This thesis addresses the imperative need for sustainable energy solutions in the residential sector which is a significant contributor to global energy consumption and greenhouse gas emissions. Focusing on modeling and optimizing residential energy systems, the study explores the integration of photovoltaic (PV) panels, heat pumps, and batteries. The purpose is extending the applications of the Photovoltaic Material and Devices (PVMD) toolbox, offering a framework for future research and advancements. The objective is to enhance energy efficiency, reduce carbon footprints, and contribute to energy security by diversifying energy sources. The research encompasses a comprehensive analysis of heat pump models, emphasizing their role in space heating, space cooling, and domestic hot water functions. Two specific models are chosen for Coefficient of Performance (COP) and Energy Efficiency Ratio (EER) calculations. These models, along with the utilization of the nPro tool, lay the foundation for integrating heat pump systems with PV production and battery storage in residential buildings. The study successfully integrates the model of the battery’s performance and the overall grid-connected energy system. Employing a mathematical modeling approach, each component is systematically incorporated into the system, including the previously developed heat pump model. This integration, coupled with the Alternating Current (AC) output of the PVMD toolbox and the battery, establishes the groundwork for subsequent economic and performance analyses of the system. The study systematically selects various locations with different environmental conditions such as Equivalent Sun Hours (ESH) and average ambient temperature to analyze the economic aspect by checking the Net Present Cost (NPC) and performance aspects by checking Self Consumption Ratio (SCR) and Self Sufficiency Ratio (SSR) of the integration model. The findings emphasize the economic viability of heat pump investments in cities with distinct heating and cooling demands. It has been demonstrated that in colder cities where heating demand is predominant, heat pumps are economically attractive, resulting having heat pumps in optimal scenarios that give the minimum NPC in Amsterdam and Lisbon. Additionally, although the individual components of the system may seem cost-ineffective, their value is derived more from integration in milder cities where heating demand is dominant, resulting having heat pump and PV integrated for the optimal scenario for Lisbon. However, cities dominated by cooling demand face challenges in achieving financially optimal designs because the operational savings for cooling cannot be accurately included such as Cairo and Dakar. The research underscores the importance of considering various system factors, including initial investment costs and electricity tariffs, to achieve financially optimal sizing. As the initial cost of the battery decreases, battery technology becomes economically appealing for Lisbon and Dakar. Moreover, changes in the tariff prove economically favorable for integrating the battery system in Lisbon, Cairo, and Dakar. This work contributes valuable insights to the field of renewable energy, providing practical solutions for the transition towards cleaner and more efficient residential energy systems.