Adaptive VSG control of flywheel energy storage array for frequency support in microgrids

0 Introduction

As renewable energy sources (RESs) continue to increase in prominence and achieve a significant penetration rate within the power grid,substantial changes have occurred in the grid structure.Microgrids,characterized by their enhanced efficiency in utilizing RESs and greater flexibility in power supply,have gradually emerged as vital components of the power system [1,2].However,microgrids are susceptible to small perturbations owing to the presence of a cluster of power-electronically interfaced RESs with less physical inertia [3].Moreover,in the event of a significant active power shock,a heightened risk of triggering under-frequency load shedding or over-frequency generation shedding exists,which exacerbates the frequency stability problems of microgrids [4-6].Therefore,the energy storage system (ESS) must be used to offer timely and stable frequency-regulation services for microgrids.In contrast to other ESSs,flywheel energy storage systems (FESS) provide distinct advantages in terms of high power density and efficiency,rapid responsiveness,and extended operational lifespan [7].Consequently,FESSs are widely utilized for peak and frequency regulation and integration of RESs [8,9].

Owing to the constraints imposed by materials,costs,technology,and other factors,the capacity of a single flywheel is limited.Consequently,interconnecting multiple modular flywheel energy storage units (FESUs) to form flywheel arrays is common practice [10].This configuration facilitates larger energy storage capacities,higher power outputs,and extended operational durations.However,challenges arise in maintaining complete consistency in the currents,friction coefficients,and motor and flywheel parameters.The prolonged operation of a flywheel energystorage array (FESA) may result in an increasing speed differential among individual units.This phenomenon can cause certain units to exceed their state of charge (SOC) limits,thereby hindering their involvement in subsequent charging or discharging processes.In [11] and [12],researchers explored topology and coordinated control methods for parallel-operating flywheel arrays with AC or DC buses.In [13],the power allocation optimization for the FESA aimed to minimize the total power loss;however,this involved a complex computational process and could exacerbate the residual energy differences among units.The authors of [14] proposed a decentralized control scheme for managing flywheel arrays;however,its practical engineering implementation presents challenges.

Numerous studies have been conducted to achieve the rapid frequency support of FESS for microgrids [15].These methodologies can be broadly categorized into communication-based and communication-free control strategies.Communication-based approaches primarily involve the issuing of frequency regulation commands from the central controller of the microgrid and directing the high-frequency portion of the required power to the FESS [16,17].However,the response of the FESS to frequency regulation commands may be adversely affected by communication delays and faults,resulting in suboptimal frequency regulation performance.By contrast,communication-free control strategies primarily rely on droop control [18] and virtual inertia control [19],thereby enabling the FESS to actively adjust the output power in response to frequency changes.In [20],an adaptive droop controller was designed to bolster the role of the FESS in providing frequency support during the initial disruption of the grid and to decrease the power output during frequency recovery,thereby extending its discharge time.In [21],a three-layer control system considering the startup process was introduced for the FESS to reduce the frequency and dc-link voltage variations.Nevertheless,the droop and virtual inertia controls depend on precise measurements of the grid frequency and synchronization of a phase-locked loop (PLL).However,there is an inherent delay in the process from the measurement of the frequency change to the response,and the PLL is prone to small-signal instability when the grid strength becomes extremely weak [22].

The virtual synchronous generator (VSG) technology imparts power to electronically interfaced equipment with inertia and damping features akin to synchronous generators (SGs),thereby offering an effective solution to the challenge of insufficient frequency support capacity resulting from the reduced share of SGs [23].VSG has already found wide applications in RESs and ESSs [24,25].However,the long-term operation of FESA results in a gradual decline in the internal consistency within the array.This deterioration negatively affects the overall power output characteristics of the system,rendering the application of existing VSG control strategies directly to the FESA challenging.Moreover,the high self-discharge rate and limited capacity of the FESA can result in SOC limits being exceeded during extended operations [18].To prolong the continuous discharge time of the FESS,an improved VSG control strategy based on transient damping was proposed in [26].This strategy enabled the FESS to provide frequency support only during dynamic grid frequency changes,resulting in suboptimal frequency regulation performance.

