This paper presents GridPACK, a unified open-source high-performance computing (HPC) platform for power grid simulation. Built on MPI and PETSc, GridPACK provides reusable parallel infrastructure, distributed networks, automated matrix assembly, and scalable solvers, upon which multiple power system applications can be developed without parallel programming expertise. Six application modules share the same network representation and solver infrastructure, enabling seamless inter-module workflows: power flow solutions directly initialize dynamic simulations, contingency analysis reuses the full power flow solver, and dynamic security assessment chains all three within a single parallel execution. The modules include power flow with voltage and reactive power controls, contingency analysis, transient stability with over 40 validated component models, electromagnetic transient simulation, state estimation, and an HPC simulation environment for reinforcement learning. The framework’s extensibility has further enabled large-scale T&D co-simulation and parallel execution of external tools on HPC clusters. This combination of HPC scalability, multi-domain coverage, and validated accuracy makes GridPACK well-suited to the emerging demands of inverter-rich grids and large-scale AI-driven power system studies.
Accurate estimation of dynamic parameters of generators is crucial for constructing high-fidelity models for dynamic studies and ensuring the reliable operation of power systems. This paper develops a physics-informed neural ordinary differential equations (ODE) approach to learn the parameters of a generator’s dynamic model using grid sensor data. A physics-informed neural network is designed to represent the ODEs governing power system dynamics. A loss function is defined as the discrepancy between the dynamic response generated by the physics-informed neural network and synthesized grid sensor data, which mimics real-world measurements. The model parameters are iteratively updated using neural ODEs and the adjoint method. Unlike moving window-based approaches, the proposed neural ODE framework enhances parameter estimation by leveraging a longer observation period with a mini-batch scheme. Numerical studies on a 3-machine 9-bus system demonstrate that the proposed model significantly outperforms state-of-the-art baseline methods in dynamic parameter estimation accuracy.
Predictions of solar power output that are close to the mark may help with grid stability, energy management, and the integration of renewable energy sources. Prediction using conventional statistical models is challenging due to the substantial influence of nonlinear meteorological variables and temporal variations on solar power output. A deep learning-based forecasting framework integrating an attention mechanism and a Temporal Convolutional Network (TCN) is proposed in this study to enhance the precision of solar energy prediction. A number of feature engineering and pre-processing approaches are used by the model, including lag features, rolling statistics, temporal indicators, and outlier reduction using the Interquartile Range (IQR) methodology. To store long-range temporal associations, the TCN architecture employs dilated causal convolutions; the attention mechanism highlights the most important time steps in the input sequence. The proposed model outperforms state-of-the-art baseline models such as Long Short-Term Memory (LSTM) and traditional TCN when tested on a publicly available solar energy dataset. It can accomplish 253.32 MW Mean Absolute Error (MAE), 325.04 MW Root Mean Square Error (RMSE), 2.30% Mean Absolute Percentage Error (MAPE), and 0.9804 Coefficient of Determination (R²). These parameters are evaluated by experimental means.
The increasing penetration of photovoltaic systems, battery storage and electric vehicles in low-voltage distribution networks poses significant operational challenges, including voltage regulation, thermal overload, and energy curtailment. This paper proposes an uncertainty-aware two-stage coordination framework. The first stage employs a LinDist3Flow-based optimisation with Monte Carlo scenario generation to determine day-ahead charging and discharging schedules for batteries and electric vehicles while accounting for uncertainties in load demand, solar irradiance, temperature, and electric vehicle availability. The second stage uses an exact nonlinear alternating current optimal power flow formulation to optimise inverters’ active and reactive power set-points in near real-time operation. The framework is evaluated on a modified IEEE European low-voltage test feeder comprising 165 loads with 100% single-phase photovoltaic penetration. Four operational approaches are compared: local Volt-Watt/Volt-Var control, direct application of scheduled set-points without real-time correction, real-time optimal power flow with fixed time-of-use schedules, and the proposed two-stage framework. The results demonstrate that the proposed approach achieves the lowest total curtailment while maintaining voltage and thermal compliance, reducing the total curtailed energy by approximately 5% compared to the optimal power flow in real-time with fixed schedules. These findings highlight the importance of integrating uncertainty-aware scheduling with real-time coordination in future low-voltage networks with a high penetration of consumer energy resources.
