Source) : Cold and Warm-Starts Unit Commitment Illinois Systems : 12 (UC12) and 24 (UC24) Time Steps Fusion and Intrepid Systems 9

11 Cold-Start UC12: 32 scenarios, 1,812,156 variables. UC24: 16 scenarios, 1,815,288 variables. Iteration Count OK but CLP performs more efficient LU factor updates Solution Time Decreased 14 Times in UC12 Solution Time Decreased 9 Times in UC14 10

12 Warm-Start UC12: 512 scenarios, 20,000,000 variables. UC24: 256 scenarios, 40,000,000 variables. Solution Time Decreased 71 Times in UC12 Solution Time Decreased 65 Times in UC14 Solution Time UC24 -Less than 2 min (amenable for B&B) 11

13 Gigantic Instance UC12: 8,162 scenarios, 463,000,000 variables - O(10 8 ) Advanced warm-start basis from solution with 4,096 scenarios Solved to optimal basis in 86,439 iterations - O(10 5 ) 4.6 Hours on 4,096 nodes of BlueGene/P (2 MPI process/node) Compare against O(10 8 ) iterations if solved in serial from scratch - 4,600 Hours Would require ~1TB of RAM in serial 12

14 Asymptotic Behavior Asymptotic Exploration Requires Solving Problems with O(10 8 ) Variables 13

15 Classical Two-Stage Formulation Key : - Captures Reliability (Robustness) - Does Not Capture Spot Market Behavior - How to Get Forward Prices and Quantities? - Is it Revenue Adequate? Spot Market Clearing 14

16 Revised Two-Stage Formulation (Pritchard, Zakeri, Philpott 2010) Definition (Revenue Adequacy): A settlement is revenue adequate in expectation if: Meaning from ISO Perspective: Market is Liquid, ISO will not run under financial deficit. Can be proved (by Construction) that Clearing Formulation Yields a Revenue Adequate Settlement and Also Is *Better* Than Deterministic 15

17 Revised Two-Stage Formulation (Zavala, Anitescu, Birge 2012) Definition (Revenue Neutrality): The market player revenue is neutral under spot price variability if Kaye, 1990: Revenue is neutral if Meaning from Player s Perspective: If forward price is an estimator of the future spot prices then remaining neutral is best strategy. Complications: It is really hard to average spot price behavior and satisfy physical constraints Constraints act as a nonconvex mapping (distorts distribution). Questions: Can Stochastic Optimization Average Prices *better*? Can it Reduce Variability of Spot Prices (Constraint Anticipation)? 16

18 Numerical Study (Zavala, Anitescu, Birge 2012) 17

19 Numerical Study (Zavala, Anitescu, Birge 2012) 18

20 Illinois System (Zavala, Anitescu, Birge 2012) Mean Field - Deterministic 19

21 Illinois System (Zavala, Anitescu, Birge 2012) Mean Field - Stochastic 20

22 Conclusions and Challenges Stochastic Optimization Cannot Be Worse than Existing (Deterministic) - Two Scenarios are Better Than One R. Wetts via J.P. Watson - Allows Anticipation of Spot Market Behavior - Necessary to use appropriate probabilistic metrics for comparison and to - Consistent Formulations Require Much Larger First Stages - Robust Optimization Scalable (Different Comp. Pattern) But Meaning of Prices? - Robust Opt = Reliability Oriented, Stochastic Opt = Economics Oriented - Can We Decompose Economics/Reliability (e.g., Hierarchical)? 21

23 Stochastic Market Clearing: Advances in Computation and Economic Implications Victor M. Zavala Assistant Computational Mathematician Mathematics and Computer Science Division Argonne National Laboratory Fellow Computation Institute University of Chicago With: John Birge (UChicago), Mihai Anitescu Contributors: Miles Lubin, Cosmin Petra, J Hall (Edinburgh) October, 2012