Adaptive linear active disturbance-rejection control strategy reduces the impulse current of compressed air energy storage connected to the grid

0 Introduction

Compressed air energy storage (CAES) is garnering increasing research attention for its large power generation capacity,long service life,high stability,and energy storage magnitude and response speed [1-4].When connected to the power grid,the voltage frequency,phase,and amplitude of the energy storage side of CAES must be consistent with those on the power grid side.However,if the existing control method,which has low precision,cannot complete the presynchronization process before the CAES device switches to the grid-connected mode,it could cause system severe disruptions during the grid-connection process.Therefore,a control strategy with higher precision and faster response speed must be adopted at the presynchronization control level to mitigate the grid-connection impact.

When applied to power grid regulation,CAES can smooth the fluctuation of renewable energy power generation,cut peaks,fill valleys,and provide voltage and frequency support [5-7].For seamless switching from the virtual synchronous-generator control mode to the constant power control mode with reduced grid-connection impact,control instructions are added to the system during the switching process to suppress fluctuations of the current controller parameters before and after the switch and reduce its impact [8,9].When a system consisting of energy and photovoltaic storage is switched to the grid-connected mode,it adopts model predictive control and introduces a weighted coefficient to optimize it,which can reduce the effect of the lack of voltage matching accuracy [10].The voltage controller is improved,and the related parameters are adjusted to address the problem in which the frequency and voltage change amplitude are excessively large due to a decrease in inertia during the switching of the microgrid operation mode,which leads to system oscillation [11].For smooth switching between operating modes,reference [12] included disturbance observation based on the conventional sag control,which can detect the current fluctuation in a very short time and reduce the current change in the switching process through the regulator.At present,research on smooth switching between operation modes is more focused on microgrids.Few studies have explored how CAES smoothly switches between off-grid and gridconnected operation modes.Therefore,studying the method to reduce the impact of CAES on grid connection when switched to the grid-connected mode must have application value.

LADRC is a control method proposed based on the modern control theory and the analysis and improvement of the essence of the PID controller [13].A bidirectional DC-DC converter-based ADRC strategy was designed,the parameters were adjusted flexibly,and the controller was optimized online by combining it with a fuzzy neural network.The strategy was verified under different simulation conditions [14].To improve the speed of instruction recognition and feedback by the LADRC,the output value of the controller was corrected,and the output error was reduced [15].For the visual servo system,reference [16] introduced a fuzzy control algorithm based on the traditional LADRC,which helped the systems adjust the parameters of the linear extended state observer (LESO) adaptively,improve the response speed of feedback to instructions,and enhance the anti-interference ability.The LESO and tracking accuracy were improved,the dynamic response of the entire system was optimized,and the problem of DC voltage instability due to system disturbances was solved [17].An improved LADRC technique was constructed,and the filtering voltage was estimated using the LESO,which improved the ability of the LADRC technique to suppress high-frequency noise [18].In these studies,the advantages of active disturbancerejection control technology were thoroughly verified.However,the fixed parameters of its controller limited its control effect in dynamic systems.Therefore,research on LADRC with adaptive parameter adjustment has practical application-guiding significance.

To solve the problem of CAES having a large impact on the power grid and threatening the safety of equipment,this study adopted the LADRC strategy with higher accuracy and faster response speed to control gridconnected presynchronization.First,the CAES system was modeled,and then the LADRC method was analyzed.The bandwidth parameters were adaptively adjusted based on the conventional controller,which improved the CAES grid-connected presynchronization speed and reduced the impulse current.Finally,an experimental verification was conducted in a hardware-in-the-loop semi-physical simulation environment.The experimental waveforms proved the superiority of the adaptive linear active disturbance-rejection control (A-LADRC) strategy in reducing the impact.

1 Structure and modeling of compressed air energy storage (CAES)

At this stage,energy storage devices can be basically divided into mechanical energy storage,electromagnetic energy storage,and chemical battery energy storage.Mechanical energy storage includes pumped energy storage,flywheel energy storage,and CAES.Pumped energy storage involves releasing water from a high elevation to drive turbines and generate electricity.During periods of low electricity demand,excess electric energy is used to pump water back to a higher elevation for storage.Flywheel energy storage utilizes the inertia of a rotating flywheel to store energy.During the energy storage phase,an electric motor accelerates the flywheel,converting energy into kinetic energy.When energy is required,the high-speed rotating flywheel’s rotational energy is transferred back to the motor,which acts as a generator to produce electricity.Electromagnetic energy storage mainly involves the use of superconducting magnets and supercapacitors.Chemical energy storage employs redox reactions of positive and negative batteries for charging and discharging.Examples of these devices include lead-acid battery,nickel-cadmium,nickel-metal hydride,and lithium electronic batteries.The following section provides a detailed introduction to CAES.

