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• Constructed an operation architecture of the coupling of energy supply and demand. • Established the comprehensive demand response mechanism based on time-sharing energy prices. • Established the minimum carbon emission cost economic scheduling model as an objective function. • The scheduling method could achieve the goal of low-carbon economic dispatch. Aiming at the problems of low energy utilization and environmental pollution in China's livestock and poultry breeding industry under the carbon peaking and carbon neutralization goals, this paper proposes an optimal scheduling model for multi-energy coupling integrated energy system with ladder-type carbon trading mechanism and demand response. First, based on the construction of a reward and punishment model with ladder-type carbon trading mechanism, this paper explores the potential interaction between the coupling ability of multiple heterogeneous energy sources and carbon emissions in consideration of the impact of carbon capture equipment on carbon emissions. Second, in view of the diversity and complexity of demands for agricultural energy supply, the energy supply side equipment model and the comprehensive demand response model of electricity, heat, and gas are established, and a low-carbon economic scheduling model of integrated agricultural energy system is proposed, aiming at minimizing the total operation cost of the system. Finally, the model is solved by CPLEX, and the coupling system of a 6-node power distribution network, a 6-node gas network, and a 4-node heat supply network is used to verify the effectiveness of the proposed model and method and optimize the operation of the integrated agricultural energy system. [ABSTRACT FROM AUTHOR]

• Taking carbon in RIES as energy flow, which is equivalent to electricity-heat-gas to ensure the carbon quota requirements of the system. • Proposing a new demand-side response mechanism to meet the purpose of reducing carbon emissions. • Scheduling RIES with comprehensive consideration of economy and low carbon. • Proposing a new RIES ladder carbon price trading mechanism to match the purpose of demand side management. Effective mitigation and reduction of carbon emissions is consistently underscored in Regional Integrated Energy Systems (RIES), aligning with the goals of carbon-neutralization. However, the inherent trade-off between carbon emissions reduction and economic operation is an obvious challenge not only in power systems but especially in the coupled electricity-gas-heat energy systems. This paper develops a bi-level low-carbon optimal scheduling model, highlighting reliable operation and the balance of supply and demand of RIESs with demand-response uncertainty. In this paper we firstly redefined the carbon emission of a RIES as a carbon flow and proposed a reward and punishment carbon trading mechanism based on the ladder carbon price. Secondly, we designed an incentive-based demand-side response policy within the subsystem encompassing electricity, gas, and heat. Concurrently, the probability density distribution functions of transferable, replaceable, and interruptible loads are computed separately. Based on the above, the deviation of the load reduction and the actual load is recalculated to delimit the constraint of the demand-side response. Finally, the mechanism of carbon trading and the demand-response is leveraged to address the economic scheduling incorporating operation cost, carbon transaction cost, imbalance costs of supply and demand, and load loss. Simulations demonstrated in the paper prove that the optimal solution with demand-response uncertain may effectively increase the economic performance and reduce carbon emissions of a RIES. [ABSTRACT FROM AUTHOR]

• Various approaches for forming the internal EMF in the VSG control of DFIG-based WTGs and their features are discussed. • A novel DFIG VSG control scheme utilizing the rotor current-induced EMF as the VSG internal EMF is proposed. • The static and dynamic characteristic of the proposed VSG control scheme is studied. • Considering the static/dynamic operating characteristic and the grid demand, recommended ranges for key parameters are given. This paper focuses on the research of virtual synchronous generator (VSG) control technology for the doubly-fed induction generator (DFIG)-based wind turbines. The key for DFIG VSG operation is to construct an internal electromotive force (EMF) with the virtual rotor motion characteristic in the stator. The existing control schemes use the rotor or mutual flux-induced EMF as the internal EMF. Since the flux corresponds to a composite magnetic field generated together by the stator and rotor current. Any variations in the stator current caused by external disturbances will reflect on the rotor current to keep the flux constant. The rotor overcurrent is inevitable under a large external disturbance, threatening the safety of the rotor-side converter (RSC). Moreover, the flux is immeasurable. The accurate flux control depends on flux observers, increasing the complexity; while the control without observers cannot ensure the effectiveness, leading to control failure. To address these problems, a novel DFIG VSG control scheme with the rotor current-induced EMF as the internal EMF is proposed in this paper. The internal EMF is corresponded to the single magnetic field generated only by the rotor current. This can lead to the following benefits: the rotor current will not vary with the stator current and can be limited under large external disturbances, ensuring the safety of the RSC; the rotor current can be directly measured without the need for extra observers, reducing the difficulty of control implementations; the underlying controlled vector is unified with the traditional grid-following DFIG, favoring the retrofit of the installed DFIGs. Compared to the existing schemes, this scheme has a larger equivalent internal impedance. An additional rotor current-terminal voltage magnitude droop control is added to effectively restrain the problems brought by this larger impedance. Simulation and analysis results demonstrate that the proposed DFIG VSG control scheme effectively addresses problems in the existing schemes. Moreover, the results also exhibit that the scheme has a robust adaptability across a wide range of short-circuit ratios and possesses the grid-forming ability independent of SGs. [ABSTRACT FROM AUTHOR]

• Propose a SMPC based voltage regulation scheme to coordinate DG, OLTC, SVR and CBs considering uncertainty of DG outputs. • Use the time-correlated scenario generation method in the proposed SMPC framework. • Consider the single-phase regulation effect of OLTC, DGs and CBs. With the increasing penetration of renewable energy resources, the uncertainty of renewable energy resources output introduces challenges to voltage control in distribution networks (DNs). To solve these problems, this paper proposes a double-time-scale voltage control scheme for unbalanced DNs based on stochastic model predictive control (SMPC) to coordinate multiple voltage control devices. In fast-time-scale control, the active and reactive power outputs of distributed generators (DGs) are optimized to minimize voltage deviation, active power curtailment and reactive power fluctuation. In the slow-time-scale control, optimal tap changes of on-load tap changers (OLTC), step voltage regulators (SVR), and switched capacitor banks (CBs) are calculated to reduce voltage deviation and tap operations. Additionally, in the fast-time-scale control, the SMPC-based scheme adopts a scenario generation approach to represent the uncertainty of DG output. Considering the temporal correlation of the DG output, different prediction scenarios and scenario probabilities are obtained by the empirical cumulative distribution function fitted by the historical measurement data. In this paper, the effectiveness of the proposed double-time-scale voltage control scheme is verified by the unbalanced IEEE123 node system. The case study demonstrates that the proposed voltage scheme can effectively keep the three-phase voltages in unbalanced DN within the secure operation range and achieve better voltage profiles. [ABSTRACT FROM AUTHOR]

In this paper, we aim to analyse the impact of hydrogen production decarbonisation and electrification scenarios on the infrastructure development, generation mix, CO 2 emissions, and system costs of the European power system, considering the retrofit of the natural gas infrastructure. We define a reference scenario for the European power system in 2050 and use scenario variants to obtain additional insights by breaking down the effects of different assumptions. The scenarios were analysed using the European electricity market model COMPETES, including a proposed formulation to consider retrofitting existing natural gas networks to transport hydrogen instead of methane. According to the results, 60% of the EU's hydrogen demand is electrified, and approximately 30% of the total electricity demand will be to cover that hydrogen demand. The primary source of this electricity would be non-polluting technologies. Moreover, hydrogen flexibility significantly increases variable renewable energy investment and production, and reduces CO 2 emissions. In contrast, relying on only electricity transmission increases costs and CO 2 emissions, emphasising the importance of investing in an H 2 network through retrofitting or new pipelines. In conclusion, this paper shows that electrifying hydrogen is necessary and cost-effective to achieve the EU's objective of reducing long-term emissions. • A new formulation is proposed for natural gas network retrofitting to hydrogen (H 2). • 30% of EU electricity in 2050 will supply 60% of the H 2 needs. • Flexible electricity-based H 2 production boosts renewables by 48%. • Using electricity for H 2 production cuts CO 2 emissions by 35%. • 11% gas network retrofit covers H 2 demand with no new pipelines required. [ABSTRACT FROM AUTHOR]

False data injection attacks (FDIAs) pose a significant threat to the healthy and safe operation of smart grids. Traditional fdia detection methods are difficult to deal with complex and harsh scenarios. Considering the increasing demand for attack location services in practical power grid management, this paper proposes a new adversarial scheme called Semi-Supervised Multi-Label Adversarial Network (SMAN). To better adapt to harsh learning conditions with only a few labeled samples, this scheme combines semi-supervised mechanisms with state-of-the-art generative adversarial networks. The showdown between generator and discriminator aims to optimize the model for high detection accuracy in semi-supervised training. Among them, for the non-Euclidean structure of the power system, we propose a graph attention-based generation mechanism to improve the generator and enhance the authenticity of the generated samples. Furthermore, the classification network based on label correlation of FDIAs is proposed to capture the inconsistency and co-occurrence dependency in the measurements due to the potential attacks, which is applied to detect the exact injection locations with high dimension data. To this end, we perform label transformation and hierarchical training on the localization task to quickly localize data attacks based on multi-label classification. Extensive simulations and comparisons implemented on IEEE 14-bus and 118-bus power systems demonstrate the superiority of this scheme in localization detection. And it has been proved that it has high robustness and generalization ability under harsh conditions. • This paper innovatively focuses on FDIAs localization in the field of semi-supervised learning. • Compared with existing methods, this paper uses semi-supervised GAN and label correlation networks to achieve accurate detection based on multi-label classification. • To reasonably model smart grid topology in non-Euclidean space, we complement and optimize a novel adversarial generator consisting of graph attention-based generative layers. • We attempt to extract the co-occurrence dependencies between injected data inherent in FDIAs, and implement question transformation based on label correlation to reduce output space dramatically. [ABSTRACT FROM AUTHOR]