This paper describes an advanced algorithm for current control in a modular multilevel power converter. The proposed algorithm is based on deadbeat model predictive control, which is further enhanced by applying an artificial neural network. Rather than supplanting the existing predictive controller, the neural network is used to supplement it, thereby improving control performance. The reference current tracking capability is enhanced under all operating conditions, particularly in cases where the reactive elements of the converter exhibit a relatively high resistive component. By introducing the neural network, the inherent delay of model predictive control in such scenarios is virtually eliminated, which reduces the overall control error. The network is trained offline on a set of control inputs obtained by optimizing the current response in a wide range of operating modes. Algorithm verification is performed for a three-phase modular multilevel converter in different steady-state and transient conditions. A state-of-the-art high-fidelity real-time simulator is used in both the algorithm development and verification stages.
This paper examines the integrated generation and transmission expansion planning (IGTEP) problem in the presence of increasing power system demand, high penetration of renewable energy sources (RES), and growing electric vehicle (EV) charging loads. The proposed framework jointly optimizes investment and operational costs for new generation units and transmission lines, while considering the environmental benefits of RES integration and the impact of EV charging on grid operation. The inherent uncertainties in load demand, EV charging, and renewable generation are addressed through a hybrid stochastic-robust optimization approach. Dynamic thermal line rating (DTLR) is incorporated through a physics-based heat balance model to capture time-varying transmission limits driven by environmental conditions. The framework also tackles the uncertainty in DTLR, incorporating a heuristic linearization technique to reduce model complexity. Unlike conventional IGTEP approaches that rely on static line ratings or treat uncertainties independently, the proposed framework provides a unified and scalable formulation that jointly captures multi-source uncertainties, including renewable variability, EV demand, and weatherdriven line ratings. The effectiveness of the proposed approach is demonstrated on the IEEE 6-bus and IEEE 118-bus systems.
Penetrations of inverter-based resources (IBRs) in power grids keep increasing. In this paper, we derived a two-port phasor-impedance circuit model for IBRs that includes the frequency coupling effect introduced by asymmetry in the dq-frame control. The physical interpretation of the related phasors of this circuit is also meticulously explained. The two-port circuit model is validated against electromagnetic transient simulation results of an IBR grid integration system subject to an unbalanced grid voltage dip. It is shown that the two-port circuit model achieves better accuracy compared to the decoupled positive- and negative-sequence circuit model (or the single-port model). We also examined the effect of IBR control on significance in frequency coupling and obtained insights regarding the application scopes of the single-port model and the two-port model.
In recent years, the rapid integration of distributed photovoltaic (DPV) systems and electric vehicles (EVs) into distribution networks has posed significant challenges to grid security and stability due to their inherent output uncertainty and volatility. Grid operators can only access net load data from households by smart meters without direct recognition of installed distributed energy resources (DERs). Therefore, accurate recognition of user-side DERs is crucial for applications such as net load disaggregation, load forecasting, and demand response. However, existing recognition methods typically rely on extensive data for model training, exhibiting insufficient accuracy and robustness in few-shot scenarios. Furthermore, these methods often overlook the coupling effects between DPV and EV, which limits the recognition performance. To address these limitations, a two-stage recognition model of DPV and EV considering weather types and electricity consumption behavior is proposed. Firstly, weather-driven features are proposed for DPV recognition, and household travel pattern-based features are introduced for EV recognition. Secondly, an unsupervised DPV output power estimation algorithm is introduced to mitigate misidentification caused by the coupling of DPV and EV during EV recognition. Finally, a Light Gradient Boosting Machine (LightGBM) algorithm improved by multi-scale data reconstruction and consensus-weighted ensemble strategies is proposed to enhance model robustness and generalization capability under few-shot scenarios. Simulation results demonstrate that the proposed model achieves a recognition accuracy of 96% for both DPV and EV. This methodology provides an effective solution for the accurate recognition of DERs under conditions of resource coupling and limited data.
