The growing complexity of power system operations has created an urgent need for intelligent, automated tools to support reliable and efficient grid management. Conventional analysis tools often require significant domain expertise and manual effort, which limits their accessibility and adaptability. To address these challenges, this paper presents X-GridAgent, a novel large language model (LLM)-powered agentic AI system designed to automate complex power system analysis through natural language queries. The system integrates domain-specific tools and specialized databases under a three-layer hierarchical architecture comprising planning, coordination, and action layers. This architecture offers high flexibility and adaptability to previously unseen tasks, while providing a modular and extensible framework that can be readily expanded to incorporate new tools, data sources, or analytical capabilities. To further enhance performance, we introduce two novel algorithms: (1) LLM-driven prompt refinement with human feedback, and (2) schema-adaptive hybrid retrieval-augmented generation (RAG) for accurate information retrieval from large-scale structured grid datasets. Experimental evaluations across a variety of user queries and power grid cases demonstrate the effectiveness and reliability of X-GridAgent in automating interpretable and rigorous power system analysis.