Luis Badesa

The Transient Stability-Constrained Optimal Power Flow (TSC-OPF) incorporates dynamic stability constraints into the OPF formulation to ensure secure and economical operation under disturbances. While discretizing system dynamics enables the use of nonlinear programming techniques, it significantly increases computational burden. To enhance scalability, many studies simplify the network by representing loads as constant admittances, allowing the use of Kron reduction. However, computing the Kron reduction outside the optimization requires a voltage-based assumption to convert loads from constant power to constant admittance. This paper proposes a practical voltage-based load admittance approximation and evaluates the errors it may introduce in rotor angle and speed deviation trajectories. Case studies on the WECC 9-bus system show that the proposed approach reproduces rotor dynamics consistent with time-domain simulations during the first few seconds while considerably reducing implementation effort and mitigating convergence issues. The proposed framework thus offers a simple and effective strategy for scalable TSC-OPF implementations.

Voltage unbalance, caused by variations in voltage magnitude and phase angle, is a significant power quality issue in three-phase systems, leading to equipment inefficiencies and increased system losses. The integration of distributed energy resources (DER) into the grid adds complexity, as DER can either reduce or worsen voltage unbalance, depending on factors such as grid configuration and the distribution of loads and DER themselves. This study explores the effects of DER penetration on voltage unbalance levels and the accuracy of the different indices most commonly used to quantify this unbalance. The results highlight the varying impacts of DER on unbalance and index performance, emphasizing the need for effective strategies to assess voltage unbalance in modern distribution systems.

Low-inertia power grids would benefit from frequency support from inverter-based generation, given the scarcity of synchronous generators as decarbonisation efforts progress. Wind turbines store kinetic energy in their rotors as they produce electric power, which can be partially released to the grid in the event of a generation loss, in order to contain the frequency drop. This paper introduces a novel fast droop control for wind turbines (WTs) based on an adaptive droop gain strategy, extracting the optimal amount of kinetic energy depending on the overall system conditions. This requires mapping the low-level inverter controls into a system-wide economic optimisation, which has not been successfully addressed yet. To overcome this challenge, we propose a data-driven methodology for integrating frequency stability constraints into an Optimal Power Flow (OPF) formulation, which is explicitly dependent on the low-level control parameters of the wind turbines’ converters. A modified Optimal Classification Tree (OCT) is used to encode frequency-security guarantees for the grid, due to its suitable structure for being included in optimisation while maintaining tractability. Through relevant case studies, we demonstrate the effectiveness of the proposed system-aware control for WTs, achieving over 8% system cost savings compared to a system-unaware controller.

The reduction in system inertia is creating an important market for frequency-containment Ancillary Services (AS) such as enhanced frequency response (e.g.,~provided by battery storage), traditional primary frequency response and inertia itself. This market presents an important difference with the energy-only market: while the need for energy production is driven by the demand from consumers, frequency-containment AS are procured because of the need to deal with the largest generation/demand loss in the system (or smaller losses that could potentially compromise frequency stability). Thus, a question that arises is: who should pay for frequency-containment AS? In this work, we propose a cost-allocation methodology based on the nucleolus concept, in order to distribute the total payments for frequency-containment AS among all generators or loads that create the need for these services. It is shown that this method complies with necessary properties for the AS market, such as avoidance of cross-subsidies and maintaining players in this cooperative game. Finally, we demonstrate its practical applicability through a case study for the Great Britain power system, while comparing its performance with two alternative mechanisms, namely proportional and Shapley value cost allocation.