The flexibility of the VSG facilitates the adjustment of the control parameters during operation to enhance the dynamic response performance.In [27],an adaptive inertia control for a VSG was proposed.Certain studies [28] and [29] explored an adaptive approach to adjust the inertia and damping coefficients within VSG control systems in real time.However,these studies did not mention the adaptive algorithm and value rule concerning the P/ω droop coefficient.In [30],adaptive VSG control considering storage capacity limitations was proposed with the parameter boundary as a function of the SOC.In [31],a fuzzy VSG control structure was designed for the FESS,thereby enabling the automatic adjustment of the VSG parameters according to the magnitude of the perturbation.However,these studies only examined the influence of SOC characteristics on the value rule without considering the adaptive adjustment of these parameters according to variations in the SOC.

The primary contributions of this study are threefold.1) A variable acceleration factor based on the SOC difference characteristics among flywheel units was integrated into the array speed balance control,which significantly improved the SOC equalization across units while adhering to power limitations.2) An improved VSG control with an energycontrol strategy for the FESA was introduced to prevent frequent output actions and avoid exceeding the SOC limit without compromising the regular operation of the FESA.3) The proposed adaptive control for the VSG-controlled FESA facilitated the flexible adjustment of the virtual inertia,damping coefficient,and P/ω droop coefficient to cope with variations in the SOC of the FESA,thereby enhancing the frequency support performance of the FESA.

This paper briefly introduces the FESA model and proposed array-speed-balance control strategy in Section 1.Section 2 provides a detailed introduction to the proposed improved VSG control method for the FESA.Section 3 describes the adaptive-control approach.Detailed timedomain simulations are presented in Section 4.Finally,Section 5 presents the conclusions of this study.

1 FESA modeling

As shown in Fig.1,Each FESU comprised a flywheel,permanent magnet synchronous motor,and flywheel converter system (FCS).The FESUs were interconnected to form a flywheel array via a DC bus.In this configuration,the flywheel array controller acquired the total output commands of the FESA using a DC bus voltage controller.Subsequently,a power command was allocated to each subunit based on the remaining energy of the individual units.The FCS regulated the FESU output to the specified power level and fed the FESU operational parameters back to the flywheel array controller.The grid-side converter adopted a VSG control strategy to impart an FESA with response characteristics similar to those of conventional generators.

Fig.1 Topology of the FESA

1.1 Model and control strategy of FESU

The charging and discharging processes of the FESU involve the use of power electronic devices to drive the motor,which propels the Maglev flywheel for acceleration or deceleration.As shown in Fig.2,the fundamental control strategy of the FESU involves synchronizing the unit output power with the power command originating from the flywheel array controller.Moreover,the d-axis current reference value of the motor was set to zero to ensure complete utilization of the stator current for generating electromagnetic torque.The current inner loop adopted grid voltage feed-forward and cross-decoupling to attain robust current tracking and dynamic performance,particularly in response to fluctuations in the power grid voltage.

Fig.2 Fundamental control strategy of FESU

Considering that the grid-connected speed of the flywheel is constrained by its maximum power and maximum electromagnetic torque,the SOC of both the FESU and the FESA was defined as shown in (1).By controlling the SOC to remain within the range of [0,1],each unit could be guaranteed to operate within its designated normal range.

where ωsi(t) is the angular velocity of the i-th flywheel.

1.2 Array-speed-balance control strategy of FESA

To ensure adherence to the upper power command and facilitate array-speed-balance control across the entire array,the flywheel array controller should allocate a power command for each unit based on the ratio of the remaining energy of each unit.The fundamental power allocation strategy considering the array speed balance control is expressed as in (2).

where is the total power instruction of the FESA,with a positive value indicating a discharge to the power grid.Further,Psi is the power distribution of the i-th FESU,and α is the acceleration factor.

