Three-level stochastic optimization framework for energy management in smart grids with integrated peer-to-peer trading

• Increases HC by 14.2% and 9.57%, respectively, reducing annual operating costs by 58% and 11.86%. • The robust model achieves a 12.4% higher HC and a 23.7% lower cost. • It yields a 9.6% HC gain and an 11.9% cost saving. • Delivering 41.75 MW HC at an annual cost of $2.72 M. The integration of peer-to-peer (P2P) energy trading into distribution networks introduces complex coordination challenges among the distribution system operator (DSO), P2P market platform, and prosumers. This paper proposes a three-level stochastic optimization framework to coordinate these actors under uncertainty in renewable generation and load demand. The upper level (DSO) designs network-access tariffs and line capacity limits to maximize expected social welfare. The intermediate level clears the P2P market using a linearized AC power-flow model to ensure physical feasibility. The lower level comprises prosumers minimizing individual expected costs, including risk aversion via conditional value-at-risk (CVaR). The tri-level stochastic program incorporates battery degradation, demand-response elasticity, renewable curtailment, and chance constraints on voltage/thermal limits. To solve this large-scale problem, a single-level reformulation is derived using Karush–Kuhn–Tucker (KKT) conditions and strong duality, with complementary slackness linearized via big-M and McCormick envelopes. A hybrid decomposition algorithm combining Benders cuts and column-and-constraint generation (C&CG) enhances tractability. In summary, this study confirms that the proposed framework yields significant performance gains. The results show a 134.4% increase in social welfare when benchmarked against the baseline (Case 1: $1,675.7), representing a substantial societal benefit. Furthermore, the framework achieves a 22.7% reduction in the total prosumer cost (Case 1 cost: $4,521.3 to Case 4 cost: $3,492.5), 18.8% reduction in network losses, robust voltage security (0% recorded in Case 4), and efficient P2P trading enabled by the framework. Key findings include the DSO’s ability to balance network constraints and prosumer flexibility, the effectiveness of the linearized power-flow model in maintaining feasibility, and the critical role of risk-averse prosumer behavior in stabilizing local energy markets