Bai Cui

Feixiang Zhang, Hongyi Li, Bai Cui et al.

The aggregate flexibility region of distributed energy resources (DERs) quantifies the aggregate power shaping capabilities of DERs. It characterizes the distribution network's potential for wholesale market participation and grid service provision at the transmission level. To enhance flexibility and fully exploit the potential of DERs, this paper proposes a method to optimize the aggregate flexibility region through distribution network reconfiguration. First, we formulate the ellipsoidal aggregate flexibility region characterization problem as a two-stage adaptive robust optimization problem and derive an exact convex reformulation with a large number of second-order cone constraints. By exploiting the problem structure, we propose a scalable Benders decomposition algorithm with provable finite convergence to the optimal solution. Finally, we propose an optimal reconfiguration problem for aggregate flexibility region optimization and solve it using the custom Benders decomposition. Numerical simulations on the IEEE 123-bus test feeder demonstrate that, compared to existing approaches, substantial improvements in the aggregate flexibility region can be achieved over multiple scenarios with the optimized topology.

Ahmed Mesfer Alkhudaydi, Bai Cui

The progression of modern power systems towards converter-rich operations calls for new models and analytics in steady-state voltage stability assessment. The classic modeling assumption of the generators as stiff voltage sources no longer holds. Instead, the voltage- and current-limited behaviors of converters need to be considered. In this paper, we develop a Wirtinger derivative-based formulation for the power flow Jacobian and derive an explicit sufficient condition for its singularity. Compared to existing works, we extend the explicit sufficient singularity condition to incorporate all bus types instead of only slack and PQ types. We prove that the singularity of the alternative Jacobian coincides with that of the conventional one. A bus-wise voltage stability index, denoted $C_{\mathrm{W}}$, is derived from diagonal dominance conditions. The condition $\min_i C_{W,i}$ being greater than one certifies the nonsingularity of the Jacobian and provides a fast, non-iterative stability margin. Case studies in standard IEEE test systems show that the proposed index yields less conservative and more localized assessments than classical indices such as the L-index, the $K_{\mathrm{R}}$ index, and the SCR index.

Puskar Neupane, Bai Cui

The solvability condition of the power flow equation is important in operational planning and control as it guarantees the existence and uniqueness of a solution for a given set of power injections. As renewable generation becomes more prevalent, the steady-state operating point of the system changes more frequently, making it increasingly challenging to verify power flow solvability by running the AC power flow solver after each change in power injections. This process can be computationally intensive, and numerical solvers do not always converge reliably to an operational solution. In this paper, we propose a sufficient condition for the solvability of the lossless real power flow equation based on the cycle space of a meshed network. The proposed condition yields a less conservative solvability certificate than existing sufficient conditions on the tested systems and can serve as a useful foundation for developing solvability conditions for the fully coupled power flow equations.

Weiqi Meng, Hongyi Li, Bai Cui

Virtual power plants (VPPs) are an emerging paradigm that aggregates distributed energy resources (DERs) for coordinated participation in power systems, including bidding as a single dispatchable entity in the wholesale market. In this paper, we address a critical operational challenge for VPPs: the day-ahead offering problem under highly intermittent and uncertain DER outputs and market prices. The day-ahead offering problem determines the price-quantity pairs submitted by VPPs while balancing profit opportunities against operational uncertainties. First, we formulate the problem as a scenario-based two-stage stochastic adaptive robust optimization problem, where the uncertainty of the locational marginal prices follows a Markov process and DER uncertainty is characterized by static uncertainty sets. Then, motivated by the outer approximation principle of the column-and-constraint generation (CC&G) algorithm, we propose a novel inner approximation-based projected subgradient method. By exploiting the problem structure, we propose two novel approaches to improve computational tractability. First, we show that under mild modeling assumptions, the robust second-stage problem can be equivalently reformulated as a linear program (LP) with a nested resource allocation structure that is amenable to an efficient greedy algorithm. Furthermore, motivated by the computational efficiency of solving the reformulated primal second-stage problem and the isotonic structure of the first-stage feasible region, we propose an efficient projected subgradient algorithm to solve the overall stochastic LP problem. Extensive computational experiments using real-world data demonstrate that the overall projected subgradient descent method achieves about two orders of magnitude speedup over CC&G while maintaining solution quality.

Zongqi Hu, Weiqi Meng, Bai Cui

Optimal transmission switching (OTS) determines which transmission lines to remove from service to minimize dispatch costs. Unlike topology design, it alters the operational status of operating lines. Sensitivity-based methods, as advanced optimization techniques, select lines whose outage yields a significant cost reduction. However, these methods overlook bus splitting, an effective congestion management strategy that our work incorporates to achieve improved economic gains. In this work, we formulate an optimal transmission reconfiguration (OTR) problem that incorporates both line switching and bus splitting. We develop a novel approach to quantify the sensitivity of the OTR objective to line switching and bus splitting, establish connections between the proposed sensitivity framework and existing heuristic metrics, prove the equivalence between bus splitting and a generalized line switching to enable unified treatment, and provide a simpler derivation of Bus Split Distribution Factor (BSDF). Simulations on nine IEEE test systems spanning 118 to 13,659 buses demonstrate the high effectiveness of our proposed sensitivity method. They also demonstrate that incorporating bus splitting into transmission reconfiguration achieves greater cost savings than line switching alone. The results confirm the economic advantage of this comprehensive approach to transmission system operation.

Ahmed Mesfer Alkhudaydi, Bai Cui

The rapid growth of large, power-electronics-rich data center (DC) loads is creating new operational challenges for bulk power systems. A key risk arises when a DC uninterruptible power supply (UPS) disconnects the facility during voltage/frequency disturbances and then reconnects it while the bulk grid is still dynamically settling to a new equilibrium point. Poorly timed reconnection can amplify electromechanical oscillations, deepen frequency deviations, and lead to repeated connect-disconnect \emph{flapping}. In this paper, we develop an analytical framework to characterize the \emph{safe reconnection time} for large DC loads after a disturbance-induced disconnection that avoids flapping. Using a model in the spirit of the classical single-machine infinite-bus system, we capture (i) swing dynamics during the disconnection interval and (ii) voltage-angle coupling at the load bus, which determines the electrical power step at reconnection under constant-power load assumptions. Using energy function method, we characterize the critical safe reconnection time such that for any reconnection time after the critical safe reconnection time, the post-reconnection trajectory is guaranteed to remain within operational limits (frequency/angle/voltage) and converge to the post-reconnection equilibrium, thereby preventing flapping. Time-domain simulations validate the effectiveness of the proposed analytical approach. The results provide a simple, physics-informed criterion that can be used to bound reconnection windows for large DC facilities and inform UPS reconnection logic.

Bai Cui, Xu Andy Sun

Variations of loading level and changes in system topological property may cause the operating point of an electric power systems to move gradually towards the verge of its transmission capability, which can lead to catastrophic outcomes such as voltage collapse blackout. From a modeling perspective, voltage collapse is closely related to the solvability of power flow equations. Determining conditions for existence and uniqueness of solution to power flow equations is one of the fundamental problems in power systems that has great theoretical and practical significance. In this paper, we provide strong sufficient condition certifying the existence and uniqueness of power flow solutions in a subset of state (voltage) space. The novel analytical approach heavily exploits the contractive properties of the fixed-point form in complex domain, which leads to much sharper analytical conditions than previous ones based primarily on analysis in the real domain. Extensive computational experiments are performed which validate the correctness and demonstrate the effectiveness of the proposed condition.