This paper addresses the problem of distributed networked set-membership filtering with ellipsoidal state estimations for a class of discrete time-varying systems in the presence of unknown-but-bounded process and measurement noises. Both global and local ellipsoidal state estimations are provided to locate the true state (target) via a distributed filtering network. A new geometric method based on Minkowski sum is proposed to produce the global ellipsoidal estimation. A novel convex optimization approach is developed to derive some sufficient conditions on the existence of local networked set-membership filters and to obtain the local ellipsoidal estimations by exchanging information among neighboring filters via communication networks. An experiment is conducted based on a 2-kW single-phase grid-connected power generation system platform to demonstrate the feasibility and the effectiveness of the proposed method in the real application.