Modern power systems with high penetration of inverter-based resources (IBRs) exhibit fast dynamics and complex harmonic interactions that challenge conventional modelling tools. Electromagnetic transient (EMT) simulations provide high fidelity but are computationally demanding for large-scale studies due to small time-step requirements, whereas conventional phasor-domain models neglect harmonic and higher-frequency effects to allow for larger time-steps. This paper proposes a unified dynamic-phasor-based framework (DQsym), implemented as a MATLAB/Simulink library, that combines dynamic phasors with multiple rotating reference frames and defines explicit algebraic rules for harmonic-domain operations compatible with state-space formulations, enabling systematic assembly of interconnected system-level models beyond isolated component representations. The formulation supports modelling across multiple harmonic orders and is expressed in state space, providing a natural pathway for future integration with small-signal analysis and control design tools, although such extensions are outside the scope of this paper. The approach is validated through (i) a benchmark case demonstrating higher-order harmonic modelling capability and (ii) simulations of an IEEE 9-bus system expanded with point-to-point HVDC transmission based on a modular multilevel converter (MMC), where the framework reproduces fundamental and second-harmonic dynamics indicating that DQsym reproduces the overall harmonic pattern and closely matches the fundamental component compared with EMT results. The proposed framework provides a structured and accurate harmonic-domain modelling tool for the analysis of IBR-rich power systems.
The increasing penetration of renewable energy sources introduces significant uncertainty into power system operation, challenging the market participation and coordination of virtual power plants. This paper proposes a risk-aware dynamic pricing framework based on a cooperative Stackelberg game to optimize the interaction between a load aggregator and multiple virtual power plants. The upper-level load aggregator employs Conditional Value-at-Risk to quantify trading risks and determines differentiated pricing signals to incentivize virtual power plants participation in energy and reserve markets. The lower-level structure separates physical operation from cooperative settlement: VPPs first solve a convex operational scheduling problem involving peer-to-peer energy trading, demand response, and continuous battery dispatch under scenario uncertainty, and the cooperative surplus is then allocated through a weighted bargaining rule. This layered structure preserves the leader--follower pricing logic while providing a mathematically consistent basis for the KKT-based reformulation of the physical dispatch subproblem. Simulation results demonstrate that the proposed framework achieves balanced pricing, fair profit distribution, and effective risk mitigation under high wind power uncertainty, providing a scalable decision-making tool for coordinating renewable-dominated electricity markets.
Automation in digital substations using the IEC 61850 standard marks a significant advancement in modern power grid management. However, the reliance on cyber components such as Intelligent Electronic Devices (IEDs) increases susceptibility to cyber intrusions, demanding enhanced substation cyber resilience. Existing research has yet to produce an integrated framework that addresses key aspects of cyber resilience, particularly with the capability of cyber recovery. This paper proposes the Smart Cyber Switching (SCS) controller to enable a novel concurrency feature that enhances cyber recovery for IEDs following a cyber intrusion. By integrating an intrusion detection system with an IEC 62351-compliant message authentication scheme, the SCS controller provides robust defense against both cryptographically authentic and unauthentic malicious GOOSE injections. The IED concurrency is implemented through concurrent IEDs (CIEDs) within the SCS architecture. Upon detecting an attack, Software-Defined Networking (SDN) capabilities of the SCS controller isolate compromised IED traffic and restore system operation via CIEDs. Additionally, a concurrency-aware Mixed-Integer Linear Programming (MILP) model is proposed to optimally allocate IED functions to CIEDs under resource constraints. The proposed IED concurrency methodology is validated through a cyber-physical substation automation testbed. The results confirm the effectiveness of the proposed techniques, particularly under high-frequency malicious GOOSE injection scenarios. The results also demonstrate compliance with the strict timing constraints of IEC 61850 and validate the MILP formulation through a practical case study.