The electricity market liberalization propelled by the increased operational flexibility observed in distribution systems urges the development of mathematical models for competitive electricity markets accounting for the participation of distribution systems operators. Most existing approaches model the interaction between the agents and the market as a bilevel programming problem, wherein the market is characterized at the lower level. Hence, the upper-level agent's objective function is favored over minimizing the costs of supplying the system's demand. In this paper, a new bilevel formulation is proposed. In the upper level, the market operator determines the optimal energy price that ensures the demand supply and maximizes the overall social welfare. In the lower level, the generation companies and distribution systems operators determine the amount of energy injected/extracted into/from the transmission system to maximize profits/minimize operational costs. A new pricing method is proposed in this paper as an alternative to the transmission system's dual variables, which are inaccessible under the proposed framework. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program. Numerical results illustrate the proposed approach's effectiveness in maintaining the minimum operational costs while distributing the payoff amongst the agents. • Bilevel formulation for wholesale markets with non-strategic price-maker agents. • New market framework with a clearing process that minimizes the total costs. • Development of a new pricing mechanism for electricity markets. • Energy storage systems and demand response minimizes the clearing prices. [ABSTRACT FROM AUTHOR]

• A new communication-less intelligent islanding detection scheme for hybrid DG systems is proposed in this research paper. • The proposed scheme utilizes time-domain FE and LSTM to detect and classify islanding and grid-connected mode events. • By reducing the reliance on communication, the proposed scheme overcomes limitations associated with remote schemes. • Extensive simulations are conducted to validate the performance of the proposed scheme. • The proposed scheme outperforms existing techniques, demonstrating superior accuracy, selectivity, and sensitivity. The proposed scheme in this research paper is a communication-less islanding detection system based on recurrent neural network (RNN) for hybrid distributed generator (DG) systems that include both synchronous and inverter-based DG devices. The scheme consists of three stages: time-domain feature extraction (FE) from the three-phase voltage signal at the point of common coupling (PCC), feature selection using the wrapper method, and detection using a long short-term memory (LSTM) RNN algorithm. To assess the performance of the proposed scheme, a comprehensive set of islanding and grid-connected scenarios was created using the IEC 61850-7-420 test system in MATLAB/Simulink. After feature extraction in MATLAB, the feature selection and LSTM model training/testing steps were conducted in Python. Thirteen features were extracted from the voltage signal, and the most significant features were selected for detection using the wrapper method. The detection process encompassed various events, such as line faults, load switching, and capacitor switching, occurring in both islanded and grid-connected modes. The proposed scheme was compared against existing techniques, artificial neural networks, and support vector machines under the same conditions. The proposed scheme demonstrated excellent accuracy (99.68 %), selectivity (99.44 %), and sensitivity (100 %) under normal conditions with all features. It also performed well in noisy environments, with accuracies of 98.94 % and 97.04 % with 40 dB and 30 dB noise, respectively. This research highlights the importance of quality and quantity of data for training intelligent RNN-based IDSs and demonstrates the effectiveness of the proposed scheme in detecting islanding in hybrid DG systems. [ABSTRACT FROM AUTHOR]

Although a finite difference-based trajectory sensitivity (FDTS) has been widely used due to its robust availability in any environment, the accuracy of FDTS-based analyses could be influenced by the perturbation size of finite difference (FD), especially in non-smooth systems. This important yet overlooked issue has not been comprehensively addressed. Here, this paper thus investigates how the analysis accuracy varies depending on the perturbation size through case studies discussing whether the FDTS-based analysis could approximate the perturbation impact of multiple parameters. Case study results demonstrate that the approximation accuracy is notably dependent on the perturbation size, which is an interesting observation that the widely used small size cannot always guarantee the best performance. The underlying cause for our finding is understood through a comprehensive causal analysis: The result of FDTS-based studies could be affected by even small perturbations or interactions caused by perturbations at multiple remote locations. Further, this paper compares the accuracy and computing burden of first- and second-order approximations, advising that linear approximation is the most suitable for practical applications. The outcomes of this paper suggest that the reliability of FDTS-based analysis could be secured even in highly non-smooth power systems if the proper perturbation size is used. • Using small perturbation sizes for trajectory sensitivity may not always be proper. • Comprehensive case studies on perturbation sizes and non-smooth behavior. • Providing practical guidelines for adequately determining the perturbation size. [ABSTRACT FROM AUTHOR]

[Display omitted] • A physics-informed fast voltage control method of distribution network is proposed. • It develops a novel deep reinforcement learning algorithm with graph knowledge. • The proposed algorithm uses multiple agents with continuous action space. With the recent rapid uptake of photovoltaic (PV) resources, the overvoltage condition during low load periods or intermittent renewable generation is one of the most critical challenges for electricity distribution networks. Traditional model-based local or centralized control methods that rely on proper system parameters are difficult to mitigate rapid changes in power systems. Utilizing model-free/data-driven multiagent deep reinforcement learning (MADRL) has been recognized as an effective solution to active voltage control. However, existing MADRL-based control approaches trained solely on data are agnostic to the underlying real-world physics principles. Therefore, this paper aims to incorporate physical knowledge of regional distribution networks into MADRL's decision-making. The main contributions of this paper are summarized as follows. First, a novel physics-informed MADRL -based distributed voltage control method is proposed, which is still under a centralized training and distributed execution framework and only requires local measurements. Second, graph neural networks are employed to help MADRL agents learn graph knowledge (node features and topological information). Further, transformer is introduced to extract discriminative representations and ensure agents' cooperative control. Third, we adopt a physics-guided architecture of neural networks in the actor network to stabilize the training process and improve sample efficiency. Finally, simulation results based upon modified IEEE 33-bus and 141-bus networks validate the proposed method's effectiveness, robustness and computation efficiency. [ABSTRACT FROM AUTHOR]

• The original contribution of the paper is a dq-real domain admittance transfer matrix model of PV-qZ systems. • The study presents some of the the two main origins of instability in multi-terminal AC grid-connected PV-qZ systems. • The study also illustrates the weakness of GNC related to stability assessment and grid partition points. Photovoltaic (PV) power systems are becoming one of the most popular green power systems. Power converters are used in these systems. Among them, quasi-Z-source inverters (qZSIs) are currently on the rise. However, instabilities can appear in multi-terminal AC grid-connected power electronics, such as PV power systems, due to the interaction between power electronic controls and the grid. Modeling of qZSI-based PV power systems is lacking in the literature and stability assessment of grid-connected qZSI-based PV power systems is not yet well understood. Accordingly, the present paper contributes with an s -domain dq -real admittance transfer matrix model of qZSI-based PV power systems derived from their small-signal state-space averaged model. The paper also describes a systematic procedure to study multi-terminal AC grid-connected qZSI-based PV power systems by the nodal admittance method, where the proposed qZSI-based PV power system model is incorporated into the nodal admittance matrix to study stability concerns. Thus, AC grid dynamics in the presence of qZSI-based PV power systems can be investigated using impedance-based stability criteria. The proposed model and the procedure are applied in a stability study of two applications where solutions for improving stability issues are presented. In these applications, the two main causes of instabilities in AC-grid connected PV-qZ systems are analyzed in detail. The study is validated by PSCAD/EMTDC simulation.. [ABSTRACT FROM AUTHOR]

• Presenting a linear thermal model for a Li-ion battery using McCormick envelopes. • Analyzing the generated heat during continuous charging and discharging. • Optimal operation and controlling the temperature of a large-scale battery pack. The growing adoption of microgrids necessitates efficient management of electrical energy storage units to ensure reliable and sustainable power supply. This paper investigates a thermal management system (TMS) for maintaining the longevity of large-scale batteries. To streamline the thermal modeling of batteries, the McCormick relaxation method is employed to linearize a nonlinear and interdependent heat generation model. The thermal model of the battery follows a nonlinear behavior where the generated heat makes the battery system temperature soar, thereby affecting the thermal performance of the battery. To showcase the efficacy of the proposed approach, four distinct case scenarios are studied, highlighting the critical importance of batteries within microgrid operations. A comparative analysis is conducted between linear and nonlinear models for TMS performance. A quantitative assessment based on simulation results demonstrates the precision of the linearized model, particularly in a multitemporal optimal power flow and day-ahead scheduling of microgrids incorporating energy storage units. Controlling the battery temperature within a permissible range (from 15 °C to 40 °C) is achieved by using a heating, ventilation, and air conditioning (HVAC) system. The paper explores the economic implications of energy storage units in microgrids by extracting and comparing daily operational costs with and without battery integration. The findings reveal that the inclusion of energy storage units yields substantial economic benefits, with potential profit margins of approximately 20 % during typical working days and 60 % on weekends. [ABSTRACT FROM AUTHOR]

• An upscaling regional photovoltaic power forecasting scheme based on ANN is proposed. • A novel method of reference PV plants selection is proposed. • A power correction method is proposed to guarantee power forecasting accuracy. • The rolling forecasting accuracy is improved by integrating multiple ANN models. • The forecasting error is 4.04%, 3.45% and 2.86% in resolution of 1, 5 and 10mins. Along with the increasing penetration of photovoltaic (PV) power generation, regional power forecasting becomes more and more critical for stable and economical operation of power system. The key challenge of regional PV power forecasting technology is the lack of complete and accurate historical power data since not all PV plants are equipped with the precise real-time output power monitoring system. Besides, the computation burden will be heavy when the number of PV plants in the target region is large. This paper therefore proposes an upscaling minute-level regional PV power forecasting scheme using the data of the selected reference PV plants. In this paper, a novel method of reference PV plants selection is proposed by comprehensively considering the prediction accuracy of artificial neural network (ANN) as well as Pearson correlation coefficient. The reference PV plant selection coefficient μ is introduced as the comprehensive indicator for reference PV plant selection, which incorporates Pearson correlation coefficient and MAPE. In addition, a PV output power correction method is assumed to guarantee the proper operation of regional power forecasting. Besides, this paper proposes a flexible approach to effectively decrease the accumulated error of rolling forecasting by integrating the forecasting results under different temporal resolutions. In specific, the power forecasting results in temporal resolutions of 1 min, 5 min and 15 min are simultaneously derived and the performance between the traditional rolling forecasting and the proposed method is compared. The validity of the proposed method is finally verified using the collected historical power data of PV plants installed in a city of Eastern China. For time resolution of 1 min, 5 mins and 10 mins, the corresponding RMSE are 6.56, 5.73 and 4.85 and corresponding MAPE are 4.04%, 3.45% and 2.86%. [ABSTRACT FROM AUTHOR]

