aggregation strategies, which are generally categorized into two exclusive clusters. Derived of equivalent thermal parameters (ETP), one cluster of aggregation methods is to analyze the transition process of the temperature and switching evolution. The on/off states of the AC population are generated to provide an overall quantification of the collective performance of aggregated ACs [6; 7]. [PERSON] and [PERSON] proposed a 2-D state bin model and utilized model predictive control to obtain the optimal control actions for AC [8]. Uncertainties regarding customer behaviors are taken into consideration in the state queuing model [9]. [PERSON] et al., developed the modified model embedded in compressor time delays to enhance collective AC performance [10]. Although massive studies on state space models have been carried out, heavy communication requirements between the control center and thermostatic control loads (TCLs) are introduced to ensure the accuracy of the dynamic model. Methods of balancing the number of AC switching states and modeling accuracy are seldom documented in the existing literature. The second cluster of aggregated methods is to characterize the flexibility of ACs as a 'virtual battery' [11; 12]. Similar to the traditional battery, thermal energy can be stored by the thermodynamic transition process in a building. A leaky storage model is proposed to model the flexibility of heterogeneous ACs [13]. The work of [PERSON] et al. presents a succinct model of stochastic dissipation storage and has established the direct load control framework for an ancillary service. Based on [14], [PERSON] et al. developed a geometric method to characterize admissible power profiles of individual ACs [15]. A thermal battery model of the AC system and the related dispatch model is proposed [16]. The comparison between the proposed thermal battery model and the conventional battery model is presented in detail. Nevertheless, the above studies focus on the application of the virtual battery model on dispatch optimizations, which is not suitable for real-time frequency control. The dynamic characteristic of energy storage modeling needs further investigation. In terms of control methods, there are three main ways for aggregated flexible resources to participate in frequency regulation. As a main category of control methods, the centralized control architectures of flexible loads are developed for frequency regulation [17]. A centralized control framework embedded with a master-slave protocol is proposed for compensating frequency deviation [18]. A priority-stacks centralized control scheme is proposed for the selection of on/off state [19]. Nevertheless, under the condition that a large number of flexible loads are integrated in the coordinated control architecture, the centralized control is deprived of handling the computational expenses and the protection of consumer privacy. Unlike the centralized control strategy, decentralized control strategies depend on instantaneous information metered by local measurement unit instead of explicit communications [20]. A decentralized control strategy is proposed to optimize the charging rates of electric vehicles [21]. The flexible loads are aggregated close to a regulation generator through a decentralized frequency control scheme [22]. Although the communication network is simplified by the local measurement, the decentralized approaches fail to handle system operational constraints in the local decision process. In order to overcome the drawbacks of centralized controls and decentralized control methods, distributed control schemes are established as alternative methods. In this control scheme, all decisions of the individual TCL are made locally based on communication with its neighbor and the agents of aggregated loads refine the control decisions iteratively by exchanging the control decisions with their neighbor agents.