To increase power transfer capacity of high-voltage direct current (HVdc) transmission, a new extra high-power HVdc architecture with multiple standard modular multilevel converters (MMCs) per substation has recently been introduced. This paper proposes a power flow model for a multi-terminal HVdc grid with this innovative substation architecture. The proposed multi-terminal HVdc power flow model can be integrated seamlessly with existing ac-dc power flow algorithms with minimal modifications. The model is applicable to various multi-terminal HVdc grid types and topologies, different numbers of dc buses, dc lines, and MMCs per substation, along with diverse control parameters. In addition, it accurately captures both balanced and unbalanced operations of the multi-terminal HVdc grid. The proposed model is verified using a 5-terminal bipole HVdc grid that spans 4 areas in the Eastern Interconnection system of the USA. The numerical solutions obtained from unified and sequential ac-dc power flow algorithms under different operating conditions closely match the time-domain simulation results in PSCAD, validating the accuracy and versatility of the proposed multi-terminal HVdc power flow model.
Wireless charging stations are gaining attention due to their ability to reduce the weight and size of the battery in the electric vehicles and increase the battery life time. Wireless charging stations are also an attractive technology for autonomous vehicle charging as they do not need human intervention. Although the design of wireless charging stations has been investigated thoroughly, the cyber-physical security posture of wireless charging stations has remained underexplored. In this paper, we examine the vulnerability of wireless charging stations to cyber-physical attacks by weaponized electric vehicles. In this paper, a weaponized EV is defined as a vehicle intentionally modified with a rogue device connected to its internal communication network capable of injecting falsified information into the electric vehicle communication controller, point-to-point communication channels, and the battery management system. Small-signal modelling is used to study the dynamics of cyber-physical systems in wireless charging, while phasor circuit analysis is used to evaluate the impact of cyber-physical attacks on wireless charging stations. A mitigation strategy is further proposed to improve the resilience of the wireless charging stations to cyber-physical attacks. Time domain simulations are employed to test and verify the analyses and the proposed mitigation strategy.
Time series forecasting has significantly advanced with the rise of deep learning models. However, recent methods often ignore the role of probabilistic state transitions in capturing temporal uncertainty. This paper introduces a novel forecasting framework based on a Probability-Adversarial Network (PAN), which leverages an adversarial architecture to embed probabilistic dynamics into neural networks. By incorporating probabilistic reasoning into a generator and discriminator architecture, the proposed PAN enhances forecasting accuracy and improves the model’s ability to handle uncertainty in sequential data. The framework is evaluated on electrical demand time series from a large-load, highly variable data center, and an average-size load, a more predictable school. Results demonstrate improved performance over probability-agnostic deep learning baselines for both load types, highlighting PAN’s versatility in addressing diverse forecasting challenges.
Harmonic excitation synchronous machines (HESMs) with brushless rotor excitation are promising for a range of applications, especially for electric vehicles, due to their compact and reliable design free from slip rings and additional exciters. However, the computer-based optimization of HESMs remains a challenging task, with effective approaches still being actively researched. This article proposes an efficient method for optimizing HESM parameters that accounts for pulse-width modulation effects, utilizing a reduced-order model and a tailored Nelder-Mead algorithm with an integrated internal optimization procedure. The proposed algorithmic enhancements significantly reduced the number of iterations required for convergence and improved key machine characteristics, namely lower losses and reduced current consumption.
Ancillary frequency controls of wind turbines (WTs) bridge the dynamic interplay between turbine mechanics and the electrical grid, enabling WTs to influence low frequency range dynamics in power systems. This work examines the impact of frequency support by grid-forming (GFM) doubly-fed induction generator (DFIG) based WT on power system ultra-low frequency oscillations (ULFOs). Accounting for different wind speed operating regions, a reduced-order small-signal model is developed to characterize GFM-DFIG’s terminal power-frequency response behavior within ULFO frequency band. This model is then integrated into the system frequency response framework. Utilizing complex torque coefficients method, the effects of various control strategies—including virtual inertia, primary frequency control, and turbine blade pitching—on the ULFO mode’s frequency and damping characteristics are analytically derived and examined. The results confirm that while the frequency support improves system frequency response, it simultaneously deteriorates ULFO damping, with high primary frequency droop gain posing a risk of instability. Lastly, simulation studies with a modified IEEE 10-machine 39-bus system are conducted to validate the theoretical findings.
