Backstepping control for a class of nonlinear differential-algebraic equations subsystems with application to power systems

Backstepping control method of nonlinear Ordinary Differential Equations (ODE) systems is extended to a class of nonlinear Differential-Algebraic Equations (DAE) subsystems, which are put forward for decentralized control analysis of power systems. The differential equations and underlying constraints of the DAE subsystems involve the interconnection inputs generated by the rest of the large-scale systems. Equivalent systems are obtained through a local differomorphism and a feedback, and then the well-known Backstepping method for nonlinear ODE systems can be extended. An asymptotic stabilization controller is designed based on such a recursive approach. Based on the design scheme proposed in this paper, a speed governor is designed for one synchronous generator set in multi-machine power systems. The simulation results illustrate the utility of the proposed scheme.