The purpose of the wind-solar complementary system (WSCS) is to couple wind power and photovoltaic (PV) in a complementary way to strengthen the ability to generate power continuously in the medium and long term. However, due to the uncertainty of natural resources, the power output of WSCS is still unstable. In recent years, hybrid energy storage systems (HESS) have been used to match the WSCS to reduce the volatility of system output, but there are still some problems leading to the system's economic cost making it difficult to control. For example, the coupling relationship between wind and solar is linear, and the premise of the fluctuation smoothing strategy is to meet the power demand of load-side or grid-connected. In order to solve the mentioned problems, this paper proposes a method that HESS smooths fluctuations of wind-solar coupling power considering multi-scenario planning. By constructing a nonlinear coupling relationship between wind and solar and optimizing the capacity allocation of power source-side hybrid energy storage, the system accommodation characteristics for power fluctuations are improved.

Firstly, the marginal distributions of the two power sources are constructed using KDE based on the historical data of wind power and PV, and the joint distribution is obtained by preferably using the Gumbel-Copula functions. The multi-scenario set obtained by random sampling of the joint distribution is able to reflect the intensity of the fluctuation changes. Secondly, the FFT and its IFFT are used to analyze the spectral analysis of the unstable power in scenarios set to determine the power borne by each energy storage unit. In this part, since the multi-scenario ensemble originates from a joint distribution, the correlation of each scenario in the ensemble is consistent, which means the cut-off frequency that distinguishes battery and super-capacitor does not change with the change of scenario. Finally, an optimization model is established with the objective function of minimum the cycle operating cost of HESS, and the capacity configuration of the HESS is calculated using an improved PSO. The result of capacity configuration provides room to accommodate fluctuations in power source-side output, which reduces the instability of the system.

The results of the simulation example show that the increase in frequency deviation before the HESS configuration is much larger than that after the HESS configuration. The change rate of RMSE for calculating the frequency deviation before and after the configuration of HESS ranges from 60.0% to 83.5%, the change rate gradually increases with the increase of the number of scenarios in the ensemble. This suggests that the role of HESS in regulating frequency increases as the number of scenarios increases. Meanwhile, with the increase in the number of scenarios in the set, the maximum growth in the rated power and rated capacity of the batteries is 77.1% and 54.9%, respectively. And that of the super-capacitors is 40.0% and 42.4%. However, this makes the increase in equipment cost of the super-capacitor more prominent. Further, the configuration of HESS makes the power fluctuation of the system at adjacent moments smoother. The fluctuation accommodation range of the power source-side within the time intervals of 10 h, 60 h, and 240 h is enhanced by 12.9%, 7.4%, and 6%, respectively. The amplification of the fluctuation accommodation range decreases with the longer of the time intervals. Nevertheless, the HESS still has rechargeable power characteristics when the power source-side output is zero.

From the simulation results, the following conclusions can be drawn: (1) Different numbers of scenarios in the set have consistent correlation, so the dividing frequency of the battery and the super-capacitor does not change with the number of scenarios, which makes the HESS can be effective for the fluctuating power to modulate frequency. (2) The more complex the frequency variations of the fluctuating power at the wind-solar coupling output, the more pronounced the capability of HESS modulating frequency. (3) The results of the HESS configuration reflect that super-capacitors and batteries have greater advantages in the rated power and rated capacity, respectively. (4) Even if the wind-solar coupling output is close to 0 or 0 after the configuration of HESS, the system is still able to ensure that there is a certain margin to counteract the fluctuating impact of sudden power changes.

Accurate prediction of the battery state of charge (SOC) is of great significance to improve the utilization efficiency and safety performance of the battery, and the monitoring of the battery state of charge is very important to help prevent overcharge and overdischarge accidents. The traditional SOC prediction methods are highly dependent on the mechanism model and statistical model, and have problems such as sensitive outliers and limited practical accuracy. In this study, a CNN-LSTM-AM (convolutional neural network - long short term memory neural network - attention mechanism) model is proposed to predict SOC variation trend through battery measurable variables.

The model first uses a one-dimensional convolutional neural network to extract spatial features of measurable variables, including battery current, voltage, temperature and average voltage, and then sends them to bidirectional long and short time memory for time series analysis. Finally, the attention mechanism is introduced to screen key features, reduce the redundancy of feature data, and improve the accuracy and generalization of the model. In addition, CNN-LSTM-AM model adopts rime optimization algorithm to optimize the hyperparameters in the training process, which effectively improves the training efficiency and reduces the training cost.

