## 1 Introduction  
### Background and Motivations  
The global energy landscape is at a critical juncture, facing the dual challenges of finite fossil fuel reserves and escalating environmental impacts [1; 2]. Traditional energy sources like coal, oil, and natural gas, while essential for meeting current global energy demands, exact a heavy toll on the environment through greenhouse gas emissions [3]. These emissions contribute significantly to global warming and climate change [4]. The consequences are profound and far-reaching, from sea-level rise and melting polar ice caps to an increase in the frequency and intensity of weather events like hurricanes, droughs, and heatwaves [5]. The urgency to transition towards sustainable energy solutions has never been clearer. Compounding these challenges are energy shortages and vulnerabilities in our existing energy infrastructure. Many regions are heavily reliant on imported fossil fuels, exposing them to economic volatility and geopolitical tensions.  
Convention power grids and transmission systems further exacerbate risks of supply disruptions and grid instability, underscoring the need for resilient and decentralized energy strategies [6]. In response to these imperatives, HEMS have emerged as a promising solution [7]. HEMS leverage cutting-edge technologies to track and improve energy usage [8; 9; 10]. By integrating data on electricity prices, demand patterns, weather forecasts, and renewable energy availability, these systems empower homeowners to make informed choices that minimize energy waste and decrease utility expenses. Through sophisticated algorithms and smart controls, HEMS adjust appliance usage, heating, and lighting to align with optimal energy efficiency practices [11].  
Moreover, HEMS play a pivotal role in facilitating the integration of RESs such as PV and small-scale WTs into the residential energy mix. This decentralized approach not only reduces reliance on centralized fossil fuel-based power generation but also enhances local energy resilience and sustainability [12; 13; 14; 15]. By generating clean energy at the point of consumption, households equipped with HEMS contribute to broader efforts to mitigate greenhouse gas emissions and combat climate change. Beyond their technical capabilities, HEMS empowers consumers by providing an actionable understanding of their energy use trends and practices. Furthermore, these systems enable participation in DR programs, where electricity consumption can be adaptively modified based on grid conditions [16]. This capability supports grid stability during peak demand periods and enhances overall system reliability as RESs become more prevalent.  
The integration of RESs into residential energy systems has been extensively studied, with numerous research efforts highlighting the benefits and challenges associated with PV and WTs [17; 18; 19]. Studies consistently show that RESs can significantly decrease dependence on fossil fuels and reduce greenhouse gas emissions. However, the inherent intermittency of solar and wind energy necessitates the inclusion of backup systems to ensure a stable energy supply [20; 21; 22; 23]. Various studies have explored the use of batteries and FCs as effective backup sources. However, there is limited research on the comprehensive integration of these elements, namely PV, wind, batteries, FCs, EVs, and TOU-based DR programs, into a cohesive energy management system for residential applications.