Harmonic coupling and the stability of modular multilevel converters (MMCs) have been extensively studied under balanced conditions. However, in practical applications, MMCs may operate under unbalanced conditions due to fac-tors such as faults and protection actions. This paper investi-gates the harmonic coupling and stability of MMC under sin-gle-phase disconnection (SPD) conditions, a scenario that, to the best of the authors' knowledge, has been relatively under-explored in the existing literature. To address this gap, the paper develops a comprehensive harmonic state-space model for an MMC-HVDC system under SPD condition. Using this model, a multi-input multi-output harmonic coupling matrix is derived to analyze the interactions between different harmon-ics and the signal-flow graph is depicted to explain the mech-anisms behind these couplings. Furthermore, the multi-input multi-output matrix is transformed into a single-input single-output impedance that encapsulates all harmonic couplings, thereby enabling the visualization of the effects of various couplings on system stability through impedance variations. Nyquist curve based stability analysis, along with the hard-ware-in-the-loop experiments, underscores the importance of incorporating SPD conditions in the parameter design of MMC-HVDC systems.

Deep learning (DL) holds significant potential for distinguishing forced oscillations (FOs) from natural oscillations (NOs) and resonances in power systems. However, most existing studies treat DL models as opaque system classifiers, and these models are often susceptible to challenges such as class imbalance among the three oscillation patterns (i.e., FOs, NOs, and resonances) and the limited size of real-world training datasets. These issues can lead to incorrect diagnoses of oscillation patterns in practical applications. To address these challenges, we propose a FO oscillation recognition framework that integrates balanced data processing, an interpretable recognition network, and a fine-tuning learning strategy. In this framework, DeepSMOTE1D is introduced to address the issue of class imbalance by oversampling features extracted from an encoder-decoder network. The interpretable DWT-CNN-LSTM recognition network incorporates multiple discrete wavelet transforms (DWT) into each convolutional and LSTM layer to enhance both interpretability and performance of the model. Finally, a fine-tuning transfer learning strategy is employed, where the recognition network is first pretrained on simulation data and subsequently retrained on limited real-world data. The effectiveness of DeepSMOTE1D and the fine-tuning strategy in the proposed framework is also evaluated. Experimental results show that the proposed recognition model not only learns effectively from simulated oscillation data but also outperforms existing related networks in real-world scenarios, achieving superior accuracy, precision, recall, and F1-score.

With the rapid advancement of power electronics, active power filters (APFs) have emerged as a preferred solution for mitigating harmonic resonance in high-voltage direct current (HVDC) systems. APFs can be broadly categorized into current compensation APFs (I-APFs) and resistive APFs (R-APFs), depending on their control strategies. Although both types have demonstrated effectiveness in practical applications, previous studies have not comprehensively compared their resonance mitigation performance, particularly under capacity-limited conditions. To address this gap, this paper establishes an equivalent harmonic model for LCC-HVDC systems with APFs connected and proposes a novel metric, capacity utilization efficiency (CUE), to compare the resonance suppression effectiveness of APFs. The variation characteristics of CUE are systematically analyzed considering factors such as resonance frequency, system damping, and APF capacity. The findings provide a practical guideline to assist utilities in selecting the optimal APF control, accounting for factors such as varying network impedances and background harmonic distortions. Finally, the developed harmonic model and the APF-selection guideline are validated using a real-life LCC-HVDC system experiencing resonance issues and a modified IEEE 39-bus system.

This paper proposes an enhanced control strategy based on a virtual factor to enhance the current-limiting capability of virtual impedance and the power-angle stability of grid-forming photovoltaic systems. Initially, the virtual synchronous generator model is examined to reveal the current-limiting characteristics of virtual impedance during faults. The impact of active power reference and line impedance on system stability is also examined. To balance the current-limiting effect while improving system stability, the strategy dynamically adjusts the active power reference based on the virtual factor, achieving coordinated control of virtual impedance and power output. This approach effectively limits current during faults, maintains power-angle stability, and ensures smooth grid recovery. Compared with conventional approaches, the enhanced strategy not only retains the inherent current-limiting capability of virtual impedance but also suppresses power-angle overshoot, improving the transient stability and dynamic performance of photovoltaic grid-forming systems, offering a promising solution for renewable energy integration.

