Residential solar photovoltaic (PV) systems play a crucial role in energy transition and climate change mitigation in urban areas. However, the adoption process shows social disparities, raising concerns about energy justice. Current research has limitations in understanding the complex mechanisms behind household solar adoption decisions. Therefore, this study explores using large language model (LLM)-based agents to simulate household solar adoption decisions. Based on a literature review, we developed a framework covering four key factor categories: technical attributes, household characteristics, personal beliefs, and external contexts. We created an LLM-based household agent model (PVAgent) that converts influencing factors into structured prompts, expanding from individual decision-making to multi-agent systems, with both decisions and reasoning statements as output. Using three neighborhoods in Amsterdam as a case study, we simulated solar adoption behavior across different social groups. Using three neighborhoods in Amsterdam as a case study, we simulated solar adoption behavior across different social groups. The result shows that the LLM agent model can generate reasonable individual decision logic and group-level structural patterns. It also shows how household adoption dynamics change over time with evolving motives and barriers. Based on these insights, we propose three principles for future policymaking: comprehensive strategic frameworks, structural innovation, and differentiated approaches for specific groups. In summary, this research contributes by introducing LLMs to energy behavior modeling. Although there are limitations, such as the subjectivity of prompt design, this research provides an innovative approach to understanding complex household decision-making. Future studies can further develop this approach and explore more extensive application scenarios with advanced methodological integration and interdisciplinary cooperation.