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The phase compensation method was proposed based on the concept of the damping torque analysis (DTA). It is a method for the design of a power system stabilizer (PSS) to suppress local-mode power oscillations in a single-machine infinite-bus power system. This paper presents the application of the phase compensation method for the design of a DC/AC converter-based stabilizer to damp inter-area mode power oscillations in a multi-machine power system. The application is achieved by examining the direct damping contribution of the stabilizer to inter-area power oscillations without relying on DTA. The simplicity and localization of the phase compensation method are retained in the application presented in the paper, as the design requires only locally available transmission line information and DC/AC converter unit parameters.