Peter Palensky

Neda Vahabzad, Kenneth Bruninx, Peter Palensky et al.

The growing penetration of distributed energy resources (DERs) intensifies congestion in distribution networks by introducing bidirectional power flows and increasing competition for limited network capacity, underscoring the need for effective and efficient congestion management, including flexible grid-access schemes. This paper proposes a bilevel optimization model for the dynamic allocation of connection capacity to DERs under non-firm connection agreements, aligning the objectives of distribution system operator (DSO) and DER owners. The upper-level problem, representing the DSO, determines the allocated connection capacity for all DERs, defined as maximum time-varying power limits, subject to distribution system constraints and the last-in-first-out (LIFO) allocation rule. The lower-level problem, representing DER owners, maximizes the profit of each DER within the allocated power limits. The proposed model is tested on a modified CIGRE medium-voltage (MV) network, demonstrating a balanced trade-off between grid utilization and economic efficiency. Furthermore, the model enhances DER integration, enforces transparent allocation rules, reduces variability in allocation patterns, and achieves up to an 80% reduction in total curtailment costs compared with benchmark methods.

Zeynab Kaseb, Rahul Rane, Aleksandra Lekic et al.

Quantum computing has emerged as a promising computational paradigm to address unresolved challenges in the modeling and control of modern power systems. However, most existing studies focus on offline simulations, and a practical framework for validating quantum algorithms in real-time operational environments remains lacking. This study proposes a quantum hardware-in-the-loop framework that integrates a real-time digital simulator with quantum and quantum-inspired hardware to solve combinatorial power flow and optimal power flow formulations under dynamic operating conditions. The proposed framework is validated using the IEEE 9-bus test system and a modified version with integrated solar and wind farms. The results confirm successful integration and convergence within a predefined tolerance. The study also identifies key limitations and challenges, such as limited access to quantum and digital annealers and current scalability limitations, that must be considered in future developments. Nevertheless, the results highlight the potential of quantum computing to significantly enhance the modeling and control of future power systems with high penetration of renewable energy sources.

Cornelius Steinbrink, Sebastian Lehnhoff, Sebastian Rohjans et al.

Smart grid systems are characterized by high complexity due to interactions between a traditional passive network and active power electronic components, coupled using communication links. Additionally, automation and information technology plays an important role in order to operate and optimize such cyber-physical energy systems with a high(er) penetration of fluctuating renewable generation and controllable loads. As a result of these developments the validation on the system level becomes much more important during the whole engineering and deployment process, today. In earlier development stages and for larger system configurations laboratory-based testing is not always an option. Due to recent developments, simulation-based approaches are now an appropriate tool to support the development, implementation, and roll-out of smart grid solutions. This paper discusses the current state of simulation-based approaches and outlines the necessary future research and development directions in the domain of power and energy systems.

Arjen A. van der Meer, Peter Palensky, Kai Heussen et al.

The gradual deployment of intelligent and coordinated devices in the electrical power system needs careful investigation of the interactions between the various domains involved. Especially due to the coupling between ICT and power systems a holistic approach for testing and validating is required. Taking existing (quasi-) standardised smart grid system and test specification methods as a starting point, we are developing a holistic testing and validation approach that allows a very flexible way of assessing the system level aspects by various types of experiments (including virtual, real, and mixed lab settings). This paper describes the formal holistic test case specification method and applies it to a particular co-simulation experimental setup. The various building blocks of such a simulation (i.e., FMI, mosaik, domain-specific simulation federates) are covered in more detail. The presented method addresses most modeling and specification challenges in cyber-physical energy systems and is extensible for future additions such as uncertainty quantification.

Thomas I. Strasser, Cyndi Moyo, Roland Bründlinger et al.

Renewables are key enablers in the plight to reduce greenhouse gas emissions and cope with anthropogenic global warming. The intermittent nature and limited storage capabilities of renewables culminate in new challenges that power system operators have to deal with in order to regulate power quality and ensure security of supply. At the same time, the increased availability of advanced automation and communication technologies provides new opportunities for the derivation of intelligent solutions to tackle the challenges. Previous work has shown various new methods of operating highly interconnected power grids, and their corresponding components, in a more effective way. As a consequence of these developments, the traditional power system is being transformed into a cyber-physical energy system, a smart grid. Previous and ongoing research have tended to mainly focus on how specific aspects of smart grids can be validated, but until there exists no integrated approach for the analysis and evaluation of complex cyber-physical systems configurations. This paper introduces integrated research infrastructure that provides methods and tools for validating smart grid systems in a holistic, cyber-physical manner. The corresponding concepts are currently being developed further in the European project ERIGrid.