The actual evaluation on CALCE (Center for Advanced Life Cycle Engineering) data set of lithium iron phosphate shows that the attention mechanism can effectively improve the training performance of the prediction model, and the rime optimization algorithm adopted can help reduce the model hyperparameters, so as to obtain higher prediction accuracy. The performance of CNN-LSTM-AM model was tested under different temperature conditions, and both RMSE and MAE were less than 1%, which was sufficient to confirm the feasibility of the model to predict SOC. In addition, even if the initial SOC is uncertain, the proposed CNN-LSTM-AM model can still accurately track SOC trend changes, and the overall prediction accuracy reaches RMSE<1.5% and MAE<1.5%. The RMSE and MAE results of the network proposed in this study are smaller than those of CNN-LSTM and CNN-LSTM-AM. It shows strong robustness and generalization ability. Finally, in order to comprehensively compare the performance of different SOC prediction methods, the CNN-LSTM-AM model proposed in this study is compared with other experimental results. It can be seen that the method proposed in this study has significantly lower RMSE compared with AT-CNN-LSTM. At the same time, considering that the proposed method uses less training set data, we can also see the advantages of the designed network. Compared with EI-LSTM-CO(extended input-LSTM-constrained output), it can be found that the error is close. In addition, EI-LSTM-CO performs some post-processing on the predicted SOC, which can also reflect the superiority of the proposed method.

The following conclusions are drawn from the simulation analysis: (1) A CNN-LSTM-AM model is proposed and applied to the SOC prediction task of battery, which can effectively capture important input features and improve the prediction accuracy. (2) Design a rime optimization algorithm, which can automatically search the optimal solution of CNN-LSTM-AM model, effectively reduce the time cost of hyperparameter optimization. (3) The influence of different ambient temperatures and initial SOC values on the prediction accuracy of CNN-LSTM-AM was studied, and the performance of CNN-LSTM-AM was compared with that of traditional prediction models to verify its strong robustness and high generalization ability.

With global climate warming, the frequency of heavy rainstorm events is increasing. During heavy rainstorms, composite suspension insulator strings are prone to reduced creepage distance utilization and potential rain flashover accidents due to the sudden increase in rain intensity and rain columns bridging the skirt gaps. Since the rod diameter and skirt diameter of composite suspension insulators are smaller than those of large-diameter composite pin insulators, and there are significant differences in skirt structure and creepage distance, the rain flashover characteristics of suspension insulators cannot be equated with pin insulators. Hence, there is insufficient data on the rain flashover characteristics of composite suspension insulators.

This paper conducts artificial rain flashover tests under strong rainfall conditions using five different skirt structures of composite insulators. It investigates the effects of rain intensity and water conductivity on insulator AC flashover characteristics by analyzing the rain column length at the skirt edge, simulation models, arc development paths, and critical leakage currents. A formula for calculating the unit insulator height AC flashover voltage under the combined effects of rain intensity and water conductivity is proposed and verified for accuracy.

Results indicate that the unit insulator height rain flashover voltage is negatively correlated with rain intensity and water conductivity, following an exponential decay function. The voltage gradient reduction can reach 41.9% and 43.8% respectively due to these factors. The rainfall intensity of 9 mm/min can be considered the tipping point between non-extreme and extreme rainfall. Additionally, composite insulators with larger skirt diameters and skirt spacings are more significantly affected by rain intensity, while the impact of water conductivity is consistent across different skirt parameters. When the rainfall intensity is low, the shorter rain column causes the arc to develop along the path of “rain column-air gap-small skirt surface”. When the rainfall intensity is high, the rain column is longer, and the vertical air gap within the rain column is directly broken down, leading to the arc development path of “rain column-vertical air gap-large skirt surface”.