The transformer inrush current has been a potential threat in wind farms connected modular multilevel converter based high-voltage direct current (WF-MMC-HVDC) system due to the low overcurrent capability of power electronic devices. To investigate this issue, this paper develops a complete harmonic state space (HSS) model of the WF-MMC-HVDC system containing saturable transformers. The severity of the inrush current is investigated under different transformer configurations and the result is compared with EMTP simulations. More importantly, key factors that influence inrush current characteristics in a WF-MMC-HVDC system are studied using the single-input single-output impedance model derived from the linearized HSS model. The results indicate that wind farms have a minor impact on the inrush current characteristics, whereas V/ F controlled modular multilevel converter (MMC) reduces its output voltage during transformer energization, thereby mitigating the severity of the inrush current. The severity of the in-rush current largely depends on the resonance point determined by the transmission line. In the case of offshore WFMMC-HVDC system, long submarine cables may cause severe harmonic amplifications and even do not attenuate for a long time.

The weak grid condition of distribution systems prevalent in remoted areas significantly constrains the enhancement of renewable energy (RE) hosting capacity (HC) and total supply capability (TSC). Coordinated charging dispatch of abundant electric vehicles (EVs) resources in demand side is a promising solution for this challenge. Thus, an ordered charging method of EV groups is proposed to improve the photovoltaic (PV) HC and TSC of the regional distribution systems in weak grid condition. A cost driven temporal-spatial EV coordinated charging dispatch model is established to proactively shift EV charging behaviors across different time and areas, so as to expand the PV HC and TSC of the target area without requiring upgrades to fixed infrastructure within the distribution system. Compared to traditional approaches relying on flexible interconnection for economical load transfer, the proposed method demonstrates superiority in PV HC expansion and TSC promotion with less cost, while safe operation of the distribution system can be maintained.

P / omega admittance modeling is one of effective techniques to analyze the low-frequency oscillation (LFO). However, existing modeling methods are typically developed for specific control strategies on a case-by-case basis, lacking a general framework. Such case-specific formulations limit the broader applicability of this model in power system studies. To address this limitation, a general P / omega admittance modeling framework is proposed based on the equivalence of controlled source and impedance (ECSI). In the proposed framework, the VSC is modeled as a controlled frequency source, which is regulated by both active power and the frequency at the filter terminal, whereas the reactive power-voltage dynamics are modeled as an equivalent admittance in parallel with the line admittance. Such a modeling strategy enables the construction of P / omega admittance models for VSCs with diversified controls, using a consistent and intuitive framework. Leveraging the model's transparency, the LFO characteristics of various VSCs are identified. The case study of a multi-VSC system demonstrates that the proposed model can accurately reflect the interactions among control loops and reveals the characteristics of LFO caused by different controls of VSCs, providing a powerful tool for stability analysis and control design. Finally, comprehensive simulations under various scenarios are conducted to verify the accuracy of the proposed model.

In five-axis machining of complex surfaces, the rotary-axis configuration directly governs nonlinear error, kinematic singularity, and dynamic performance. Existing studies usually investigated the above three issues separately and cannot synthesize the rotary-axis configuration from task-specific features. This paper reveals the topological mismatch between the physical rotary axes and the ideal elementary motion axes (EMAs) as the common kinematic origin of these three issues. It proposes a forward design framework in which the elementary motion manifold (EMM) extracted from workpiece toolpath directly drives the rotary-axis configuration synthesis. The directional velocity gain (DVG) is established as the unifying optimization criterion. Spectral decomposition of the EMM structure tensor yields the optimal non-orthogonal axis directions in closed form. A propeller blade case study confirms that the synthesized non-orthogonal configuration (β=84.73∘) avoids the kinematic singularity encountered by the conventional CA configuration and, relative to it, reduces the RMS orientation nonlinear error by 96.5% and the RMS angular acceleration by 88.0%. This work shifts the design paradigm from ‘structure adapts to task’ to ‘task defines structure’.

This study investigates the small-signal stability of centralized energy storage systems (CESSs) using grid-following (GFL) and grid-forming (GFM) controls, particularly focusing on bidirectional power flow and multiple energy storage systems (ESSs). To address the issue of complex dynamics in CESSs when comprehensive GFL and GFM control loops are considered, high-order dynamics are simplified using the virtual damping method by focusing on the dominant oscillation mode. Damping analysis verifies that CESSs using a single-type control (either GFL or GFM) have dynamic superimposition characteristics. Specifically, as ESS number increases, the damping of GFM-CESSs improves but that of GFL-CESSs decreases. The damping sensitivity shows that the damping of GFM-CESSs is more sensitive to bidirectional power flow and all control loops, whereas that of GFL-CESSs is more sensitive to d-axis control loop. Consequently, GFM-CESSs are preferred for large-scale integration but are limited in scenarios with significant power reversal. If GFL and GFM controls are hybridized in CESSs, the ratio of GFM-CESSs should be constrained to avoid instability from modal resonance between GFL-CESSs and GFM-CESSs. This highlights that implementing GFM-CESSs necessitates considering scenario limitations rather than pursuing maximal integration under hybrid integration conditions. The conclusions are validated through modal analysis and time-domain simulations.

