This paper investigates the impact of adaptive activation functions on deep learning-based power flow analysis. Specifically, it compares four adaptive activation functions with state-of-the-art activation functions, i.e., ReLU, LeakyReLU, Sigmoid, and Tanh, in terms of loss function error, convergence speed, and learning process stability, using a real-world distribution network dataset. Results indicate that the proposed adaptive activation functions improve learning capability over state-of-the-art activation functions. Notably, adaptive ReLU activation shows the most improved learning process, with convergence speed up to twice as fast as ReLU. Adaptive Sigmoid and Tanh activation functions exhibit superior performance in terms of loss function error, outperforming ReLU and LeakyReLU by up to two orders of magnitude. Furthermore, the proposed adaptive activation functions lead to smoother and more stable learning processes, especially during early training, improving convergence. The practical implications of this study include the potential application of these adaptive activation functions in distribution network modeling, forecasting, and control, leading to more accurate and reliable power system operation.

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The heterogeneous distribution of frequency support from dispersed renewable generation sources results in varying inertia within the system. The effects of disturbances exhibit non-uniform variations contingent upon the disturbance's location and the affected region's topology and inertia. A screening method for inertia-zone identification is proposed considering the combination of network structure and generator inertia distribution that will aid in comprehending the response of nodes to disturbances. The nodes' dynamic nodal weight (DNW) is defined using maximal entropy random walk that defines each node's spreading power dynamics. Further, a modified weighted kmeans++ clustering technique is proposed using DNW to obtain the equivalent spatial points of each zone and the system to parameterize the inertia status of each zone. The impact of the proposed scheme is justified by simulating a modified IEEE 39 bus system with doubly-fed induction generator (DFIG) integration in the real-time digital simulator.

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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 IEEE 14-bus system and 48 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 power flow, 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.

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Under new EU regulation, as of 2035 all new cars and vans registered in the EU are set to be zero-emission. This ambitious target will be an important driver for a large-scale rollout of e-mobility across European cities. To ensure the successful planning of the energy infrastructure and optimized operation of the expanding e-mobility systems, smart and robust tools will be in high demand for various stakeholders, such as industry, city planners, or researchers. As part of the EU-funded research and innovation project DriVe2X, an interactive open-source prediction tool for Vehicle-to-Grid (V2G) operation and planning has been conceptualized and is under development. The main functions of this tool are the prediction of energy balance and flexibility at the public charging station level for a day-ahead operation and providing useful customized analytics for long-term planning purposes.@en

This paper explores the potential application of quantum and hybrid quantum–classical neural networks in power flow analysis. Experiments are conducted using two datasets based on 4-bus and 33-bus test systems. A systematic performance comparison is also conducted among quantum, hybrid quantum–classical, and classical neural networks. The comparison is based on (i) generalization ability, (ii) robustness, (iii) training dataset size needed, (iv) training error, and (v) training process stability. The results show that the developed hybrid quantum–classical neural network outperforms both quantum and classical neural networks, and hence can improve deep learning-based power flow analysis in the noisy-intermediate-scale quantum (NISQ) and fault-tolerant quantum (FTQ) era.@en

The power generation and consumption of distributed energy resources (DERs) offer significant flexibility potential, which can be utilized to provide services such as peak and frequency regulation. DERs introduce a vast number of variables and constraints, making it complicated to directly integrate them into upper-level dispatch. To address this challenge, virtual power plants (VPPs) emerge, which treat diverse DERs as a collective entity and use aggregated flexibility envelopes to reduce the variable and constraint scale, facilitating upper-level optimization. In VPPs, unified DER modeling and efficient DER aggregation play a crucial role but are challenging. This paper first introduces a novel unified polytope model to represent heterogenous DERs' flexibility region. A coordination transformation is utilized to eliminate redundant variable dimensions and maintain DERs' interface characteristics. A sample-based projection method is then developed, further removing all state variables, resulting in a unified flexibility region. This method is then utilized to calculate the Minkowski sums of individual flexibility polytopes for aggregation. The results of numerical tests demonstrate a considerable reduction in computation time and maintain satisfactory accuracy when the proposed modeling and aggregation approach is adopted.

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Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave’s Advantage™ quantum annealer, Fujitsu’s digital annealer V3, D-Wave’s quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.@en

This work seeks to reduce the severity of congestion in the medium voltage (MV) cyber-physical systems (CPES) by optimising the network topology in line with seasonal variations in the supply and demand of electricity. To this aim a two-stage reconfiguration algorithm is proposed. In the first stage, the positions of the normally open switches within the network are optimised in to adjust the power flow therein. These optimised positions are subsequently used in the second stage to calculate the network variables. The first stage is implemented as a mixed-integer linear program (MILP) optimisation in Python, whereas the second stage consists of a Newton-Raphson calculation in DIgSILENT PowerFactory software package. The benefit of network reconfiguration is that it is a short-term and low-cost solution which can be implemented by a distribution system operator (DSO) without relying on other external parties. The presented case study addresses the need of seasonal reconfigurations to accommodate for the manual operation of the switches present within a synthetic model of MV CPES, which is implemented inspired from CPES in the Netherlands. The application of the algorithm significantly reduces the frequency by which reconfiguration actions can be performed. Furthermore, the algorithm is able to consistently reduce congestion within the analysed synthetic CPES, completely removing it or reducing its severity. It also outperforms two alternative optimisation options implemented in PowerFactory with regard to the objective function value. Those being an iterative exploration of meshes and a genetic algorithm.