Shengren Hou, Shuyi Gao, Weijie Xia et al.

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. Additionally, RL-ADN incorporates the Laurent power flow solver, significantly reducing the computational burden of power flow calculations during training without sacrificing accuracy. The effectiveness of RL-ADN is demonstrated using in different sizes of distribution networks, showing marked performance improvements in the adaptability of DRL algorithms for ESS dispatch tasks. This enhancement is particularly beneficial from the increased diversity of training scenarios. 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.

Panos Kotsampopoulos, Nikos Hatziargyriou, Thomas I. Strasser et al.

Traditional power systems education and training is flanked by the demand for coping with the rising complexity of energy systems, like the integration of renewable and distributed generation, communication, control and information technology. A broad understanding of these topics by the current/future researchers and engineers is becoming more and more necessary. This paper identifies educational and training needs addressing the higher complexity of intelligent energy systems. Education needs and requirements are discussed, such as the development of systems-oriented skills and cross-disciplinary learning. Education and training possibilities and necessary tools are described focusing on classroom but also on laboratory-based learning methods. In this context, experiences of using notebooks, co-simulation approaches, hardware-in-the-loop methods and remote labs experiments are discussed.

Hou Shengren, Edgar Mauricio Salazar, Pedro P. Vergara et al.

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.

Sohail Khan, Mohsin Shahzad, Usman Habib et al.

The potential of demand side as a frequency reserve proposes interesting opportunity in handling imbalances due to intermittent renewable energy sources. This paper proposes a novel approach for computing the parameters of a stochastic battery model representing the aggregation of Thermostatically Controlled Loads (TCLs). A hysteresis based non-disruptive control is used using priority stack algorithm to track the reference regulation signal. The parameters of admissible ramp-rate and the charge limits of the battery are dynamically calculated using the information from TCLs that is the status (on/off), availability and relative temperature distance till the switching boundary. The approach builds on and improves on the existing research work by providing a straight-forward mechanism for calculation of stochastic parameters of equivalent battery model. The effectiveness of proposed approach is demonstrated by a test case having a large number of residential TCLs tracking a scaled down real frequency regulation signal.

Weijie Xia, Gao Peng, Chenguang Wang et al.

Electricity Consumption Profiles (ECPs) are crucial for operating and planning power distribution systems, especially with the increasing numbers of various low-carbon technologies such as solar panels and electric vehicles. Traditional ECP modeling methods typically assume the availability of sufficient ECP data. However, in practice, the accessibility of ECP data is limited due to privacy issues or the absence of metering devices. Few-shot learning (FSL) has emerged as a promising solution for ECP modeling in data-scarce scenarios. Nevertheless, standard FSL methods, such as those used for images, are unsuitable for ECP modeling because (1) these methods usually assume several source domains with sufficient data and several target domains. However, in the context of ECP modeling, there may be thousands of source domains with a moderate amount of data and thousands of target domains. (2) Standard FSL methods usually involve cumbersome knowledge transfer mechanisms, such as pre-training and fine-tuning, whereas ECP modeling requires more lightweight methods. (3) Deep learning models often lack explainability, hindering their application in industry. This paper proposes a novel FSL method that exploits Transformers and Gaussian Mixture Models (GMMs) for ECP modeling to address the above-described issues. Results show that our method can accurately restore the complex ECP distribution with a minimal amount of ECP data (e.g., only 1.6\% of the complete domain dataset) while it outperforms state-of-the-art time series modeling methods, maintaining the advantages of being both lightweight and interpretable. The project is open-sourced at https://github.com/xiaweijie1996/TransformerEM-GMM.git.

Shuyi Gao, Stavros Orfanoudakis, Shengren Hou et al.

Optimal dispatch of energy storage systems (ESSs) in distribution networks involves jointly improving operating economy and voltage security under time-varying conditions and possible topology changes. To support fast online decision making, we develop a topology-aware Reinforcement Learning architecture based on Twin Delayed Deep Deterministic Policy Gradient (TD3), which integrates graph neural networks (GNNs) as graph feature encoders for ESS dispatch. We conduct a systematic investigation of three GNN variants: graph convolutional networks (GCNs), topology adaptive graph convolutional networks (TAGConv), and graph attention networks (GATs) on the 34-bus and 69-bus systems, and evaluate robustness under multiple topology reconfiguration cases as well as cross-system transfer between networks with different system sizes. Results show that GNN-based controllers consistently reduce the number and magnitude of voltage violations, with clearer benefits on the 69-bus system and under reconfiguration; on the 69-bus system, TD3-GCN and TD3-TAGConv also achieve lower saved cost relative to the NLP benchmark than the NN baseline. We also highlight that transfer gains are case-dependent, and zero-shot transfer between fundamentally different systems results in notable performance degradation and increased voltage magnitude violations. This work is available at: https://github.com/ShuyiGao/GNNs_RL_ESSs and https://github.com/distributionnetworksTUDelft/GNNs_RL_ESSs.

