In the face of an increasingly prominent “double-high” market environment

the current DC/linearized AC power flow-driven power system supply-demand balance analysis mechanism struggles to effectively support market settlement requirements under renewable energy uncertainty. This paper proposes a convex relaxation AC power flow-based energy-reserve co-optimization framework with network loss compensation for locational marginal pricing (LMP). Firstly

this paper develops a second-order cone programming (SOCP) relaxation AC optimal power flow

which accurately captures the marginal cost of network losses without requiring iterative computations. Secondly

considering the uncertainty of renewable energy sources

a distributionally robust optimization approach for joint energy-loss-reserve co- optimization is developed. By constructing generalized affine analytical functions based on AC power flow and employing duality theory

this paper reformulates the original problem into an AC-solvable form. Subsequently

based on Karush- Kuhn- Tucker (KKT) conditions and shadow price theory

an uncertainty-inclusive LMP method is established

with the explicit decomposition of LMP components. Finally

comprehensive simulations are conducted on test systems of varying scales. The results demonstrate that the proposed approach not only accurately delineates the operational regulation boundaries of renewable-penetrated power systems under uncertainty

but also establishes a paradigm for resource allocation optimization in high-renewable power markets while providing actionable guidance for market participants to enhance their investment decisions and operational strategies.