Physics-informed data-driven modeling of AC optimal power flow via quadratic approximation

Parameters in alternating-current optimal power flow (AC-OPF) models evolve with operating conditions and equipment aging, which can create a gap between analytical models and field behavior. To mitigate this effect, this paper leverages field measurements within a physics-informed, data-driven framework that preserves the OPF structure while learning high-fidelity quadratic surrogates of network physics. Two complementary models are proposed. The Convex Quadratic Approximation Model (CQAM) replaces non-convex constraints with data-driven convex under-estimators and concave over-estimators constructed via sparsity-promoting semidefinite programming (SDP), yielding a tractable convex program that admits globally optimal solutions for the convexified problem. The Non-convex Quadratic Approximation Model (NQAM) learns explicit quadratic equalities through regularized quadratic programming (QP), closely matching the AC-feasible set and producing solutions that satisfy power flow constraints within numerical tolerances. A cooperative workflow exploits their strengths: CQAM provides fast screening and dispatch when tractability is critical, whereas NQAM refines solutions and supports feasibility recovery. Experiments on standard OPF benchmarks demonstrate improvements in optimal value and constraint satisfaction compared to representative baseline surrogates, while maintaining competitive runtimes. • Data-driven, physics-guided optimal power flow using learned quadratic surrogates. • Convex quadratic model enables fast, tractable optimization with guarantees. • Non-convex quadratic model restores near-exact feasibility with high fidelity. • Cooperative workflow balances speed and fidelity for practical applications.