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Modeling, Simulation, And Optimization for the
21st Century Electric Power Grid
Proceedings
Fall 10-22-2012
Stochastic Market Clearing: Advances in
Computation and Economic Impacts
Victor Zavala
Argonne National Laboratory
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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). http://dc.engconfintl.org/power_grid/14
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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
Deterministic Market Clearing
Zavala, Constantinescu, Wang, and Botterud, 2009
2
Market Volatility
Prices at Illinois Hub, 2009
Constraint Anticipation
Effect of Foresight on Economic Dispatch Performance
Deterministic Clearing Formulation
Classical Two-Stage Stochastic Formulation
5
Illinois System
Constantinescu, Zavala, Anitescu 2011, Lubin, Petra, Anitescu, Zavala 2011
1900 Buses
261 Generators
24 Hours
6
Simplex
7
Parallel Simplex
Implementation Non-Trivial : Numerical Stability, Communication, Load Balancing
8
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
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
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
Gigantic Instance
UC12: 8,162 scenarios, 463,000,000 variables - O(108)
Advanced warm-start basis from solution with 4,096 scenarios
Solved to optimal basis in 86,439 iterations - O(105)
4.6 Hours on 4,096 nodes of BlueGene/P (2 MPI process/node)
Compare against O(108) iterations if solved in serial from scratch - 4,600 Hours
Would require ~1TB of RAM in serial
12
Asymptotic Behavior
Asymptotic Exploration Requires Solving Problems with O(108) Variables
13
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
Revised Two-Stage Formulation (Pritchard, Zakeri, Philpott 2010)
Definition (Revenue Adequacy): A settlement
adequate in expectation if:
is revenue
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
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
Numerical Study (Zavala, Anitescu, Birge 2012)
17
Numerical Study (Zavala, Anitescu, Birge 2012)
18
Illinois System (Zavala, Anitescu, Birge 2012)
Mean Field - Deterministic
19
Illinois System (Zavala, Anitescu, Birge 2012)
Mean Field - Stochastic
20
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
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