This paper proposes a bi-level, learning-enabled control framework for power systems with high penetration of inverter-based resources (IBRs) and dynamic loads. The framework couples physics-based differential–algebraic models with a structured neural-network residual model, creating a feedback loop in which measurement-driven parameter and residual updates refine the underlying dynamics used for control. At the lower level, a distributed multi-timescale optimization scheme coordinates synchronous generators, grid-forming and grid-following IBRs, and dynamic loads via an alternating direction method of multipliers (ADMM)-based algorithm with trust-region convexification of AC power-flow constraints and time-varying barrier functions for operational limits. Communication uncertainty is handled through a consensus update with prediction-based recovery, enabling operation under delays and packet losses. On the analytical side, we establish local well-posedness of the hybrid model and derive practical stability guarantees for the closed-loop system using a composite device-level Lyapunov function and a perturbed ADMM contraction argument. The framework is validated through real-time hardware-in-the-loop experiments on the IEEE 39-bus system and large-scale co-simulation on a 1332-bus southern regional power grid (SRPG) model. The results indicate improved frequency and voltage performance, reduced constraint violations, and enhanced robustness under non-ideal communication conditions, while satisfying the relevant real-time execution constraints.
Conventional carbon emission flow (CEF) tracing solves each operating scenario independently, which becomes inefficient in large-scale multi-point evaluation along operating trajectories. This paper develops a matrix-recursive holomorphic embedding (HE) framework that converts pointwise power and carbon tracing into a reusable analytical mapping along a prescribed one-dimensional path. Without altering the allocation rule, the nodal outflow reciprocals, distribution and tracing matrices, and node-allocated carbon flow rates are solved recursively from the embedded AC power flow coefficients. A multi-germ scheme restarts the expansion at branch direction changes or residual violations and routes uncertified queries to a pointwise solver. The resulting piecewise analytical trajectory enables rapid online evaluation and yields pathwise carbon sensitivity. Tests on IEEE systems and a 399-bus provincial grid verify reconstruction, carbon conservation, sensitivity accuracy, and wind power uncertainty propagation. For 10,000 common queries, the protected online stage achieves speedups of 2.55–10.49× over HE power flow with pointwise CEF and 49.49–166.00× over AC power flow with pointwise CEF, with a maximum relative discrepancy below 7 × 10⁻11.
This paper investigates the problem of resilient load frequency control with prescribed performance for power systems subject to multiple actuator failures and gain perturbations. For the first time, a novel robust control scheme incorporating dynamic performance constraints is proposed using auxiliary matrices. This method improves upon conventional robust control techniques by explicitly accounting for transient closed-loop dynamics, which are often overlooked in existing designs. To simplify the controller design, auxiliary matrices are introduced alongside a variable substitution technique. Through this approach, sufficient conditions are derived to ensure closed-loop stability in the presence of actuator failures and gain perturbations while satisfying prescribed performance constraints. Finally, the effectiveness of the proposed method is verified through simulations on a three-area power system.
Load dynamics can significantly deteriorate a power system's transient stability under contingencies. However, the diversity and time-varying nature of load behaviors make accurate parameter estimation highly challenging, potentially compromising the transient stability guarantees of dispatch solutions. This paper proposes a robust transient stability-constrained multi-objective optimal power flow (RTSC-MOPF) model that explicitly considers uncertainty in load dynamic parameters. The model aims to balance dispatch costs and transient stability risks while maintaining system stability under critical contingencies. Transient stability is evaluated based on the Extended Equal-Area Criterion (EEAC) method, formulated as a function of generation scheduling decisions and uncertain load parameters represented by a polyhedral uncertainty set. To solve this problem, the model is reformulated into a single-objective min-max-min problem using the Normal Boundary Intersection (NBI) method and penalty terms for stability constraint violations. Subsequently, a novel dual-loop iterative solution framework is developed, which integrates the Column-and-Constraint Generation (C&CG) algorithm with the sequential method that linearizes stability constraints based on Trajectory Sensitivity Analysis (TSA). Numerical studies are conducted on the IEEE New England 39-bus system to demonstrate the effectiveness of the proposed method.
Traditionally, distribution planners and the transmission planner used to solve their expansion planning problems independently, which kept their data privacy at the expense of suboptimal plans. In contrast, in current studies on the coordinated transmission and distribution systems expansion planning (CTDSEP), optimality is mainly achieved through monolithic approaches at the expense of privacy, which is crucial in practical settings. To address the issue of privacy preservation, a practical algorithm based on the combination of the alternating direction method of multipliers (ADMM) and the coordinate descent method (CDM) is proposed in this paper to solve the non-convex instances of CTDSEP. The approach is general enough to accommodate different formulations for the transmission system (TS) and distribution systems (DSs), with the coordination among planners limited to exchanging information only related to the interface nodes. Similar to the ADMM algorithm, the centralized formulation is decomposed into individual subproblems for the TS and for each DS. Additionally, the CDM ensures the convergence of practical large-scale non-convex problems, which is not guaranteed for ADMM. Finally, the simulation results involving up to 550-node test systems show the effective performance of the proposed approach both in terms of solution quality and computation time.
