Wasserstein Distributionally Robust
Look-Ahead Economic Dispatch
Bala Kameshwar Poolla, Ashish R. Hota, Saverio Bolognani,
Duncan S. Callaway, and Ashish Cherukuri
Automatic Control Laboratory
Bala K. Poolla
Ashish Cherukuri
Duncan S. Callaway
Ashish R. Hota
Saverio Bolognani
Grid operators need to schedule traditional power plants without knowing tomorrow's solar power generation
Weather ensembles: possible realizations of tomorrow's irradiation based on sophisticated weather models
Even preparing for the worst-case would lead to
frequent violations of the safety constraints of the grid!
Distributionally robust optimization: satisfaction of constraints for a range of uncertain events which are statistically close to the forecasts
minimize economic cost as long as...
...the worst-case probability
(for statistically similar uncertainty)...
...of satisfying all safety constraints...
...is at least
99.9%
Key technical idea: a notion of distance between probability distributions that makes the optimization problem tractable.
empirical samples
"similar" probability distributions
Wasserstein metric
Earth Mover's distance between probability distributions
Key findings
- This class of problems is computationally tractable
- The degree of robustness can be tuned to obtain the desired tradeoff between risk and economic cost
- Historical data instead of weather forecasts can also be used to estimate risk
higher cost
higher risk
30-year historical weather forecasts provided by
To appear in the IEEE Transactions on Power Systems
https://doi.org/10.1109/TPWRS.2020.3034488
Open-access preprint
https://arxiv.org/abs/2003.04874
CVar optimization - Chance-constrained optimization - Distributionally robust programming - Wasserstein uncertainty set - Stochastic optimal power flow - Real data experiments - Renewable power integration