• The paper proposes combining DWT and RBFNN for fault detection in microgrids. • The approach achieves precise fault detection, notably for high-resistance single-phase-to-ground faults, with minimal error. • RBFNN and GRNN excel in accuracy and performance, while SVM handles high-dimensional datasets efficiently. • RBFNN exhibits high correlation coefficients, validating its robustness in fault classification. • RBFNN is the optimal choice for microgrid fault detection, balancing accuracy, training time, and simplicity. Microgrids are essential for integrating renewable energy sources into the power grid. However, fault detection is challenging due to bidirectional energy flow. Traditional relay-based systems struggle in microgrids, primarily because of limited fault currents from grid-connected renewable energy inverters. To address these challenges, this paper proposes a new methodology for fault detection and classification in a renewable microgrid. The main contributions encompass two key aspects. Firstly, it enhances fault detection performance in microgrids characterized by nonlinear relationships, including photovoltaic, hydrokinetic, and variable electric load systems. Secondly, the combination of the discrete wavelet transform with various types of neural networks and supervised learning techniques provides a robust methodology for fault detection and classification. The proposed approach is evaluated using an IEEE-5 feeder test bed representing a realistic ring network configuration. The results show that the radial basis function neural network model exhibited promising outcomes, yielding a low prediction error of 1.31 e-31, highlighting its practical potential for enhancing system reliability and performance. Furthermore, various test cases were conducted by altering the ground resistance to train the neural networks, demonstrating the effectiveness of this neural network in accurately identifying fault conditions. Additionally, this research achieved promising outcomes with other models, including support vector machine and nonlinear autoregressive with external input, emphasizing the adaptability of these models in fault detection. [ABSTRACT FROM AUTHOR]

• A two-stage risk dispatching model for integrated transmission and distribution networks is proposed. The day-ahead phase focuses on the economics of the transmission and distribution network, while the intra-day phase focuses on operational safety. • The four dimensions of regulable resources, such as power side, grid side, load side and energy storage side, are coordinated to optimally dispatch the transmission and distribution network. • An improved particle swarm (PSO) algorithm solution model is proposed. In this paper, the dynamic adjustment of the inertia weight factor and learning factor can improve the ability to globally search for optimal values and increase the convergence speed of the algorithm. With the incorporation of more renewable energy sources, distribution networks are shifting from passive to active. The interconnection of the transmission and distribution networks will increase and the tidal currents will become bidirectional, affecting the stable operation of the transmission and distribution networks. This paper proposes a multi-timescale risk dispatch study for transmission and distribution networks that have a high proportion of distributed energy access to meet the rising demand for coupling between the two types of networks. First, a day-ahead scheduling model that takes into account various operational risks is developed with the goal of minimizing total operating costs, and it optimizes the source network load and storage of multiple adjustable resources of the transmission network and distribution network jointly under the risk limit constraint. Second, an intraday scheduling model is built with the goal of minimizing the risk cost of the transmission network and distribution network, and the day-ahead scheduling plan is modified by considering the day-ahead forecast error and the different operational risks of the transmission network and distribution network. Finally, the effectiveness of the proposed multi-time-scale risk dispatch model is verified through the analysis of arithmetic cases, and it is proved that the model can enable the interaction and coordination between transmission and distribution networks as well as the synergistic optimization of operating costs and operating risks. [ABSTRACT FROM AUTHOR]

This paper assesses the difference of optimal operation of energy communities (ECs) with respect to economic and technical goals. ECs have emerged as a promising solution for accelerating the transition to more sustainable energy systems and therefore climate change mitigation. While cost optimization (economic goal) is most commonly used in ECs, optimizing their resilience (technical goal) can be an important part of operating a distribution grid with high photovoltaic (PV) and electrical vehicle (EV) penetration in the future. This paper presents a comparative analysis of the impact of those two objective functions on overall EC costs as well as individual member costs. The findings highlight the trade-off between the flexibility measures required for a resilient EC and the cost associated with them. This study helps quantify the subsidies that would be required to incentives EC to operate in a resilient matter as a form of grid service. • An energy community optimization model with multiple objective function options. • Energy production, flexibility and grid constraints in single energy community model. • Considering grid tariffs and energy allocation to members. • Cost optimization results show high demand/production peaks. • Resiliency optimization results show high financial burden on members. [ABSTRACT FROM AUTHOR]

• This paper presents an enhanced computational optimizer of the Social Network Search Technique (ESNST) for multi-dimension Optimal Power Flow problem. • The proposed ESNST is introduced with two strategies. • The multi-dimension OPF in EPGs is considered with several minimization objectives of fuel costs, grid Losses, and produced emissions. • The performance of the SNST and ESNST are evaluated on two systems. • The results reveal the solution quality and robustness of the proposed ESNST and recent algorithms. This paper presents an enhanced computational optimizer of the Social Network Search Technique (ESNST) for multi-dimension Optimal Power Flow (OPF) in Electrical Power Grids (EPGs). The SNST is motivated by social network users who have various moods: conversation, imitation, innovation, and disputation. The proposed ESNST is introduced with two strategies. The first is the aggressive exploit process, which aims to increase the number of people seeking the best possible perspective to develop SNST performance. The second strategy proposes an adaptive parameter to aid in higher exploitation towards the end of iterations. This paper considers the multi-dimension OPF in EPGs with several minimization objectives for fuel costs, grid losses, and produced emissions. Not only that but also the system's power demands and losses must be satisfied. The performance of the proposed SNST and ESNST is evaluated on IEEE standard 30-bus, 57-bus, 118-bus, and practical West Delta Region EPGs. The results reveal the solution quality and robustness of the proposed ESNST compared with the SNST and other relevant techniques reported in the literature. [ABSTRACT FROM AUTHOR]

• A stochastic coordinated generation and transmission expansion planning model is proposed. • The planning model takes into account the impact of demand response programs and renewable energy development. • The detailed demand response model with operating characteristics such as power, energy, reserve, response period, and response number is established. • The chance-constrained method is introduced into the planning model to flexibly control the participation level of DR programs. The integration of high-penetration renewable energy has led to a significant increase in the uncertainties of power systems, and coordinated generation and transmission expansion planning has attracted more and more attention. Demand response resources are regarded as a kind of virtual power supply, which can improve the flexibility of power systems and delay generation and transmission investment to a certain extent. This paper establishes a stochastic coordinated generation and transmission expansion planning model taking into account the impact of demand response programs. In particular, the demand response model describes the operating characteristics such as power, energy, reserve, response period, and response number in detail. Considering the difference in the degree of invocation of demand response programs by different power systems, the chance-constrained method is adopted, which can make the planning schemes flexibly adapt to different demand response levels and improve the practicability of the model. In the case study, numerical results of construction and operation indicate that demand response programs can play a role in replacing generation and transmission capacity. Specifically, although the response energy does not exceed 0.3% of the total load energy, the investment cost can be saved up to more than 20%. Moreover, the response level, flexibility parameters, response capacity, and the proportion of renewable energy will all affect the capacity substitution effect of demand response, which verifies the rationality and necessity of considering these factors in this paper. [ABSTRACT FROM AUTHOR]

• The proposed voltage control method provides optimal voltage profiles in various LVDC and MVDC electric railway systems by minimizing inter-area voltage drops. • The proposed voltage control method maximizes the release of the line capacity and minimizes the power losses by minimization of inter-area current. • The proposed voltage control method is a decentralized and distributed voltage control method that employs the DC voltage of DC electric railway networks rather than telecommunication systems. • The proposed voltage control method benefits from simplicity, cheapness, high reliability, expandability and modularity. • Any changes in the power, number and location of trains, traction substations, distributed generators, ESS's and the length of electric lines in LVDC and MVDC electric railway systems cannot perturb the performance of the proposed voltage control method. The medium voltage DC (MVDC) electric railway system is one of the most interesting options for future high-speed rail (HSR) lines. The dc voltage control is one of the most critical challenges of MVDC electric railway systems due to various reasons such as simultaneous, continuous and considerable changes in the power and location of trains, regenerative brake energy of trains, long power lines, the application of ESS's and RES's. In this paper, a voltage control, i.e., the optimal-voltage voltage-power (OVVP) control method, is presented for MVDC electric railway systems. OVVP control method is a practical, reliable, automatic, and modular distributed voltage control method. The proposed voltage control method satisfies the nearest voltage to the nominal value in each node and the smoothest voltage profile in different MVDC electric railway systems. Although the analyses carried out in this paper analytically prove the significant performance of the presented voltage control method, different challenging scenarios are considered to verify OVVP control method more. In addition, the results of the proposed voltage control method are successfully validated by GAMS software. [ABSTRACT FROM AUTHOR]

