## 1 Introduction  
With the fast development of non-synchronous renewable energy sources (RESs), such as wind turbine generators (WTGs) and photovoltaic (PV) panels, the characteristics of power system dynamic response have changed significantly. The RESs have strong volatility and uncertainty and low inertia, which reduces the controllability of power systems [1, 2, 3]. So, power systems are facing great challenges on the accommodation of RESs. On the other hand, the prices of energy storage systems (ESSs) have decreased rapidly and become accessible in large-scale industrial application [4]. Additionally, the continuous development of electric vehicle (EV) technology increases the number of users and makes the vehicle-to-grid (V2G) possess the potential of bidirectional power regulation when power systems are subjected to large disturbances [5, 6]. Thus, the non-synchronous RESs, ESSs, and EVs complicate the interaction mechanisms of power system dynamics, and may aggravate power system security and stability. The distributed form is a more flexible way than the centralized one to integrate RESs, ESSs, and EVs. The distributed energy resources (DERs) have become an essential part of power systems. Moreover, the micro-grid and active distribution network (ADN) have been widely used. The micro-grid is a small autonomous system to realize the efficient utilization of DERs, which disconnects from the power systems under contingencies to keep its secure operation [7, 8]. With the flexible adjustment of network topology and DERs, the ADN is designed to manage power flow and smooth exchange power at the point of common coupling (PCC) [9, 10]. To a certain degree, the micro-grid and ADN can promote the accommodation of DERs. However, there are few researches on the power support for power systems after large disturbances. As the penetration of DERs increases, the ability of these resources to participate in power system security and stability control becomes necessary and urgent. Based on the advanced communication and control technologies, the virtual power plant (VPP) has been proposed to aggregate DERs for power and auxiliary service markets [11, 12, 13]. VPPs can include different types of DERs, such as traditional generators, RESs, ESSs, and EVs. These DERs can have different installed capacities and geographical sites, which are virtually aggregated through advanced communication and control methods. More specially, the optimal planning [14, 15, 16], bidding [17, 18, 19], dispatching [21, 22, 23, 24], and communication architecture design [25, 26, 27, 28] of VPPs have been studied. As for the planning of VPPs, the volatility and complementarity of RESs should be taken into account, and the investments, risks, and profits should be traded off. An equivalent VPP model has been proposed using the probability density function, of which the performance is assessed from different aspects [14]. Then, the ESSs are added in the above VPP model, and the performance of augmented VPPs in improving generation adequacy is quantified [15]. Moreover, the installed capacities of DERs and electricity prices have been optimized considering the economic and secure operation of a power system [16]. The VPP has been widely used in electricity and auxiliary service markets, and various bidding methods have been proposed. A three-stage mixed-integer stochastic programming model has been proposed for the bidding of VPPs, in which the uncertainties and battery degradation of EVs are considered [17]. In order to minimize the cost of VPPs in the day-ahead market, a stochastic optimization model has been established [18]. Based on the game theory, both the models for a single VPP and multiple VPPs have been proposed, where the interactive coordination between VPPs and energy consumers is considered [19]. Moreover, a two-stage robust optimization approach is provided to obtain the bidding strategy of a VPP in the day-ahead and real-time markets [20].