## 7 Load Data  
To assess the proposed problem, a medium-sized household is utilized. Table 3 illustrates the load profile for different household appliances, detailing their daily energy usage and operational times. This case study examines a residential home in Liaoning Province, China. The location of the home is indicated on the map of Liaoning shown in Figure 5. The table presents the energy consumption of different appliances, showing their power usage and the number of hours they typically operate each day. For instance, the home uses two air conditioners, each with a power consumption of 1500 watts. These air conditioners operate for approximately 11 h daily, resulting in a combined daily energy consumption of 33,000 Wh. This substantial energy use reflects the necessity for cooling in the regional climate. Additionally, the household includes two refrigerators, each consuming 100 watts. These refrigerators operate for an estimated 22 h daily, leading to a total energy consumption of 4400 Wh per day. The extended operation time accounts for the refrigerators' intermittent cycling to maintain optimal cooling while efficiently managing energy use. Fans contribute significantly to the household's energy profile. The home is equipped with five fans, each consuming 80 watts. Due to the climate in Liaoning, these fans are used extensively, operating for about 19 h a day and contributing 7600 Wh to the daily energy usage. The frequent use of fans highlights the household's efforts to maintain comfort in varying temperatures. In addition to cooling devices, the washing machine and space heater also play notable roles in energy consumption. The washing machine, with a power usage of 700 watts, is used for about 4 h each day, resulting in a daily energy consumption of 2800 Wh. During colder periods, the space heater, which consumes 1500 watts, operates for around 6 h daily, contributing 9000 Wh to the household's energy usage. These figures underscore the varying energy demands depending on the season and household activities. Figure 5: Location of the residential home in Liaoning Province, China, examined in this case study. The intelligent HEMS seeks to enhance the efficiency of appliance operations to reduce operation and maintenance costs, sustain energy balance, ensure user comfort, and prevent elevated demand during peak periods. This study explores HEMS from the viewpoints of both consumers and suppliers, with the goal of developing a system that effectively handles both energy production and consumption. Decisions are made based on the demand for and generation of energy, with the status of devices being updated regularly. In the context of home energy management, appliances can be classified into three distinct types according to their operational flexibility and energy consumption patterns: Elastic, Shiftable, and Fixed. Understanding these categories is crucial for optimizing energy usage, particularly in systems incorporating RESs and DR programs. Elastic appliances are those whose energy consumption can be modulated or adjusted within certain limits without affecting their core functionality. These appliances are highly adaptable to fluctuations in energy supply and can operate under variable power conditions. Elastic appliances play a crucial role in DR programs by providing the flexibility to increase or decrease electricity usage in response to the grid conditions or energy prices, thereby helping maintain grid stability and energy cost savings. Shiftable appliances are those whose operation can be delayed or rescheduled to a different time without impacting their overall functionality. These appliances are typically used for tasks that do not require immediate attention and can be deferred to periods of lower energy demand or higher renewable energy availability. Shiftable appliances enhance the efficiency of HEMSs by aligning energy consumption with periods of lower demand or higher supply, reducing overall energy costs and improving the utilization of RESs.