• This paper proposes a concept that utilizes historical time-series data from transmission system operators (TSOs) to estimate the optimal day-ahead energy-mix proportion for a power system dominated by converters. • This paper employs a long short-term memory (LSTM) network as a data-driven model to forecast the day-ahead values of key parameters. • To ensure secure system functioning, an energy-mix operation and reserve scheduling model is developed. • This paper emphasizes the importance of power system security in incorporating inverter based resources (IBRs). Advancements in various scientific fields have encouraged the development of novel tools, techniques, components, methodologies, and innovations aimed at addressing the challenges encountered in modern power systems dominated by inverter-based resources (IBRs). This paper focuses on a concept that leverages historical time-series data obtained from transmission system operators (TSOs) to enhance the secure management and operation of power systems. By employing a data-driven model, the day-ahead values of power generation and load consumption are estimated and integrated with a dynamic model of the power system for further analysis. To optimize energy generation and ensure grid stability, an energy-mix operation and reserve scheduling model is utilized. This model optimally combines different power-generating technologies, including synchronous generators (SGs), grid-following converters (GFLs), and grid-forming converters (GFMs), to meet the energy demands of the day while enhancing the overall system strength. The findings are supported by quantitative analysis utilizing variables such as frequency, power production, terminal voltages, and system non-synchronous penetration (SNSP). Simulation results demonstrate that implementing the proposed concept enables the power system under consideration to operate securely, even in the face of a 38% increase in immediate load, with a maximum SNSP ratio of 59%. These findings highlight the effectiveness of the proposed approach in addressing the reliability, system dynamics, stability, control efficiency, and security challenges posed by IBR-dominated power systems. Furthermore, it is believed that this research contributes to the ongoing efforts in decarbonization, renewable energy integration, and combating global warming by facilitating the secure and optimized operation of renewable energy-dominated power systems. [ABSTRACT FROM AUTHOR]

• This study is the first to comprehensively investigate the conflicting effects of virtual inertia on VSG transient stability under different severities of grid voltage sag, providing new insights into the control of VSG. • Faults, such as grid voltage sags, are classified into two types: transient tolerable faults and transient intolerable faults. The proposed fault-type classification provides a clear insight into the transient impact of virtual inertia on VSG under different severities of faults. • We propose a fault-type identification method based on LVQ neural networks, which can distinguish between the two types of faults within 5 ms, enabling timely control strategy adjustment. The virtual synchronous generator (VSG) control, widely used for voltage source inverters, is prone to the loss of synchronization (LOS) under large disturbances such as grid voltage sags. Despite the significant amount of research that has been conducted on the transient stability of VSGs, the existing conclusions on the influence of virtual inertia under different fault conditions remain controversial. In this paper, the conflicting effect of virtual inertia on VSG transient stability under different severities of grid voltage sag is comprehensively investigated. Faults, like grid voltage sags, are classified into two types in this paper: transient tolerable faults and transient intolerable faults. Moreover, a unified control framework for rapid fault-type identification and transient stability improvement is proposed. The Learning vector quantization (LVQ) neural networks are used to distinguish fault types within 5 ms. Based on the fault-type identification results, the proposed control strategies are applied to enhance the transient stability of VSG. Finally, simulations and control-hardware-in-loop experimental validations are carried out to demonstrate the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

Climate change introduces a new set of vulnerabilities. It might cause unexpected voltage and frequency violation problems that can damage the existing power system configurations. Identifying the zones containing more critical violations in a bulk system under different climatic conditions and contingencies is crucial to securing the power system operation and infrastructure safety. This paper presents an advanced critical zone identification framework that can retrieve information from extensive data yielded by dynamic contingency analysis results from a large interconnected power grid. A machine learning (ML) based clustering approach is applied to identify the critical zone under hundreds of scenarios. The developed framework is tested using the 2028 western electricity coordinating council (WECC) system, and the detailed results are discussed in this paper. • The primary contribution of this work is the development of an ML-based methodology to detect the critical zone that experiences the majority of constraint violations across various scenarios. • This is achieved by grouping all critical zones using an ML-based clustering approach, effectively resolving the time to localize the critical zones for a bulk electric grid. • The innovation of this work lies in the robust integration of the independently developed models and tools to evaluate the existing system under severe events and extreme weather scenarios, coupling the ML approaches and engineering planning strategy with quantifiable metrics, which returns concise and accurate information for relevant stakeholders such as power system analytic engineers. [ABSTRACT FROM AUTHOR]

• A comprehensive evaluation and comparison of the stability performances of the GFL and GFM control schemes of the cascaded hybrid converter under weak grids is implemented for the first time. • Different impacts of the coupling between LCC and MMC in the cascaded hybrid converter on the GFL and GFM control schemes are revealed and two control schemes' sensitivities to parameters detuning of the system are analysed It is found that, • Both the GFL and GFM control schemes considerably improve the stable regions of the system under extremely weak grids (SCR < 2). Although the GFM control scheme is better than the GFL one, there is a certain limitation. The improvement of the GFM control scheme in the system's capability to withstand a low wind power output compared to the GFL one is gradually less noticeable with the decrease of SCR of the power grid. • The coupling between LCC and MMC in the cascaded hybrid converter has a significant impact on the stability of the system under the GFL control scheme. Both LCC and MMC are involved in the dominant mode of the system. In contrast, under the GFM control scheme, the dominant mode of the system is almost exclusively related to MMC, with a negligible relationship to the rest of the system. • The GFL control scheme has a high sensitivity to the control parameters of LCC and MMC, and is prone to instability due to parameters detuning of either converter. Whereas the GFM control scheme is only sensitive to the control parameters of MMC and is more robust to parameters detuning. The conventional line commutated converter based high voltage direct current (LCC-HVDC) system is no longer suitable for transmitting wind power integrated with weak grids. Therefore, a cascaded hybrid converter consisting of LCC and modular multilevel converter (MMC) connected in series is considered as a promising solution in this paper. And a grid-following (GFL) control scheme and a grid-forming (GFM) control scheme are designed for the cascaded hybrid converter. To investigate the stability performances of the proposed two control schemes, this paper develops a small-signal model of the cascaded hybrid HVDC system for wind power integrated with weak grids. Then, based on the eigenvalue analysis method, several issues of concern are investigated for the proposed GFL and GFM control schemes, including their tolerance to a weak grid and a low wind power output, significant participants and sensitivity to parameter detuning. Based on the analysis results, one of the two that is more suitable for weak grids is recommended. The time-domain simulations implemented in PSCAD/EMTDC confirm the validity of the model and analysis results. Index Terms —Cascaded hybrid converter, grid-following, grid-forming, wind power, weak grids. [ABSTRACT FROM AUTHOR]

• An experiment for comparison of three different current limiting topologies is conducted. For the same tape consumption of 17 m, the limiting rates of R-SFCL, FC-SFCL and H-SFCL are 10 %, 28 % and 58 % respectively within the DC voltage range of 240–440 V. Both FC-SFCL and H-SFCL have good current limiting effect. Compared with FC-SFCL, the H-SFCL has stronger flexibility and adaptability, and there is no quenching recovery time, which makes it better cooperate with the DC circuit breaker to realize automatic reclosing. Therefore, H-SFCL is the most suitable superconducting current limiter for MVDC SPS. • This paper puts forward an optimal allocation method of H-SFCL on MVDC SPS. To solve the problem of optimizing the number and position of current limiters, a dual objective hierarchical optimization configuration method is proposed with the goal of minimizing the maximum allowable current and inductance energy of circuit breakers. The optimization of the number, position, and internal component parameters of current limiters is achieved on a four-terminal system. The results show that the proposed hierarchical optimization configuration method can effectively achieve the optimization of position and component parameters. • An improved four objective optimal allocation method suitable for circuit breakers and H-SFCLs is proposed to address the issue of the breaking sequence between the internal switch in H-SFCL and the external circuit breaker. The results showed that the maximum effective individual ratio within the first 20 generations of improvement was 88%; The improved iteration speed has significantly increased, and the effective individual ratio in the 5th generation can reach 100%, effectively improving the effective individual ratio in the optimization iteration process and achieving overall optimization of isolation and current limiting equipment. Medium voltage direct current shipboard power system (MVDC SPS) is the development trend of navy in the future. At present, one of the bottlenecks restricting the development of MVDC SPS is that the short fault. There is a lack of effective means to limit short fault current to protect MVDC SPS. This paper presents a method of applying a hybrid type superconducting fault current limiter (H-SFCL) to MVDC SPS protection. The architecture and system modeling of MVDC SPS are introduced, and the mechanism of bipolar DC short fault is analyzed. The topology and working principle of H-SFCL are introduced. The small-scale prototype experiment is done, the current limiting effect of H-SFCL is compared with resistive type superconducting fault current limiter (R-SFCL) and flux-coupling type superconducting fault current limiter (FC-SFCL) in the prototype test, so as to verify the superiority of H-SFCL. A dual objective hierarchical optimization configuration method is proposed, and the number and position of H-SFCLs are verified on a four-terminal system, as well as multi-objective optimization for H-SFCLs. A fault isolation and H-SFCL optimal allocation evaluation model is proposed; An improved method suitable for fault isolation and multi-objective optimal allocation of H-SFCLs is proposed to address the issue of breaking timing between internal switches in H-SFCLs and external circuit breakers in the optimization process. The research results indicate that the proposed optimal allocation method can optimize the inductance, resistance, and switch breaking time inside the current limiter, and can match the timing with the external circuit breaker; The proposed multi-objective optimization configuration method has a maximum effective individual ratio of 88% in the first 20 generations of improvement, and the improved iteration speed has significantly increased. In the 5th generation, the effective individual ratio can reach 100%. [ABSTRACT FROM AUTHOR]