Chenguang Wang, Simon H. Tindemans, Peter Palensky

Generating power system states that have similar distribution and dependency to the historical ones is essential for the tasks of system planning and security assessment, especially when the historical data is insufficient. In this paper, we described a generative model for load profiles of industrial and commercial customers, based on the conditional variational autoencoder (CVAE) neural network architecture, which is challenging due to the highly variable nature of such profiles. Generated contextual load profiles were conditioned on the month of the year and typical power exchange with the grid. Moreover, the quality of generations was both visually and statistically evaluated. The experimental results demonstrate our proposed CVAE model can capture temporal features of historical load profiles and generate `realistic' data with satisfying univariate distributions and multivariate dependencies.

Shengren Hou, Edgar Mauricio Salazar Duque, Peter Palensky et al.

The optimal dispatch of energy storage systems (ESSs) presents formidable challenges due to the uncertainty introduced by fluctuations in dynamic prices, demand consumption, and renewable-based energy generation. By exploiting the generalization capabilities of deep neural networks (DNNs), deep reinforcement learning (DRL) algorithms can learn good-quality control models that adaptively respond to distribution networks' stochastic nature. However, current DRL algorithms lack the capabilities to enforce operational constraints strictly, often even providing unfeasible control actions. To address this issue, we propose a DRL framework that effectively handles continuous action spaces while strictly enforcing the environments and action space operational constraints during online operation. Firstly, the proposed framework trains an action-value function modeled using DNNs. Subsequently, this action-value function is formulated as a mixed-integer programming (MIP) formulation enabling the consideration of the environment's operational constraints. Comprehensive numerical simulations show the superior performance of the proposed MIP-DRL framework, effectively enforcing all constraints while delivering high-quality dispatch decisions when compared with state-of-the-art DRL algorithms and the optimal solution obtained with a perfect forecast of the stochastic variables.

Kutay Bölat, Simon H. Tindemans, Peter Palensky

Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation mechanism as a probability distribution to assess the data quality and generate more data, if needed. Kernel density estimation (KDE) based models are popular choices for this task, but they fail to adapt to data regions with varying densities. In this paper, an adaptive KDE model is employed to circumvent this, where each kernel in the model has an individual bandwidth. The leave-one-out maximum log-likelihood (LOO-MLL) criterion is proposed to prevent the singular solutions that the regular MLL criterion gives rise to, and it is proven that LOO-MLL prevents these. Relying on this guaranteed robustness, the model is extended by adjustable weights for the kernels. In addition, a modified expectation-maximization algorithm is employed to accelerate the optimization speed reliably. The performance of the proposed method and models are exhibited on two power systems datasets using different statistical tests and by comparison with Gaussian mixture models. Results show that the proposed models have promising performance, in addition to their singularity prevention guarantees.

Zeynab Kaseb, Matthias Moller, Giorgio Tosti Balducci et al.

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.

Nan Lin, Peter Palensky, Pedro P. Vergara

High-resolution time series data are crucial for the operation and planning of energy systems such as electrical power systems and heating systems. Such data often cannot be shared due to privacy concerns, necessitating the use of synthetic data. However, high-resolution time series data is difficult to model due to its inherent high dimensionality and complex temporal dependencies. Leveraging the recent development of generative AI, especially diffusion models, we propose EnergyDiff, a universal data generation framework for energy time series data. EnergyDiff builds on state-of-the-art denoising diffusion probabilistic models, utilizing a proposed denoising network dedicated to high-resolution time series data and introducing a novel Marginal Calibration technique. Our extensive experimental results demonstrate that EnergyDiff achieves significant improvement in capturing the temporal dependencies and marginal distributions compared to baselines, particularly at the 1-minute resolution. EnergyDiff's universality is validated across diverse energy domains (e.g., electricity demand, heat pump, PV, multiple time resolutions (1 minute, 15 minutes, 30 minutes and 1 hour), and at both customer and transformer levels.

Chenguang Wang, Ensieh Sharifnia, Simon H. Tindemans et al.

