Electrical grid congestion has emerged as an immense challenge in Europe, making the forecasting of load and its associated metrics increasingly crucial. Among these metrics, peak load is fundamental. Non-time-resolved models of peak load have their advantages of being simple and compact, and among them Velander's formula (VF) is widely used in distribution network planning. However, several aspects of VF remain inadequately addressed, including year-ahead prediction, scaling of customers, aggregation, and, most importantly, the lack of probabilistic elements. The present paper proposes a quantile interpretation of VF that enables VF to learn truncated cumulative distribution functions of peak loads with multiple quantile regression under non-crossing constraints. The evaluations on non-residential customer data confirmed its ability to predict peak load year ahead, to fit customers with a wide range of electricity consumptions, and to model aggregations of customers. A noteworthy finding is that for a given electricity consumption, aggregations of customers have statistically larger peak loads than a single customer.

Electrical grid congestion is a growing challenge in Europe, driving the need for accurate prediction of load, particularly of peak load. Non-time-resolved models of peak load offer the advantages of simplicity and compactness, and among them, Velander's formula (VF) is a traditional method that has been used for decades. Moreover, VF can be adapted into a quantile VF, which learns a truncated cumulative distribution function of peak load based on electricity consumption. This paper proposes a mathematical model based on extreme value theory to characterize the probability distribution of peak load for large non-residential customers. The model underpins the quantile VF as demonstrated through multiple quantile regression and reduces its representation to just four parameters without sacrificing predictive performance. Moreover, using maximum likelihood estimation and the likelihood ratio test, we validate that the probability distribution of peak load of analysed groups belongs to the heavy-tailed Fréchet class.

Ensuring electricity grid reliability becomes increasingly challenging with the shift towards renewable energy and declining conventional capacities. Distribution System Operators (DSOs) aim to achieve grid reliability by verifying the n-1 contingency criterion, ensuring reconfiguring and restoring power distribution through switching strategies. While DSOs operate radial grids, government regulations and reliability metrics, such as the average minutes without power, necessitate achieving continuity as closely as possible through reconfiguration. Despite the critical role of reliability assessment, current methods such as mathematical optimisation approaches are often computationally expensive and impractical for large-scale grids. This paper addresses these limitations by proposing a novel application of Graph Neural Networks (GNNs) to tackle the n-1 contingency criterion, directly leveraging the inherent graph structure of electrical networks. Unlike traditional machine learning methods, GNNs directly handle graph-structured data, making them well-suited for complex grid topologies. This study introduces a Graph Isomorphic Network (GIN)-inspired framework designed to incorporate both node and edge features, enabling amore comprehensive representation of grid assets and connectivity. The GIN-inspired framework not only generalises effectively to unseen grid structures but also significantly reduces computation times, demonstrating prediction times up to 1000 times faster compared to traditional optimisation-based approaches. These findings indicate that our approach provides a computationally efficient and scalable solution for DSOs, enhancing the reliability and operational efficiency of energy grid assessments, and opening up the way for more robust real-time contingency planning.

Reactive power plays a vital role in the stability and efficiency of electrical systems, yet it is often overlooked in favour of active power in grid management practices. Standard power factors are used which lead to inefficient grid usage at most locations and possible unnoticed reliability risks at a few exceptional spots. Here, we investigate the challenges of estimating reactive power for large-scale customers where direct measurements are limited or unavailable. Using a dataset comprising fifteen-minute resolution measurements of active and reactive power for approximately 3,000 Dutch large customers, we developed machine learning models with the aim to accurately estimate reactive power. Traditional methods, which rely on fixed power factor assumptions, often result in inefficient and conservative grid utilization. By integrating customer metadata and monthly reactive power totals, we investigated the use of different approaches, achieving a fourfold reduction in estimation error compared to standard methods. With a model using LightGBM the mean absolute error decreases 13% further. These findings highlight the potential of machine learning to improve reactive power estimation, optimize grid usage and enhance grid reliability.

In this paper we present novel methodology for automatic anomaly and switch event filtering to improve load estimation in power grid systems. By leveraging unsupervised methods with supervised optimization, our approach prioritizes interpretability while ensuring robust and generalizable performance on unseen data. Through experimentation, a combination of binary segmentation for change point detection and statistical process control for anomaly detection emerges as the most effective strategy, specifically when ensembled in a novel sequential manner. Results indicate the clear wasted potential when filtering is not applied. The automatic load estimation is also fairly accurate, with approximately 90% of estimates falling within a 10% error margin, with only a single significant failure in both the minimum and maximum load estimates across 60 measurements in the test set. Our methodology’s interpretability makes it particularly suitable for critical infrastructure planning, thereby enhancing decision-making processes.

