Coordinated frequency -constrained stochastic economic dispatch for integrated transmission and distribution system via distributed optimization

The increasing penetration of renewable energy challenges frequency stability due to high variability and declining inertia. Traditional frequency-security-constrained dispatch methods fail to capture regional frequency heterogeneity and spatially correlated stochastic disturbances, resulting in inaccurate frequency security enforcement. To address this, a regional frequency-constrained dispatch method is proposed, considering the spatial-joint stochastic disturbances and contingencies. Firstly, a multi-regional frequency response model is constructed, incorporating the Vine-Copula-based characterization of regional stochastic disturbances and regional frequency support. Then, a progressive latent-bottleneck physics-informed neural network is applied to characterize differential frequency nadir terms and regional frequency support integral terms via an encoder-decoder architecture, which enables optimization compatible expressions of system frequency dynamics. Finally, a day-ahead dispatch model is developed in which regional stochastic frequency constraints are embedded using a CVaR-based formulation. A case study on the IEEE 118-bus system shows that the proposed method outperforms the unified center-of-inertia–embedded approach in mitigating regional frequency violations, with the regional frequency nadir and RoCoF improved by 32.76% and 2.06%, respectively.