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Uncertainties from deepening penetration of renewable energy resources haveposed critical challenges to the secure and reliable operations of futureelectric grids. Among various approaches for decision making in uncertainenvironments, this paper focuses on chance-constrained optimization, whichprovides explicit probabilistic guarantees on the feasibility of optimalsolutions. Although quite a few methods have been proposed to solvechance-constrained optimization problems, there is a lack of comprehensivereview and comparative analysis of the proposed methods. Part I of thistwo-part paper reviews three categories of existing methods tochance-constrained optimization: (1) scenario approach; (2) sample averageapproximation; and (3) robust optimization based methods. Data-driven methods,which are not constrained by any particular distributions of the underlyinguncertainties, are of particular interest. Part II of this two-part paperprovides a literature review on the applications of chance-constrainedoptimization in power systems. Part II also provides a critical comparison ofexisting methods based on numerical simulations, which are conducted onstandard power system test cases.

Data-driven Decision Making with Probabilistic Guarantees (Part 1): A Schematic Overview of Chance-constrained Optimization