Variational autoencoder (VAE) neural networks can be trained to generate power system states that capture both marginal distribution and multivariate dependencies of historical data. The coordinates of the latent space codes of VAEs have been shown to correlate with conceptual features of the data, which can be leveraged to synthesize targeted data with desired features. However, the locations of the VAEs' latent space codes that correspond to specific properties are not constrained. Additionally, the generation of data with specific characteristics may require data with corresponding hard-to-get labels fed into the generative model for training. In this paper, to make data generation more controllable and efficient, an oriented variation autoencoder (OVAE) is proposed to constrain the link between latent space code and generated data in the form of a Spearman correlation, which provides increased control over the data synthesis process. On this basis, an importance sampling process is used to sample data in the latent space. Two cases are considered for testing the performance of the OVAE model: the data set is fully labeled with approximate information and the data set is incompletely labeled but with more accurate information. The experimental results show that, in both cases, the OVAE model correlates latent space codes with the generated data, and the efficiency of generating targeted samples is significantly improved.

Zeynab Kaseb, Matthias Moller, Peter Palensky et al.

The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability and offer performance advantages for large-scale optimization problems. Therefore, we propose a novel combinatorial optimization framework that reformulates continuous energy and power system problems into a format executable on quantum/digital annealers. The proposed framework accommodates both real and complex numbers and can represent both linear and nonlinear equations. As a proof of concept, we demonstrate its use in three applications: (i) 2D steady conductive heat transfer for a plate with constant temperature at each edge, where coefficient and boundary condition matrices are developed to solve linear system of equations, (ii) power system parameter identification, where the admittance matrix is estimated given voltage and current measurements, and (iii) power flow analysis, which solves the governing equations for active and reactive power balance. As a proof of concept, the applications are run on small test cases. The results show that the framework effectively and efficiently addresses the three applications and therefore suggest its potential to solve a wide range of energy and power system problems.

Runyao Yu, Viviana Kleine, Philipp Gromotka et al.

Batteries with silicon-graphite-based anodes, which offer higher energy density and improved charging performance, introduce pronounced voltage hysteresis, making state-of-charge (SoC) estimation particularly challenging. Existing approaches to modeling hysteresis rely on exhaustive high-fidelity tests or focus on conventional graphite-based lithium-ion batteries, without considering uncertainty quantification or computational constraints. This work introduces a data-driven approach for probabilistic hysteresis factor prediction, with a particular emphasis on applications involving silicon-graphite anode-based batteries. A data harmonization framework is proposed to standardize heterogeneous driving cycles across varying operating conditions. Statistical learning and deep learning models are applied to assess performance in predicting the hysteresis factor with uncertainties while considering computational efficiency. Extensive experiments are conducted to evaluate the generalizability of the optimal model configuration in unseen vehicle models through retraining, zero-shot prediction, fine-tuning, and joint training. By addressing key challenges in SoC estimation, this research facilitates the adoption of advanced battery technologies. A summary page is available at: https://runyao-yu.github.io/Porsche_Hysteresis_Factor_Prediction/

Weijie Xia, James Ciyu Qin, Edgar Mauricio Salazar Duque et al.

Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC) based power flow (PF) simulations or simplified analytical approximations. While MC approaches are computationally intensive and demand substantial data storage, analytical approximations often compromise accuracy. In this paper, we propose a novel analytical PPF framework that eliminates the dependence on MC-based PF simulations and, in principle, enables an approximation of the analytical form of arbitrary voltage distributions. The core idea is to learn an explicit and invertible mapping between stochastic power injections and system voltages using invertible neural networks (INNs). By leveraging the Change of Variable Theorem, the proposed framework facilitates direct approximation of the analytical form of voltage probability distributions without repeated PF computations. Extensive numerical studies demonstrate that the proposed framework achieves state-of-the-art performance both as a high-accuracy PF solver and as an efficient analytical PPF estimator.

Dong Liu, Sander Timmerman, Yu Xiang et al.

Most existing phase balancing and topology reconfiguration problems are formulated as mixed-integer optimization problems that depend on network topologies~\cite{10098964,11017695,10571996}. However, these topologies are often inaccurate and outdated for distribution system operators~(DSOs) due to missing recordings, topology maintenance and reconfiguration, such as congestion management ~\cite{vanin2024phase}. Thus, the topology of the low-voltage distribution network (LVDN) needs to be checked and corrected when it is outdated. The increasing uncertainty of distributed energy resources (DERs), including household photovoltaic (PV), heating pumps, etc., impacts the frequency of topology reconfiguration and challenges the correction of the low-voltage distribution network topology~\cite{10026490, 10347462, 10475702}. Moreover, the available smart meter (SM) datasets are often limited due to privacy concerns and random communication channel failure, challenging the topology correction~\cite{9696306, costa2022identification, dande2025consumer}. Synthetic European networks and benchmark models presented in~\cite{birchfield2016grid,2020Non} are benchmarks for research but insufficient to represent the diversity of European LVDNs for practical use by DSOs (e.g., state estimation). Thus, practical topology identification and correction approaches are required for real-time topology updating for active management of LVDNs.