• Investment portfolio and planning strategy under limited budget for resilience enhancement to realize adaption and mitigation to the risk of extreme disasters under climate change are discussed. • Insurance incorporated as a supplementary strategy to enhance resilience is co-optimized with security investment from the perspective of distribution system operators in the planning stage. • Both emergency power support under extreme disaster scenarios and efficient renewable energy consumption under normal operation scenarios of energy storage are considered. • Entire normal-failure-recovery-loss process to address climate change is considered and modeled as a stochastic mixed integer linear optimization problem based on scenarios. Severe damage and high economic losses caused by frequent extreme disasters are becoming unbearable for distribution system operators (DSOs) under climate change. In order to cope with extreme disasters, this paper proposes an investment portfolio and planning framework of multi-resource for resilience enhancement. In the investment portfolio and planning framework, insurance is incorporated to mitigate high economic losses as a risk sharing and resilience enhancement supplementary strategy, and co-optimized with security investment from the perspective of DSOs. Firstly, the insurance investment is modelled based on Gordon-Loeb model according to insurance industry principles and formulated as constraints by piecewise linearization techniques. Secondly, the investment portfolio and planning framework proposed in this paper is modeled as a scenario-based two-stage stochastic mixed integer linear optimization program (MILP). In the first stage, DSO makes investment and planning decisions including energy storage (ESS) allocation, line hardening strategy and insurance investment. Both operation strategies of normal operation scenarios and extreme disaster scenarios under climate change are optimized in the second stage. Finally, progressive hedging (PH) algorithm is applied to solve the two-stage stochastic MILP model. The proposed model and algorithm are tested on the modified IEEE 33-bus test system. The results verify the validity of investment portfolio and planning framework, and the results show that portfolio investment considering insurance can realize resilience enhancement in both load shedding and economic losses. [ABSTRACT FROM AUTHOR]

• Traditionally, assessment of static voltage stability for distribution power networks with distributed generation (DG) utilizes the continuous power flow (CPF) method by calculating load margin index (LMI) at various load levels, which suffers from slow calculation speed and low accuracy when power flow calculation becomes ill-conditioned. • To overcome this issue, this paper presents a novel holomorphic embedding load flow method (HELM)-based approach that calculates voltage stability indices for various types of nodes in distribution network. • Different orders of sensitivity information are calculated using the HELM method, and the criteria for assessing voltage stability are derived, which are used as constraints to optimize the location and capacity of DG. • Such formulation of the optimization problem does not need to calculate the maximum load margin using CPF that can be effectively solved using the Genetic Algorithm and easily adaptable to various operating conditions of DG. • The effectiveness of the proposed approach is verified on IEEE 33-node and 69-node distribution power network model. • Results show that considering the HELM VSI, the location and capacity of DG in the distribution network can be better optimized. Traditionally, assessment of static voltage stability for distribution power networks with distributed generation (DG) utilizes the continuous power flow (CPF) method by calculating load margin index (LMI) at various load levels, which suffers from slow calculation speed and low accuracy when power flow calculation becomes ill-conditioned. To overcome this issue, this paper presents a novel holomorphic embedding load flow method (HELM)-based approach that calculates voltage stability indices for various types of nodes in a distribution network. Different orders of sensitivity information are calculated using the HELM method, and the criteria for assessing voltage stability are derived, which are used as constraints to optimize the location and capacity of DG. Such formulation of the optimization problem does not need to calculate the maximum load margin using CPF. Moreover, it can be effectively solved using the Genetic Algorithm and easily adaptable to various operating conditions of DG, which improve the calculation speed of the stability index. The effectiveness of the proposed approach is verified on IEEE 33-node and IEEE 69-node distribution power network models. Results show that considering the HELM VSI, the location, and capacity of DG in the distribution network can be better optimized. For the IEEE 33-node model, the total cost is reduced by approximately 2.33%, the network loss is reduced by 1.2%, and the HELM voltage stability criteria index is increased by about 4.23%; while for the IEEE 69-node system, the total cost is reduced by about 2.98%. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of how corona losses on transmission lines depend on weather conditions in their vicinity. Two years of synchronized phasor measurement data has been collected to monitor corona losses over a longer period of time. From the same time period, both hourly and 10 min weather monitoring data has been obtained for comparison. The dependence between various weather parameters and corona losses is presented with graphical data analysis. In addition, feature importance methods have been applied to rank the weather parameters and determine which of them have the largest influence on the occurrence of significant corona losses. The results presented in this paper are directly applicable for transmission systems operators for adequate planning of system operation. • Transmission network corona loss monitoring using Phasor Measurement Units. • Analysis of corona loss dependency on various weather parameters. • Ranking of weather parameters based on importance. • Dependency of data availability on corona loss estimation results. [ABSTRACT FROM AUTHOR]

• The proposed joint demand response and dynamic pricing strategies can make the net grid demand curve smoother and have practical significance. • The dynamic pricing strategy helps to realize the joint dispatch of multiple demand response resources in the region and alleviate the grid pressure during peak hours. • A two-layer optimization model is proposed to not only realize the economy of joint operation of multiple energy stations, but also make the net grid demand curve smoother through joint demand response. In recent years, countries around the world have made great efforts to coordinate energy green and low-carbon development and energy supply. In this context, it is of great significance to build energy stations that can greatly absorb renewable energy. The coordinated operation of multi-energy stations in the region can expand the role of energy stations and strengthen energy complementarity between regions. Aiming at the problem of energy interaction and coordinated operation of multi-energy stations in regional integrated energy system, this paper proposes a two-layer scheduling optimization model, which can effectively reduce the system operation cost and carbon emissions. At the same time, considering the joint demand response, it can effectively reduce the peak power supply pressure of the power grid. In addition, in order to ensure the accuracy and efficiency of the solution, this paper improves the traditional NSGA-II algorithm, greatly improving the overall performance of the algorithm. Finally, the simulation analysis is carried out through an example. The results show that the operation optimization model proposed in this paper can effectively reduce the total energy cost of the system, reduce carbon dioxide emissions, and reduce the peak pressure of the power grid. The coordinated operation optimization method is effective and feasible. [ABSTRACT FROM AUTHOR]

• BESS model which can accurately describe BESS's power regulation behavior and provide a correct state of charge. • Simplifying method to enable the proposed model to finish 24 h-simulation within a few minutes. • BESS-based strategy to improve the AGC performance of wind farms. Battery energy storage system (BESS) is being widely integrated with wind power systems to provide various ancillary services including automatic generation control (AGC) performance improvement. For AGC performance studies, it is crucial to accurately describe BESS's power regulation behavior and provide a correct state of charge (SOC). In addition, BESS model is required to maintain a sufficiently high simulation speed, since it usually is involved in hour- or day-scale simulations. Different from existing models, this paper develops a new BESS model which considers DC-AC converter control, DC link circuit and switching loss, thus providing an accurate power regulation behavior. In addition, it also considers the nonlinear relationship between open-circuit voltage and SOC of battery so that it provides a correct SOC. As a whole, the BESS is simplified as a controlled current source with fundamental frequency (50/60 Hz) and described by algebraic phasor equations to reduce computational burden. This makes the proposed model capable of finishing hour- or day-scale simulations within a few minutes. Time-domain simulations are used to validate and compare the simulation accuracy with the classical first-order transfer function model and electromagnetic model. Based on the proposed model, this paper also introduces and verifies a new BESS-based strategy to improve the AGC performance of wind farms. [ABSTRACT FROM AUTHOR]

This paper introduces a pilot protection method for two-terminal transmission lines based on the measurement residual of an extended Kalman filter designed to track alternate current signals. Transmission lines that interconnect generation plants to consumers are the primary equipment most susceptible to faults, and failing to isolate them correctly and promptly may lead to system collapse. In this context, the measurement residual allows for rapid fault identification and tripping. In addition, the proposed solution requires computing and communication resources typically available for pilot protection since it uses conventional sampling rates and has a low computational burden. This paper details the theory and application of the extended Kalman filter and the results of the proposed method when tested against different simulation scenarios. These scenarios were built on an extra-high voltage transmission system implemented in ATP/EMTP, varying fault impedance, inception angle, distance, phases involved, and fault type. It also presents a statistical analysis of these scenarios, including channel asymmetry, errors in the current transformers' conversion rate, and noise. Besides, it describes an analysis of the proposed method regarding current transformer saturation, high impedance faults, zero-crossing faults, external breaker opening, and power-swing. Finally, it compares the solution with other algorithms in the literature. The results indicate that the proposed solution is fast, accurate, secure, and dependable. • Transmission lines are susceptible to faults that need fast isolation. • Fast isolation preserves stability, avoids equipment damage, and reduces life risk. • The method is based on the extended Kalman filter; estimates the signals' behavior. • Method tested against simulations from an existing 500 kV system. • Faster than conventional protection algorithms, secure, dependable, and accurate. [ABSTRACT FROM AUTHOR]

Accurate wind power forecasting can enhance the safety, stability, economy and controllability of the power system. Traditional physical methods and statistical methods are easily affected by data quality and extraction methods in wind power forecasting. The commonly used recursive neural network method may have memory decline phenomenon in wind power forecasting and does not support parallel calculation, thus limiting the forecasting accuracy. To solve the above problems, in this paper, a wind power forecasting method based on EMD-CCTransformer is proposed. The network model is based on an encoder–decoder structure, where the encoder is used to parse historical wind power sequences, the decoder generates future wind power, and the encoder and decoder are connected using an attention mechanism. In this method, the EMD algorithm is used to decompose the wind power series and obtain the changes of power signals in different time scales, which improves the ability of Transformer to maintain long-term information. Meanwhile, in view of the partial unknowability of the Transformer model, the convolutional attention mechanism is introduced to replace the dot product attention mechanism to form the CCTransformer model, which further improves the forecasting accuracy. We use large-scale wind power data (annual data of the year of 2020) to train and test the proposed model. Experimental results show that compared with commonly used wind power forecasting methods, the forecasting error of the proposed EMD-CCTransformer forecasting method in this paper is lower and its model training time is further shortened. • The ability of local feature extraction is improved by causal convolution. • Features of different time scales are generated based on EMD algorithm. • A Transformer model combining EMD and causal convolution has significant advantages in forecasting accuracy. [ABSTRACT FROM AUTHOR]