Ensuring electricity grid reliability becomes increasingly challenging with the shift towards renewable energy and declining conventional capacities. Distribution System Operators (DSOs) aim to achieve grid reliability by verifying the n-1 principle, ensuring continuous operation in case of component failure. Electricity networks' complex graph-based data holds crucial information for n-1 assessment: graph structure and data about stations/cables. Unlike traditional machine learning methods, Graph Neural Networks (GNNs) directly handle graph-structured data. This paper proposes using Graph Isomorphic Networks (GINs) for n-1 assessments in medium voltage grids. The GIN framework is designed to generalise to unseen grids and utilise graph structure and data about stations/cables. The proposed GIN approach demonstrates faster and more reliable grid assessments than a traditional mathematical optimisation approach, reducing prediction times by approximately a factor of 1000. The findings offer a promising approach to address computational challenges and enhance the reliability and efficiency of energy grid assessments.

Identifying future congestion points in electricity distribution networks is an important challenge distribution system operators face. A proven approach for addressing this challenge is to assess distribution grid adequacy using probabilistic models of future demand. However, computational cost can become a severe challenge when evaluating large probabilistic electricity demand forecasting models with long forecasting horizons. In this paper, Monte Carlo methods are developed to increase the computational efficiency of obtaining asset overload probabilities from a bottom-up stochastic demand model. Cross-entropy optimised importance sampling is contrasted with conventional Monte Carlo sampling. Benchmark results of the proposed methods suggest that the importance sampling-based methods introduced in this work are suitable for estimating rare overload probabilities for assets with a small number of customers.

Since the volatility of the power load is expected to keep increasing due to new energy technologies, modelling the stochastic properties of the power loads becomes increasingly important for distribution network operators. Due to limited measurements in these grids, often bottom-up methods are used to create load estimations with which the peak load of the power customers is calculated. However, in average electricity consumption profiles, as used in most bottom-up methods, the stochastic behaviour of the customers energy consumption is neglected. In this study, the effect of neglecting the stochastic behaviour is investigated and is shown to be particularly strong in situations with a low number of consumers. To cope with this problem, several efficient methods to quantify the uncertainty and to determine peak loads have been evaluated. These methods were applied and validated on a data set with nearly thousand consumer measurement series, measured over 3.5 years on a 15 min resolution. In low-voltage networks with <10 power consumers, the conventional methods are shown to be at least a factor 2 too low. The suggested ‘individual rescaling method’ is accurate within 10%.

An aging asset population and a less predictable volatile electricity consumption and production pattern urge DSOs to get insight in the condition of their medium voltage (MV) and low voltage (LV) networks. Because visual inspections of underground networks are impossible and the number of measurements is still very limited, this paper proposes a method to rank underground assets by looking for trends and patterns in historical outages with help of Machine Learning methods. Nine years of outages of MV and LV cables and joints in the network of a large Dutch DSO are analysed. A model is developed that couples each outage to the asset most probable responsible. Twenty-two different datasets are coupled with the asset database, ranging from load estimates of the asset to distance-to-a-railway. Each set could contain data that explains or correlates to some of the outages. Several Machine Learning techniques are benchmarked. The final model, created by the Random Forest algorithm, is applied to rank current assets. It is operational to determine the positioning of an online monitoring system in the DSO's MV network.

Fast escape of charged particles due to the presence of large magnetic islands limits the performance of modern tokamaks, toroidally-shaped fusion-energy devices. Magnetic islands are closed magnetic fieldline topologies that form in a fusion plasma because of magnetic reconnection. When magnetic islands grow in size, they are commonly called neoclassical tearing modes (NTMs) by plasma physicists. The theoretical work that describes the growth-rate of NTMs is called the generalized Rutherford equation (GRE). The GRE assumes that in the poloidal coordinate the perturbation of the helical flux, responsible for the generation of the magnetic island, can be described by a single Fourier mode. In this work, we developed a two-dimensional MHD simulation to test this assumption of the GRE. The goal is to produce a clear understanding of the plasma effects internal to the magnetic island that are neglected in the GRE. To develop a simulation relevant to tokamak plasma conditions that also successfully produces magnetic islands, we must formulate new boundary conditions. The formulation of these boundary conditions is a significant step forward for this type of simulation, and was not theoretically clear from the beginning of this work. We describe in detail the options and consequences of these boundary conditions on the plasma, and present the results of a benchmarking study performed with the code. We discuss possible future extensions to the code to investigate the localized character of a non-inductive current, which could be added to the simulation to suppress growing magnetic islands.