Stabilization of structure-preserving power networks with market dynamics

This paper studies the problem of maximizing the social welfare while stabilizing both the physical power network as well as the market dynamics. For the physical power grid a third-order structure-preserving model is considered involving both frequency and voltage dynamics. By applying the primal-dual gradient method to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. After interconnection with the physical system a closed-loop port-Hamiltonian system of differential-algebraic equations is obtained, whose properties are exploited to prove local asymptotic stability of the optimal points.Comment: IFAC World Congress 2017, accepted, 6 page

Convergence of Projected Primal-Dual Dynamics with Applications in Data Centers

This paper studies the convergence of projected primal-dual dynamics under mild conditions on the (general) optimization problem. In particular, we do not require strict convexity of the objective function nor uniqueness of the optimizer. By regarding the inequality constraints as hard constraints, we construct a suitable primal-dual dynamics in the complementarity formalism. We establish pointwise asymptotic stability of the set primal-dual optimizers by a suitable invariance principle involving two different Lyapunov functions. In addition, we show how these results can be applied for online optimization in data centers