The study simulated the behaviour of power system stabilizer (PSS) on automatic voltage regulator (AVR) and excitation system. It also developed an algorithm to investigate the transient and dynamic stability of the power systems. This was with a view to providing information of damping rotor oscillations of synchronous generators. Three types of power systems were investigated: a single-machine-infinite-bus system with and without PSS, two generators connected to a load with various types of excitation controls and a multimachine power system typified by Nigerian 330-kV electrical network. Tabu-search technique was used to tune the PSS-parameters for a single machine connected to an infinite bus operating at three different loading conditions. The objective function allowed the selection of the stabilizer parameters to optimally place the closed-loop eigenvalues in the left-hand side of a vertical line in the complex s-plane. The effectiveness of this suggested technique was confirmed through eigenvalue analysis. Time-domain simulations were also carried out on two generators connected to a load using MATLAB/Simulink. Two types of PSS were used for these simulations: generic and multiband. The power systems were subjected to a balanced three-phase fault (most severe fault). The investigation was further extended to Nigerian 330-kV electrical network.