LLM-based autonomous agents have demonstrated outstanding performance in solving complex industrial tasks. However, in the pursuit of carbon neutrality and high-performance renewable energy systems, existing AI-assisted design automation faces significant limitations in explainability, scalability, and usability. To address these challenges, we propose LP-COMDA, an LLM-based, physics-informed autonomous agent that automates the modulation design of power converters in Power Electronics Systems with minimal human supervision. Unlike traditional AI-assisted approaches, LP-COMDA contains an LLM-based planner that gathers and validates design specifications through a user-friendly chat interface. The planner then coordinates with physics-informed design and optimization tools to iteratively generate and refine modulation designs autonomously. Through the chat interface, LP-COMDA provides an explainable design process, presenting explanations and charts. Experiments show that LP-COMDA outperforms all baseline methods, achieving a 63.2% reduction in error compared to the second-best benchmark method in terms of standard mean absolute error. Furthermore, empirical studies with 20 experts conclude that design time with LP-COMDA is over 33 times faster than conventional methods, showing its significant improvement on design efficiency over the current processes.