This paper proposes PE-GPT, a custom-tailored large language model uniquely adapted for power converter modulation design. By harnessing in-context learning and specialized tiered physics-informed neural networks, PE-GPT guides users through text-based dialogues, recommending actionable modulation parameters. The effectiveness of PE-GPT is validated through a practical design case involving dual active bridge converters, supported by hardware experimentation. This research underscores the transformative potential of large language models in power converter modulation design, offering enhanced accessibility, explainability, and efficiency, thereby setting a new paradigm in the field.