This article investigates the problem of accelerating average consensus in undirected and connected networks. The protocol using the information of second-order neighbours with communication delays is proposed and the delay effects on stability and the convergence speed are analysed, respectively, under an assumption about the network topologies. It is proved that, for appropriate communication delays, networks reach average consensus faster under the proposed protocol than the standard protocol using only the information of first-order neighbours. Finally, a simulation example is presented to illustrate the proposed results.

This paper presents a model predictive control (MPC) strategy for electric spring (ES) to address the power quality problems, especially voltage regulation and harmonic suppression, which are more acute for a growing proportion of renewable energy generation to the grid. A Kalman filter is used to estimate the random variation of the supply voltage and extract the fundamental and harmonic components of the supply voltage, respectively. In this way, the supply voltage, which is treated as an external disturbance for the plant, can be established in the state‐space model form. Such processing brings great convenience to the application of MPC and also lays a foundation for MPC to achieve an ideal control effect. Based on an integrated state‐space model of the supply voltage and the ES, an MPC controller is designed for power quality improvement. Simulation studies are carried out and the simulation results are presented to verify the effectiveness and accuracy of the control strategy.