According to (2),the value of α determines the speed of SOC balancing.A small α value slows SOC balancing,whereas a larger one poses a high risk of individual units exceeding their maximum power capacity.Thus,considering the power constraints and SOC balancing speed of the FESA,this study proposed the multistage SOC balancing strategy as in (3).

As evident from (3),the value of α is linked to the total power instruction of the array and the state of charge (SOC) of each unit.This adjustment of α occurs during different stages of array SOC equilibrium.In addition,the proposed array speed-balance control enables each unit to operate at the maximum power even in case of differences in their SOCs,ensuring that the capacity of the FESA is fully utilized.

2 Proposed VSG control for the FESA

The overall control structure of the FESA based on the VSG is depicted in Fig.1.The grid-side converter adopted VSG control to provide a system with inertial and primary frequency regulation capabilities.The flywheel array served as energy support for the VSG frequency response,ensuring the stability of the DC bus voltage through the flywheel array controller.However,because of the inevitable deterioration in consistency within the flywheel array during prolonged operation,the total output command of the flywheel array must undergo array speed balance control before being distributed to each subunit.The control structure of the flywheel array controller is illustrated in Fig.3.

Fig.3 Control scheme of the flywheel array controller

2.1 Control Structure of the improved VSG

The control strategy of the grid-side converter based on the VSG control,which includes power control loops,a virtual impedance loop,and dual closed voltage-current control loops,is shown in Fig.4.The voltage and current control loops follow classical vector control,and the virtual impedance loop can realize active and reactive power decoupling and enhance the performance during transient and grid faults [32].

Fig.4 Overall control scheme of the grid-side converter

The active power loop (APL) of the improved VSG is illustrated in Fig.5.The traditional VSG primarily employs a second-order swing equation to synchronize the virtual angular frequency generated by the converter with the angular frequency of the grid.This study retained the inertia characteristics and replaced the traditional damping link with a transient damping strategy based on a power differential term [33] to ensure the output power stability.Thus,the reference angular frequency of the VSG was determined using the following formula:

Fig.5 APL of the improved VSG

where Pe and Pref are the actual and reference values of the active power,respectively;Jv and Dh are the virtual inertia and transient damping coefficient,respectively;ωn is the rated angular frequency;θv and ωv are the virtual angular frequency and phase angle of the output voltage of the inverter,respectively;and Th is the time constant for the low-pass filter.

Droop control was applied to the FESA to emulate the primary frequency regulation behavior of the SGs without requiring frequency measurements,as shown in (5).Simultaneously,the frequency dead zone was set to (50±0.033) Hz to prevent the depletion of flywheel energy during prolonged frequency deviations.

where Dv is the P/ω droop coefficient.

An additional energy control loop facilitated the FESA in autonomously managing energy during operation,thereby preventing the overlimiting of the SOC from excessive frequency regulation energy consumption and/or prolonged self-discharge.The dead zone ensured that FESA adjusted its output only after an SOC warning.In this study,the SOC was set to a reference value of 0.5 with a dead zone size of 0.45.Therefore,when the SOC was between 0.05 and 0.95,the energy control loop did not interfere with the normal operation of the FESA.

The reactive power loop (RPL) of the VSG emulated the droop characteristics of the excitation regulator,which can be expressed as

where Un is the rated voltage;Qe and Qset are the actual and reference values of the reactive power,respectively;and Kq is the Q–U proportional coefficient of the virtual excitation regulator.

2.2 Control mechanism analysis

Owing to the significantly faster response of the dualvoltage-current loops,the dynamic process of the impact of the double inner loops on the power outer loop can be ignored [34].Therefore,the output active power of the VSG can be expressed as

where Ug is the grid voltage,XΣ is the equivalent impedance of the line and the virtual impedance of the VSG,and δ is the phase angle difference between the output voltage of the VSG and the grid voltage.