In addition, the maximum length of the rain column at the skirt increases with rain intensity and varies with skirt diameter and spacing. The arc development path differs significantly among insulators with different skirt parameters. Insulators with larger skirt diameters and spacings exhibit a combined air gap and skirt surface discharge path, with reduced rain column bridging the skirt gap due to effective skirt coverage, resulting in higher creepage utilization. Therefore, insulators with larger skirt diameters and spacings can effectively enhance the insulation strength. Due to the influence of the number of charged particles in the water and the area covered by the water film, the average critical leakage current increases with rain intensity and water conductivity, which increases the energy gained by the electric arc and promotes the development of local arcs and the formation of discharge channels. During heavy rainstorms, to reduce surface leakage current on composite insulators and prevent rainwater from bridging the skirts to form a “rain pillar-vertical air gap” continuous arc path, it is recommended to use composite insulators with larger inter-skirt spacing and skirt diameters in regions prone to frequent heavy rainfall.

Similar to synchronous generators, the grid-forming converter mostly uses power synchronization or inertial synchronization control strategies, which can provide inertia and damping support to the grid. However, the similar external characteristics of the grid-forming converter and synchronous generator result in its susceptibility to sub-synchronous oscillations when connected to the grid through aseries capacitor compensation line. In view of this, this paper carries out a comprehensive research work on the stability analysis and sub-synchronous oscillation suppression strategy for the grid-forming converter connected to the grid via a series capacitor compensation line.

Firstly, the self-impedance and the accompanying impedance models of the grid-forming converter are established by using the complex variable representation method. The self-impedance and the accompanying impedance are verified using the frequency scanning method, and the scanning results were consistent with the analytical model, verifying the correctness of both. The established the self-impedance and the accompanying impedance models can accurately explain and characterize the single-frequency input and dual-frequency output of the grid-forming converter. Afterwards, the equivalent impedance model of the system with single input and single output of the grid-forming converter is derived, taking into account the frequency coupling effect and the influence of the series complementary lines.

Secondly, the stability of the grid-connected system at different series compensation degrees is analysed by using the Nyquist stability criterion based on an equivalent impedance model that accounts for thefrequency coupling effect. It is found that the larger series compensation degree is, the worse the system stability is. In addition, the impedance stability analysis taking into account the frequency coupling effect is more accurate under certain operating conditions.

Then, a current feedback-based impedance reshaping strategy is proposed for the phenomenon of sub-synchronous oscillations generated by the interaction between the grid-forming converter and the series-complementary line. The strategy is that the grid-connected current passes through the notch filter and the feedback coefficient as part of the modulation wave output to achieve system impedance reshaping. The function of the trap filter is to maintain the fundamental frequency output impedance and avoid the working point offset of the converter. And the current feedback coefficient was introduced into the equivalent impedance model, the feedback coefficient-frequency binary equivalent impedance model was established, and the amplitude-phase contour stability criterion was used to parameterize the current feedback coefficients. It is found that the larger the feedback coefficient k is, the larger the phase margin of the system is, and the more stable the system is. In addition, after the system is shaped by impedance, the phase-frequency curve moves down as a whole, especially in the frequency band below 50 Hz, the phase-frequency curve moves down greatly, resulting in the phase difference at the resonance point less than 180°, and the oscillation is suppressed.

Finally, the grid-connected system model of the grid-forming converter via series-complementary line is built through simulation and experiment, and the impedance remodeling control strategy is implemented on the damping controller to verify the correctness of the theoretical analysis as well as the parameter design. This study draws the following conclusions. (1) The interaction between the grid-forming converter and the series compensation line is easy to cause sub-synchronous oscillation, and the greater the series compensation degree, the higher the oscillation risk. In addition, under certain operating conditions, impedance analyses that take into account frequency coupling effect are more accurate and their influence cannot be ignored. (2) The amplitude-phase contour plot can be used to determine intuitively the influence of the feedback coefficient k on the operating characteristics of the system and to derive the range of values of the feedback coefficient k parameter when the system is in a stable or unstable state.

As modern power system toward high renewable energy integration with wind, solar, and storage sources, the increasing share of inverter-based resources leads to stability challenges dominated by multi-loop control with wide-band frequency characteristics. In systems with high penetration of renewable energy, converter-based systems have presented new features, such as large-scale integration and long-distance transmission, causing system faults to exhibit large-signal transient characteristics. The hybrid connection of grid-following (GFL) and grid-forming (GFM) converters has emerged as a potential solution to enhance the stability and efficiency of new energy transmission. However, the high order and strong nonlinearity of these hybrid systems pose challenges to the assessment of their transient stability. Therefore, this study is dedicated to designing an effective method for evaluating the transient stability of GFL/GFM converter hybrid systems.