Nan Lin, Yanbo Wang, Jacco Heres et al.

Smart meter data is the foundation for planning and operating the distribution network. Unfortunately, such data are not always available due to privacy regulations. Meanwhile, the collected data may be corrupted due to sensor or transmission failure, or it may not have sufficient resolution for downstream tasks. A wide range of generative tasks is formulated to address these issues, including synthetic data generation, missing data imputation, and super-resolution. Despite the success of machine learning models on these tasks, dedicated models need to be designed and trained for each task, leading to redundancy and inefficiency. In this paper, by recognizing the powerful modeling capability of flow matching models, we propose a new approach to unify diverse smart meter data generative tasks with a single model trained for conditional generation. The proposed flow matching models are trained to generate challenging, high-dimensional time series data, specifically monthly smart meter data at a 15 min resolution. By viewing different generative tasks as distinct forms of partial data observations and injecting them into the generation process, we unify tasks such as imputation and super-resolution with a single model, eliminating the need for re-training. The data generated by our model not only are consistent with the given observations but also remain realistic, showing better performance against interpolation and other machine learning based baselines dedicated to the tasks.

Runyao Yu, Julia Lin, Derek W. Bunn et al.

Accurate and efficient imbalance electricity price forecasting is critical for industrial energy trading systems, especially as battery assets and automated bidding pipelines increasingly participate in balancing markets. However, real-time forecasting is complicated by nonlinear market-rule-based price formation, heterogeneous input signals, and incomplete data availability caused by communication delays, publication lags, and measurement outages. This paper proposes a market-rule-informed neural forecasting framework that embeds imbalance price formation rules into the latent space of an expressive neural network. The proposed framework preserves raw signal information while exploiting transparent market-rule priors. We further analyze operational robustness by removing price-component information and characterize how forecasting performance scales with input length and forecasting horizon. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines. Experimental results show that the proposed model achieves competitive forecasting performance with substantially fewer trainable parameters and shorter training time than generic deep learning baselines, demonstrating that market-rule priors and expressive neural networks should be jointly used for accurate and computationally sustainable forecasting in industrial energy trading applications. The implementation is publicly available at https://runyao-yu.github.io/MRINN/.

Stavros Orfanoudakis, Cesar Diaz-Londono, Yunus E. Yılmaz et al.

As electric vehicle (EV) numbers rise, concerns about the capacity of current charging and power grid infrastructure grow, necessitating the development of smart charging solutions. While many smart charging simulators have been developed in recent years, only a few support the development of Reinforcement Learning (RL) algorithms in the form of a Gym environment, and those that do usually lack depth in modeling Vehicle-to-Grid (V2G) scenarios. To address the aforementioned issues, this paper introduces the EV2Gym, a realistic simulator platform for the development and assessment of small and large-scale smart charging algorithms within a standardized platform. The proposed simulator is populated with comprehensive EV, charging station, power transformer, and EV behavior models validated using real data. EV2Gym has a highly customizable interface empowering users to choose from pre-designed case studies or craft their own customized scenarios to suit their specific requirements. Moreover, it incorporates a diverse array of RL, mathematical programming, and heuristic algorithms to speed up the development and benchmarking of new solutions. By offering a unified and standardized platform, EV2Gym aims to provide researchers and practitioners with a robust environment for advancing and assessing smart charging algorithms.

Zhisheng Xiong, Dimitris Boskos, Bo Zeng et al.

This paper studies the robust optimal operation of distribution networks (DNs) under renewable generation and load demand uncertainties, seeking an improved trade-off between robustness and economic performance. Building upon information gap decision theory (IGDT), a generalized uncertainty modelling is proposed to enhance the expressiveness of the uncertainty characterization. The proposed modelling captures both symmetric and asymmetric uncertainty features, and supports linear or nonlinear expansion of the uncertainty sets driven by confidence level. This advancement leads to the development of a confidence-level-based IGDT (CL-IGDT) framework for DN operation. To solve the resulting model, its equivalence to a family of two-stage robust optimization problems (TSROs) is established, enabling a Fibonacci search over the confidence level. To further improve computational efficiency, a cut-recycling strategy is proposed to exploit invariant information across TSROs. These techniques are integrated into a novel Fibonacci-Parametric Column-and-Constraint Generation algorithm with guaranteed asymptotic convergence. Case studies validate the effectiveness of the proposed framework and demonstrate the performance advantages of the proposed algorithm.