Linearizing (4),(5),and (7) at the steady-state operating point of the system and then applying the Laplace transform yields

Therefore,the transfer functions from the grid angular frequency to the output active power of the VSG can be expressed as

where

Equation (9) suggests that incorporating a powerdifferential term is equivalent to adding a zero and a pole to a traditional VSG.This adjustment altered the distribution of zeros and poles,thereby affecting the APL response characteristics.Considering that the value of Th is generally excessively small to maintain the filtering effect,the influence of the first-order low-pass filter is temporarily ignored,thus reducing the order of (9) to a second-order system.The corresponding natural oscillation angular frequency ωn1 and damping ratio ξ1 are

According to (9),if the frequency ωg deviates,the steady output active power of the VSG is

Hence,the natural oscillation angular frequency of the VSG is exclusively associated with the virtual inertia Jv.An increase in Jv reduces the bandwidth,resulting in a slower dynamic response for the APL.Nevertheless,Dh can be adjusted to alter the damping ratio of the system without affecting steady-state characteristics.

Consequently,when the system needs to respond to AGC commands,the FESA can operate in power control mode for precise output power regulation.During this period,the power differential branch serves as transient damping to ensure damping demand.When the FESA is required to automatically participate in the frequency regulation,it can operate in the frequency support mode,and Jv and Dv are adjusted based on the grid inertia and primary frequency regulation requirements.Moreover,dynamic performance can be enhanced by adjusting Dh to modify the damping ratio of the system.

2.3 Small-signal analysis and parameter design

2.3.1 Small signal modeling

To investigate the impact of the key parameters in the proposed strategy on system stability,we constructed the small-signal model (SSM) of the improved VSG,as depicted in Fig.4.Considering that the energy control loop serves the same function as adjusting the active power reference value of the VSG and that the droop control loop enhances system damping,the following stability analysis does not consider these two loops.The state equations of the power control loops of the VSG are

The specific modeling process for the other parts of the VSG can be found in [35] and will not be repeated here.By combining with (14),the SSM can be described as follows:

where x is the state-variable matrix,A is the state matrix,and B is the coefficient matrix;Δu=[ΔPset ΔQset]T.

2.3.2 Validation of the established small-signal model

In this section,we establish an electromagnetic transient model in MATLAB/Simulink and the small-signal model at the steady-state operating points corresponding to Pset=0.5 pu and Qset=0 pu.The detailed parameters are listed in Table A1.As shown in Fig.6,when the power instructions changed at t =0.5 and 1.5 s,the dynamic responses of the output power from these two models completely coincided.This alignment confirmed the accuracy of the small-signal model.

Fig.6 Step response comparisons between the small-signal model and the electromagnetic transient model

2.3.3 Stability analysis

The eigenvalues of the coefficient matrix A can be obtained using MATLAB to investigate the impact of the parameters on the system stability.As shown in Table 1,all 14 eigenvalues of the system exhibited negative real parts,indicating system stability.

Table 1 Eigenvalues of the tested system

For varying Th values,the locus of the dominant eigenvalues when Dh increases is shown in Fig.7.Despite the different Th values,the overall trend of the root loci in the system remained the same.As Dh increased from 0.01 to 0.03,λ7 and λ8 progressively moved away from the virtual axis,thereby signifying an enhancement in system damping and stability.Conversely,as Th varied from 0.001 to 0.02,the λ7 and λ8 gradually shifted to the right,thus indicating that the control delay introduced by Th would reduce the damping of the system and intensify oscillation.Moreover,if Th were excessively small,λ5 and λ6 would cross the imaginary axis into the right half plane,presenting a high risk of high-frequency oscillation.Therefore,the stability of λ5,6,and λ7,8 should be both considered when designing Th.In the study,a Th value of 0.008 was used.

