Power-to-gas (P2G) systems can provide multifaceted services within Multi-Energy Systems (MES) beyond traditional roles. When strategically deployed, P2G systems can mitigate congestion in the electricity grid, advance the heat transition through the utilization of their waste heat, and optimize the usage of existing gas grids. This research introduces a joint operations and planning model for P2G facilities, including the expansion of electricity, gas, and heat distribution systems. The model is formulated as a mixed integer second order cone program (MISOCP). It incorporates the variable efficiency of electrolyzers and a detailed representation of the electrolyzer waste heat extraction system (EHES), addressing spatial, temporal, and temperature mismatches between heat demand and supply. The model is demonstrated on a 22-node interconnected electricity–gas test network and a 95-node real-world electricity–gas network in the Netherlands. Results reveal tradeoffs in alleviating congestion in the electricity grid, preventing congestion in the gas grid, and maximizing waste heat sales. Optimally distributed P2G reduced congestion in the electricity distribution grid, but induced congestion in the gas distribution grid. Future research should focus on managing such Active Gas Distribution Networks (AGDNs) with distributed P2G and finding a balance between the benefits and challenges of P2G deployment in MES.

This article presents the theoretical and practical foundation of a spherical lower dimensional representation for daily medium voltage load profiles, based on principal component analysis. The objective is to unify and simplify the tasks for (i) clustering visualisation, (ii) outlier detection and (iii) generative profile modelling under one concept. The lower dimensional projection of standardised MV load profiles unveils a latent distribution in a three-dimensional sphere. This spherical structure allows us to detect outliers by fitting probability distribution models in the spherical coordinate system, identifying measurements that deviate from the spherical shape. The same latent distribution exhibits an arc shape, suggesting an underlying order among load profiles. We develop a principal curve technique to uncover this order based on similarity, offering new advantages over conventional clustering techniques. This finding reveals that energy consumption in a wide region can be seen as a continuously changing process. Furthermore, we combined the principal curve with a von Mises-Fisher distribution to create a model capable of generating profiles with continuous mixtures between clusters. The presence of the spherical distribution is validated with data from four municipalities in the Netherlands. The uncovered spherical structure implies the possibility of employing new mathematical tools from directional statistics and differential geometry for load profile modelling.

In response to increasing grid congestion in the Netherlands, non-firm connection and transport agreements (CTAs) and capacity restriction contracts (CRCs) have been introduced, allowing consumer curtailment in exchange for grid tariff discounts or per-MW compensations. This study examines the interaction between an electrolyzer project, facing sizing and contracting decisions, and a network operator, responsible for contract activations and determining grid connection capacity, under the new Dutch regulations. The interaction is modeled using two bilevel optimization problems with alternating leader-follower roles. Results highlight a trade-off between CRC income and non-firm CTA tariff discounts, showing that voluntary congestion management by the network operator increases electrolyzer profitability at CRC prices below €10/MW but reduces it at higher prices. Furthermore, the network operator benefits more from reacting to the electrolyzer owner's CTA decisions than from leading the interaction at CRC prices above €10/MW. Ignoring the other party's optimization problem overestimates profits for both the network operator and the electrolyzer owner, emphasizing the importance of coordinated decision-making.

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 (PFs) in distribution systems. The presented algorithms are the base for a new TensorPowerFlow (TPF) tool and shine for their simplicity, benefiting from multicore Central processing unit (CPU) and Graphics processing unit (GPU) parallelization. We also focus on the mathematical convergence properties of the algorithm, showing that its unique solution is at the practical operational point. The proof is validated using numerical simulations showing the robustness of the FPI algorithm compared to the classical Newton–Raphson (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. Finally, a set of applications is described, highlighting the potential of the proposed formulations over a wide range of analyses in distribution systems.