• Power transformers have a non-linear behavior due to the magnetic core saturation. • Saturation must considered because it affects their performance and efficiency. • This paper proposes a transformer model based on the inverse Jiles-Atherton theory. • Experimental results show that this model predicts core losses with accuracy. • The proposed model can be applied to many other magnetic devices. Power transformers are devices with non-linear behavior due to the saturation of the ferromagnetic core. When modelling such devices, the saturation effect must be taken into account because it greatly affects their performance and efficiency. In this paper, an electromagnetic model for power transformers is proposed and experimentally validated using an electrical T-model coupled with a reluctance network to model the magnetic part. The electrical circuit and the reluctance network are linked by two B–H approaches. The B–H relationships are modelled by the full hysteresis cycle based on the inverse Jiles-Atherton theory and by the initial magnetization curve. The results obtained with the inverse Jiles-Atherton theory model reproduce the magnetic core behavior with more accuracy than the one based on the initial magnetization curve, especially at low load conditions where saturation plays a more prominent role on the no-load current. The proposed model can be applied to other magnetic devices such as inductors for power electronic applications or electromechanical relays, among others. [ABSTRACT FROM AUTHOR]

• The papers accepted by the guest editor team of the special issue " Flexible and Resilient Urban Energy Systems " are reviewed. • This Special Issue is devoted to collection of the state-of-the-art on the original research and approaches in FRUES to improve the flexibility and resilience of urban energy systems to address and minimize the impact of multi-vector uncertainties, cyberattacks and natural disasters. • Data-analytic methodologies published in this Special Issue have clearly shown the superiority of new technologies such as recovery and restoration strategy as well as situational awareness, flexible planning and robust operation. This guest editorial summarizes the topics and the papers selected for the Special Issue on Flexible and Resilient Urban Energy Systems. After rigorous reviewing process, 21 papers are accepted for publication. These 21 accepted papers cover various aspects of urban energy systems and are distributed as following: situational awareness of urban energy systems (2 papers), quantification metrics of flexibility and resilience of urban energy systems (3 papers), vulnerability modeling of urban energy systems under various extreme events (3 papers), planning of flexible and resilient urban energy systems (4 papers), robust and resilient operation and control of urban energy systems (4 papers), recovery and restoration strategy of urban energy systems (2 papers), and coordination and interoperability of interconnected energy systems (3 papers). The Guest Editorial Board hopes this Special Issue can provide a valuable information for future research and advancements in the field of flexible and resilient urban energy systems. [ABSTRACT FROM AUTHOR]

• A novel concept of mobile energy storage is proposed in this paper. • A detailed modeling of mobile compressed air energy storage with higher dispatchability and storage capacity is presented. • In concern to routing challenges, Google map's Application Programming Interface is used to find the target location. • A new heuristic-based technique that overcomes deficiencies of traditional constraint handling methods is proposed. • The proposed framework is tested through the IEEE 33-bus and 136-bus networks with different scenarios. • Various reliability indices and operating profits are measured to demonstrate the applicability of the proposed technology. Efficient energy storage technology is one of the key elements to enhance the flexibility, economy, and security of the power system. With the continuous development of energy storage technology, containerized mobile energy storage is coming into view, which has offered promising opportunities to improve distribution network (DN) performances and grid operating factors against emergencies. This paper proposes the concept of mobile compressed air energy storage (CAES) for an electric DN. The movable air storage tanks with stored energy are transported by trucks and placed at some distribution nodes/buses to improve DN performance. To overcome routing challenges for trucks, the configuration of the grid is mapped on the urban region of the city of Sydney, Australia, using Google map's Application Programming Interface. This approach can accurately model distances between current and targeted locations, unavailability of tanks during traveling, route congestions, and fuel consumptions. A new heuristic mathematical method is proposed in this paper to convert the constraints of the mobile CAES (MCAES) model into feasible search spaces, which significantly improves the convergence quality and speed. Operating results for both stationary and mobile CAESs are presented and compared. The methodology is applied to IEEE 136-bus DN in addition to IEEE 33-bus DN to demonstrate the competence of MCAES for larger-scale grids in optimizing the total operating profit, active power loss, energy not supplied, and voltage stability index of the grid. The crucial application of the proposed model can deal with natural disasters to avoid large-scale power outages and, eventually, mitigate the power system damages. [ABSTRACT FROM AUTHOR]

• Fusing uncertainties divide-and-conquer and multi-attribute adversarial learning. • Design a divide-and-conquer mechanism for multi-source uncertainties problem. • Design an adversarial learning mechanism for temporal and spatial characteristics. • The proposed method is validated with real-world datasets. The rapid development of the Internet of Things and device-level meters provides accurate energy consumption data for various household devices, and making full use of these data to achieve higher accuracy of residential load forecasting is an open problem. Moreover, the uncertainties and insufficient feature extraction of variables make it challenging for individual residential load forecasts. In this regard, this paper proposes a novel short-term residential load forecasting method. It has the following aspects: (1) Considering the multi-source uncertainties, a multi-source uncertainties divide-and-conquer mechanism is proposed, which classifies the residential load from the device level according to different sources of uncertainties and forecasts separately. (2) Considering the multiple attributes of influencing variables, a multi-attribute adversarial learning mechanism based on the conditional Wasserstein generative adversarial network with gradient penalty (cWGAN-GP) is designed. In cWGAN-GP, this paper uses a long short-term memory network to implement the generator and uses a convolutional neural network to implement the discriminator. The former is used to extract temporal features, while the latter is used to extract spatial features, and they realize the fusion of multiple attributes through adversarial training to improve prediction accuracy. Compared with existing load forecasting methods, our proposed method's mean absolute percentage error decreased by 1.5–38.9%, mean square error decreased by 3.5–35.9%, normalized root MSE decreased by 1.7–19.9%, and mean absolute error decreased by 3.7–27.0%. [ABSTRACT FROM AUTHOR]

This paper investigates the energy management of an Energy Internet (EI) that integrates multiple energy networks. Based on the structure of EI and the fluctuation of load, an optimal energy management model considering part of the load as time-varying factor is proposed. Under the influence of load, the actual energy management problem (EMP) is formulated as a time-varying optimization problem subject to a set of global and local constraints. Its optimal solution varies continuously with time, which leads to difficulties in obtaining optimal solutions by conventional algorithms. Consequently, to obtain better tracking performance, this paper proposes a distributed inertial projection neurodynamics algorithm (DIPNA) based on the Nesterov accelerated gradient descent method. This algorithm tracks the optimal solution of the EMP with a fast convergence rate O 1 / t 2 , providing a referenceable active power for each energy unit in real time. Finally, the performance evaluation results demonstrated the effectiveness and fast convergence of the proposed algorithm. • Collaborative management of multiple energy sources throughout the energy internet system is achieved. • The model takes into account the fluctuation of load • Proposes a distributed reach dynamics algorithm with fast convergence characteristics. [ABSTRACT FROM AUTHOR]

• It is proposed a topology consisting of an input step-up stage, followed by a step-down stage and an unfolding inverter. • A decentralized control strategy of the DC-DC stage allows maximizing the renewable energy harvest and synthesizing an output current to be injected into the grid with low harmonic distortion. • The grid current controller proposed in this paper consists of a reduced number of resonant stages meeting the energy quality required by standards. • The article introduces a novel extension of a formerly presented design strategy for Proportional + Resonant controllers, to include harmonics compensation. • A 500 W prototype converter was implemented, and the experimental results show a fast transient response to step changes in both the input current and the phase angle reference. Also, the multi-resonant controller design presented in this article resulted in an injected current with a THD of 3.37%, compliant with the IEEE Std. 1547–2018. This paper presents a two-stage current-source DC-AC converter for grid-connected PV applications which is composed of an input step-up stage, followed by a step-down stage and an unfolding inverter. A decentralized control strategy of the DC-DC stage allows maximizing the renewable energy harvest using an Incremental Conductance MPPT algorithm and synthesizing an output current to be injected into the grid with low harmonic distortion. Double-loop PI controllers are used for the boost stage. The DC bus voltage of the buck stage is regulated using a PI controller, and an inner Proportional-Resonant (PR) controller tracks a sinusoidal reference. The PR controller proposed in this paper, includes a reduced number of resonant stages meeting the energy quality required by standards, which results in good stability margins. Finally, a SOGI-FLL algorithm synchronizes the inverter operation with the grid. Experimental results show an excellent dynamic response of the system, and the injected current complies with the IEEE Std. 1547–2018 specifications regarding harmonic content using a control law with a low computational burden. [ABSTRACT FROM AUTHOR]

• The restoration processes in electricity and gas systems are coordinated in both spatial and temporal scales to enhance restoration efficiency and security. • The electricity and gas system coordination are achieved in a decentralized manner to preserve their information privacy. • A high-accuracy gas flow dynamics model is proposed. • An efficient solution algorithm is proposed with great calculation performance. The ever-increasing couplings between electricity and gas systems highlight the coordinated restoration decisions for interdependent electricity and gas system (IEGS) to enhance resilience. However, the distinct timescales of power and gas flow rates as well as information privacy concern cause additional complexities in making restoration decisions, and large calculation scale and nonconvexity also results in computational obstacles. To address these issues, this paper proposes a hybrid spatio-temporal scale decentralized restoration strategy for IEGS to enhance restoration efficiency and security. First, in the spatial scale, the network sectionalizing and the restoration processes in sectionalized electricity and gas systems are coordinated in a decentralized manner with limited boundary information interactions to respect information privacy. Next, the impacts of distinct timescales of power and gas flow rates are explored to accelerate restoration, and a linear gas flow dynamics model is also proposed to capture the gas transmission dynamics with high accuracy, enhancing restoration security. Furthermore, a decomposition-based alternating direction method of multipliers algorithm is proposed to efficiently solve the proposed IEGS restoration strategy, showing good calculation time and convergence performance. Finally, the effectiveness of the proposed restoration strategy is validated in a T118N20 test system and a real-world system, demonstrating the enhanced restoration efficiency, security alongside commendable computational performance. [ABSTRACT FROM AUTHOR]

