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.

As the adoption of electric vehicles (EVs) accelerates, addressing the challenges of large-scale, city-wide optimization becomes critical in ensuring efficient use of charging infrastructure and maintaining electrical grid stability. This study introduces EV-GNN, a novel graph-based solution that addresses scalability challenges and captures uncertainties in EV behavior from a Charging Point Operator’s (CPO) perspective. We prove that EV-GNN enhances classic Reinforcement Learning (RL) algorithms’ scalability and sample efficiency by combining an end-to-end Graph Neural Network (GNN) architecture with RL and employing a branch pruning technique. We further demonstrate that the proposed architecture’s flexibility allows it to be combined with most state-of-the-art deep RL algorithms to solve a wide range of problems, including those with continuous, multi-discrete, and discrete action spaces. Extensive experimental evaluations show that EV-GNN significantly outperforms state-of-the-art RL algorithms in scalability and generalization across diverse EV charging scenarios, delivering notable improvements in both small- and large-scale problems.

The optimal dispatch of energy storage systems (ESSs) in distribution networks poses significant challenges, primarily due to uncertainties of dynamic pricing, fluctuating demand, and the variability inherent in renewable energy sources. By exploiting the generalization capabilities of deep neural networks (DNNs), the deep reinforcement learning (DRL) algorithms can learn good-quality control models that adapt to the stochastic nature of distribution networks. Nevertheless, the practical deployment of DRL algorithms is often hampered by their limited capacity for satisfying operational constraints in real time, which is a crucial requirement for ensuring the reliability and feasibility of control actions during online operations. This paper introduces an innovative framework, named mixed-integer programming based deep reinforcement learning (MIP-DRL), to overcome these limitations. The proposed MIP-DRL framework can rigorously enforce operational constraints for the optimal dispatch of ESSs during the online execution. This framework involves training a Q-function with DNNs, which is subsequently represented in a mixed-integer programming (MIP) formulation. This unique combination allows for the seamless integration of operational constraints into the decision-making process. The effectiveness of the proposed MIP-DRL framework is validated through numerical simulations, demonstrating its superior capability to enforce all operational constraints and achieve high-quality dispatch decisions and showing its advantage over existing DRL algorithms.

Deep Reinforcement Learning (DRL) presents a promising avenue for optimizing Energy Storage Systems (ESSs) dispatch in distribution networks. This paper introduces RL-ADN, an innovative open-source library specifically designed for solving the optimal ESSs dispatch in active distribution networks. RL-ADN offers unparalleled flexibility in modeling distribution networks, and ESSs, accommodating a wide range of research goals. A standout feature of RL-ADN is its data augmentation module, based on Gaussian Mixture Model and Copula (GMC) functions, which elevates the performance ceiling of DRL agents, achieving an average performance improvement of 21.43%, 1.08%, 2.76%, by augmenting five-year, one-year and three-month data, respectively. Additionally, RL-ADN incorporates the Tensor Power Flow solver, significantly reducing the computational burden of power flow calculations during training without sacrificing accuracy, maintaining voltage magnitude with an average error not exceeding 0.0001%. The effectiveness of RL-ADN is demonstrated using distribution networks with size varying, showing marked performance improvements in the adaptability of DRL algorithms for ESS dispatch tasks. Furthermore, RL-ADN achieves a tenfold increase in computational efficiency during training, making it highly suitable for large-scale network applications. The library sets a new benchmark in DRL-based ESSs dispatch in distribution networks and it is poised to advance DRL applications in distribution network operations significantly. RL-ADN is available at: https://github.com/ShengrenHou/RL-ADN and https://github.com/distributionnetworksTUDelft/RL-ADN.

The integration of distributed energy resources (DERs) has escalated the challenge of voltage magnitude regulation in distribution networks. Model-based approaches, which rely on complex sequential mathematical formulations, cannot meet the real-time demand. Deep reinforcement learning (DRL) offers an alternative by utilizing offline training with distribution network simulators and then executing online without computation. However, DRL algorithms fail to enforce voltage magnitude constraints during training and testing, potentially leading to serious operational violations. To tackle these challenges, we introduce a novel safe-guaranteed reinforcement learning algorithm, the DistFlow safe reinforcement learning (DF-SRL), designed specifically for real-time voltage magnitude regulation in distribution networks. The DF-SRL algorithm incorporates a DistFlow linearization to construct an expert-knowledge-based safety layer. Subsequently, the DF-SRL algorithm overlays this safety layer on top of the agent policy, recalibrating unsafe actions to safe domains through a quadratic programming formulation. Simulation results show the DF-SRL algorithm consistently ensures voltage magnitude constraints during training and real-time operation (test) phases, achieving faster convergence and higher performance, which differentiates it apart from (safe) DRL benchmark algorithms.

