Virtual synchronous generator (VSG) control is a promising control method in microgrid (MG) for the inertia support characteristic. However, the VSG inherits the oscillation feature of synchronous generator (SG), thus the active power and frequency oscillation may be observed when VSG control is applied. In MG, the oscillation may cause the unreasonable dynamic active power sharing among VSGs. Subsequently, the VSGs are prone to overload and even unstable, and the existing works based on

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... us control cannot suppress the oscillation effectively. In order to tackle this problem, this paper proposes an enhanced second-order-consensus-based distributed secondary frequency controller by introducing the active power second-order consensus control, and reveals the oscillation suppression capacity of the second-order consensus algorithm in depth. Since there is no specific control requirement for the second-order variables, i.e., the change rate of active power and frequency of MG in steady state, the proposed controller can be simplified by replacing the integral control of second-order variables with the proportional control of first-order variables, i.e., active power and frequency, thus the communication data volume will not increase comparing to the traditional first-order-consensus-based controller. This paper also provides a small-signal model of MG with the proposed controller to evaluate the system dynamic performance and design the parameters. Finally, the simulation results verify the effectiveness of the proposed controller. (X. Wan). economy principle. But the primary control may introduce frequency and voltage deviation in steady state, which deteriorates the power quality when the load is heavy. Fortunately, it can be corrected by the secondary control. The tertiary control focus on the economic dispatch and power optimizations through day-ahead scheduling, for establishing the acceptable and costeffective operational conditions. This paper, we will focus on the secondary control. Due to advances of distributed control in multi-agent systems (Olfati-Saber et al., 2007) , the distributed consensus-based secondary control has been considered in isolated MG (Yazdanian and Mehrizi-Sani, 2014) . The methods can achieve general agreements among connected agents by exchanging local information only, thus it needs less requirement on communication infrastructure, and marvelous robustness with switching topology and single point of failure (Bevrani and Uok, 2020). The distributed secondary control of MG can be seen as a synchronous tracking problem (Li et al., 2010) . It exploits the sparse communication, and restores the frequency and voltage magnitude of DERs while achieving the accurate active and reactive power sharing among DERs (Simpson-Porco et al., 2015; Xu et al., 2019b; https://doi.