Electrical power distribution systems are experiencing a deep penetration of renewable energy integration, which is reversing the power flow during some periods and modifying their conventional operation. In this context, the curtailment of renewable distributed generation is needed to consider the electrical limitations of transformers and lines, mainly voltage deviations and power overloads. Multiport converters with energy storage stand as a potential solution for enhancing power flow operation in the distribution system and minimising renewable generation curtailments. This paper presents an optimisation-based methodology to size multiport power converters and a techno-economic comparison to other conventional approaches. The optimisation includes energy storage components and AC power flow constraints. Moreover, specific days are considered to reduce computational requirements. This methodology is evaluated in a case study based on a medium voltage benchmark network from CIGRE to identify the best scenarios where multiport converters can be considered as a potential solution. Results conclude that the multiport converter provides clear advantages and is economically viable specially in scenarios with unbalanced distributed generation in the feeders, where their rated power is around 25 MVA, or if batteries are initially installed in the feeders. [Display omitted] • Optimisation-based methodology to size a multiport converter. • Multiport converter comparison with other solutions to reduce renewable curtailment. • Multiport converter can reduce curtailment the same or more than battery solutions. • High renewable penetration scenarios are feasible to install a multiport converter. [ABSTRACT FROM AUTHOR]

• Incorporates market-based flexibility procurement to distribution system planning. • Hybrid approach that combines binary particle swarm and linear programming. • Case study for real 500 bus MV grid in Spain. • Procurement of flexibility services reduces network reinforcement investment by 14% • Sensitivity to calculate cost and availability thresholds that make flexibility competitive. Flexibility services enable distribution system operators to actively manage the grid for accommodating demand and generation growth while potentially reducing or delaying investments in grid reinforcements. This paper proposes a novel hybrid particle swarm optimization and linear programming methodology that analyzes explicit flexibility procurement as an alternative to conventional network reinforcements in electricity distribution network planning. The distribution system planning problem is decomposed into a master problem and an inner problem. Binary particle swarm optimization (BPSO) is used to determine the optimal investment decisions, binary variables, from a set of candidate grid reinforcements in the master problem. At the inner linear programming optimization problem, a market-based procurement of flexibility services is performed. The inner optimization problem obtains the total cost of flexibility and the volume of flexibility at each network bus required to defer or avoid part of the grid reinforcements. A real 500-bus medium voltage network is used to validate the proposed methodology. Results illustrate cost-effective network plans that combine flexibility procurement with network reinforcements. A sensitivity to the cost and availability of flexibility services is also conducted to calculate the thresholds where flexibility becomes an efficient alternative to reinforcing the network. [ABSTRACT FROM AUTHOR]

DC microgrids, considered building blocks of smart grid technologies, are subjected to small-signal instability due to the extensive introduction of power electronics devices. Therefore, in this paper, a sequence Virtual Filter (VF) controller, which considers not only the longitudinal virtual parameters but also the lateral capacitance and resistance, is first developed to increase the flexibility of system stability adjustment compared to the Virtual Impedance (VI) controller. Then, as distribution feeders are normally unbalanced and the application of the proposed sequence VF controller may amplify the distortion of imbalances on DC voltage, a novel Reference Current Generation (RCG) strategy considering the VF controller is proposed for Grid-Connected Converter (GCC) to improve DC microgrid power quality. The double-frequency fluctuation of the DC-link voltage is eliminated by regulating the oscillation of the active power flowing into the converter instead of the Point of Common Coupling (PCC) to 0. The PSCAD simulation results illustrate that the sequence VF controller can enhance the stability adjustment since, in some cases, the system can only be stabilized by adjusting lateral parameters. On the other hand, the proposed RCG strategy can significantly reduce DC voltage fluctuations compared to the traditional approach. Furthermore, incorporating the proposed strategy with the sequence VF controller offers greater flexibility in reducing the negative-sequence current while maintaining a power transfer capacity for GCCs in a master–slave-based DC microgrid, comparable to that of the traditional strategy. • Develop a sequence VF controller for GCC operating under unbalanced conditions to increase the flexibility of stability adjustment compared to the VI controller. • Propose a novel RCG strategy considering the sequence VF controller to improve the power quality of DC microgrids interconnected with unbalanced grids. • Simulation results demonstrate the effectiveness of the proposed controllers. Furthermore, the proposed controllers offer greater flexibility in reducing the negative-sequence current while maintaining power transfer capacities for GCCs in a master-slave-based DC microgrid, comparable to that of the traditional strategy. [ABSTRACT FROM AUTHOR]

• Traditional energy hub models often focus solely on the energy perspective during the establishment process. However, in the context of wind and solar fluctuations, the conductance of subsystems in DC off-grid hydrogen systems exhibits a nonlinear changing pattern. Therefore, this model introduces a nonlinear admittance model for subsystems, enhancing its applicability to real-world conditions. • The dynamic responses among electrical, hydrogen, and thermal multi-energy flows in DC off-grid hydrogen systems demonstrate highly coupled and nonlinear characteristics. This model, building upon the working mechanisms of subsystems, establishes a nonlinear dynamic transformation characteristics matrix to describe the intricate energy transmission laws in hydrogen production systems. • Under wind and solar fluctuations, extensive calculations are performed on a DC off-grid hydrogen system comprising subsystems such as wind turbines, solar cells, FC, DC inverters, inverters, rectifiers, electrolyzers, batteries, and hydrogen storage tanks. The paper evaluates the energy transmission laws of the system under dynamic conditions, providing valuable insights into its performance. The dynamic response characteristics between the multiple energy flows of electricity-hydrogen-heat in the renewable energy DC off-grid hydrogen production system are highly coupled and nonlinear, which leads to the complexity of its energy conversion and transmission law. This study proposes a model to describe the dynamic nonlinear energy conversion and transmission laws specific to such systems. The model develops a nonlinear admittance framework and a conversion characteristic matrix for multi-heterogeneous energy flow subsystems, based on the operational characteristics of each subsystem within the DC off-grid hydrogen production system. Building upon this foundation, an energy hub model for the hydrogen production system is established, yielding the electrical, thermal, and hydrogen energy outputs along with their respective conversion efficiencies for each subsystem. By discretizing time, the energy flow at each time node within the hydrogen production system is computed, revealing the system's dynamic energy transfer patterns. Experiments were conducted using measured wind speed and irradiance data from a specific location in eastern China. Results from selected typical days were analyzed and discussed, revealing that subsystem characteristics exhibit nonlinear variation patterns. This highlights the limitations of traditional models in accurately capturing these dynamics. Finally, a simulation platform incorporating practical control methods was constructed to validate the model's accuracy. Validation results demonstrate that the model possesses high accuracy, providing a solid theoretical foundation for further in-depth analysis of DC off-grid hydrogen production systems. [ABSTRACT FROM AUTHOR]

• A two-layer location and capacity planning method of charging stations is proposed. • A fuzzy logic-based charging decision-making model of electric vehicles is proposed. • The impact of private charging piles is considered when predicting charging demand. The planning of public charging stations is crucial for the growth of electric vehicles (EVs). To improve the accuracy of predicting EV charging demand in urban areas, we propose a charging decision-making model based on fuzzy logic. Meanwhile, the influence of private charging piles is considered to further enhance the accuracy of predicting public charging demand. To address the issue of optimization algorithms easily getting stuck in local optima due to the vast quantity of variables involved in the location and capacity planning process, this paper introduces a two-layer planning method. In specific, the upper-level location model optimizes the locations of charging stations, while the lower-layer capacity model determines the number of charging piles within each station, leading to a reduction in the number of variables for each layer. Moreover, through iterative exchange results between the upper-layer location model and lower-layer capacity model, the optimal solution can be attained. The simulation results demonstrate that the proposed method can simultaneously consider the perspectives of both EV drivers and charging station investors, while also enhancing the utilization rates of public charging piles. [ABSTRACT FROM AUTHOR]

Virtual power plants (VPPs) are encountering multiple challenges due to market uncertainties and power network instability. In this paper, a novel probabilistic prediction-based multi-objective optimization framework for VPP is proposed to maximize operating profit while minimizing pollutant emissions and voltage deviations in the distribution network, which considers the uncertainties of wind power and electricity price. In this framework, the VPP that participates in the energy and ancillary service markets firstly aggregates the wind farms, the electric vehicle charging stations (EVCS), and the combined cooling, heating, and power subsystems to improve the utilization efficiency and operational flexibility of multiple energy sources. Then, a new Pareto optimizer, called multi-objective hybrid sand cat swarm optimization and strength firefly algorithm, is proposed to tackle the multi-objective optimization model of VPP. The proposed hybrid algorithm utilizes the advantages of sand cat swarm optimization and strength firefly algorithm mechanisms to facilitate local exploitation and global exploration. Finally, a new deep reinforcement learning probabilistic prediction approach based on quantile regression deep deterministic policy gradient is modeled to evaluate the uncertainties. The proposed models and methods have been thoroughly discussed on a modified distributed network. It is calculated that compared with the VPP without EVCS, the operating profit of the proposed VPP increases by 18.69%, and the emissions and voltage deviation of the proposed VPP are reduced by 3.42% and 10.44%, respectively. Experimental results also prove that the performance of the proposed Pareto optimizer and probabilistic prediction approach is superior to other benchmark techniques. [Display omitted] • A new VPP consisting of the wind farm, EVCS, and CCHP is proposed. • Multi-market trading of VPP with uncertainties is formulated as an MOO model. • Optimization of voltage deviation can reduce the instability of VPP operation. • The Pareto solution of VPP optimal operation can be effectively obtained by MOSCSFA. • A QRDDPG probabilistic prediction model is used to predict the VPP uncertainties. [ABSTRACT FROM AUTHOR]