Zeynab Kaseb, Stavros Orfanoudakis, Pedro P. Vergara et al.

This study introduces PINN4PF, an end-to-end deep learning architecture for power flow (PF) analysis that effectively captures the nonlinear dynamics of large-scale modern power systems. The proposed neural network (NN) architecture consists of two important advancements in the training pipeline: (A) a double-head feed-forward NN that aligns with PF analysis, including an activation function that adjusts to the net active and reactive power injections patterns, and (B) a physics-based loss function that partially incorporates power system topology information through a novel hidden function. The effectiveness of the proposed architecture is illustrated through 4-bus, 15-bus, 290-bus, and 2224-bus test systems and is evaluated against two baselines: a linear regression model (LR) and a black-box NN (MLP). The comparison is based on (i) generalization ability, (ii) robustness, (iii) impact of training dataset size on generalization ability, (iv) accuracy in approximating derived PF quantities (specifically line current, line active power, and line reactive power), and (v) scalability. Results demonstrate that PINN4PF outperforms both baselines across all test systems by up to two orders of magnitude not only in terms of direct criteria, e.g., generalization ability, but also in terms of approximating derived physical quantities.

Stavros Orfanoudakis, Peter Palensky, Pedro P. Vergara

Maintaining grid stability amid widespread electric vehicle (EV) adoption is vital for sustainable transportation. Traditional optimization methods and Reinforcement Learning (RL) approaches often struggle with the high dimensionality and dynamic nature of real-time EV charging, leading to sub-optimal solutions. To address these challenges, this study demonstrates that combining Large Language Models (LLMs), for sequence modeling, with Graph Neural Networks (GNNs), for relational information extraction, not only outperforms conventional EV smart charging methods, but also paves the way for entirely new research directions and innovative solutions.

Weijie Xia, Chenguang Wang, Peter Palensky et al.

Residential Load Profile (RLP) generation and prediction are critical for the operation and planning of distribution networks, especially as diverse low-carbon technologies (e.g., photovoltaic and electric vehicles) are increasingly adopted. This paper introduces a novel flow-based generative model, termed Full Convolutional Profile Flow (FCPFlow), which is uniquely designed for both conditional and unconditional RLP generation, and for probabilistic load forecasting. By introducing two new layers--the invertible linear layer and the invertible normalization layer--the proposed FCPFlow architecture shows three main advantages compared to traditional statistical and contemporary deep generative models: 1) it is well-suited for RLP generation under continuous conditions, such as varying weather and annual electricity consumption, 2) it demonstrates superior scalability in different datasets compared to traditional statistical models, and 3) it also demonstrates better modeling capabilities in capturing the complex correlation of RLPs compared with deep generative models.

Zeynab Kaseb, Matthias Moller, Lindsay Spoor et al.

The Newton-Raphson (NR) method is widely used for solving power flow (PF) equations due to its quadratic convergence. However, its performance deteriorates under poor initialization or extreme operating scenarios, e.g., high levels of renewable energy penetration. Traditional NR initialization strategies often fail to address these challenges, resulting in slow convergence or even divergence. We propose the use of reinforcement learning (RL) to optimize the initialization of NR, and introduce a novel quantum-enhanced RL environment update mechanism to mitigate the significant computational cost of evaluating power system states over a combinatorially large action space at each RL timestep by formulating the voltage adjustment task as a quadratic unconstrained binary optimization problem. Specifically, quantum/digital annealers are integrated into the RL environment update to evaluate state transitions using a problem Hamiltonian designed for PF. Results demonstrate significant improvements in convergence speed, a reduction in NR iteration counts, and enhanced robustness under different operating conditions.

Ali Rajaei, Peter Palensky, Jochen L. Cremer

Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer non-linear problem for large-scale systems in near-real-time is currently intractable with existing solvers. Machine learning (ML) approaches have emerged as a promising alternative, but they have limited generalization to unseen topologies, varying operating conditions, and different systems, which limits their practical applicability. This paper formulates NTO for congestion management problem considering linearized AC PF, and proposes a graph neural network (GNN)-accelerated approach. We develop a heterogeneous edge-aware message passing NN to predict effective busbar splitting actions as candidate NTO solutions. The proposed GNN captures local flow patterns, achieves generalization to unseen topology changes, and improves transferability across systems. Case studies show up to 4 orders-of-magnitude speed-up, delivering AC-feasible solutions within one minute and a 2.3% optimality gap on the GOC 2000-bus system. These results demonstrate a significant step toward near-real-time NTO for large-scale systems with topology and cross-system generalization.

