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.

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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 (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.

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The massive integration of renewable-based distributed energy resources (DERs) inherently increases the energy system’s complexity, especially when it comes to defining its operational schedule. Deep reinforcement learning (DRL) algorithms arise as a promising solution due to their data-driven and model-free features. However, current DRL algorithms fail to enforce rigorous operational constraints (e.g., power balance, ramping up or down constraints) limiting their implementation in real systems. To overcome this, in this paper, a DRL algorithm (namely MIP-DQN) is proposed, capable of strictly enforcing all operational constraints in the action space, ensuring the feasibility of the defined schedule in real-time operation. This is done by leveraging recent optimization advances for deep neural networks (DNNs) that allow their representation as a MIP formulation, enabling further consideration of any action space constraints. Comprehensive numerical simulations show that the proposed algorithm outperforms existing state-of-the-art DRL algorithms, obtaining a lower error when compared with the optimal global solution (upper boundary) obtained after solving a mathematical programming formulation with perfect forecast information; while strictly enforcing all operational constraints (even in unseen test days).@en

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.

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This paper introduces an energy management system (EMS) aiming to minimize electricity operating costs using reinforcement learning (RL) with a linear function approximation. The proposed EMS uses a Q-learning with tile coding (QLTC) algorithm and is compared to a deterministic mixed-integer linear programming (MILP) with perfect forecast information. The comparison is performed using a case study on an industrial manufacturing company in the Netherlands, considering measured electricity consumption, PV generation, and wholesale electricity prices during one week of operation. The results show that the proposed EMS can adjust the prosumer's power consumption considering favorable prices. The electricity costs obtained using the QLTC algorithm are 99% close to those obtained with the MILP model. Furthermore, the results demonstrate that the QLTC model can generalize on previously learned control policies even in the case of missing data and can deploy actions 80% near to the MILP's optimal solution.@en

Taking advantage of their data-driven and model-free features, Deep Reinforcement Learning (DRL) algorithms have the potential to deal with the increasing level of uncertainty due to the introduction of renewable-based generation. To deal simultaneously with the energy systems’ operational cost and technical constraints (e.g, generation-demand power balance) DRL algorithms must consider a trade-off when designing the reward function. This trade-off introduces extra hyperparameters that impact the DRL algorithms’ performance and capability of providing feasible solutions. In this paper, a performance comparison of different DRL algorithms, including DDPG, TD3, SAC, and PPO, are presented. We aim to provide a fair comparison of these DRL algorithms for energy systems optimal scheduling problems. Results show DRL algorithms’ capability of providing in real-time good-quality solutions, even in unseen operational scenarios, when compared with a mathematical programming model of the energy system optimal scheduling problem. Nevertheless, in the case of large peak consumption, these algorithms failed to provide feasible solutions, which can impede their practical implementation.@en

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%.

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To guarantee a successful deployment of a droop-based control strategy to mitigate overvoltage problems caused by solar photovoltaic (PV) generation, Distribution System Operators (DSOs) will need to estimate the amount of active power curtailed by the PV inverters for billing purposes. This paper provides a structural elaboration on the development of data-driven approaches in Python to estimate the PV curtailed power as a provision of voltage support services by residential users using droop-based voltage control strategies. The use of the total input data, available for a DSO, would be impractical for an all-regression approach for the estimation of the PV curtailed power. Since in the majority of the data no active power is curtailed, the data-driven models would in this case partly be trained and fitted for situations where there is no active power curtailment. The regression models for the curtailed power prediction are therefore preceded by a classification model. The developed combined classification-regression model was able to estimate the PV curtailed power with an error of less than 4%, for test data from the network on which the model was trained.@en