This paper presents two novel nonlinear fractional-order sliding mode controllers for power angle response improvement of multi-machine power systems. First, a nonlinear block control is used to handle nonlinearities of the interconnected power system. In the second step, a decentralized fractional-order sliding mode controller with a nonlinear sliding manifold is designed. Practical stability is achieved under the assumption that the upper bound of the fractional derivative of perturbations and interactions are known. However, when an unknown transient perturbation occurs in the system, it makes the evaluation of perturbation and interconnection upper bound troublesome. In the next step, an adaptive-fuzzy approximator is applied to fix the mentioned problem. The fuzzy approximator uses adjacent generators relative speed as own inputs, which is known as semi-decentralized control strategy. For both cases, the stability of the closed-loop system is analyzed by the fractional-order stability theorems. Simulation results for a three-machine power system with two types of faults are illustrated to show the performance of the proposed robust controllers versus the conventional sliding mode. Additionally, the fractional parameter effects on the system transient response and the excitation voltage amplitude and chattering are demonstrated in the absence of the fuzzy approximator. Finally, the suggested controller is combined with a simple voltage regulator in order to keep the system synchronism and restrain the terminal voltage variations at the same time.

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