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.

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.

Metal oxide surge arresters are crucial for overvoltage protection in power systems, determining the insulation level of electrical equipment, with their core component being the ZnO varistor. However, modern stable ZnO varistors exhibit an anomalous decrease in power loss during aging, contradicting the increase in power loss predicted by the classical ion migration model. This discrepancy poses challenges for the condition assessment and life prediction of ZnO varistors due to a lack of theoretical foundations, thereby presenting a potential threat to the power system. Consequently, the study of the anomalous aging mechanism of stable ZnO varistors has been identified as a major challenge for the varistor community by CIGRE in both 2013 and 2017.

In this paper, stable ZnO varistors are subjected to accelerated DC aging at elevated aging temperatures to investigate their long-term stability transition. With increase in aging temperature, power loss trend transitions from a continuous decrease at 120℃ to an initial decrease followed by an increase at 150℃, and a sustained rise at 180℃. The decreasing power loss trend can be fitted by a double exponential decay function, while the increasing power loss is proportional to the square root of the aging time t^0.5. After transitioning to a mixed stable type at 150℃, the aging of stable ZnO varistors becomes irreversible. In-situ high-temperature dielectric measurements reveal that the interface space charge polarization relaxation process shifts to higher frequencies with decreased relaxation time and activation energy decreasing from 0.583 eV to 0.560 eV, indicating the destruction of the grain boundary structure. Low-temperature dielectric tests show that intrinsic point defects of zinc interstitials undergo irreversible consumption after aging. Upon transitioning to an instable type at 180℃, the "crossover" phenomenon of the forward current-voltage (I-U) characteristics disappears at 180℃, and both forward and reverse I-V characteristics shift towards increased leakage current region as a whole. Severe deterioration in reverse electrical parameters was observed, as breakdown voltage U_1mA decreases from 200.5 V to 92.9 V, the nonlinear coefficient α decreases from 16.3 to 2.0, and the leakage current rises from 19.5 μA to 479.3 μA. More importantly, offline physical and chemical structural tests show a reduction in the diffraction angles of ZnO crystal planes and decreased peak intensities. Additionally, a significant decrease in the binding energy of the Zn_2p orbital is observed, with Zn_2p3/2 and Zn_2p1/2 orbitals decreasing from 1 022.5 eV and 1 045.9 eV to 1 022.1 eV and 1 045.2 eV, respectively. This indicates the reduction of zinc interstitials and confirming that the interface states cannot maintain stability at high temperatures, thus becoming neutralized and consumed with zinc interstitials.

These findings demonstrate that the essence of the decreasing power loss in stable ZnO varistors lies in the stable interface states at the grain boundary, which, however, cannot maintain stable at certain high temperatures. The interface states would then neutralize with the zinc interstitials due ion migration, subsequently leading to the reduction of zinc interstitials and the destruction of the ZnO lattice, resulting in significant deterioration of ZnO varistors. Therefore, optimizing the high-temperature stability of the interface states is crucial for enhancing the long-term stability of ZnO varistors.

In substation robot inspection tasks, high-precision semantic segmentation of 3D point cloud data is one of the key technologies. Traditional point cloud semantic segmentation algorithms have certain limitations, making it difficult to handle complex 3D scenes. Deep learning methods have compensated for the shortcomings of traditional point cloud semantic segmentation algorithms and have become the main method for achieving point cloud semantic segmentation. However, existing point cloud segmentation methods for substations face issues such as high complexity, low accuracy, and gradient vanishing. To address these issues and achieve accurate segmentation of the main equipment point cloud in substations, this paper proposes a high-precision semantic segmentation method for substation main equipment point clouds based on DI-PointNet.