The research methodology starts with the construction of a detailed fourth-order nonlinear model of the hybrid system, integrating phase-locked loops and virtual synchronous generators, which serves as the basis for the proposed transient stability solution method based on alternating calculation. Further, by calculating the mutation portion at the failure moment, the method derives the computed initial values for each system of the transient process. The essence of the rotation calculations lies in performing energy calculations and resolving the angular velocities in the power angle domain, subsequently mapping them back to the time domain. In the method implementation, energy calculations are first performed for a certain converter system, the dynamics of this system is used to further estimate the motion of the other system in this step, and the order of calculations for the two systems is exchanged to perform the alternating calculations. In this process, the correspondence between the power angles of GFL and GFM control is established, which enables the complex interactive motion patterns of the hybrid system under severe disturbances to be evaluated. During the alternating computation process, for the GFL/GFM system, the equivalent kinetic energy change over the step is computed by integrating the relevant equations that take into account the damped power and kinematic properties, avoiding the uncertainty associated with neglecting damping. During the continuous iterative computation process, the computed values are exchanged and updated between the two systems to ensure accurate transient behavior of the system. Eventually, the computation is stopped after the judgment condition of stability is satisfied.

The experimental and simulation results confirm the feasibility and effectiveness of the proposed method. It accurately depicts the variations in power angles, angular velocities, and GFM converter voltages during the transient processes of the hybrid system. The computational time of this method is significantly reduced compared to existing numerical methods, with at least an order of magnitude improvement. Additionally, the method is applicable to calculating the critical clearing time (CCT), achieving a resolution within 5 ms in the presented examples. It can also accurately characterize the out-of-sync operation of GFL and GFM converters during the fault recovery process.

In conclusion, this study provides a practical solution for evaluating the transient stability of hybrid converter systems. The developed method based on alternating calculation in the discrete domain exhibits clear physical mechanisms and relatively low computational requirements. It has the potential to be incorporated as a subsystem in large-scale simulations to accelerate the simulation speed.

Insulator is one of the most common and widely used electrical components in transmission lines, which plays a critical role in electrical insulation and mechanical support, ensuring that the current flows along the specified path and reducing electromagnetic interference with the surrounding environment. Since insulators are installed outdoors, they are exposed to wind, sunlight, rain, ice, frost and other bad weather for a long time, and their surface defects are inevitable. If the insulator appears self-explosion or drop string, which will cause leakage due to the loss of insulation, leading to electric shock accidents, thus resulting in huge economic losses. Relying on computer vision and deep learning technology, insulator defect detection from massive UAV aerial images has become an urgent problem for power operation and maintenance. However, the backgrounds of aerial images from overhead transmission line corridors are complex. Under different lighting conditions, shooting angles, shooting distances, etc., the scale of insulators in aerial images varies greatly, and the insulator strings are prone to occlusion, the defect area of the insulator is much smaller than the insulator itself. Therefore, there are numerous difficulties in detecting insulator defects in practical applications.

In recent years, compared with the traditional object detection methods, deep learning methods can quickly and accurately identify insulators and their defects from power inspection images. There is still a lack of comprehensive review of the latest progress in insulator defect detection in existing literature, without introducing object detection algorithms such as anchor free algorithm, YOLOv7, Transformer, and knowledge extraction techniques. In view of this, this article summarizes and analyzes a large number of visual methods for insulator defects detection, systematically reviews deep learning methods for insulator defect detection in drone aerial images, aiming to select appropriate detection methods for specific insulator defects and provide valuable reference for researchers engaged in transmission lines fault diagnosis.

