  Uncertainties from deepening penetration of renewable energy resources have
posed critical challenges to the secure and reliable operations of future
electric grids. Among various approaches for decision making in uncertain
environments, this paper focuses on chance-constrained optimization, which
provides explicit probabilistic guarantees on the feasibility of optimal
solutions. Although quite a few methods have been proposed to solve
chance-constrained optimization problems, there is a lack of comprehensive
review and comparative analysis of the proposed methods. Part I of this
two-part paper reviews three categories of existing methods to
chance-constrained optimization: (1) scenario approach; (2) sample average
approximation; and (3) robust optimization based methods. Data-driven methods,
which are not constrained by any particular distributions of the underlying
uncertainties, are of particular interest. Part II of this two-part paper
provides a literature review on the applications of chance-constrained
optimization in power systems. Part II also provides a critical comparison of
existing methods based on numerical simulations, which are conducted on
standard power system test cases.