1.1 Structure of CAES

The connection mode and components of the CAES system are shown in Fig.1.

Fig.1 Topology of CAES system

The topology of the system primarily constitutes a motor that drives the compressor operation,a two-stage compressor unit divided into high-and low-pressure units,a gas storage unit,a two-stage turbine unit,a generator,a heat storage tank divided into two types,and a heat exchanger.During low electricity demand,the surplus wind power is used to drive the motor.The compressor compresses the ambient air driven by the electric motor.This air is stored in a gas reservoir.During peak hours of power demand,the gas reservoir releases the high-pressure air using a demand control valve,which then passes through the two-stage turbine to drive the generator.The two stages of compressed and released air are equipped with heat exchangers.The heat exchangers and heat storage tank jointly complete heat exchange between the air and the heat-exchange medium [19].

1.2 Mathematical model of CAES

A mathematical model of each component of the advanced adiabatic CAES system was developed based on the working principles of the devices involved them,under reasonably simplified conditions [20-22].

1.2.1 Mathematical model of compressor

We disregarded the volume of gas within the compressor,assumed no internal pumping and venting,neglected the influence of fluid flow in the compressor,and ignored heat exchange with the external environment.Consequently,the outlet air temperature of the stage i compressor can be expressed as (1).

where and represent the outlet and inlet air temperatures,respectively,ηc,i is the adiabatic efficiency,βc,i is the single-stage compressor pressure ratio,and k is the air specific heat ratio.

By ignoring the loss,the total work Wc done by the compressed air in the gas storage chamber can be expressed as (2).

where cpa is the specific heat capacity of air at constant pressure,ma,c is the air mass flow rate,ts is the energystorage duration,and n is the compressor level.

1.2.2 Mathematical model of turbine Ignoring the loss,the influence of the fluid is ignored.The outlet air temperature is expressed as (3).

where and are the outlet and inlet air temperatures of a class i turbine,respectively,ηt,i is the adiabatic efficiency and βt,i denotes the expansion ratio.

The work Wt of the two-stage turbine can be expressed as (4).

where ma,t denotes the air mass flow rate,tr is the release time,and m is the turbine level.

1.2.3 Mathematical model of heat exchanger

Assuming the gas is ideal,the chemical reaction of the fluid in the process of flow and heat transfer was ignored,and the heat loss was disregarded.Thus,the outlet air temperature is expressed as (5).

where and denote the outlet and inlet air temperatures,respectively,And ε is the heat transfer efficiency.

During gas compression,the heat stored in heat reservoir Qs can be expressed as (6).

1.2.4 Mathematical model of gas storage

We assumed that the volume did not change when the gas was stored.Hence,the pressure loss of the gas was neglected.The change trends of pressure and temperature when compressed air was used can be expressed as (7).

The change trends in pressure and temperature when air is released can be expressed as (8).

where hac is the heat transfer efficiency,Ac denotes the wall area,T and Tac are the air and chamber wall temperatures,respectively,m is the mass of gas,and V is the volume of the gas storage chamber.

2 Adaptive linear active disturbance rejection control (A-LADRC) strategy and parameter design method

When the CAES system is connected to the grid,it must have the same voltage amplitude,phase,and frequency as those of the power grid.Presynchronization based on traditional PI control could not achieve the goals of high adjustment precision and fast response time in practice.Therefore,this study adopted the LADRC with higher immunity and accuracy to replace the PI control.However,because changes in frequency and phase influence each other,excessively fast phase synchronization will result in large frequency fluctuations,which is not conducive to stability.Based on the LADRC,an A-LADRC strategy was proposed to adjust the controller bandwidth parameters in real time by determining the relationship between the phase angle difference and the set value,and further optimizing the grid-connection impact problem.

2.1 Method of LADRC

The LADRC linearizes the nonlinear LESO and adopts a simple PD control combination.Simultaneously,it also linearizes and simplifies the design of the linear state error feedback (LSEF) [23].The basic structure of the LADRC is shown in Fig.2.In this figure,R is the reference input value,u0 is the output control quantity,b0 is the gain coefficient,u is the control quantity,y is the output value,and z1,z2,and z3 are state variables.