This paper reviews the research progress of deep learning methods for insulator defect detection in UAV aerial images. Firstly, the current research status of transmission lines inspection based on deep learning is briefly reviewed. Then, the insulator defect detection methods based on deep learning are explained, mainly from the target detection models, lightweight network models, cascade detection models and other methods are summarized, which is conducive to the comparison between different deep learning methods and more helpful for power inspection personnel to select appropriate deep vision detection methods for fault diagnosis of specific electrical component. And the target detection models based on two-stage algorithms, one-stage algorithms and anchor-free algorithms are elucidated. The lightweight network models based on model pruning, knowledge distillation, low-rank decomposition, network quantization and the target detection model based on Transformer are summarized. Next, the self-built and public datasets for insulator defect detection are introduced. Due to the lack of training samples and unified dataset for insulator defect detection, scholars mostly conduct defect detection research through self-built datasets in different detection scenarios. Finally, the challenges faced by insulator defect detection methods based on deep learning are elucidated, including insufficient defect samples, low defect detection accuracy, difficulty in detecting small target defects, and feature extraction, etc. Based on existing deep learning techniques and recent research ideas, several important research directions in the future are pointed out, including expanding insulator defect samples, establishing unified performance evaluation indicators, small and zero sample learning, new defect detection frameworks, multi-level detection of small defects, deep fusion of multiple learning technologies, cloud-edge-end collaborative fusion, and improving network model stability and real-time performance.

The output characteristics of magnetostrictive devices usually show a strong bias condition dependence. The bias magnetic field provided by constant current will change nonlinearly with the change of the material permeability under stress excitation (manifested as non-constant bias magnetic field). This change affects the accurate characterization of material magnetization process and the rational design of bias points. At present, the inverse effect models of magnetostriction mainly focus on material characterization under constant bias magnetic field. Models that solely consider a constant magnetic field fail to accurately reflect the output characteristics of devices in their actual operating environments. Establishing a hysteresis model that accounts for the inverse magnetostrictive effect with dynamic variations in the bias magnetic field holds significant research importance.

The models established in this paper include the average model of non-hysteresis energy, the hysteresis constitutive model and the equivalent magnetic circuit model taking into account the variation of the bias magnetic field. Firstly, based on the free energy theory, the expression of the non-hysteretic magnetization is derived, and the average model of the non-hysteretic energy is established. Secondly, using the modeling idea of J-A model for positive hysteresis phenomenon, the first order differential equations of irreversible component M_irr, λ_irr and stress are introduced. The hysteresis constitutive model which can characterize the inverse effect of magnetostrictive materials is obtained. Based on the equivalent theory of magnetic circuit, the influence of stress on magnetic field strength is reflected by the change of magnetoresistance. Finally, an energy average hysteresis model is established which can account for the change of bias magnetic field. Hysteresis models often have difficulty in parameter identification. An improved cuckoo search-grey wolf optimizer (CS-GWO) hybrid algorithm is proposed by introducing nonlinear adaptive step factor α(t). Comparing the optimization results of the traditional optimization algorithms of CS, GWO, and PSO, the CS-GWO algorithm has the highest accuracy and the fastest convergence speed, and can accurately and efficiently identify the globally optimal parameters of the energy-averaged hysteresis model. Model validation is performed in two steps. First, the basic parameters of the model were extracted based on the experiments of Fe₈₁Ga₁₉ alloy bar under -115~0 MPa compressive stress and 22.3~446 Oe constant bias magnetic field. The error between the B-σ curve simulated by the model and the existing experimental data is only 3.85%, which is better than the error calculated by the traditional model of 6.79%. The error of ε-σ curve simulated by the model is 2.93%. Then, based on the experimental data of Fe₈₁Ga₁₉ alloy bar under constant current bias, the parameter H_s is further extracted. The errors of the simulated H-σ curve, B-σ curve and ε-σ curve with experimental data are 4.74%, 4.31% and 3.97%, respectively. The simulation results can accurately describe the tendency of the bias field to increase nonlinearly with the increase of stress, which also leads to a shallower sensing response under constant current bias than under constant field bias.

The proposed model, in addition to predicting the sensing response of the device, can also be used to track the optimal bias conditions of the material as well as to predict the trend of the ΔE effect of the material. The model can provide theoretical guidance for the performance tuning and variable stiffness design of devices such as sensors and energy harvesters based on the inverse effect of magnetostrictive materials.

The dynamic characteristic of grid-forming inverter (GFM) is mainly affected by the control strategy, and the interaction with the power grid may cause instability such as oscillation. At the same time, the interactive coupling between different time-scale controllers in GFM makes the stability analysis more complicated. Modal analysis based on the state-space model (MASS) uses the participation factor (PF) to quantify the contribution of each state variable to a particular pattern. However, the number of electrical components in new power systems is increasing explosively, and the difficulty of state-space modeling of the whole system is increasing rapidly. In addition, state-space modeling requires detailed system structure topology and complete control parameters of each electrical component, and inverters usually only have impedance models that describe the characteristics of voltage and current ports, with gray box or black box characteristics.

