Data-Driven Distributionally Robust Stochastic Control of Energy Storage for Wind Power Ramp Management Using the Wasserstein Metric

Abstract

The integration of wind energy into the power grid is challenging because of its variability, which causes high ramp events that may threaten the reliability and efficiency of power systems. In this paper, we propose a novel distributionally robust solution to wind power ramp management using energy storage. The proposed storage operation strategy minimizes the expected ramp penalty under the worst-case wind power ramp distribution in the Wasserstein ambiguity set, a statistical ball centered at an empirical distribution obtained from historical data. Thus, the resulting distributionally robust control policy presents a robust ramp management performance even when the future wind power ramp distribution deviates from the empirical distribution, unlike the standard stochastic optimal control method. For a tractable numerical solution, a duality-based dynamic programming algorithm is designed with a piecewise linear approximation of the optimal value function. The performance and utility of the proposed method are demonstrated and analyzed through case studies using the wind power data in the Bonneville Power Administration area for the year 2018.

On Affine Policies for Wasserstein Distributionally Robust Unit Commitment

“…As the most important contribution of this paper, this subsection provides a tractable exact reformulation of (7). The reformulation is based on the following theorem:…”

“…Fig. 2 summarizes the DA decisions of the RUC model (2), the exact WDRUC model (4), and the proposed model (7); all have the same DM process at the RT stages, which is described in Fig. 1.…”

“…Recently, distributionally robust optimization (DRO) has attracted great interests in the field of power system planning and control (e.g., [4]- [7]), which builds on the idea that the This work was supported by in part by the National Research Foundation of Korea funded by the MSIT(2020R1C1C1009766), and Samsung Electronics.…”

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“…In the setting of multi-stage stochastic optimal power flow problem, a framework is proposed to solve multi-stage feedback control policies with respect a Conditional Value at Risk (CVaR) objective Guo, Baker, Dall'Anese, Hu and Summers (2018). A control policy for wind power ramp management is solved via dynamic programming by reformulating the distributionally robust value function with a tractable form: a convex piecewise linear ramp penalty function Yang (2019). For linear quadratic problems, a deterministic stationary policy is determined by solving an data-irrelevant discrete algebraic Riccati equation Yang (2020).…”

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“…In practice, estimating an accurate distribution from such observations is technically challenging due to insufficient data and inaccurate statistical models, among others. Using inaccurate distribution information in the construction of an optimal policy may significantly decrease the control performance [3], [4] and can even cause unwanted system behaviors, in particular, violating safety constraints [5]. The focus of this work is to develop and analyze a discrete-time minimax control method that is robust against uncertainties or errors in such distribution information.…”