Fig.2 Basic structure of linear ADRC

2.1.1 LESO

If the controlled object is regarded as a second-order system,it can be expressed as (9).

where y and u denote the system output and input,respectively,a1 and a0 are the controller parameters,b is the system gain,And ω is the disturbance.When b0 in b is known,(9) can be expressed as (10) and (11):

where f denotes the total disturbance.As the correction term can estimate the perturbation by ignoring f,the observer equation is given by (12).

where A,B,and C are coefficient matrices,L is the error feedback gain matrix of the bandwidth parameter,and uc is the input matrix.The matrices described above can be expressed as (13) -(15).

The observer state vector is (16).

where β1=3ω0,

Assuming the bandwidth of the observer as ω0 and assigning the pole of the observer characteristic equation at -ω0,the characteristic equation can be expressed as (17).

where I is the identity matrix.

2.1.2 LSEF

The control form of LSEF can be expressed as (18) and (19).

where z1,z2 and z3 are the observer states from the LESO.The value of R is known.

The closed-loop transfer function of the system is expressed as (20).

Assuming the controller bandwidth as ωc and assigning the pole at–ωc [24],kp and kd be expressed as (21).

2.2 A-LADRC control parameter setting

The observer bandwidth ω0 and controller bandwidth ωc were adjusted.For observer bandwidth ω0,the larger the ω0,the faster the extended state observer can observe and be compensated by the controller.Simultaneously,the sensitivity of the observer to noise will increase.The value of ω0 also affects the inertia of the system;typically,the larger the inertia,the smaller the ω0,and vice versa [25].For controller bandwidth ωc,the larger the ωc,the faster the system response.However,excessive ωc may cause severe overharmonic oscillation in the system [24].For most engineering objects,ω0 is approximately 3-10 times ωc.

When the CAES system is switched to the grid mode,owing to the interaction between the output phase and frequency,the fixed controller bandwidth parameters of LADRC may cause instability in the system frequency due to its extremely fast phase synchronization speed.Therefore,to consider both the phase synchronization speed and system frequency stability,the LADRC parameters were adaptively tuned.From the above analysis,we observe that controller bandwidth ωc had the strongest influence on the phase synchronization response speed and system stability.Additionally,a certain quantitative relationship between observer bandwidth ω0 and controller bandwidth ωc was observed,while LADRC is highly robust to b0.If b0 is offset by ±50%,the system may still have good stability if the bandwidth is appropriate.Simultaneously,the system output gain b was difficult to identify,and because of the uncertainty compensation of LESO,only the order of magnitude of b can be determined.Therefore,this study designed a LADRC strategy with adaptive adjustment of bandwidth parameters,collected the output phase of the CAES side,compared it with the phase of the power grid side and calculated the difference.This difference was compared with the critical phase difference,and accordingly the system bandwidth ωc was adjusted in real time through the control strategy.This process can be expressed as (22).

where ωc0 is the value of the system bandwidth under normal working condition,k is an additional adaptive adjustment parameter that is greater than 0,and θk is the critical phase difference.When the phase difference is greater than θk,the system response should accelerate the phase synchronization speed.When the phase difference is less than θk,the phase on both sides is close to synchronization,and the system response should be slow to maintain the stability.Under operating conditions,a CAES with a phase difference of less than 15° can be connected to the grid to improve accuracy,i.e.,if θk=5°,k=10.Thus,the A-LADRC strategy can adjust the presynchronization speed in real time according to the magnitude of phase difference,considering the presynchronization speed and frequency stability.

3 Smooth grid-connection strategy of CAES system based on A-LADRC

Unlike batteries,which use an equivalent circuit model to describe their dynamic external characteristics,CAES is a physical energy storage system that is composed of multiple devices.Compared with electrochemical energy storage,it offers high scalability,long life,safety,and stability.In terms of energy storage control,the battery generally adopts a fixed power control mode or DC voltage control for the converter,whereas the CAES system has no converter device and is connected to the power grid through a synchronous generator.Thus,the released air flow can be controlled by regulating the valve of the gas storage tank,which in turn controls the output power of the CAES.

