In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions can be easily constructed. Interestingly enough, for linear systems the resulting Lyapunov function is the incremental energy; thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given.

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Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation

We provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances. More specifically, we consider the full 3n-dimensional model of the n-generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements which, as is well known, hamper the assignment of simple "gradient" energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state-modulated interconnections that play the role of multipliers in classical passivity theory.

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Transient stabilization of multimachine power systems with nontrivial transfer conductances

Brief An energy-shaping approach to the design of excitation control of synchronous generators

Brief Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems

This paper deals with the problem of L2 disturbance attenuation for Hamiltonian systems. We first show that the L2 gain from the disturbance to a penalty signal may be reduced to any given level if the penalty signal is defined properly. Then, an adaptive version of the controller will be presented to compensate the parameter perturbation. When the perturbed parameters satisfy a suitable matching condition, it is easy to introduce the adaptive mechanism to the controller. Another contribution of this paper is to apply the proposed method to the excitation control problem for power systems. An adaptive L2 controller for the power system is designed using the proposed method and a simulation result with the proposed controller is given.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1934-6093.2003.tb00105.x

R. Ortega

Papers

A Passivation Approach to Power Systems Stabilization