Firstly, on the basis of the PointNet++ network structure, a double-layer consecutive transformer (DLCTransformer) module is introduced. Key points are sampled through the DLCTransformer to enhance information interaction between point clouds and expand the effective receptive field. Secondly, a hierarchical key sampling strategy is adopted. The point cloud data is divided into the original dense point cloud space and a sparse point cloud space formed after farthest point sampling. These are then divided into multiple non-overlapping 3D windows, ultimately generating key values required for self-attention mechanism calculations, thereby reducing computational complexity, improving the model’s receptive field, and aggregating long-range context to achieve information interaction of substation-associated point clouds. Finally, an inverted residual module (InvResMLP) based on residual connections and inverted bottleneck design is added to the network. This enhances the model’s ability to extract complex structural features from substation point clouds while effectively reducing the gradient vanishing problem, making the algorithm more robust in handling complex substation scenarios and improving the accuracy of semantic segmentation of substation main equipment point clouds.

Additionally, to validate the segmentation effectiveness of the algorithm, this paper uses Avia LiDAR equipment to collect point cloud images of different devices at substations such as the Baobei substation in Baoding City. The original data includes transformers, switchgear, steel towers, insulators, maintenance equipment, and others (mainly vegetation and buildings). To simplify the point cloud data while filtering noise, the original input point cloud is first subjected to grid sampling with a grid size of 0.03 m. Data augmentation methods such as z-axis rotation, scaling, perturbation, and color reduction are employed. The initial window size is set to 0.12 m and is doubled after each down-sampling layer. The DI-PointNet is trained using the cross-entropy loss function and Adam optimizer with the following hyperparameters: initial learning rate of 0.001, batch size of 2, and 100 epochs. To ensure the reasonableness and accuracy of the experiments, the comparative algorithms used in this paper are trained using the same hardware platform, environment version, loss function, optimizer, hyperparameters, and training strategies as DI-PointNet.

Through ablation experiments and comparative analysis, the DI-PointNet algorithm proposed in this paper improves the overall accuracy (OA) value of substation point cloud segmentation by 3.4 percentage points compared to before the improvement, while reducing algorithm complexity. The proposed algorithm outperforms other mainstream deep learning algorithms and other point cloud segmentation algorithms in the power sector. The performance of this algorithm is close to the accuracy of manual segmentation and can achieve precise segmentation of substation point clouds.

AC/DC hybrid system has become an effective solution for large-scale new energy consumption because of its characteristics of multiple power sources, multiple drop points, large capacity and cross-regional flexible transmission. However, the wide-frequency oscillation problem of AC/DC hybrid power system with high proportion of power electronics is prominent, which threatens the safe and stable operation of the system. At present, the stability analysis of hybrid system is mainly faced with the problem of how to take into account the AC and DC sections of the hybrid system at the same time and how to cover the system equipment with different impedance characteristics, so as to realize the unified analysis of the AC/DC hybrid network with multiple power electronic equipment. To address the above issues, this paper establishes a unified immittance network model for system-level stability assessment of hybrid systems.

First, based on the voltage/current source type device characteristics of the network devices, the impedance/ admittance forms of each network module of the system are standardized to avoid the problem of solving for the right half-plane poles in the process of system stability analysis. Secondly, from the perspective of the AC and DC ports of the system equipment, the AC/DC hybrid system can be divided into mono immittance subsystem and hybrid immittance subsystem. Finally, based on the interaction relationship between system immittance networks, a unified immittance network model containing complete oscillation information of the hybrid system is established. Under the premise of covering the stability information at each AC and DC port of the hybrid system, the unified immittance network model reduces the dimension of the system network model, at the same time expands the system network matrix from a single AC or DC system to an AC/DC system. Furthermore, combined with the derivation and change process of the immittance network, and through the modularization of the system expansion, this paper makes the immittance network applicable to the analysis of objects with different topologies,and extends the unified immittance network to general AC/DC hybrid systems. In addition,in contrast to the matrix model that merely aggregates a single impedance feature or a single admittance feature, the unified immittance network encompasses the AC/DC systems with various impedance characteristics, accomplishing the mutual unification of the new energy unit with admittance properties and the load network with impedance properties. This facilitates the precise establishment of the network mathematical model when confronted with the AC/DC system that concurrently incorporates equipment with current/voltage source characteristics, and realizes the unified coverage of equipment models with dissimilar impedance characteristics.