In order to explore the interaction characteristics among all electrical components of the system, the dynamic model of the whole system is constructed by the closed-loop feedback formula of the whole system dynamic matrix. Based on this foundation, the modal analysis based on impedance model (MAI) can evaluate the contribution of each power device to oscillation modes at the device level. However, MAI treats inverters as single, holistic components, which limits its ability to identify dominant system dynamics at the control loop or state variable level. Decomposing different control loops into equivalent circuit components enables the stability analysis of internal inverter dynamics. However, the decomposition of synchronization control loops remains to be explored. This paper proposes an extended modal analysis based on impedance model (EMAI) method to address the current challenges faced by MAI.

First, a decomposition method for the GFM impedance model based on the matrix inversion lemma was proposed, dividing GFM dynamics into synchronous dynamics (SD), dominated by the power frequency synchronization loop (PFL), and electromagnetic dynamics (ED), governed by the voltage control loop (VCL). The detailed categorization of dynamics facilitates an in-depth exploration of the complex coupling mechanisms among controllers operating on different time scales. Subsequently, overall impedance participation factors and participation ratios (PR) were introduced to characterize different internal dynamics of GFM, enabling the evaluation of SD and ED contributions at the control loop level. These metrics help identify the dominant system dynamics and trace the root causes of system instability. Finally, an explicit parameter PF was introduced to precisely locate the critical control parameters of identified loops, serving as a metric for optimizing control parameters and enhancing system damping.

The analysis yields the following conclusion: as the frequency of oscillation modes decreases, the dominant dynamics within each GFM gradually shift from ED to SD. MAI can provide an overall assessment of GFM participation but fails to capture the dominant dynamics of individual GFMs. EMAI not only identifies interactions between various GFMs and the grid but also evaluates the contributions of ED and SD within GFM through overall impedance participation factors, thereby pinpointing the primary causes affecting system dynamics to specific control loops. Moreover, the results of EMAI and MASS in assessing the participation levels of different GFM dynamics are highly consistent, validating the effectiveness of the EMAI method. Furthermore, the explicit parameter PF provides effective recommendations for improving system damping and enhancing stability. EMAI offers nuanced insights into system stability analysis, enabling the rapid identification of the root causes of system instability.

The global consensus has emerged to replace traditional fossil fuel-based power generation with renewable energy sources such as photovoltaic and wind power, leading to the formation of renewable energy delivery systems (REDSs). Within these systems, a trend towards the integration of grid-following (GFL) and grid-forming (GFM) devices has emerged. The REDS incorporating GFL and GFM devices exhibit high dynamic order, with complex dynamic interactions between heterogeneous equipment clusters and between equipment clusters and the network, posing challenges for the mechanism analysis and quantitative computation of small-signal stability. This paper proposes an eigen-subsystem computation method for the small-signal stability analysis of REDSs. It defines the double-infeed eigen-subsystem (DIES), which includes a GFL device and a GFM device. By equivalently reducing the complex, high-dimensional REDS to several low-dimensional DIES, the method preserves the dynamic interactions both between devices and between devices and the network. This approach enables efficient and accurate small-signal stability analysis of REDSs.

Firstly, for a REDS incorporating GFL and GFM devices, a full-order small-signal model of the system is constructed. The general approach for deriving the eigen-subsystem is briefly outlined, which involves reducing the complex high-dimensional system to several simple low-dimensional eigen-subsystems through decoupling. Subsequently, for a REDS with an equal number of n GFL devices and n GFM devices, based on the full-order model of the system, a matrix block diagonalization method is proposed on top of the matrix diagonalization method. A fast algorithm based on the Givens method is presented to solve for P⊗I₄ (P∈R^n×n), thus decoupling the REDS into n DIESs. Stability criteria for the DIES are also provided. When the device parameters are given, the stability operating region Ω of the DIES can be determined. The DIES remains stable if its network impedance falls within Ω. Thirdly, for more generalized scenarios, a node-splitting method is introduced to increase the number of less abundant devices, addressing the imbalance in the number of GFL and GFM devices. An eigen-subsystem-based method for small-signal stability analysis of REDSs is proposed. The REDS is stable if the set of network impedances Ω₁, formed by all decoupled DIESs, lies within the stability region Ω. Otherwise, the REDS becomes unstable and exhibits the same stability issues as the unstable DIES. Finally, time-domain simulations are conducted, and a 3-machines 9-nodes system as well as a 54-machines system are used to validate the effectiveness and correctness of the proposed method in the small-signal stability analysis of REDSs incorporating GFL and GFM devices. Experimental comparisons show that, compared to traditional eigenvalue analysis methods, the proposed method significantly improves computational efficiency.

