Stability and Optimality of Distributed Secondary Frequency Control Schemes in Power Networks

Abstract

We present a systematic method for designing distributed generation and demand control schemes for secondary frequency regulation in power networks such that stability and an economically optimal power allocation can be guaranteed. We consider frequency dynamics given by swing equation along with generation, controllable demand, and a secondary control scheme that makes use of local frequency measurements and a locally exchanged signal. A decentralized dissipativity condition is imposed on net power supply variables to provide stability guarantees. Furthermore, economic optimality is achieved by explicit steady state conditions on the generation and controllable demand. A distinctive feature of the proposed stability analysis is the fact that it can cope with generation and demand dynamics that are of general higher order. Moreover, we discuss how the proposed framework captures various classes of power supply dynamics used in recent studies. In case of linear dynamics, the proposed dissipativity condition can be efficiently verified using an appropriate linear matrix inequality. Moreover, it is shown how the addition of a suitable observer layer can relax the requirement for demand measurements in the secondary controller. The efficiency and practicality of the proposed results are demonstrated with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus and a 9-bus system.