Faced with the dual pressures of increasingly frequent extreme disasters and a high penetration of renewable energy, power systems are encountering significant challenges in maintaining secure and stable operation. Conventional transmission network expansion planning (TNEP) methods, which rely on simulations of typical steady-state scenarios, fall short in ensuring system reliability under severe disaster conditions. To address this issue, this paper introduces an extreme disaster simulation method tailored for the planning stage of hybrid AC/DC power grids, along with an intelligent TNEP strategy based on reinforcement learning. The research follows three main steps: (1) constructing a representative set of extreme scenarios and quantitatively evaluating grid damage in each case; (2) proposing a stepwise Markov decision process (MDP) model suited to the characteristics of TNEP tasks; and (3) developing a reinforcement learning-based intelligent agent to derive optimal wide-area grid expansion schemes. Simulation results on representative systems confirm that the proposed approach significantly improves the reliability of hybrid AC/DC grids in the face of extreme disasters.

To address the critical voltage stability of industrial DC microgrids serving sensitive loads, virtual capacitor control is a promising technique for inertia enhancement. However, conventional virtual capacitor control, with its fixed parameters and limited disturbance rejection capability, struggles to maintain qualified voltage quality, threatening the reliable operation of industrial equipment. This paper proposes a novel adaptive virtual capacitor control strategy based on linear active disturbance rejection control (LADRC). The key contribution is a novel control architecture where the virtual capacitor is not predetermined but is adaptively modulated by real-time disturbance estimated by LADRC. This unique feedback mechanism allows the system to proactively counteract both external load changes and internal parameter uncertainties, achieving superior voltage regulation. Furthermore, an integrated sliding time window filter ensures smooth control action by mitigating oscillations from voltage ripple. The proposed strategy's effectiveness in simultaneously enhancing voltage deviation suppression, ripple mitigation, and dynamic inertia support is validated through simulation and hardware-in the-loop (HIL) experiments.

Traditional homogeneous transform matrix (HTM) method for geometric error modelling of five-axis machine tools (FAMTs) has some misuse problems in applications including possible distortion and low adaptiveness to variations due to its complexity. Hence, a novel, unified and parameterized framework for geometric error modelling is proposed. Initially, the idea of expressing deviations with transfer vectors is introduced. Novel definitions led by local transfer vector and transition matrix are then proposed to enable the calculation of transfer vectors without HTM process. Subsequently, a transfer vector table with the configuration parameters of FAMTs, i.e., ParamSet, as input is created. Finally, by identifying ParamSet of various FAMTs and specifying each parameter in the transfer vector table, the corresponding geometric error model can be directly generated. With the transfer vector table being reusable, this modelling method can reconstruct rapidly to adapt to different configurations of FAMTs. The application of this method to BC-type and AC-type dual rotary table FAMTs generated error models with accuracy consistent with traditional models, while the modelling process is greatly simplified and the computational time is significantly reduced, validating the feasibility of the proposed framework. Applying this framework in the design phase is beneficial to infuse FAMTs with resilience.

This paper addresses the dual challenges of harmonic/unbalanced power sharing and voltage quality improvement in microgrids. A consensus-theoretic analysis shows that the traditional consensus algorithm framework—widely used in distributed power sharing—does not necessarily improve the voltage quality at the point of common coupling (PCC). Building on this insight, a novel distributed control strategy is developed based on a leader-follower consensus framework. The consensus-variable is constructed using the remaining capacity of each distributed generator, enabling optimal utilization of inverter capacity. A virtual leader node is introduced to coordinate the virtual impedance of inverters and steer the absorbed harmonic and unbalanced power toward the leader-assigned target. As a result, the proposed strategy achieves a practical balance between harmonic/unbalanced power sharing and PCC voltage quality improvement.

To address rapid frequency decline, transient voltage violations, and excessive configuration costs caused by competition between active and reactive power support in weak grids, this paper proposes an optimal configuration method that incorporates the fault-period voltage-support capability of photovoltaic (PV) inverters into the planning of a grid-forming energy storage system (ESS). A coordinated response model for the ESS and PV inverter is developed, in which the PV inverter provides reactive power through Q-V droop control while smoothing its active power output. An optimization model is then formulated to minimize the annualized ESS cost while satisfying constraints on transient frequency security, voltage recovery, islanded operation, and state of charge (SOC). Frequency security indices, including the rate of change in frequency, frequency nadir, and quasi-steady-state frequency deviation, are explicitly linked to the rated power and energy capacity of the ESS. A hierarchical solution framework integrating capacity search, scheduling while connected to the grid, stepwise transient verification, and steady-state assessment under islanded operation is adopted to improve computational efficiency. Case studies on a weak distribution network show that PV transient voltage support reduces the reactive power requirement of the grid-forming ESS and lowers its configuration cost by approximately 5.2%. Meanwhile, all frequency and voltage indices remain within the prescribed security limits. Further multi-scenario evaluations and sensitivity analyses confirm the broader applicability of the proposed method across different operating conditions.

