Based on the Lyapunov stability theorem and sliding mode control technique, a design of the nonlinear controller is proposed for the dual-excited and steam-valving control of the synchronous generators with matched and mismatched perturbations in this paper. By using some constant gains designed in the sliding surface function, the perturbations in the power system can be suppressed, and the property of asymptotical stability of the rotor angle and the voltage can be achieved at the same time. 1. Introduction To achieve a high degree of reliability in the power systems, many works [1–11] have studied the stability of generators. In general, there are two ways to stabilize the generators: the excited control [1–3] and the steam-valving control [4–7]. Using the excited control, Xie et al. [1] designed a linear matrix inequality (LMI) controller for a class of multimachine power systems with uncertain parameters to achieve the property of asymptotical stability. Galaz et al. [2] proposed a passivity-based controller and discussed the domain of attraction of the equilibria in power systems. Huang et al. [3] utilized a physical exact linearization method to design a controller for a dual-excited synchronous generators. For the steam-valving control, Zhang and Sun [4], Fu [5], Li et al. [6], and Li et al. [7] designed the adaptive backstepping controller for single machine infinite bus system in the presence of internal and external disturbances to achieve the property of asymptotical stability. As for the systems with both steam turbine dynamics and the excited generator, Xi et al. [8] and Ma et al. [9] presented a novel nonlinear controller based on Hamiltonian energy theory steam for the turbine dynamics and single excited generator to achieve the property of asymptotical stability. The dual-excitation means the system has -axis and -axis field winding simultaneously. Each field voltage can be adjusted separately and hence the control objectives can be achieved more flexibly. Based on the passive lemma, Wang and Lin [10] designed the bounded passivity controller for the synchronous generators to achieve the property of asymptotical stability. Using the coordinated passivation technique, Chen et al. [11] designed backstepping controller for steam-valving and dual-excited synchronous generators to achieve the property of asymptotical stability. However, the perturbations were not considered in the works [10, 11]. Sliding mode control (SMC) is well known to possess several advantages, for example, fast response, good transient performance, robustness of
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