In Part I of this paper, we have proposed the new concept of generalized voltage damping (GVD) and derived the system-wise GVD (sGVD) index for the global assessment of voltage stability and system strength. Part II of this paper extends this concept to develop a port-wise index for quantifying the voltage damping characteristics locally. To this end, we decompose the sGVD index into individual ports (or buses), there-by forming the port-wise GVD (pGVD) index, which can be computed using local measurements. By inheriting the interpretation of the system-wise index, we further prove that the average of pGVD indices across all ports is approximately identical to the sGVD index. Moreover, it exhibits favorable properties absent in existing indices based on the maximum Lyapunov exponents (MLEs) of terminal voltages, empowering its application as an assessment metric for the supportive capability of devices to short-term voltage stability. The model-independent feature enables the assessment considering the complex and nonlinear dynamics of inverter-based resources (IBRs) such as wind turbines, photovoltaics (PVs), and battery energy storages. Experimental simulations conducted on a heterogeneous IEEE 39-bus system and two practical power systems with massive renewable resource integration confirm the theoretical results. The influence of voltage control strategies of IBR., control parameters, integration locations, and active power control parameters are also analyzed, providing a new perspective for understanding the individual support of devices for short-term voltage stability.

The growing electricity demand, combined with the increasing integration of photovoltaic (PV) generation into the distribution system, requires higher flexibility from the demand side. This paper proposes a customized scheduling approach for demand response (DR) of customers with dispatchable inverters in distribution-level PV facilities. Based on the Chilean context, the proposed approach enables these energy resources to provide flexibility in the technical and economic management of the distribution system operator (DSO). Specifically, a bi-level optimization model is introduced. At the upper level, the DSO minimizes distribution system costs by determining daily price signals for customers based on their response profile classes (RPCs) and active and reactive power set points for PV facilities. At the lower level, customers aim to reduce their electricity bills. In addition, the proposed approach ensures the reliable operation of the distribution system with high probability by ad-dressing uncertainty through chance constraints (CCs). Incorporated CCs in the distribution system modeling include the squared magnitude of nodal voltage, complex power flow in lines, and apparent power of inverters. Finally, two case studies are presented, involving 420 residential and commercial Chilean customers with two distribution-level PV facilities using real-world market prices and daily consumption profiles on the IEEE 37-node test feeder. Results demonstrate how the proposed model enables the customized scheduling of customers and PV facilities, highlighting its effectiveness over the uniform price scheme.

Accurate load profile data are essential for optimizing energy systems. However, real-world datasets often suffer from low resolution and significant missing values. To address these challenges, this paper introduces physics-informed loss generative adversarial network (PIL-GAN), a model that combines generative adversarial networks (GANs) with physics-informed losses (PILs) derived from physics-informed neural networks (PINNs) that are integrated directly into the generator. High-resolution load profiles are generated that not only fill in missing data but also ensure that the generated profiles adhere to physical laws governing the energy systems, such as energy conservation and load fluctuations. By embedding domain-specific physics into the generation process, the proposed model significantly enhances data quality and resolution for low-quality datasets. The experimental results demonstrate notable gains in data accuracy, resolution, and consistency, making PIL-GAN an effective tool for energy management systems. The PIL-GAN also has broader applicability in other fields such as generating and inpainting high-resolution datasets for energy systems, industrial processes, and any domain in which data must comply with real-world physical laws or operational requirements.

Time-domain distance protection shows superior performance for transmission lines integrated with renewable energy sources (RESs). However, in 35–110 kV renewable power transmission systems, the inhomogeneity of the mixed overhead lines (OHLs) and underground cables (UGCs) negatively affects the feasibility of distance protection. This paper proposes a robust algorithm of time-domain distance protection for renewable power transmission system with the mixed OHLs and UGCs. First, based on the time-domain mathematical model, the accuracy and robustness of the conventional algorithm under inhomogeneous line parameters are evaluated. To solve the “0/0” problem caused by weak signals, the singular value decomposition-based least squares method (SVD-LSM) is adopted to avoid calculation outliers and improve the protection reliability. Meanwhile, a weighting method based on Euclidean norm is designed to overcome the problem of computational non-convergence. It also ensures the protection operation speed by using a short time window. In addition, a distance correction method is designed for mixed lines to improve the accuracy of fault location. On the basis, a prototype of the protection device is developed, and extensive hardware-in-the-loop (HIL) tests are performed to verify its feasibility and superiority. In addition, the prototype of the protection device has been applied to actual renewable power transmission systems.

