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This paper presents a comprehensive survey on the research of a specific topic in power system engineering, power system oscillation stability and control by FACTS (Flexible AC Transmission System) and ESS (Energy Storage System). The paper firstly reviews the problem of power system oscillation. Then it addresses the issue of analysis of power system oscillation, focusing on two of most commonly-used methods, damping torque analysis (DTA) and modal analysis. This is followed by an examination of research on damping power system oscillation, i.e., control of power system oscillation stability. Finally the paper reviews the most recent progress on the research topic, applications of FACTS and ESS to enhance power system oscillation stability. A comprehensive list of research publications (mainly journal papers) are provided at the end of the paper.