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.

Residential load profiles (RLPs) play an increasingly important role in the optimal operation and planning of distribution systems, particularly with the rising integration of low-carbon energy resources such as PV systems, electric vehicles, small-scale batteries, etc. Despite the prevalence of various data-driven models for generating consumption profiles, there is a lack of clear conclusions about their relative strengths and weaknesses. This study undertakes a comprehensive comparison of frequently used data-driven models in recent research, including Generative Adversarial Networks (GANs), Variational Autoencoders (VAE), Wasserstein GANs (WGAN), WGANs with Gradient Penalty (WGANGP), Gaussian Mixture Models (GMMs), and Gaussian Mixture Copulas (GMC). The presented comparison explores the effectiveness of the above-mentioned models on transformer- and consumer-level consumption profiles, as well as for different time resolutions (15-min, 30-min, and 60-min). The objective of this research is to elucidate the respective advantages and drawbacks of these models, thereby providing valuable insights for subsequent research in this field.

Reinforcement Learning (RL) has emerged as a promising solution for defining the optimal dispatch of Energy Storage Systems (ESS) in distributed energy systems. However, a notable gap exists in the literature: a lack of comprehensive and fair comparisons between different RL algorithms, particularly between linear and nonlinear approaches. This study critically evaluates the trade-offs between computational efficiency and operational accuracy among various Linear RL (LRL) strategies and compares them against the nonlinear Deep-Q-Network (DQN) algorithm. Through a comprehensive analysis, this study benchmarks the model-based Mixed-Integer Linear Programming (MILP) results to assess and compare these algorithms' convergence, training efficiency, and optimization accuracy. Results indicate that while LRL approaches the operational cost accuracy of DQN, it faces significant trade-offs in computational efficiency and struggles with generalization across larger and varied datasets. The results illuminate critical areas for further development in LRL methodologies, particularly in enhancing their adaptability and generalization capabilities.

This article proposes a framework to identify, visualize, and quantify risk of potential over/under voltage due to annual energy consumption and PV generation growth. The stochastic modeling considers the following: (i) Active and reactive power profiles for distribution transformers, dependent on annual energy consumption and activity in the serviced areas. (ii) Variable solar irradiance profiles that allow a broader range of PV generation scenarios for sunny, overcast, and cloudy days. The proposed framework uses multivariate-t copulas to model temporal correlations between random variables to generate synthetic scenarios. A probabilistic power flow is computed using the generated scenarios to define critical static operating regions. Results show that classical approaches may underestimate the maximum PV capacity of distribution networks when local irradiance conditions are not considered. Moreover, it is found that including annual energy consumption growth is critical to establishing realistic PV installation capacity limits. Finally, a sensitivity analysis shows that taking a 5% of overvoltage risk could increase up to 15% of the PV installed capacity limits.

The operation of a community energy storage system (CESS) is challenging due to the volatility of photovoltaic distributed generation, electricity consumption, and energy prices. Selecting the optimal CESS setpoints during the day is a sequential decision problem under uncertainty, which can be solved using dynamic learning methods. This paper proposes a reinforcement learning (RL) technique based on temporal difference learning with eligibility traces (ET). It aims to minimize the day-ahead energy costs while maintaining the technical limits at the grid coupling point. The performance of the RL is compared against an oracle based on a deterministic mixed-integer second-order constraint program (MISOCP). The use of ET boosts the RL agent learning rate for the CESS operation problem. The ET effectively assigns credit to the action sequences that bring the CESS to a high state of charge before the peak prices, reducing the training time. The case study shows that the proposed method learns to operate the CESS effectively and ten times faster than common RL algorithms applied to energy systems such as Tabular Q-learning and Fitted-Q. Also, the RL agent operates the CESS 94% near the optimal, reducing the energy costs for the end-user up to 12%.