Fully decentralized conditions for local convergence of DC/AC converter network based on matching control

Abstract

We investigate local convergence of identical DC/AC converters interconnected via identical resistive and inductive lines towards a synchronous equilibrium manifold. We exploit the symmetry of the resulting vector field and develop a Lyapunov-based framework, in which we measure the distance of the solutions of the nonlinear power system model to the equilibrium manifold by analyzing the evolution of their tangent vectors. We derive sufficient and fully decentralized conditions to characterize the equilibria of interest, and provide an estimate of their region of contraction. We provide ways to satisfy these conditions and illustrate our results based on numerical simulations of a two-converter benchmark.

Steady state characterization and frequency synchronization of a multi-converter power system on high-order manifolds

“…that is, for all z * ∈ M, it holds that [z * ] ⊂ M. Note that all steady states z * ∈ M, correspond to the synchronization of all converters, as a result of the adopted dq-transformation. For more details, we refer the reader to Lemma 2.1 in [1].…”

“…, n s . To analyze the behavior of the linearized trajectories on the tangent bundle T D of the variational system (22), we define a parameterized Lyapunov function V : T D → R, measuring the squared distance from a tangent vector δ z ∈ T z D, to the span{v(z * s,i )}, based on ideas from [1], [22] and given by,…”

“…This allows us to define an equivalence class that identifies the trajectories pertaining to the continuum, generated under these actions and defines a quotient system, where trajectories starting on the same equivalence class, remain in the same class for all times. We identify all the stable eigenspaces based on the study of the system Jacobian governing the dynamics on the tangent space of the steady state manifold at a steady state trajectory, by relaxing a technical assumption from [1], [22]. Hence, via curve integration, all the stable sets on the steady state manifold are characterized.…”

“…Compared to [1], we further provide a comprehensive study of the system behavior and stability including the relaxation of the condition on asymptotic stability of the eigenspace of Jacobian restricted the the steady state manifold, as well as the investigation of the characteristics and properties of the induced steady state manifold with emphasis on the role of the input in shaping the steady state and vice versa. Our contribution in comparison to [22] lies in the analysis of local convergence of nonlinear trajectories of the power system model, initialized in a neighborhood of a synchronous steady state set.…”

“…Section III studies the symmetry of its vector field, characterizes an equivalence relation identifying its trajectories,quotient non-degenerate, stable and unstable steady state sets and formulates an optimization problem to find a feasible input. Section IV studies the local asymptotic contraction of the nonlinear power system model based on the stability analysis conducted in [1], [22] and the theory of Finsler-Lyapunov functions in [13] and identifies the region of contraction. Section V provides interpretations of our results.…”