Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition

We consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then a global random attractor and the existence of a stationary measure are obtained via the Birkhoff ergodic theorem and the Chebyshev inequality

Leveraging Two-Stage Adaptive Robust Optimization for Power Flexibility Aggregation

To effectively harness the significant flexibility from massive distributed energy resources (DERs) for transmission-distribution interaction, power flexibility aggregation is performed for a distribution system to compute the feasible region of the exchanged power at the substation. Based on the adaptive robust optimization (ARO) framework, this paper proposes a novel methodology for aggregating system-level power flexibility, considering heterogeneous DER facilities, network operational constraints, and unbalanced power flow model. In particular, two power flexibility aggregation models with two-stage optimization are developed for application: one focuses on aggregating active power and computes its optimal feasible intervals over multiple periods, while the other solves the optimal elliptical feasible regions for the aggregate active-reactive power. By leveraging ARO technique, the disaggregation feasibility of the obtained feasible regions is guaranteed with optimality. The numerical simulations conducted on a real-world distribution feeder with 126 multi-phase nodes demonstrate the effectiveness of the proposed method.Comment: 8 Page