Fig.7 Root locus of Dh varying from 0.01–0.03 when Th varies from 0.001,0.005,0.01,and 0.02

3 Adaptive control

3.1 Adaptive VSG control for frequency support

Considering the capacity limitations of the FESA,during significant power deficits in the system,a premature exit from frequency regulation due to flywheel-triggered SOC protection control may cause secondary frequency dips.Therefore,applying adaptive control to key VSG parameters based on changes in the system frequency and flywheel SOC was a more reasonable approach.The previous analysis showed that Jv and Dh exclusively influenced the power output dynamics,whereas Dv affected the steadystate output power.Therefore,comprehensively analyzing the impacts of Jv,Dh,and Dv on the frequency regulation services and the dynamic performance of the FESA—a critical aspect of their adaptive design—is necessary.

3.1.1 Adaptive virtual inertia

Because the appropriate design of the DC voltage controller of the FESA rendered the machine-side dynamics negligible [36],the VSG-controlled FESA could simulate the frequency response characteristics of the SGs.Considering that the RESs in the microgrid operated at maximum power,the equivalent system frequency response (SFR) of the islanded microgrid is illustrated in Fig.8.Here,HG is the inertia time constant of the equivalent SG,and KG,TR,and FH are the droop coefficient,inertial time constant,and characteristic coefficient of the equivalent governor,respectively.Further,DL is the load-damping coefficient,and ηG is the proportion of SGs.

Fig.8 SFR model of islanded microgrid

Fig.9 Dynamics of the frequency under a load step with increasing inertia constants

In the absence of generator governors and load frequency regulation effects during the initial stage of the disturbance,only the inherent moment of inertia of the SGs prevented the frequency changes.Thus,the level of inertia is crucial for ensuring the secure and reliable operation of power systems.Figure 9 shows the frequency-dynamic characteristics of the microgrid after experiencing the same disturbanceas changing the equivalent inertia HG.As HG increased,the maximum rate of change in frequency (ROCOF) decreased,and the steady-state frequency remained unchanged.However,the inertial response and frequency recovery times of the system increased.

Considering the relationship between the dynamics of the frequency and different equivalent inertia levels during disturbances,this study proposed an adaptive algorithm for the virtual inertia of a VSG-controlled FESA without the need for a direct measurement of the grid frequency,which can be expressed as

where J0 and Kj represent the initial value and adjustment coefficient of virtual inertia,respectively;and Jt is the change threshold,with a value of 0.02 as adopted in this study;Δω =ωv-ωn.

Considering that the derivative term may generate control noise,the derivative of the angular frequency is calculated in moving 50 ms windows.Furthermore,an inertia link was integrated to facilitate a smooth transition of the virtual inertia.This approach aimed to prevent unnecessary disturbances to the system frequency caused by sudden changes in the virtual inertia.

3.1.2 Adaptive P/ω droop coefficient

The energy emitted or absorbed by the VSG in response to grid frequency fluctuations was primarily determined by the P/ω droop coefficient.Excessive charge and discharge cycles do not affect the performance of the FESA;however,deviations in the SOC from the optimal range are of concern.If the FESA consistently responds to the primary frequency-regulation demands of the power grid at its rated power output,the SOC may quickly exceed its limit.This can result in sudden changes in the FESA output power,resulting in secondary frequency drops and system shocks.Therefore,it is imperative to correct Dv according to the SOC,which is expressed as

where kSOC is the participation factor of frequency control.

For practical reasons,this study adopted a linear piecewise function to define ksoc.This approach ensured a smooth output and simplified the calculations.The adaptive curve for ksoc is shown in Fig.10.

Fig.10 Adaptive curve of kSOC

3.1.3 Adaptive damping coefficient

The damping coefficient effectively mitigated the power oscillations without introducing steady-state errors.Therefore,adjusting the damping coefficient ensured that the VSG maintained exceptional responsiveness and operational stability.The adaptive strategy for the damping coefficient Dh can be derived using (11) by leveraging the optimal damping ratio.

