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In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore \gls{cpu} and \gls{gpu} parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the practical operational point, which is the solution of high-voltage and low-current. The proof is validated using numerical simulations showing the robustness of the FPI algorithm compared to the classical \gls{nr} approach. In the case study, a benchmark with different PF solution methods is performed, showing that for applications requiring a yearly simulation at 1-minute resolution the computation time is decreased by a factor of 164, compared to the NR in its sparse formulation.

Accurate and efficient power flow (PF) analysis is crucial in modern electrical networks' operation and planning. Therefore, there is a need for scalable algorithms that can provide accurate and fast solutions for both small and large scale power networks. As the power network can be interpreted as a graph, Graph Neural Networks (GNNs) have emerged as a promising approach for improving the accuracy and speed of PF approximations by exploiting information sharing via the underlying graph structure. In this study, we introduce PowerFlowNet, a novel GNN architecture for PF approximation that showcases similar performance with the traditional Newton-Raphson method but achieves it 4 times faster in the simple IEEE 14-bus system and 145 times faster in the realistic case of the French high voltage network (6470rte). Meanwhile, it significantly outperforms other traditional approximation methods, such as the DC relaxation method, in terms of performance and execution time; therefore, making PowerFlowNet a highly promising solution for real-world PF analysis. Furthermore, we verify the efficacy of our approach by conducting an in-depth experimental evaluation, thoroughly examining the performance, scalability, interpretability, and architectural dependability of PowerFlowNet. The evaluation provides insights into the behavior and potential applications of GNNs in power system analysis., Comment: 10 pages, 7 figures

This paper introduces a stochastic AC-OPF (SOPF) for the flexibility management of electric vehicle (EV) charging pools in distribution networks under uncertainty. The SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks. An application of the proposed SOPF is described where a distribution system operator (DSO) requires flexibility to each charging pool in a day-ahead time frame, minimizing the cost for flexibility while guaranteeing technical limits. Flexibility areas are defined for each charging pool and calculated as a function of a risk parameter involving the solution's uncertainty. Results show that all players can benefit from this approach, i.e., the DSO obtains a risk-aware solution, while charging pools/tasks perceive a reduction in the total energy payment due to flexibility services.

Compensation mechanisms are used to counterbalance the discomfort suffered by users due to quality service issues. Such mechanisms are currently used for different purposes in the electrical power and energy sector, e.g., power quality and reliability. This paper proposes a compensation mechanism using EV flexibility management of a set of charging sessions managed by a charging point operator (CPO). Users' preferences and bilateral agreements with the CPO are modelled via discrete utility functions for the energy not served. A mathematical proof of the proposed compensation mechanism is given and applied to a test scenario using historical data from an office building with a parking lot in the Netherlands. Synthetic data for 400 charging sessions was generated using multivariate elliptical copulas to capture the complex dependency structures in EV charging data. Numerical results validate the usefulness of the proposed compensation mechanism as an attractive measure both for the CPO and the users in case of energy not served.