Power System Operations with Probabilistic Guarantees

This study is motivated by the fact that uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electrical grids. Among various tools for decision making in uncertain environments, this study 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. In this work, we provide a detailed tutorial on existing algorithms and a survey of major theoretical results of chance-constrained optimization theory. Data-driven methods, which are not constrained by any specific distributions of the underlying uncertainties, are of particular interest. Built upon chance-constrained optimization, we propose a three-stage power system operation framework with probabilistic guarantees: (1) the optimal unit commitment in the operational planning stage; (2) the optimal reactive power dispatch to address the voltage security issue in the hours-ahead adjustment period; and (3) the secure and reliable power system operation under uncertainties in real time. In the day-ahead operational planning stage, we propose a chance-constrained SCUC (c-SCUC) framework, which ensures that the risk of violating constraints is within an acceptable threshold. Using the scenario approach, c-SCUC is reformulated to the scenario-based SCUC (s-SCUC) problem. By choosing an appropriate number of scenarios, we provide theoretical guarantees on the posterior risk level of the solution to s-SCUC. Inspired by the latest progress of the scenario approach on non-convex problems, we demonstrate the structural properties of general scenario problems and analyze the specific characteristics of s-SCUC. Those characteristics were exploited to benefit the scalability and computational performance of s-SCUC. In the adjustment period, this work first investigates the benefits of look-ahead coordination of both continuous-state and discrete-state reactive power support devices across multiple control areas. The conventional static optimal reactive power dispatch is extended to a “moving-horizon” type formulation for the consideration of spatial and temporal variations. The optimal reactive power dispatch problem is further enhanced with chance constraints by considering the uncertainties from both renewables and contingencies. This chance-constrained optimal reactive power dispatch (c-ORPD) formulation offers system operators an effective tool to schedule voltage support devices such that the system voltage security can be ensured with quantifiable level of risk. Security-constrained Economic Dispatch (SCED) lies at the center of real-time operation of power systems and modern electricity markets. It determines the most cost-efficient output levels of generators while keeping the real-time balance between supply and demand. In this study, we formulate and solve chance-constrained SCED (c-SCED), which ensures system security under uncertainties from renewables. The c-SCED problem also serves as a benchmark problem for a critical comparison of existing algorithms to solve chance-constrained optimization problems