3.2 Adaptive parameter design

Owing to the frequency variation limit of ±0.5 Hz,the initial value of the P/ω droop coefficient was set to ensure that when the system frequency changed by 0.5 Hz,the FESA fully released power to provide primary frequency support.Therefore,Dv0 can be set as

During the initial phase of the system disturbance,the frequency deviation in the microgrid was minimal,whereas the ROCOF was significant.Consequently,the droopcontrol loop initially produced a low output.To utilize the output power capability of the inverter,the virtual inertia Jv should satisfy

An increase in Jv results in a longer system settling time and slower response speed.Therefore,by setting the maximum settling time to 0.4 s,the virtual inertia Jv should satisfy

The range of the virtual inertia Jv can be determined by combining (18) and (19).

4 Simulation analysis and evaluation

4.1 System with an ideal AC grid

To assess the effectiveness of the proposed flywheel array control strategy,a simulation model of the FESA connected to an ideal AC grid was established using MATLAB/Simulink,as shown in Fig.1.The FESA comprised three units,each with a capacity of 600 kW/5 kWh and an energy conversion efficiency of 85%.The detailed parameters of FESA are provided in Appendix A.

First,the grid frequency was set to 50 Hz,and charging and discharging simulations of the FESA were conducted.The array speed-balance control described in Section 1.2 and the equal-proportion distribution strategy outlined in [12] were adopted.As shown in Fig.11,the response time of the FESA in power control mode was within 0.5 s,showcasing its ability to swiftly and accurately track the reference power.Owing to the larger discharge power at 0–5 s,the power allocated by FESU1 exceeded its rated value in the equal proportional distribution strategy.Such an occurrence is impermissible in practical applications and may result in errors or even failures in the power control of the entire array.Furthermore,the time required for the maximum SOC difference among the FESUs to reach 1% was notably shorter with the proposed array speed balance strategy (58.90 s) than with the method outlined in [12] (83.28 s).These findings underscore the superiority of the proposed array speed balance control in achieving faster balancing of the SOC across all the FESUs.

Fig.11 Simulation results during the charging and discharging of the FESA

The frequency of the ideal AC grid was set to 49.97 Hz.Fig.12 illustrates the output power and SOC of the FESA during standby periods.As shown in Fig.12(a),traditional VSG control results in the FESA continuing to output active power within the frequency-regulation dead zone.This arises from the virtual damping link of the traditional VSG control,which introduces a discrepancy between the reference angular frequency and the virtual angular frequency in the power command link,resulting in inaccurate tracking of the power command.Furthermore,the self-discharge of the flywheel exacerbated the discharge loss of the system,leading to the SOC surpassing the prescribed limit during prolonged standby periods.Conversely,the improved VSG control avoided the introduction of the drooping power of the damping link and instead provided transient damping through the power differential term.This modification eliminated the discharge behavior of the FESA in the frequency-regulated dead zone.Moreover,the energy feedback loop automatically adjusted the output power following the SOC warning,preventing the SOC from exceeding the limit without affecting the regular operation of the FESA.

Fig.12 Simulation results of the FESA during standby periods

4.2 System with the revised IEEE 13-bus

In this section,simulations are conducted to evaluate the effectiveness and superiority of the proposed adaptive VSG control for the participation of FESA in frequency regulation within a microgrid based on the revised IEEE 13-bus system [37].The tested microgrid comprised a generator,wind farm,two photovoltaic plants,and an FESA,as shown in Fig.13.Four distinct cases were investigated using this test system for comparison.

Fig.13 Network of the microgrid adopted

Case I:No FESA.

Case II:FESA controlled by traditional VSG.

Case III:FESA controlled using adaptive droop control,as proposed in [20].

Case IV:FESA in frequency support mode controlled using an adaptive VSG,as proposed in this study.

4.2.1 Scenario A:Sudden islanding of the microgrid

In this scenario,we assumed that the RESs always operated at rated power.Circuit breaker S1 abruptly opened at t =10 s,and the microgrid drew approximately 5 MW of power from the external grid.

