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In this paper, it is proposed to apply the mayfly optimization algorithm (MOA) to perform the coordinated and simultaneous tuning of the parameters of supplementary damping controllers, i.e., power system stabilizer (PSS) and power oscillation damping (POD), that actuate together with the automatic voltage regulators of the synchronous generators and the static synchronous series compensator (SSSC), respectively, for damping low-frequency oscillations in power systems. The performance of the MOA is compared with the performances of the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm for solving this problem. The dynamics of the power system is represented using the current sensitivity model, and, because of that, a current injections model is proposed for the SSSC, which uses proportional-integral (PI) controllers and the residues of the current injections at the buses, obtained from the Newton–Raphson method. Tests were carried out using the New England system and the two-area symmetrical system. Both static and dynamic analyses of the operation of the SSSC were performed. To validate the proposed optimization techniques, two sets of tests were conducted: first, with the purpose of verifying the performance of the most effective algorithm for tuning the parameters of PSSs, PI, and POD controllers, and second, with the purpose of performing studies focused on small-signal stability. The results have validated the current injections model for the SSSC, as well as have indicated the superior performance of the MOA for solving the problem, accrediting it as a powerful tool for small-signal stability studies in power systems. [ABSTRACT FROM AUTHOR]