The massive integration of intermittent renewable generation and the increasing variability of demand raise concerns about the high level of uncertainty in the security assessment of power systems. In this context, the main contribution of this study is the proposal of a new definition of contingency criticality, which takes into account the violation probability of the voltage security margin (VSM) while considering correlated uncertainties in both system loads and wind power generation. From this new definition, a contingency ranking can be derived and used to determine preventive control actions. To calculate this probability for each contingency, a new approach based on the cross-entropy (CE) method is developed and applied. The CE method is well-suited to handle high levels of uncertainty, as it typically provides faster and more accurate results compared to Monte Carlo simulation, particularly for cases with low violation probabilities of the VSM. Another innovative feature of this approach is the consideration of correlated uncertainties through the use of multivariate normal distributions and Gaussian copulas. Furthermore, the proposed definition is implemented using a formulation that is capable of detecting either saddle-node or limit-induced bifurcations to accurately identify the maximum loadability point. A proof of concept is presented for a comprehensive explanation of the proposed definition, followed by an application of this definition to the IEEE 118-bus test system. The findings of this paper highlight the need to carefully select critical contingencies for voltage security assessment in the context of increasing uncertainties.

Joint operation optimization for electric vehicles (EVs) and on-site or adjacent photovoltaic generation (PVG) are pivotal to maintaining the security and economics of the operation of the power system concerned. Conventional offline optimization algorithms lack real-time applicability due to uncertainties involved in the charging service of an EV charging station (EVCS). Firstly, an optimization model for real-time EV charging strategy is proposed to address these challenges, which accounts for environmental uncertainties of an EVCS, encompassing EV arrivals, charging demands, PVG outputs, and the electricity price. Then, a scenario-based two-stage optimization approach is formulated. The scenarios of the underlying uncertain environmental factors are generated by the Bayesian long short-term memory (B-LSTM) network. Finally, numerical results substantiate the efficacy of the proposed optimization approach, and demonstrate superior profitability compared with prevalent approaches.

This paper proposes a method for obtaining nonlinear models of distribution grid based on available measurements from the power grid. We formulate a maximum likelihood estimation (MLE) problem that estimates unknown line parameters—specifically, the impedance between nodes—using measured voltage magnitudes and net active and reactive power injections at each node. The nonlinear model for the distribution grid uses a nonlinear approximation of the DistFlow model, which includes line losses and is parameterized by the unknown line impedances. We solve the resulting MLE problem using an expectation maximization (EM) algorithm, tailored for the nonlinear model, and provide a numerically robust implementation. The proposed method is demonstrated on the IEEE 37-node test network, and we compare it with the state-of-the-art methods. The proposed method achieves a 70% reduction in voltage error and an error for state variables that is more than 10000 times smaller. A final comparison uses data from a real network, and the proposed method achieves parameter estimates with errors 100 times smaller than competing methods.

This paper proposes a grid synchronization control strategy for the grid-connected voltage source converters (VSCs) based on the voltage dynamics of the DC-link capacitor in the VSC. The voltage dynamics of the DC-link capacitor are used to regulate the frequency and phase angle of the inner potential of the VSC, synchronizing the VSC with grid. Firstly, in the proposed strategy, the active power regulation and grid synchronization of the VSC are combined, which are separated in the traditional control strategy. This can avoid the instability of the VSC in a weak grid with a low short circuit ratio (SCR), aroused by the dynamic interaction between the separated control loops in traditional control strategies. Secondly, the energy stored in the DC-link capacitor is directly coupled with the grid via the inner potential of the VSC, and the inertia characteristic is naturally featured in the inner potential by the proposed strategy. With the increase of the capacitance, the natural inertial response of the VSC is helpful to improve the grid frequency dynamic. Finally, simulation results are presented to validate the correctness and effectiveness of the proposed strategy on the enhancement of the grid frequency and voltage dynamic support capability.

Interval state estimation (ISE) can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements, thereby analyzing the impact of uncertain pseudo-measurements on states. However, predicted pseudo-measurements have prediction errors, and their confidence intervals do not necessarily contain the truth values, leading to estimation biases of the ISE. To solve this problem, this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression (GPR) model, thereby improving the prediction accuracy of pseudomeasurement confidence intervals. Besides, a weight assignment strategy for improving the robustness of weighted least squares (WLS) ISE is proposed. This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudomeasurement intervals with larger deviations, thereby improving the estimation accuracy and robustness of the ISE. This paper adopts the data from the supervisory control and data acquisition (SCADA) system of the New York Independent System Operator (NYISO). It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods. In addition, this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case. Finally, the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.

Electric power grids are evolving into complex cyber-physical power systems (CPPSs) that integrate advanced information and communication technologies (ICTs) but face increasing cyberspace threats and attacks. This study considers CPPS cyberspace security under distributed denial of service (DDoS) attacks and proposes a nonzero-sum game-theoretical model with incomplete information for appropriate allocation of defense resources based on the availability of limited resources. Task time delay is applied to quantify the expected utility as CPPSs have high time requirements and incur massive damage DDoS attacks. Different resource allocation strategies are adopted by attackers and defenders under the three cases of attack-free, failed attack, and successful attack, which lead to a corresponding consumption of resources. A multidimensional node value analysis is designed to introduce physical and cybersecurity indices. Simulation experiments and numerical results demonstrate the effectiveness of the proposed model for the appropriate allocation of defense resources in CPPSs under limited resource availability.