As shown in Fig.14,when the microgrid lacked the FESA,the frequency of the disturbance reached 49.496 Hz.In Case II,with traditional VSG control,the FESA effectively provided inertial support and damping power in response to grid frequency disruptions,leading to an increase in the frequency nadir to 49.633 Hz.However,the output of the FESA remained unchanged despite a decrease in the SOC,resulting in the SOC rapidly exceeding its limit,followed by a secondary drop in frequency.In Case III,the FESA reduced its output power during the frequency recovery phase to extend its operating time.However,this adjustment caused a secondary drop in grid frequency,leading to oscillations in the FESA output power.

Fig.14 Simulation results of the microgrid during sudden isolation

When the FESA adopted the improved VSG control strategy,the virtual inertia parameters and droop coefficient were adaptively adjusted based on changes in the VSG angular frequency and SOC of the FESA,as shown in Fig.14(d).The frequency nadir increased to 49.631 Hz,and the FESA reduced the power output during periods of low SOC to prevent a secondary frequency drop.The proposed multiparameter adaptive control strategy significantly enhanced the dynamic response characteristics of the FESA and reduced the frequency offset of the islanded microgrid.

4.2.2 Scenario B:Long-term operation of the islanded microgrid

In this scenario,the microgrid remained in island mode,and the initial SOC of the FESA was 0.7.The actual wind speed,sunlight intensity,and temperature data were imported into the simulation system to study the frequencyregulation effect of the FESA under a fluctuating output power from the RESs.The frequency deviation curve is displayed in Fig.15(a),and the SOC variation curve is shown in Fig.15(b).To quantitatively describe the frequency regulation effect of the FESA under various control strategies,we used the root mean square (RMS) of the frequency as an evaluation index to reflect the degree of frequency deviation from the reference value.The calculation method for this evaluation index is expressed as (20) in Appendix B,and the results are presented in Table 2.

Table 2 Frequency regulation evaluation index

Fig.15 Simulation results of the long-term operation of the islanded microgrid

The simulation results showed that the frequency regulation index was worst when the microgrid was operated without an ESS.The frequency regulation effects of the FESA under the three aforementioned control strategies did not differ significantly.However,the SOC retention effect was best under the control strategy proposed in this study.Considering the period of 70–100 s as an example,the frequency curve of the system is shown in Fig.15(c),and the output active power curve of the FESA is displayed in Fig.15(d).As evident,the control strategy proposed in this study enabled the flywheel to remain inactive within the frequency regulation dead zone.Simultaneously,the output power of the FESA adapted according to the SOC,thereby extending the discharge time while ensuring a frequency regulation effect.Because SOC retention is more important in long-term operations,the control strategy proposed in this study offers more obvious advantages.

5 Conclusion

This study proposed an optimized control strategy for a high-power FESA to enhance the frequency performance and validated the effectiveness of the proposed strategy through simulations.The primary conclusions are summarized as follows:

1) Throughout the array speed balancing process,the balancing speed decreased as the SOC disparity among the units diminished.To address this challenge,the control strategy for array speed balancing introduced a variable acceleration factor.This factor considered both the power limit of the flywheel and the SOC balancing speed,resulting in significantly improved practicability.

2) In comparison with the droop-control strategy,the VSG-controlled FESA circumvented the need for frequency measurement and could promptly offer inertial support during disturbances,resulting in more desirable frequency response results.

3) Traditional VSG control overlooks the capacity constraint of ESSs and lacks provisions for the frequency dead zone to prevent the depletion of the flywheel energy during prolonged frequency deviations.In this study,the transient damping branch of the VSG was designed,and the VSG parameters were adaptively adjusted according to changes in the output angular frequency of the VSG and the SOC,thereby enhancing the frequency regulation performance of the FESA.

Appendix A

Table A1 Parameters of the SSM

Table A2 Parameters of the flywheel

Appendix B

where Qf is the frequency regulation evaluation index.

Acknowledgments

National Natural Science Foundation of China (51977160)“Voltage Self balancing Control Method for Modular Multilevel Converter Based on Switching State Matrix”.

Declaration of Competing Interest

We declare that we have no conflict of interest.