A block diagram of the proposed A-LADRC-based CAES off-grid-to-grid-connected operation control is shown in Fig.3.When the CAES system is operated solely with a load,the control mode is V/f control,with switches S1 and S2 are set to state 0 and switches S3 and S4 disconnected.When CAES is connected to the grid for presynchronization,switches S1,S2,and S4 are turned off,switch S3 is closed,and the A-LADRC strategy is used for presynchronization.When the grid-connection conditions are satisfied after presynchronization,S3 and S4 are switched off,the CAES control mode is switched to PQ control,S1 and S2 are switched to state 1,and the grid connection is completed.

Fig.3 Block diagram of control for switching of CAES from off-grid to grid-connected mode based on A-LADRC

3.1 Grid-connected mode and off-grid control strategy of CAES system

The CAES system adopts fixed power control in the grid-connected mode.It outputs power directly based on the reference values of the active and reactive powers.Voltage frequency fluctuations caused by abrupt load increases or decreases are absorbed by the power-grid side.The CAES adopts the V/f control in the off-grid mode to avoid frequency and voltage instability,ensuring that it can supply power to the load normally and maintain overall system stability.

As shown in Fig.3,in the grid-connected mode,S1 and S2 are set to state 1,S3 and S4 are turned off.The deviation between the CAES output active power P and the reference value Pref enters the speed control system to control the air mass flow into the turbine and control the work done by the turbine according to the reference power value,i.e.,the input mechanical power Pm of the generator.In Fig.3,Kp is the magnified image of the PID regulator,TD is the differential time constant,and T1 and Te are the integral time constants of the corresponding links.Similarly,the deviation between the actual reactive-power value and its reference value was input to the excitation system to generate the excitation voltage.Under normal circumstances,a negative feedback link is introduced into the excitation system to improve its quality and ensure its operational stability.The basic equations of the system are expressed as (23)-(25) [26].

where TA and TL are the time constants of the corresponding links,UR is the excitation voltage of the exciter,KA is the amplification factor,SE is the saturation coefficient,KL is the self-shunt coefficient,KF is the magnification of the excitation negative feedback link,and TF is the time constant.In Fig.3,TB and TC represent the time constants of the lead and lag links,respectively.

In the off-grid mode,as shown in Fig.3,the active power and frequency control switch S1 and the reactive power and voltage control switch S2 are set to state 0.Switches S3 and S4,which are connected to the grid,were disconnected.In contrast to the grid-connected mode,the active power control link was converted into frequency control and the reactive power control link into voltage control,while the remaining link is unchanged.Simultaneously,it was disconnected from the grid in the off-grid mode,and the CAES operated separately with the load.

3.2 Stability analysis

Equation (26) can be obtained from (12),(18),and (19).

where N(s),G(s),and H(s) are represented by (27).

According to (10),the second-order controlled object system can be expressed as (28).

A block diagram of the LADRC model was obtained through the above analysis,as shown in Fig.4.

Fig.4 LADRC transfer function-equivalent block diagram

According to Fig.4,the closed-loop transfer function of the system can be expressed as (29).

where the system output Y(s) is related to the input term R(s) and disturbance term F(s).The performance of LADRC mainly depends on the influence of a perturbation term,which is related to both the observer bandwidth ω0 and controller bandwidth ωc.Therefore,the observer bandwidth ω0 was set to 2,500,and different controller bandwidths ωc were used to draw a Bode diagram for the interference terms,as shown in Fig.5.Controller bandwidths ωc were set to 200,400,600,800,and 1,000 in sequence.

Fig.5 Bode diagram of the transfer function of the CAES system with increasing ωc

Overall,in the low-frequency band,the curve amplitude and absolute slope values were larger,the steady-state error was smaller,and the steady-state accuracy was higher.The middle frequency band reduced the cutoff frequency and occupied a wide frequency band,ensuring better stability.The amplitude of the high-frequency curve was low and the attenuation rapid,which enhanced the anti-interference ability of the system.With the increase of controller bandwidth ωc,the disturbance suppression ability of the system increased in the low-frequency band.In the middlefrequency band,the bandwidth,phase angle margin,system stability,and dynamic performance were all increased.Therefore,to ensure that the system did not undergo severe overharmonic oscillation,the controller bandwidth ωc can be appropriately increased to achieve the optimal antiinterference ability of the system.