Inverter-based resources (IBRs) are a new type of generators entering power systems. Industries are concerned about the harmonic impact caused by IBR plants. How to model IBRs for harmonic studies has, therefore, become an important topic. This industry application-oriented tutorial paper presents a comprehensive review and analysis of the harmonic behaviors of IBR units, covering their harmonic characteristics, advanced and practical harmonic models, methods for model parameter determination and more. Lab test results on a physical IBR unit are presented to substantiate the findings. It is hoped this paper will clarify the confusion between the harmonic models of VSC (voltage source converter) based IBR units versus LCC (line commutated converter) based loads. Furthermore, a comparison between IBRs and synchronous generators reveals many similarities in their harmonic behaviors.

Elevator faults can cause significant harm, especially in high-speed elevators. However, obtaining fault samples from in-service high-speed elevators by monitoring sensors is challenging due to high simulation costs and limited efficiency, which hinders the development of fault diagnosis. To address this, a scalable fault simulation model is proposed, offering a cost-effective and efficient approach to generate fault samples. Leveraging this model, an innovative fault methodology that combines variational mode decomposition (VMD) and graph convolutional network (VGCN) is proposed to enhance the extraction and representation of deep features from the fault data. This approach consists of two core components: a variational-mode-decomposition layer (V-Layer) that decomposes and reconstructs vibration signals, effectively mitigating noise interference, and a graph convolution layer (GC-Layer) that uses Hermite polynomials to adaptively fit the graph convolution kernel, ensuring robustness in high-noise conditions. Faults are then classified through a fully connected layer with a softmax classifier. The proposed method is validated using both a simulated fault dataset and a real-world high-speed elevator dataset, demonstrating superior performance in fault diagnosis.

This paper investigates the transient stability of the grid-forming and grid-following (GFM-GFL) paralleled system based on the Lyapunov direct method. To achieve this goal, an improved sum-of-squares (SOS) programming method is proposed to construct the low-conservativeness Lyapunov function for the GFM-GFL paralleled system. The proposed method simplifies the conventional SOS constraints and enables adaptive tuning of SOS parameters according to the conservativeness of the domain of attraction (DOA). Compared with existing numerical Lyapunov methods, the proposed method achieves faster computation and lower conservativeness, thus enabling more precise evaluation of the transient stability. Furthermore, the influence of system parameters on the transient stability of the GFM-GFL paralleled system is quantitatively analyzed using the volume of DOA as a metric. Finally, the effectiveness of the proposed method is verified through comparative studies.

Distributed photovoltaic storage charging piles in remote rural areas can solve the problem of charging difficulties for new energy vehicles in the countryside, but these storage charging piles contain a large number of power electronic devices, and there is a risk of resonance in the system under weak grid conditions. Firstly, the topology of a photovoltaic storage charging pile is introduced, including a bidirectional DC/DC converter, unidirectional DC/DC converter, and single-phase grid-connected inverter. Then, the maximum power tracking control strategy based on improved conductance micro-increment is derived for a photovoltaic power generation system, and a constant voltage and constant current charge–discharge control strategy is derived for energy storage equipment. Additionally, a segmented reflective charging control strategy is introduced for charging piles, and the quasi-PR controller is introduced for single-phase grid-connected inverters. In addition, an improved second-order general integrator phase-locked loop (SOGI-PLL) based on feed-forward of the grid current is derived. Finally, a simulation model is built to verify the performance of the solar–storage charging pile and lay the technical groundwork for future integrated control strategies.

For a $100 \%$ renewable energy generation base supported by wind, photovoltaic (PV), concentrated solar power (CSP) and BESS, optimizing the capacity configuration of thermal and battery storage is crucial for improving the renewable energy integration rate and the stability of the power system. This paper proposes a coordinated optimization method for thermal storage(TES)/battery storage capacity, considering the green certificate(GC) trading mechanism. It takes into account the operational constraints of direct current(DC) channels, various power sources, and energy storage devices, and establishes a bilevel stochastic optimization model with the objective of maximizing the system’s annual integrated revenue. Using simulation data from a wind-PV-CSP-BESS renewable energy base in northwest China and typical daily profiles obtained through K-means clustering, the model is solved to determine the optimal configuration of TES and battery storage that balances system economics, reliability, and environmental sustainability. Additionally, the impact of factors such as GC trading, TES cost and battery storage costs on the configuration results is further quantified and analyzed.