## 1 Introduction  
Power system frequency stability is an important indicator of the power system quality and safety [1, 2], upon which power system frequency regulation is mainly achieved by automatic generation control (AGC), which can guarantee satisfactory frequency quality and safe operation of the electric power system by maintaining the real-time balance between power generation and loads of the electric power system. Besides, with large-scale intermittent energy such as wind energy [3] being connected to the power grid, higher requirements for frequency regulation [4] and spinning reserve capacity are in urgent need to balance the unexpected power disturbance [5] to alleviate power quality problems [6] and ensure the power systems can operate under a safe and economical condition [7]. Hence, the intermittent energy can be operated at their maximum power point [8] most of the time by various control techniques [9]. In particular, when numerous electric vehicles (EVs) are connected to the power grid, that is, vehicle to grid (V2G), the utilization of EVs to provide auxiliary services such as frequency regulation for power system will be a popular research topic. With the decrease of battery equipment costs, the advancement of charging and discharging technology, the gradual improvement of charging infrastructure, and the successive issuance of government supporting policies, the growth of EVs has become an inevitable trend that has aroused widespread attention [10]. Moreover, when numerous EVs are connected to the power grid, they are not only regarded as loads that can absorb electricity from the power grid, but can also be utilized as discharge units to provide electricity to the power grid. Hence, EVs can be regarded as a controllable energy storage equipment to participate in economic dispatch [11] and peak-load shifting [12]. Particularly, recent studies show that it is a promising V2G commercial operation mode [13] to provide a frequency regulation service for a power system via centralized or decentralized control [14; 15]. According to the literature [16], compared with the traditional generators, the participation of EVs in frequency regulation has the advantages of short frequency regulation delay, low frequency regulation cost, as well as fast and accurate responses to frequency regulation instructions. Besides, the literature [17] proposed the concept of EV agents, which can realize cluster dispatching to numerous EVs to meet the demand of power system frequency regulation capacity. Meanwhile, the feasibility of EVs participating in power system frequency regulation can also be verified. Hence, through controlling the charging and discharging behaviour of large-scale EVs, a series of auxiliary services, for example, power system frequency regulation, can be provided to effectively smoothen the load fluctuations of the power grid and to eliminate excess intermittent energy [18], while the generation efficiency of the renewable energy can be maximized [19]. Generally speaking, the application of exchanging battery mode in bus and taxi charging stations can be regarded as a reasonable business mode to cope with the large-scale development of EVs. This is because a bus or taxi can directly exchange a fully charged battery from the charging station without waiting. Particularly, charging stations are always equipped with a large number of batteries, which means they possess high frequency regulation capacity through making full use of retired batteries [20]. Consequently, the charging stations can be regarded as independent EV agents to participate in the frequency regulation service [21], which is crucial for power quality adjustment [22], while the power quality parameters can be estimated by the curve fitting algorithm [23].