Solver Success Is Not Enough: Verification-Grounded LLM Agents for Distribution-Grid Model Reconstruction

Updating a distribution-grid optimization model from a natural-language operational request is not a code-generation task alone. A single request may jointly change device states, parameters, constraints, objectives, and priorities, creating dependencies across interpretation, formulation, implementation, and execution. A candidate may execute and solve successfully while misrepresenting the request or producing a solution that violates nonlinear AC power-flow constraints. Existing evaluations of LLM agents do not jointly test such coupled modifications against both requirement fidelity and physical feasibility. We introduce a benchmark with 36 request types spanning parameter edits, formulation changes, and coupled state-and-formulation changes. To evaluate the same reconstruction tasks across different network structures, we instantiate all 36 request types under four operating conditions on three distribution networks, yielding 432 cross-network instances, each paired with executable requirement and physical checks. We also propose GridRecon, a verification-grounded multi-agent framework in which Planning, Formulation, Coding, and Review Agents exchange structured requirement specifications and mathematical change plans. Deterministic tools check requirement implementation, program execution, topology, AC power flow, and SOC relaxation quality, while a controller uses the resulting evidence to accept verified candidates, trigger bounded, targeted self-refinement for actionable failures, or reject unresolved cases. As a result, our GridRecon outperforms the strongest adapted baseline for each of four LLM backbones on IEEE 69 by 7.6 to 34.0 percentage points and passes 329 of 432 instances in the common cross-network evaluation on IEEE 33, IEEE 69, and case136ma.