## 1 Introduction  
As an important supplement to centralized renewable energy stations, distributed renewable energy generators are close to electricity consumers and easily approved by the government for project construction. They have become an important part of promoting the energy revolution and building a low-carbon modern energy system [1]. The rapid development of distributed renewable energy brings new challenges to power quality and power flow distribution optimization. There are many operation challenges when the distributed renewable energy generators are connected to the distribution network. Hence a large number of scholars have paid attention to the power flow calculation methods for the distribution network with large-scale renewable energy generators [2]. In the meantime, many distributed, decentralized, and centralized control methods have been proposed and validated for distributed renewable energy consumption [3,4]. With the gradual increase in the penetration rate of distributed renewable energy, smart microgrid technologies have become the key measures to realize the friendly access of distributed renewable energy to the power grid [5, 6, 7]. Microgrids can operate in off-grid or on-grid mode. Based on the output prediction of distributed renewable energy and electricity load, microgrids can optimize the power of controllable distributed conventional power supply, distributed energy storage, and flexible, controllable loads to achieve optimized local consumption of distributed renewable energy with the goal of minimizing network loss, operating costs, and maximizing the utilization rate of distributed renewable energy [8,9]. Microgrids have been widely used all over the world and have become the most important power supply mode in areas with a high proportion of distributed renewable energy. However, in one microgrid, all aggregated resources should be controlled and dispatched by one strategy [10,11]. This idea of dealing with the problem ignores the conflict of interest among the power network, distributed renewable energy sources, energy storage devices, and consumers [12, 13, 14]. In the case of a further increase in the penetration of distributed renewable energy, it is impossible to realize the interests of all market players in a fair manner. Under the existing electricity spot market environment, it is impossible to further promote the participation of distributed renewable energy as a market subject in the electricity market if the distributed renewable sources are located in the microgrid [15, 16, 17]. Electricity connection and inverter control methods are the main tasks to carry out in microgrids. In contrast to microgrid concerns, various types of virtual power plants (VPPs) are proposed to aggregate distributed resources and participate in the electricity spot market [18, 19, 20]. These VPPs can aggregate demand-side response resources, distributed renewable energy, and other supply-side resources, as well as multiple types of resources. How to construct a VPP has been first studied, including VPP aggregated resources [21,22] and communication architecture [23,24]. And then, the business model of VPPs has become one of the most important problems to be solved for the promotion of VPPs in the world [25, 26, 27]. For the VPP with demand-side response resources, such as electric vehicles, the dynamic load behavior characteristics and optimal demand response of VPPs are studied under the electricity spot market [28,29]. In the meantime, the optimal operation of VPPs with other resources, including energy storage systems and the uncertainty of renewable energy, are also studied in the literature [30, 31, 32]. The optimal operation of a virtual power plant relies on the scheduling and management of all types of resources. Under the electricity spot market, dynamic time-of-use pricing (TOU) is an important means for VPP to participate in external transactions and internal resource aggregation.