## 1 Introduction  
New energy power generation, particularly wind power generation, has been developed rapidly around the world in recent years because it may offer clean and cost-effective electric energy. According to the description from the U.S. Department of Energy, by 2030, 20% of the state's electricity could be generated by wind farms [1]. However, wind power outputs are fluctuating and intermittent [2] because of the wind velocity variation. In addition, wind farms would generate more electricity during valley load periods and less electricity during peak-load periods. In terms of the controllability relative to conventional units, wind power outputs are equivalent to a negative load. As a result, the load peak-valley gap has been significantly widened in wind energy-integrated power systems compared to the traditional power system. Such a gap has brought enormous challenges to the reliable operation of power systems [3; 4; 5]. In order to supply the excessive load during the peak period, many approaches have been proposed. The traditional approach was to set up new power plants with the capability of peak addition, requiring huge capital investment and planning time [6]. A recently proposed approach was to utilize electric energy storages to adjust the peak load [7; 8]. With the rapid development of smart grid techniques, demand response (DR) has been gaining acceptance among practitioners as one of the most useful load shedding methods [9; 10]. Moreover, DR is also an efficient measure to coordinate the wind power fluctuation. The DR is described as a resource that originates from the behavior and usage changes of electricity customers in response to rate variations [11] or incentive mechanisms [12]. Generally, there are two types of DR programs: incentive-based and price-based programs. Electric power companies usually carry out incentive-based DR programs to manage the electric load. According to a Federal Energy Regulatory Commission (FERC) report, in the United States, the incentive-based DR programs account for the majority of the total potential peak reduction reported in 2012 [13]. Additionally, direct load control (DLC) has been reported to be one of the most popular methods of incentive-based DR for peak-load shedding. The DLC [14] projects utilize advanced control technology and remote controllers to switch the on/off state of specific appliances during peak-load periods. The direct control objects are usually the thermostatically controlled loads (TCLs) from residential and small commercial customers, such as heating, ventilation, air-conditioning [15; 16] and water heaters. In the past years, the usage of air-conditioning loads (ACLs) has been steadily increasing [17; 18]. In China, for example, during peak-load periods in summer, ACLs account for 30-40% of total load [19] in some large cities, such as Beijing and Shanghai. Research also indicates that turning off the air conditioner or changing the temperature setting for a short period of time has little impact on customer comfort [20]. Therefore, the ACL can be viewed as a potential DR resource in reducing the peak load. Many studies have described and modeled the load characteristics and behaviors of ACLs. For instance, [PERSON] et al. [21] adopted the Monte Carlo and the Fokker-Planck methods to analyze the probability distribution function of TCLs. [PERSON] and [PERSON] [22] utilized thermostat offset signals to control ACLs and used a novel partial differential equation framework to model ACLs. Additionally, [PERSON] and [PERSON] [23] used the statistical approach to model the dynamic behavior of aggregated air conditioners. Nonetheless, most of these works were based on statistical approaches, which require a large amount of data to be collected. Our research, by contrast, is based on an equivalent thermal parameter model of the home heating system, which physically describes the relationship between temperature and ACL power output. In [16], DCL was implemented to control centralized TCLs for providing continuous regulation reserves.