  To address the challenge of the renewable energy uncertainty, the ISO New
England (ISO-NE) has proposed to apply do-not-exceed (DNE) limits, which
represent the maximum nodal injection of renewable energy the grid can
accommodate. Unfortunately, it appears challenging to compute DNE limits that
simultaneously maintain the system flexibility and incorporate a large portion
of the available renewable energy at the minimum cost. In addition, it is often
challenging to accurately estimate the joint probability distribution of the
renewable energy. In this paper, we propose a two-stage distributionally robust
optimization model that co-optimizes the power dispatch and the DNE limits, by
adopting an affinely adjustable power re-dispatch and an adjustable joint
chance constraint that measures the renewable utilization. Notably, this model
admits a second-order conic reformulation that can be efficiently solved by the
commercial solvers (e.g., MOSEK). We conduct case studies based on modified
IEEE test instances to demonstrate the effectiveness of the proposed approach
and analyze the trade-off among the system flexibility, the renewable
utilization, and the dispatch cost.