The following conclusions can be drawn: (1) The REDS is mode-equivalent to its DIESs, and the stability characteristics of the original system can be traced back through DIESs. (2) For general REDS with n GFL devices and m GFM devices, the system can be decoupled and reduced in order by constructing a mode-equivalent system through node-splitting. This results in m DIESs, and (n-m) eigen-subsystems of single GFL devices (where n>m, or vice versa). (3)When the device parameters are given, the stability operating region Ω of the device-side characteristics can be determined. The network-side information of the eigen-subsystems obtained from the decoupling of the REDS forms a set of network impedances Ω₁. By checking whether Ω₁ belongs to Ω, the stability of the original system can be quickly assessed. Currently, small-signal synchrony stability has primarily been analyzed for the DIES. A future challenge is how to comprehensively analyze system stability under interactions among different components and quantify the stability margin of hybrid delivery systems.

Under the impetus of "dual carbon" targets, new energy sources are increasingly integrated into the power grid through power electronic converters, leading to a gradual decline in the proportion of synchronous machines. To enhance the stability of "highly renewable and highly flexible" systems, the flexible controllability of converters can be leveraged by employing grid-forming control to provide reliable voltage and frequency support to the system. Virtual synchronous generator (VSG) control emulates the operating characteristics of synchronous generators to achieve voltage and frequency regulation, providing active frequency and voltage support capabilities while effectively increasing the inertia level of new energy units. VSG control has garnered significant attention due to its active support features; however, the factors influencing its voltage support capability are not yet fully understood, necessitating further research on VSG control strategies that balance voltage support with short-circuit current limitations.

To address these issues, this paper first analyzes the equivalent impedance of each control stage of grid-forming converters based on VSG control during steady-state operation and establishes an equivalent circuit model of the system. Secondly, based on the system's equivalent circuit, the expression for terminal voltage is derived, quantifying the relationship between terminal voltage, internal electromotive force, and system impedance, and analyzing the factors affecting the voltage support capability of VSG. Subsequently, improvements to VSG control are made considering both current limitation requirements and voltage support capability, proposing adaptive control strategies for virtual impedance and voltage compensation coefficients. Finally, the accuracy of the theoretical analysis and the effectiveness of the proposed strategy are verified using the Matlab/Simulink electromagnetic simulation platform.

The analysis results show that reducing virtual impedance, reactive power voltage droop coefficient, or increasing the voltage compensation coefficient can enhance the voltage support capability of VSG. However, decreasing virtual impedance and reactive power voltage droop coefficient reduces the system's equivalent impedance, while increasing the voltage compensation coefficient increases the system's internal electromotive force, thus imposing higher demands on the system's current-limiting capacity. By adopting the proposed adaptive control strategy for virtual impedance and voltage compensation coefficients, virtual impedance can be self-adaptively configured according to the system state, ensuring voltage support capability under the premise of meeting current-limiting requirements.

Through theoretical analysis and simulation experiments, the following conclusions can be drawn: (1) When the grid-forming converter system based on VSG control enters a steady state, its various control stages can be represented by equivalent impedance, which characterizes the relationship between terminal voltage, internal electromotive force, and system impedance. (2) The voltage support capability of VSG is related to virtual impedance, reactive power voltage droop coefficient, and voltage compensation coefficient. Reducing the reactive power voltage droop coefficient, decreasing virtual impedance, and adding voltage compensation control to the reactive power loop can all improve voltage support capability. (3) Voltage support capability and short-circuit current limitation of VSG interact. Through adaptive control of virtual impedance and voltage compensation coefficients, short-circuit currents can be fully utilized, maximizing the voltage support capability of VSG without exceeding the short-circuit current limit.