Grid-forming energy storage technology serves as a critical solution for enhancing power system stability. Transformerless energy storage systems, characterized by high efficiency, modularity, and direct medium/high-voltage grid integration, have emerged as the preferred choice for large-scale grid-connected energy storage. However, the reduced electrical distance between transformerless systems and the grid results in significantly lower grid impedance, posing severe challenges to the stability of grid-forming control. The underlying mechanism lies in the voltage-source operation of grid-forming converters: under low grid impedance conditions, minor voltage deviations between the converter and grid can trigger substantial current surges, ultimately leading to instability. To address these challenges, this study establishes a full order small signal model to analyze the impact of low grid impedance on stability and proposes impedance enhancement strategies.

The research begins by developing a dynamic model that integrates virtual synchronous generator (VSG) control, voltage-loop regulation, and grid interactions. Pole trajectory analysis reveals two critical instability mechanisms: 1) Excessively low grid inductance shifts system poles to the right-half plane, inducing instability; 2) Insufficient grid resistance reduces damping ratios, exacerbating oscillatory behavior. These combined effects diminish system stability margins and may provoke subsynchronous oscillations. To mitigate these issues, a dual-layer impedance enhancement strategy is proposed: (1) Physical impedance reconstruction: The equivalent internal voltage control strategy repurposes filter inductance as coupling impedance by relocating the controlled voltage from the point of common coupling (PCC) to the converter side. This hardware-free modification enhances physical coupling impedance without requiring additional components. (2) Adaptive virtual impedance: A composite virtual impedance module combines static impedance for damping optimization and a dynamic current-limiting component. The static virtual impedance elevates damping ratios near to 0.707, while the current-limiting module dynamically adjusts impedance parameters based on real-time overcurrent thresholds, ensuring fault current suppression.

In the analysis of impedance enhancement effect, it is shown that equivalent internal voltage control causes the dominant pole of the system under strong power grid to shift to the left into the stable region, while the introduction of adaptive virtual impedance further enhances damping characteristics and improves dynamic response performance. The proposed impedance enhancement strategy enhances the system stability by introducing filtering impedance at the physical level and superimposing virtual impedance at the control level, thereby increasing the equivalent coupling impedance of the system from a single grid impedance to the combined effect of the three.

Experimental validation on a cascaded H-bridge transformerless energy storage platform under zero grid impedance conditions confirms the strategy's effectiveness. The proposed method eliminates oscillatory instability observed in conventional approaches, achieving smooth active power step responses without overshoot. During grid frequency fluctuations (±0.5 Hz), the system provides 0.67(pu) active power support, demonstrating effective grid-forming capabilities. Under symmetrical voltage sags (0.5(pu)), it delivers 0.5(pu) reactive power while constraining currents within 1.2(pu) safety thresholds, validating robust fault ride-through performance. Experimental and theoretical analyses confirm: (1) The proposed impedance enhancement architecture synergizes physical-layer reconstruction with control-layer virtual compensation, demonstrating superior stability improvement over conventional methods through coordinated impedance augmentation. (2) A pole trajectory analysis-based parameter optimization framework achieves concurrent enhancement of stability and dynamic performance, with virtual impedance implementation optimizing damping ratios to eliminate oscillatory instabilities. This work validates the effectiveness of the proposed strategy in extreme low-impedance scenarios, providing technical support for grid-forming transformerless energy storage applications in power grids.

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.

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.

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.

In China, the current renewable energy resources mainly use grid-following converters as grid-connected interfaces, which cannot provide inertia and damping support for power systems. In order to enhance the support capacity of renewable energy resources, grid-forming inverters are emerging as a promising solution as they can emulate the dynamic property of synchronous generator and provide support. However, the grid-forming inverter faces significant risks of transient synchronous instability. Current research primarily focuses on single grid-forming inverter systems, which cannot be applied to multi-machine systems due to complex interactions between converters. Quantitative transient analysis and the method of stability region estimation for multiple paralleled grid-forming inverter systems are absent.

To fill this gap, taking transient interaction and power coupling into consideration, the large-signal equivalent model of multiple grid-forming inverters system is established. Based on this model, a set of Lyapunov functions is constructed, which accounts for damping dissipation, reactive power loop dynamics, and transient interactions, enabling intuitively and accurately plotting the stability region for multi-machine system. Then, by comparing the sizes of the stability regions, the impact of control parameters and grid parameters on the stability boundaries of grid-forming multi-machine systems is quantified. Furthermore, the influence of damping dissipation, reactive power loop dynamics, and transient interactions on the transient stability margin is explored. Finally, hardware-in-the-loop experiments validate the accuracy of the estimated maximum stability region.

The following conclusions can be drawn from the analysis in this paper: (1) Due to the complex interaction, the equivalence model and transient characteristics of multi-machine system are more complex than those of single-machine system. (2) The Lyapunov function set, which takes into account voltage dynamics, damping dissipation and transient interaction, can accurately estimate the maximum stability region of multiple grid-forming inverter systems, and predict the transient synchronization stability via the location of the fault clearing point. (3) By comparing the size of the stability region, the increase of reference power, fault depth, and line impedance will reduce the stability region, and the increase of damping coefficient, inertia, and reactive droop coefficient will enlarge the stability region. The voltage dynamics and damping dissipation can increase the stability margin of the system, and the transient interaction between units can reduce the stability margin.

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.

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.

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.

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.

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.