Optimal generation in structure-preserving power networks with second-order turbine-governor dynamics

Recently we have been exploring the role of passivity and the internal model principle in power network control in the presence of uncertainties due to unmeasured demand and supply. In this work we continue this line of research and extend our results to include more complex dynamics at the generation side. Namely, we study frequency stabilization by primary control and frequency regulation by optimal generation control, where we additionally incorporate second-order turbine-governor dynamics. The power network is represented by the structure-preserving Bergen-Hill model [1]. Distributed controllers that require local frequency measurements are proposed and are shown to minimize the generation costs. Asymptotic convergence is proven when the generators satisfy a local matrix condition. The effectiveness of proposed controllers is demonstrated in a case study