Kutay Bölat, Peter Palensky, Simon Tindemans

Accurate intraday forecasts are essential for power system operations, complementing day-ahead forecasts that gradually lose relevance as new information becomes available. This paper introduces a Bayesian updating mechanism that converts fully probabilistic day-ahead forecasts into intraday forecasts without retraining or re-inference. The approach conditions the Gaussian mixture output of a conditional variational autoencoder-based forecaster on observed measurements, yielding an updated distribution for the remaining horizon that preserves its probabilistic structure. This enables consistent point, quantile, and ensemble forecasts while remaining computationally efficient and suitable for real-time applications. Experiments on household electricity consumption and photovoltaic generation datasets demonstrate that the proposed method improves forecast accuracy up to 25% across likelihood-, sample-, quantile-, and point-based metrics. The largest gains occur in time steps with strong temporal correlation to observed data, and the use of pattern dictionary-based covariance structures further enhances performance. The results highlight a theoretically grounded framework for intraday forecasting in modern power systems.

Kutay Bölat, Tarek Alskaif, Peter Palensky et al.

As the number of rooftop photovoltaic (PV) installations increases, aggregators and system operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. This method encodes each PV system's characteristic power generation patterns and uncertainty as a probability distribution, then groups systems by their statistical distances and agglomerative clustering. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness.

Stavros Orfanoudakis, Nanda Kishor Panda, Peter Palensky et al.

Reinforcement Learning (RL) methods used for solving real-world optimization problems often involve dynamic state-action spaces, larger scale, and sparse rewards, leading to significant challenges in convergence, scalability, and efficient exploration of the solution space. This study introduces GNN-DT, a novel Decision Transformer (DT) architecture that integrates Graph Neural Network (GNN) embedders with a novel residual connection between input and output tokens crucial for handling dynamic environments. By learning from previously collected trajectories, GNN-DT tackles the sparse rewards limitations of online RL algorithms and delivers high-quality solutions in real-time. We evaluate GNN-DT on the complex electric vehicle (EV) charging optimization problem and prove that its performance is superior and requires significantly fewer training trajectories, thus improving sample efficiency compared to existing DT and offline RL baselines. Furthermore, GNN-DT exhibits robust generalization to unseen environments and larger action spaces, addressing a critical gap in prior offline and online RL approaches.

Chenguang Wang, Ensieh Sharifnia, Zhi Gao et al.

For planning of power systems and for the calibration of operational tools, it is essential to analyse system performance in a large range of representative scenarios. When the available historical data is limited, generative models are a promising solution, but modelling high-dimensional dependencies is challenging. In this paper, a multivariate load state generating model on the basis of a conditional variational autoencoder (CVAE) neural network is proposed. Going beyond common CVAE implementations, the model includes stochastic variation of output samples under given latent vectors and co-optimizes the parameters for this output variability. It is shown that this improves statistical properties of the generated data. The quality of generated multivariate loads is evaluated using univariate and multivariate performance metrics. A generation adequacy case study on the European network is used to illustrate model's ability to generate realistic tail distributions. The experiments demonstrate that the proposed generator outperforms other data generating mechanisms.

Kaikai Pan, Peter Palensky, Peyman Mohajerin Esfahani

The main objective of this article is to develop scalable dynamic anomaly detectors when high-fidelity simulators of power systems are at our disposal. On the one hand, mathematical models of these high-fidelity simulators are typically "intractable" to apply existing model-based approaches. On the other hand, pure data-driven methods developed primarily in the machine learning literature neglect our knowledge about the underlying dynamics of the systems. In this study, we combine tools from these two mainstream approaches to develop a diagnosis filter that utilizes the knowledge of both the dynamical system as well as the simulation data of the high-fidelity simulators. The proposed diagnosis filter aims to achieve two desired features: (i) performance robustness with respect to model mismatch; (ii) high scalability. To this end, we propose a tractable (convex) optimization-based reformulation in which decisions are the filter parameters, the model-based information introduces feasible sets, and the data from the simulator forms the objective function to-be-minimized regarding the effect of model mismatch on the filter performance. To validate the theoretical results, we implement the developed diagnosis filter in DIgSILENT PowerFactory to detect false data injection attacks on the Automatic Generation Control measurements in the three-area IEEE 39-bus system.

Chenguang Wang, Simon Tindemans, Kaikai Pan et al.

