In this paper, we formulate a two-stage distributionally robust (DR) model for the optimal power flow (OPF) problem in the presence of uncertainties from wind power generation and load-based reserves. Assuming ambiguous distributions of the random variables, we minimize the costs of generation, reserves, and the worst-case expected value of the penalty cost of violating constraints. We consider a lifted support and a distributional ambiguity set parameterized by empirical means and absolute deviations of the random variables. We adopt an enhanced linear decision rule (ELDR) to derive a quadratic programming reformulation of the DR-OPF model, and compare its performance to that of a DR chance-constrained OPF model. We study the optimal solution patterns of the two approaches, compare their performance in out-of-sample simulations, and also numerically justify the use of the ELDR.
|Original language||English (US)|
|Title of host publication||2017 IEEE Manchester PowerTech, Powertech 2017|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|State||Published - Jul 13 2017|
|Event||2017 IEEE Manchester PowerTech, Powertech 2017 - Manchester, United Kingdom|
Duration: Jun 18 2017 → Jun 22 2017
|Name||2017 IEEE Manchester PowerTech, Powertech 2017|
|Conference||2017 IEEE Manchester PowerTech, Powertech 2017|
|Period||6/18/17 → 6/22/17|
Bibliographical noteFunding Information:
This work was supported by NSF Grant #CCF-1442495.
© 2017 IEEE.
- distributionally robust optimization
- enhanced linear decision rule
- load control