Wasserstein Distributionally Robust Look-Ahead Economic Dispatch

Abstract

We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability.

Chance Constrained Economic Dispatch Considering the Capability of Network Flexibility Against Renewable Uncertainties

“…Here we take d ij = 0.7, ∀(i, j) ∈ E flex . For line capacity, we set (7,9), and f max ij = 200MW for all the other lines.…”

“…The AC power flow-based CCED formulations are emerging and solved by more sophisticated methods such as convex relaxation [4], sequential linearization [5] and polynomial chaos expansion [6]. In addition, the CCED is being extended to the distributionally robust version [7][8][9] to make the solution work under a set of probability distributions for renewables.…”

Wasserstein distributionally robust chance-constrained optimization for energy and reserve dispatch: An exact and physically-bounded formulation

“…Several works exist in the literature that use metric-based distributionally robust chanceconstrained programs for power system applications, e.g., Duan et al (2018); Guo et al (2019); Poolla et al (2020) and Ordoudis et al (2021). To the best of our knowledge, all these works approximate DRCCs, e.g., using a Conditional Value-at-Risk (CVaR) reformulation, as proposed by Zymler et al (2013) and.…”

Distributionally Robust Optimal Power Flow with Contextual Information

“…Therefore, Distributionally Robust Chance-Constrained Optimal Power Flow (DRCC-OPF) models seek the optimal dispatch such that all the model constraints are satisfied with a pre-fixed confidence level for all the probability distributions within the ambiguity set built either by means of the Wasserstein metric ( [1], [2], [8], [15], [12], [25], [26], [36]) or using moments ( [17], [18], [19], [21], [29], [33]). In addition, the system operator can not only tune the robustness of the resulting chance-constrained DRO model by adjusting the probability of constraint violation, but also, and very importantly, through the specificity degree of the ambiguity set.…”

“…Unfortunately, the consideration of joint chance constraints in a DRO framework ( [13], [34]) renders an intractable optimization problem in general. For this reason, researchers have considered DRO-OPF models based on the well-known conservative, but far more tractable approximation given by the concept of conditional-value-at-risk (CVaR), see, for example, [1], [8], [12], [15], [25], [26] and references therein. The authors in [7] show that the CVaR offers a tight convex approximation of the chance constraints under the DRO framework, which justifies its popularity.…”