State estimation is of considerable significance for the power system operation and control. However, well-designed false data injection attacks can utilize blind spots in conventional residual-based bad data detection methods to manipulate measurements in a coordinated manner and thus affect the secure operation and economic dispatch of grids. In this paper, we propose a detection approach based on an autoencoder neural network. By training the network on the dependencies intrinsic in 'normal' operation data, it effectively overcomes the challenge of unbalanced training data that is inherent in power system attack detection. To evaluate the detection performance of the proposed mechanism, we conduct a series of experiments on the IEEE 118-bus power system. The experiments demonstrate that the proposed autoencoder detector displays robust detection performance under a variety of attack scenarios.

Kaikai Pan, Elyas Rakhshani, Peter Palensky

Power systems are moving towards hybrid AC/DC grids with the integration of HVDC links, renewable resources and energy storage modules. New models of frequency control have to consider the complex interactions between these components. Meanwhile, more attention should be paid to cyber security concerns as these control strategies highly depend on data communications which may be exposed to cyber attacks. In this regard, this article aims to analyze the false data injection (FDI) attacks on the AC/DC interconnected system with virtual inertia and develop advanced diagnosis tools to reveal their occurrence. We build an optimization-based framework for the purpose of vulnerability and attack impact analysis. Considering the attack impact on the system frequency stability, it is shown that the hybrid grid with parallel AC/DC links and emulated inertia is more vulnerable to the FDI attacks, compared with the one without virtual inertia and the normal AC system. We then propose a detection approach to detect and isolate each FDI intrusion with a sufficient fast response, and even recover the attack value. In addition to theoretical results, the effectiveness of the proposed methods is validated through simulations on the two-area AC/DC interconnected system with virtual inertia emulation capabilities.

Arjen van der Meer, Cornelius Steinbrink, Kai Heussen et al.

The complex and often safety-critical nature of cyber-physical energy systems makes validation a key challenge in facilitating the energy transition, especially when it comes to the testing on system level. Reliable and reproducible validation experiments can be guided by the concept of design of experiments, which is, however, so far not fully adopted by researchers. This paper suggests a structured guideline for design of experiments application within the holistic testing procedure suggested by the European ERIGrid project. In this paper, a general workflow as well as a practical example are provided with the aim to give domain experts a basic understanding of design of experiments compliant testing.

Kaikai Pan, André Teixeira, Milos Cvetkovic et al.

A class of data integrity attack, known as false data injection (FDI) attack, has been studied with a considerable amount of work. It has shown that with perfect knowledge of the system model and the capability to manipulate a certain number of measurements, the FDI attacks can coordinate measurements corruption to keep stealth against the bad data detection. However, a more realistic attack is essentially an attack with limited adversarial knowledge of the system model and limited attack resources due to various reasons. In this paper, we generalize the data attacks that they can be pure FDI attacks or combined with availability attacks (e.g., DoS attacks) and analyze the attacks with limited adversarial knowledge or limited attack resources. The attack impact is evaluated by the proposed metrics and the detection probability of attacks is calculated using the distribution property of data with or without attacks. The analysis is supported with results from a power system use case. The results show how important the knowledge is to the attacker and which measurements are more vulnerable to attacks with limited resources.

Kaikai Pan, André Teixeira, Milos Cvetkovic et al.

Understanding smart grid cyber attacks is key for developing appropriate protection and recovery measures. Advanced attacks pursue maximized impact at minimized costs and detectability. This paper conducts risk analysis of combined data integrity and availability attacks against the power system state estimation. We compare the combined attacks with pure integrity attacks - false data injection (FDI) attacks. A security index for vulnerability assessment to these two kinds of attacks is proposed and formulated as a mixed integer linear programming problem. We show that such combined attacks can succeed with fewer resources than FDI attacks. The combined attacks with limited knowledge of the system model also expose advantages in keeping stealth against the bad data detection. Finally, the risk of combined attacks to reliable system operation is evaluated using the results from vulnerability assessment and attack impact analysis. The findings in this paper are validated and supported by a detailed case study.

Kaikai Pan, André Teixeira, Claudio López et al.

It is challenging to assess the vulnerability of a cyber-physical power system to data attacks from an integral perspective. In order to support vulnerability assessment except analytic analysis, suitable platform for security tests needs to be developed. In this paper we analyze the cyber security of energy management system (EMS) against data attacks. First we extend our analytic framework that characterizes data attacks as optimization problems with the objectives specified as security metrics and constraints corresponding to the communication network properties. Second, we build a platform in the form of co-simulation - coupling the power system simulator DIgSILENT PowerFactory with communication network simulator OMNeT++, and Matlab for EMS applications (state estimation, optimal power flow). Then the framework is used to conduct attack simulations on the co-simulation based platform for a power grid test case. The results indicate how vulnerable of EMS to data attacks and how co-simulation can help assess vulnerability.