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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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Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and (ii) an adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (iii) a scalability study of the AQPF algorithm; and (iv) an extension of the AQPF algorithm for larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave’s Advantage™ quantum annealer, Fujitsu’s digital annealer V3, D-Wave’s quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.@en

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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A photovoltaic (PV)-rich low-voltage (LV) distribution network poses a limit on the export power of PVs due to the voltage magnitude constraints. By defining a customer export limit, switching off the PV inverters can be avoided, and thus reducing power curtailment. Based on this, this paper proposes a mixed-integer nonlinear programming (MINLP) model to define such optimal customer export. The MINLP model aims to minimize the total PV power curtailment while considering the technical operation of the distribution network. First, a nonlinear mathematical formulation is presented. Then, a new set of linearizations approximating the Euclidean norm is introduced to turn the MINLP model into an MILP formulation that can be solved with reasonable computational effort. An extension to consider multiple stochastic scenarios is also presented. The proposed model has been tested in a real LV distribution network using smart meter measurements and irradiance profiles from a case study in the Netherlands. To assess the quality of the solution provided by the proposed MILP model, Monte Carlo simulations are executed in OpenDSS, while an error assessment between the original MINLP and the approximated MILP model has been conducted.@en

With a growing share of electric vehicles (EVs) in our distribution grids, the need for smart charging becomes indispensable to minimise grid reinforcement. To circumvent the associated capacity limitations, this paper evaluates the effectiveness of different levels of network constraints and different dynamic tariffs, including a dynamic network tariff. A detailed optimisation model is first developed for public charging electric vehicles in a representative Dutch low voltage (LV) distribution network, susceptible to congestion and voltage problems by 2050 without smart charging of EVs. Later, a detailed reflection is made to assess the influence of the modelled features on the distribution system operator (DSO), charge point operator (CPO) costs, and the EVs' final state-of-charge (SOC) for both mono- (V1G) and bi-directional (V2G) charging. Results show that the dynamic network tariff outperforms other flat tariffs by increasing valley-filling. Consequently, compared to regular day-ahead pricing, a significant reduction in the frequency of congestion in the lines is achieved. In addition, V2G ensures the joint optimum for different stakeholders causing adequate EV user satisfaction, decreased CPO costs compared to conventional charging and fewer violations of grid constraints for the DSOs.

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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

This paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newton-like iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch R/X ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm.@en

With the enforcement of governmental regulations and incentives, the share of electric vehicles (EVs) in the mobility sector is on the rise, impacting significantly the grid and its operation. This paper aims to investigate and find solutions to mitigate the impacts of EV charging on Dutch residential grids, namely the impacts of voltage magnitude regulation and distribution transformer loading. This paper proposes a decentralized coordinated charging strategy with local voltage control at its essence. The proposed charging strategy effectively allocates the charging power by prioritizing users based on their current State-of-Charge (SOC) and/or Time of Departure (ToD), or the current loading on the distribution transformer. These parameters are communicated to the charge controller through an Internet-of-Things (IoT) platform. The proposed charging strategy was simulated on a real Dutch residential grid that serves 86 household users, assuming every household has its own controllable EV charger. Based on the obtained results, the proposed charging strategy has eliminated all voltage magnitude violations, reduced the loading on the distribution transformer, while also achieving a SOC that is 2.5% less than that of the uncontrolled charging strategy.@en

Door middel van een zo representatief mogelijk rekenmodel voor het middenspanningsnet van de Amsterdamse gebieden Buiksloterham-Zuid/Overhoeks (BZOH), heeft het onderzoeksteam een detailanalyse kunnen uitvoeren naar de verwachte leveringscongestie in dit gebied zoals aangekondigd door Liander op 24 juni 2021. De detailanalyse laat een grootschalige toename in elektriciteitsverbruik in 3 jaar tijd zien, voornamelijk vanwege de stedelijke ontwikkeling in Overhoeks. Uit de beperkte beschikbare data en de resultaten uit het rekenmodel blijkt dat deze toename in vermogensvraag in het middenspanningsnet boven de normale beleidsgrenzen komt totdat de realisatie van de geplande netuitbreiding halverwege 2023 gereed is. De capaciteit is vooral ontoereikend in storings- en/of onderhoudssituaties, ook wel verschakelde toestand genoemd, in bepaalde delen van het netwerk. De studie laat zien dat het effectief verschakelen van het netwerk door Liander een groot deel van het capaciteitsprobleem vermindert. Er bestaan meerdere mogelijkheden om de configuratie van het net aan te passen om zowel in normaal bedrijf als in storings- en/of onderhoudssituaties belastingen beter in het netwerk te kunnen integreren. Een optimale netwerktopologie is daarom noodzakelijk om capaciteit vrij te spelen. In combinatie met een alternatieve reservestelling voor storing en onderhoud (t.o.v. de huidige reservecapaciteit in het netwerk) blijkt dat kritieke netsituaties voorkomen kunnen worden. Om tot een kosteneffectieve en uitvoerbare inschatting te komen voor de dimensionering en locatie van de alternatieve reservestelling, is het detailniveau van netanalyse cruciaal en is voor het toepassen van een alternatieve reservestelling in BZOH een kalibratie van deze studie door Liander noodzakelijk. Daarbij kan de detailanalyse inzichten bieden om in tijden van congestie het overschrijden van de normale beleidsgrenzen omtrent kabelbelasting tijdelijk toe te staan onder de veilige omstandigheden. Op basis van de resultaten uit deze studie zijn deze opties voor reservestelling vanuit energetisch perspectief kansrijk voor BZOH, zonder een verdere uitwerking te bieden voor implementatie.@en

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