Power-electronic contributions of inherent inertia require grid-forming (GFM) control schemes such as ‘virtual synchronous machine’. In order to minimize cost and expenditure, the available resources should be fully exploited. Constraints of the resource at/behind the DC link require an AC behaviour slightly or strongly deviating from that of a synchronous machine. For two outstanding aspects of those deviations, this article proposes clear-cut approaches. The notion ‘complementary grid forming’ (C-GFM) is proposed for contributors of inherent inertia which cannot fully comply with scientific GFM criteria, be it due to only one or several deviations. The definition of C-GFM draws a sharp demarcation towards GFL (grid following) and a soft line towards full GFM. To reflect the particularities of power-electronic inherent inertia, the P-contribution time constant TP is proposed for general use. For controller-agnostic description and reporting of inertia, a minimal set of rules called tailored TP covers the parameterization and operation of power-electronic inertia contributors. Tailored TP allows for the shaping of inertia with a maximum of degrees of freedom. Utilization examples are oriented at constraints of resources and also depict novel possibilities of shaping inertia contributions in order to keep the maximum of network participants operational during extreme events.
In recent years, research on power-electronic contributions of inherent inertia via grid-forming (GFM) control schemes has made significant progress. But several technical hurdles still stand against major progress towards an optimized use of resources and minimized cost on the way of providing enough power-electronic inertia for the next decade. Oriented at basic properties of virtual synchronous machines (VSMs), this article indicates generic technical solutions for respecting active-power (P) constraints of devices, tapping all working-point-dependent potentials of P variation for inertia, implementing RoCoF dead bands, circumventing the inherent slowness of a VSM to follow setpoint changes while retaining the GFM characteristic, and maximizing the combined P variation ranges of inertia and P(f) control. The overall objective is to tap the full P-variation potential of resources at/behind the DC link, even and particularly of the fluctuating ones. The described implementation example of tailored inertia is kept as generic as possible to allow for selective adoption and/or combination with other approaches. After explanation of the technical concepts in sufficient detail, simulations demonstrate the feasibility of tailoring inertia, yielding adequate behaviour in challenging circumstances.
A high-altitude electromagnetic pulse (HEMP) or geomagnetic disturbance (GMD) can disrupt power grids by inducing low-frequency common-mode (CM) currents. When these currents flow through grounded transformers, they can bias the magnetic core, driving it into saturation and reducing performance or damaging equipment. This work presents a solid-state transformer (SST) to replace vulnerable assets and improve grid resilience. The paper reviews half-cycle saturation in conventional transformers, then describes an SST architecture that neutralizes and redirects CM currents during HEMP/GMD events. A prototype SST is built and validated, demonstrating stable CM-disturbance operation and protection of nearby transformers. Finally, large-scale simulations show how coordinated SST deployment mitigates CM disturbances and strengthens overall grid resilience.
The holomorphic embedding (HE) method has gained significant attention in power flow analysis. However, there is no consensus regarding its computational efficiency compared to the traditional Newton-Raphson (NR) method. This paper presents a comprehensive analysis of the computational complexity of the HE method focusing on key steps such as matrix factorization, higher-order power series calculation, and Padé approximation. A theoretical investigation of these steps is conducted, followed by the implementation of multi-core parallel computing using Numba to enhance performance. Case studies on test systems ranging from 300 to 25,000 buses are used to evaluate the parallel strategies for accelerating computation. The results show a significant improvement in the computational efficiency of the HEM, demonstrating its scalability and practical applicability for large-scale power flow calculations. This study provides both theoretical and practical foundations for the broader adoption of the HE method in power system analysis.