4 Experimental verification

This section verifies the proposed A-LADRC strategy through a semi-physical simulation experiment to simulate the actual situation as accurately as possible.A semiphysical hardware-in-the-loop simulation platform,including RT-LAB,DSP controller,host computer,and wave recorder,was constructed (Fig.6).The grid-connected simulation model of the CAES system was downloaded to the RT-LAB simulator through an upper computer,and the A-LADRC strategy to be adopted for presynchronization was loaded into the DSP controller.During operation,the DSP controller generated a pulse width modulation pulse and transmitted it to RT-LAB and controlled the simulation model in the simulator,while the wave recorder recorded the experimental waveform [10].

Fig.6 Controller level hardware in the ring test platform

The static data of each major component during steadystate operation in the energy storage and release stages are listed in Tables 1 and 2,respectively.Table 3 lists the other device parameters.

Table 1 Static data of compressor and heat exchanger during steady-state operation in the energy storage stage

Table 2 Static data of turbine and heat exchanger during steady state operation during energy release stage

Table 3 Other equipment parameters

4.1 Analysis of grid-connected CAES under different control strategies

In the same system,the PI control,LADRC,and A-LADRC with adaptive bandwidth parameter adjustment were used to presynchronize the CAES connected to the grid.The phase-difference changes in the grid-connected presynchronization process are shown in Fig.7.Examining the phase-difference change waveform revealed that the three strategies reduced the phase difference to 0,i.e.,they can track the phase of the grid side.However,with A-LADRC,the phase on the side of the net can be tracked in the shortest time at approximately 0.5 s,and the time for tracking the phase on the side of the net under LADRC was approximately 0.9 s.The time for tracking the phase on the side of the net under PI control was the longest at approximately 5.3 s.As observed in the figure,the speed of the A-LADRC for phase tracking is evidently better than that of the other two control methods,and the response speed of the LADRC is notably improved after the adaptive adjustment of the bandwidth parameters.

Fig.7 Phase difference changes under different controls compared waveforms

To study the impact reduction of the A-LADRC strategy,the impact current and junction voltage waveforms under the three types of control were displayed on the same interface.The junction current and voltage waveforms are shown in Fig.8(a) and Fig.9(a).To clarify the waveform,it has been locally enlarged and illustrated in Fig.8(b) and Fig.9(b).

Fig.8 Impulse current contrast waveform under different controls

Fig.9 Voltage comparison waveform at grid connection under different controls

The analysis of the current waveform shows that the current under different controls oscillates when the CAES is connected to the power grid but eventually stabilizes to the same value.When PI control was adopted,the impulse current was the largest,its maximum amplitude was approximately 4.5 kA,and the time from grid connection to stability recovery was longer.The maximum impulse current under LADRC was close to 3.3 A.The maximum impulse current under A-LADRC decreased again to approximately 3.1 kA based on the working of LADRC.The analysis of the voltage waveform shows that when PI control is adopted,the voltage oscillates significantly after being connected to the grid,whereas the voltage at the junction points under both LADRC and A-LADRC rises to a certain extent and then recovers to a stable state.When the A-LADRC strategy was adopted,the oscillation amplitude was small after the junction point voltage increased,and the voltage quickly recovered to a stable state.

By analyzing the system frequency waveform in Fig.10,we conclude that the system frequency oscillates after completion of the grid connection and eventually stabilizes.However,the frequency oscillation was the most severe and the oscillation time was the longest under PI control.However,the frequency offsets of LADRC and A-LADRC were small.Under the A-LADRC strategy,the maximum frequency offset did not exceed 50.1 Hz,the minimum frequency offset was 49.7 Hz,the oscillation amplitude was small,and the frequency quality was good.Similarly,by analyzing the output power waveform of CAES in Fig.11,we conclude that the output power under PI control oscillates significantly after the grid connection,whereas under the A-LADRC strategy,it exhibits minimal oscillation and returns to a more stable state swiftly.

Fig.10 System frequency comparison waveform under different controls

Fig.11 Comparison waveform of CAES output power under LADRC and A-LADRC

This analysis reveals that under the A-LADRC strategy,the phase synchronization speed is faster,the impulse current and voltage generated by the grid connection are smaller,the grid-connection process is smoother,and the frequency and CAES output power fluctuations in the entire process are minimal.Thus,the A-LADRC strategy has been validated.

4.2 Simulation analysis of the influence of adaptive adjustment additional parameter k on the control effect of A-LADRC strategy

According to the adaptive adjustment formula for bandwidth parameters designed in this paper,i.e.,(22),the selection of an additional parameter k for adaptive adjustment will affect the system bandwidth ωc.To study the influence of k on A-LADRC and select its value under an optimal control effect,we tested the control effect of the strategy by varying the value of k to 5,10,and 15.Fig.12-15 shows the grid-connected impulse current,voltage,system frequency,and output power of the CAES system at different k values.

