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This paper presents the tuning of a proportional-integral (PI) damping controller for static var compensator (SVC) to enhance the dynamic stability of power systems over a wide range of voltage-dependent load models. The gains settings of the PI controller are tuned using the eigenvalues assignment technique. A closed formula was derived to allocate the electro-mechanical mode eigenvalues to a prescribed value. Tuning of SVC damping controllers traditionally assumes that the system loads are voltage dependent with fixed parameters. However, the load model parameters are generally uncertain. This uncertainty behavior of load model parameters can de-tune the gains of the PI controller; consequently, SVC damping controller tuned with fixed gain-settings can be adequate for some load models but contrarily can reduce system damping and contribute to system instability with loads having other models. The effect of typical load model parameters on the tuning gains of SVC PI damping controller is investigated and it is found that load models have a considerable influence on the PI controller tuning gains. The time domain simulations performed on the system show that the SVC damping controller tuned at fixed load models reduce the system damping under other load parameters and could lead to system instability.