Based on the immittance network model, a unified immittance network stability criterion covering the interaction relationship of each AC/DC port of the hybrid system is derived. Combined with the expansion analysis of the immittance network, the criterion is extended to the general AC/DC hybrid system. The stability criterion comprehensively covers the stability problems of the AC/DC system, and avoids solving the problem of poles in the right half-plane, simplifying the analysis process. Furthermore, an oscillation traceability method for the hybrid system is given based on the immittance network model. Finally, based on the application examples of the AC/DC hybrid system, the immittance network model and its stability analysis method proposed in this paper are evaluated and verified.

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.

With a high proportion of power electronic devices connected to the power system, the new power system presents low inertia, low impedance, weak stability and other characteristics, and the risk of operational security increases. In this regard, the grid-forming energy storage converter should be emerged, the grid-forming energy storage converter gives inner loop voltage control the amplitude and phase angle through the power external loop control, presenting the voltage source characteristics. It has active anti-interference, active support characteristics, can effectively solve the problems faced by the new power systems. However, when the system is disturbed and the voltage falls to different degrees, the grid-forming energy storage is limited by the power angle curve of the power outer loop and the fixed active and reactive reference values, which will result in a large power angle instability and a disturbance current of more than 5 times. It threats the security and stability of the system operation. To address this problem, this paper firstly establishes a model of grid-forming energy storage converter. Based on the established model, the droop control power angle curve is plotted, and the transient destabilization mechanism of the grid-forming energy storage converter is analyzed under large disturbances. After analyzing the system, it is known that the stability of the system during large disturbances depends on the existence of an intersection between the system power angle curve and the active power reference value. At the same time, the size of the system disturbance current is affected by the degree of power angle change to a certain extent. Secondly, the disturbance current characteristics and its determining factors are analyzed, and the effect of direct current limiting control on the transient stability of the system is revealed. The analysis results show that the direct current limiting control tends to destabilize the system and cannot be directly used to limit the disturbance current. After theoretical analysis in this paper, it is found that the disturbance current size of the system is positively correlated with the difference between the converter out put voltage and the grid-side voltage, and the converter out put voltage size is correlated with the reference value of the power outer loop reactive power of the structural network type control. Therefore, during the disturbance period, the disturbance current can be limited by adjusting the system reactive power and then controlling the converter out put voltage. Based on the above theoretical analysis, an adaptive low-voltage ride-through (LVRT) control strategy for grid-forming energy storage converter is proposed, which can adjust the active and reactive reference values according to the degree of system perturbation, without switching the control strategy and changing the structure of the grid-forming control strategy. The energy storage converter still exhibits the characteristics of the voltage source during the distribution period, and it has the ability of active support for the system. It realizes effective limitation of the distribution current in the course of maintaining the stability of the system. At the same time, the disturbance current is effectively limited. Finally, the effectiveness of the proposed control strategy is verified by simulation and semi-physical experiment.

At present, renewable energy generation mainly use grid-following (GFL) control, which is prone to cause small signal stability problems such as broadband oscillation when connecting to the weak grid system. What’s more, the GFL units have insufficient support capacity for the grid. Grid-forming (GFM) technology construct the grid voltage independently through power synchronization control.When the system is disturbed, GFM units can actively support the grid voltage and frequency to improve the stable operation of the system. Under the situation of rapid development of renewable energy, it’s important to carry out GFM technological transformation and upgrading with renewable energy clusters/stations as the main body. How to reasonably plan the access capacity and location of GFM units of renewable energy grid-integration systemand improve the system stability characteristics, has become a key concern for engineering applications. The paper studies the configuration problem of the GFM unitsin renewable energy grid-integration system, with the focus on the small signal stability constraints.