Fig.12 Current waveform vs.adaptive adjustment parameter k

Fig.13 Voltage waveform vs.k

Fig.14 Frequency waveform vs.k

Fig.15 Output power of CAES waveform vs.k

According to the waveform observation,when θk is assigned a certain value,the maximum impulse current generated during grid connection will decrease with an increase in k.However,owing to the drop in the instantaneous current during the grid connection,the current oscillation amplitude increases when k is excessively small or large.Similarly,when the k value is small,the voltage increment at the instance of grid connection is small,but subsequently rises to a larger value.The system frequency decreases by a greater margin,and the CAES output power has a large impact.When the value of k is large,the voltage surge at the instance of grid connection is large,but eventually drops to a smaller value.Although the system frequency does not decrease significantly,it increases to a certain extent at the instance of grid connection.Meanwhile,the output power of CAES also declines,albeit with a small impact.When k was small,the impact of each electrical volume increased.When k was large,although the impact of CAES was small,a certain degree of overshot was observed at grid connection.If k is excessively large or small,the waveform oscillation amplitude will be larger;therefore,the value of k should not be exceedingly large or small.

The reason for this situation is that when the k value increases,bandwidth ωc also increases,the system response is faster,and the CAES system tracks the grid phase more accurately.Thus,the impact is reduced when the grid is connected.However,when ωc is exceedingly large,the system will experience severe overshooting and large oscillation amplitudes.When ωc is small,the adaptive adjustment ability of the system decreases,and the controller adjustment performance tends to be LADRC with fixed bandwidth parameters.Therefore,to prevent large overshoots and oscillation amplitudes under the requirement of a small shock,the value of k was selected as 10,which is an intermediate value.

4.3 Simulation analysis of load sudden change in presynchronization process

To verify the anti-interference performance of the proposed A-LADRC,sudden increases and decreases were set in the presynchronization process under the A-LADRC strategy,and the voltage,current,and frequency waveforms were compared to those without abrupt load changes.When the simulation time was set to 1 s,the load abruptly increased by 10 MW.At 1.5 s,it suddenly decreased by 10 MW.After the presynchronization,the CAES system was connected to the grid at 2.8 s.The current,voltage,and frequency waveforms obtained from the simulations are shown in Fig.16-18.

Fig.16 Current contrast waveform

Fig.17 Voltage contrast waveform

Fig.18 Frequency contrast waveform

By observing the waveform,we observe that after the abrupt load increase,the current and voltage in the presynchronization process undergo a minor amplitude change.The frequency also declined,with the change amplitude not exceeding 0.1 Hz.When the load was restored to the original value,the current,voltage,and frequency eventually returned to the state without sudden load changes.At the time of grid connection,the impulse current in the case of abrupt load changes was less than 10 A and the frequency change was only 0.01 Hz compared with the normal condition.Despite the abrupt load change,the system did not become unstable nor did it oscillate.The current,voltage,and frequency changed insignificantly and rapidly recovered its stability compared with the behavior under normal conditions.Therefore,this analysis demonstrates the anti-interference performance of A-LADRC.

5 Conclusion

The CAES has great potential for development and large-scale adoption.To optimize the performance of a CAES system connected to the power grid and reduce the impulse current,an A-LADRC strategy was proposed.The conclusions are as follows:

1) In view of the large impact of CAES on the gridconnection process and the coupling of frequency and phase,system bandwidth ωc was adaptively adjusted,and the stability of the designed active disturbance-rejection control was analyzed.The results show that ωc can be appropriately increased to improve the anti-interference ability of the system.

2) By establishing a hardware-in-the-loop simulation experiment platform,we verified that the A-LADRC strategy can effectively accelerate the phase synchronization speed,and reduce the grid connection impulse current and voltage and frequency and power fluctuations during the grid connection process to achieve a smooth grid connection.

3) The influence of parameter k in the adaptive adjustment formula on the control effect of the A-LADRC strategy was analyzed through simulation.An additional adaptive adjustment parameter k =10 is recommended.During the presynchronization process under the A-LADRC strategy,disturbances due to abrupt load increase and decrease were simulated.The results demonstrated the antiinterference performance of A-LADRC.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Project No.52077079).

Declaration of competing interest

We declare that we have no conflict of interest.