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In order to understand how an energy storage system (ESS)-based stabiliser suppresses a power system inter-area oscillation in a multi-machine power system, this study proposes a tie-line power oscillation-related ESS linearised model. Based on the linearised model, a general conclusion is established to assess the capability of the ESS-based stabiliser to affect the damping of the inter-area power oscillation. Analysis derived from the general conclusion explains how and why the robustness of the ESS stabiliser is different to the variations of the loading conditions of the tie transmission line when the stabiliser is realised by controlling the exchange of either active or reactive power between the ESS and the rest of the power system. It is analytically concluded that when the stabiliser is implemented via controlling the exchange of active power, the stabiliser is of better robustness. The study presents an example multi-machine power system installed with a battery energy storage system (BESS)-based stabiliser. Results of eigensolutions computation and non-linear simulation demonstrate and confirm the analytical conclusion about the robustness of the ESS-based stabiliser in suppressing the inter-area power oscillation.