Firstly, the singlerenewable energy converter grid-integration system was established. Based on the small signal model of the renewable energy converter grid-integration system, a closed-loop power-voltage feedback model was constructed, and the consistency between the former and the current-voltage closed-loop feedback model was verified in analyzing the stability characteristics of the system. Secondly, based on the impedance network circuit model, the system stability characteristic analysis method was extended to the multi-machine system. What’s more, the GFM units access capacity and distribution configuration problem of the multi-machine system was set. The objective of the problem is to minimize the total capacity of GFM units in the system, the constraints are that the system has sufficient small signal stability margin and stability support capability. Finally, the small signal stability margin index, the small signal stability support gain growth rate index, the GFM units access point selection index and the configuration method for GFM units of the system were proposed respectively. An analytical example was constructed based on the real renewable energy cluster grid-integration system, and the effectiveness of the proposed method was verified by time-domain simulation.

The conclusions are as follows: (1) Under the constraint of system small signal stability, the reasonable configuration of the capacity and location of GFM units can ensure that the whole system has sufficient small signal stability margin and stability support capability. Furthermore, reducing the capacity of the GFM units configuration can minimize the economic cost of the system. (2) The proposed configuration methodcan enhance the system's stable operation capability, particularly within a specific range of weak grid strength. It appears that when the capacity proportion of GFM units is constant, the weaker the grid characteristics, the more GFM units needs to be accessed. (3) The higher the percentage of GFL units with poor dynamic characteristics in the system, the larger the proportion of GFM units needs to be accessed. Optimization of system control parameters or control strategies, and explore the configuration method of GFM units in complex system scenarios will be the future research direction.

With the continuous development of the new energy vehicle industry, lithium-ion batteries are used in large quantities as on-board power batteries. The battery management system (BMS) is responsible for monitoring, evaluating, maintaining, and optimizing the performance and life of Li-ion batteries, and the prediction of c is an important part of the BMS. Accurate prediction of a battery's RUL helps identify batteries that are nearing the end of their life to prevent potential safety risks such as overheating, combustion, or explosion, and allows O&M personnel to schedule battery maintenance and replacements based on the battery’s actual state of health, rather than on a pre-determined schedule, thereby reducing unnecessary O&M costs. However, lithium-ion batteries exhibit nonlinear aging trends due to their complex internal chemical reactions during use, and the aging process of batteries usually exhibits multi-stage degradation, which increases the difficulty of RUL prediction. In view of this, this paper proposes a RUL prediction method for lithium-ion batteries based on public battery data from the University of Maryland and lithium iron phosphate battery data collected by the group's own laboratory, and the main research contributions are as follows:

Aiming at the problem that battery capacity is difficult to be measured directly, and the poor ability of traditional network models to capture multi-feature input information, a method is proposed to optimize the bidirectional gated recurrent unit (BiGRU) network based on the fusion feature and the osprey optimization algorithm (OOA) for RUL prediction of lithium-ion batteries. Simple and easy-to-measure current, voltage and time data during battery aging are collected, from which the health factors that can reflect the aging trend of the battery are extracted. The Savitzky-Golay filtering method is selected to reduce the influence of noise on the prediction accuracy. A fusion feature screening strategy combining filter and wrapper is proposed to reduce the complexity of the model and prevent model overfitting. Considering the insufficient ability of the traditional model to capture battery aging information when dealing with multi-feature inputs, the GRU network, which predicts only based on historical information, is upgraded to the BiGRU network, which is capable of handling both forward and backward information of the sequences. The BiGRU network is able to understand the overall structure and dynamic properties of the sequences in a more in-depth manner, better integrate the multi-dimensional features, and adapt to dependencies in different time scales. OOA is used to effectively optimize the hyper parameters inside the BiGRU model, which improves the prediction accuracy of the model and also realizes the automatic configuration of the parameters. Different types of battery data are used to compare the proposed method with traditional network models to verify the reliability of the proposed OOA-BiGRU model. In addition, the effect of the proposed fusion feature prediction is compared with all feature prediction and filtered feature prediction, which proves that the fusion feature better represents the aging degree of the battery and improves the accuracy of the model prediction.

The research results of this paper provide a new method and idea for RUL prediction of lithium-ion power batteries, which can be applied to the BMS system of new energy vehicles and is of practical significance.

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.