• A DL-based WF prediction model with CNN-Transformer architecture was established. • A fully decentralized DL-based data-driven control framework is developed. • A DL-DOVC method for WF is proposed to minimize the voltage deviation. The random fluctuations of wind energy and external grid voltage disturbances can both lead to serious voltage fluctuations and voltage deviations in the wind farm (WF). Voltage/reactive power control is an effective way to improve the voltage stability of WF. The existing research is based on complex physical models with prior parameter information, and the accuracy and calculation speed of the WF model are difficult to guarantee. To address this issue, this paper explores a decentralized optimal voltage control method for WF with deep learning-based (DL) data-driven modeling (DL-DOVC). A hybrid convolutional neural network (CNN)-Transformer architecture is proposed to establish the data-driven model of WF, leveraging its enhanced capabilities for extracting time series correlation, to learn complex patterns and dynamics from time series data. Then, we develop a fully decentralized voltage control method for WF to regulate the terminal bus voltage of wind turbines (WTs) within a feasible range. A DL-based data-driven predictive controller is specially designed to solve the established data-driven voltage optimization problem, it eliminates the necessity for frequent manual model maintenance and is suitable for real-time application. Additionally, the difficulty of WF decentralized optimal voltage control arises from the inability of local controllers to fully consider the impact of all non-local WTs on the local WT states. By designing the DL-based auxiliary state-feedback controller, the effects of non-local WTs are implicitly considered in the auxiliary feedback control law. A WF with 32*6.25 MW WTs is used to test the proposed DL-DOVC method. Simulation results show that the proposed DL-based model can efficiently learn and predict the WF dynamics under different operating scenarios. The near-global optimal voltage control performance is achieved only with local measurements by employing the DL-DOVC method. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel MPPT method under partial shading conditions is proposed. • The SCSO-based MPPT technology effectively addresses complex partial shading conditions. • The SCSO-based MPPT technology exhibits faster tracking speed, higher convergence accuracy, and increased robustness. • The SCSO-based MPPT technology has been validated through simulations under random shading conditions and experimental verification. Maximum power point tracking (MPPT) plays a crucial role in photovoltaic systems (PVS). In partial shading conditions (PSCs), the P-V characteristic curves of PVS exhibit multiple peaks. Traditional MPPT algorithms, like perturbation and observation (P&O), may fall into local maximum power points (LMPP) and fail to identify the global maximum power point (GMPP). To address the drawbacks of conventional optimal search algorithms, this paper introduces a bio-inspired approach named Sand Cat Swarm Optimization (SCSO) for maximizing the power output of individual PVS. The SCSO can mitigate the adverse effects of partial shadows on PVS performance by precisely identifying the GMPP. In comparison to other bio-inspired algorithms, SCSO exhibits lower complexity and higher efficiency by utilizing only one optimization parameter. SCSO's performance is evaluated in four scenarios: uniform irradiance, complex partial shading conditions, step-varying stochastic irradiance, and gradual irradiance. A comparative analysis is conducted with Particle Swarm Optimization (PSO), Cuckoo Search Algorithm (CSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Moth-Flame Optimization (MFO), Crow Search Algorithm (CSA), Slap-Swarm Optimization (SSA) and P&O, focusing on factors such as high efficiency, accuracy, convergence time, and implementation simplicity. Simulation results demonstrate that, on average, the tracking time improves by 19.91%, achieving an efficiency of over 98% while maximizing energy yield. Simultaneously, experimental results indicate that the SCSO is capable of tracking to a larger power output in a shorter time, with an average tracking efficiency improvement of 3.16%. [ABSTRACT FROM AUTHOR]

Small-signal stability analysis is essential for the safe operation and parameter design of power electronic-dominated grids. Unbalanced conditions introduce more frequency-coupling terms, which are unneglectable in the stability assessment. This paper proposes a novel Linear Time-Periodic (LTP) theory-based stability analysis method and focuses on grid-connected voltage-source converters (VSCs) without improved unbalancing controls. Firstly, the analysis of fundamental solutions of the LTP system reveals that each LTP mode is characterized by a unique damping factor and multiple oscillation frequencies, defined by LTP eigenvalues and related transformation vectors, i.e., (λ i , V i (t)). Then, a method for calculating (λ i , V i (t)) is proposed using the characteristic matrix of the Harmonic State-Space (HSS) model. An iterative sorting method based on the time-domain interpretation of HSS eigenvalues/eigenvectors is proposed to determine accurate (λ i , V i (t)) in the case of the minimum truncation order. Finally, generalized definitions and calculation methods of the widely used indicators for modal analysis are presented to assess system stability and guide the parameter design. Numerical and simulation results verify the proposed stability analysis method and indicate its advantages compared to the existing Floquet and HSS methods. • Proposes a novel LTP theory-based time-domain stability analysis method. • Fundamental solutions of the LTP system are analyzed, revealing that each LTP mode is characterized by a unique damping factor and multiple oscillation frequencies, defined by LTP eigenvalues and related transformation vectors. • A method for computing LTP eigenvalues and related transformation vectors is proposed using the characteristic matrix of the HSS model. • Generalized definitions and calculation methods of the damping ratio, PFs, and EPSs for LTP systems are proposed for the guidance of parameter design. [ABSTRACT FROM AUTHOR]

• A DVRU is defined to grasp the communication right and act as a master to maintain the system voltage under faults. The other DERs will follow after the DVRU to form a dynamically master–slave architecture to avoid phase conflict and realize proper transient power sharing among grid-forming DERs. • A local FCDDM is proposed to realize the autonomous selection of the DVRU among various DERs under real-time faults. Moreover, when the current DVRU undergoes communication failure, a new one will automatically replace it to enhance the transient reliability. • Compared with conventional methods, it is the switching signals rather than the phase signals that transferred by the communication bus. Therefore, the low-bandwidth communication can meet the timeliness and accuracy requirements under transient state. • The system mathematical mode is developed to optimize the voltage tracking control parameters to avoid the PCC over-voltage during the recovery stage, where the adaptive capability to various fault situations is considered. Additionally, compatibility with MG protection is also discussed by referring to the existing protection configurations. The ever-expanding inverter-based microgrids (MGs) require the grid-forming distributed renewable energy resources (DERs) to enhance the system safety. However, the different types of grid-forming DERs are prone to have transient conflicts with each other under short circuit faults, leading to unexpected outage or even system collapse. The fast response and poor overcurrent capability of DERs make transient coordination a challenge. This paper proposes a dynamic master–slave architecture for transient coordination control in islanded MGs under asymmetric faults. A dynamic reconfigurable voltage reference unit (DVRU) is designed according to the real faults. In this manner, the other DERs could comply with this DVRU to achieve both system voltage support, inrush current restraining, and power oscillation suppression. It is action signals instead of phase signals need to be transferred by the communication bus with the proposed local fault current differential time delay method (FCDDM). Thus, the low-bandwidth and the enhanced robust communication could be met under transient state. Additionally, the feasibility of the proposed method to combined with relay protection is analyzed. Finally, case study results on islanded MGs consisting of various grid-forming and grid-following DERs demonstrate the effectiveness and robustness of the proposed method under short circuit faults as well as communication failures. [ABSTRACT FROM AUTHOR]

• A restoration flexibility quantification method is developed for EB clusters. • A two-step collaborative restoration strategy for the resilient DS is proposed. • Uncertainties associated with the EB cluster dispatch time and renewables power outputs are well addressed by using rolling optimization method. The widespread deployment of electric buses (EBs) offers substantial flexibility resources to support the service restoration and enhance the resilience of distribution system (DS). Therefore, this paper presents a comprehensive and collaborative service restoration strategy for resilient DS, considering the support of EBs. First, the restoration flexibility model for EBs is derived, which quantifies the restoration capability of EBs by dividing effective EB clusters. This model is integrated into the DS restoration process. Then, a two-step collaborative restoration method of DS is proposed with the aim of minimizing the load curtailment cost. The first step addresses the restoration planning problem to determine the dispatch decisions for EB clusters. Based on above planning solutions, the second step focuses on the real-time restoration problem of DS, obtaining optimal restoration results through coordinating EB clusters and other local resources. In this stage, the impact of natural disasters on the EB cluster dispatch in transportation system is considered, and a rolling optimization method is employed to deal with uncertainties from renewables, load, and EB cluster dispatch time. Finally, numerical simulations are conducted using the modified IEEE 33-bus distribution test system and a 29-node transportation system to verify the effectiveness of the proposed restoration method. [ABSTRACT FROM AUTHOR]

• Unique Augmentation Algorithm: Combines variational autoencoders with metric learning for time series. • Normalization of Irregularities: Normalizes heteroscedastic and non-stationary data effectively. • Advanced VAE Integration: Integrates GRU into VAE, enhanced by metric learning for better representation. • Improved Data Interpretability: Maintains temporal structure through multi-seasonal decomposition. • Superior Performance: Shows enhanced accuracy and fidelity in data-limited scenarios. In the field of time series classification, deep learning techniques have shown remarkable performance; however, their effectiveness is often compromised when confronted with challenges of insufficient data and class imbalance. To address this challenge, we propose an interpretable time series data augmentation algorithm integrating variational autoencoders (VAE) and metric learning. The core contribution of this algorithm is manifested in three aspects: First, it eliminates the heteroscedasticity and non-stationarity of the data, ensuring that the data satisfies the hypothesis of normal distribution in the potential space of the encoder, and effectively avoids the approximation error of the real data distribution; Secondly, the algorithm constructs a discriminant VAE potential space, suitable for data augmentation, with metric learning, ensuring that the hidden variable distribution accurately reflects the characteristics of the original data. Finally, this paper explores the multi-seasonal decomposition algorithm of time series to seamlessly integrate the structural features of the original time series in the generated data, thereby enhancing the interpretability of data generation. Through experimental verification on four multivariate time series data sets, including the electrical energy data set, the results demonstrate that the proposed algorithm outperforms existing methods in fidelity and prediction performance, exhibiting high stability and generalization ability, particularly in cases of limited data volume. The introduction of this algorithm not only contributes to enhancing the overall performance of time series classification models but also substantially reduces the cost of data collection and labeling, thereby demonstrating its significant value in practical applications. [ABSTRACT FROM AUTHOR]