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Compressed-air energy storage (CAES) is considered a promising energy storage system for many grid applications, including managing renewable variability and grid capacity concerns. However, compared with conventional generation such as coal or hydro, the cost of storage power of CAES is still high, which impedes its deployment. Therefore a standing question is how to operate CAES in the most efficient and economical fashion, that is, to exploit the system functions for maximum-possible benefit. This study investigates the CAES dynamic reactive capability used to stabilise wind farms under grid fault conditions. Two considered operation modes are motor mode with leading power factor and synchronous condenser mode. Analysis with a 60-MW wind farm and two types of popular wind turbines, namely stall-regulated and doubly fed induction-generator-based WTs, shows that the CAES performance is comparable or better than that of an static var compensator in most situations investigated. Therefore the reactive-power-supply function should be considered in CAES design and operation to increase the system efficiency and value.