ADRC‐based control strategy for DC‐link voltage of flywheel energy storage system

The direct current (DC)‐link voltage control of the flywheel energy storage system plays an important role in realizing high‐quality grid connection. With the traditional proportional‐integral control, the DC‐link voltage cannot track its reference value quickly and smoothly when the flywheel energy storage system switches from the charging stage to other working stages. Therefore, a DC‐link voltage control strategy for the flywheel energy storage system based on active disturbance rejection control is proposed in this paper to deal with this issue. The DC‐link voltage and its differential value are considered as the state variables in this strategy. The internal and external disturbances, such as load power, switching loss, and parameter uncertainty, are regarded as an expanded state. By inputting the voltage error and the observed disturbance into the nonlinear state feedback control law, the rapidity and anti‐interference of the DC‐link voltage control are ensured under different States of Charge of the flywheel energy storage system. Then, the coefficient freezing method is used to analyze the effects of the disturbance observation bandwidth by nonlinear gain and pole position changes. The DC‐link voltage can track the reference value over a wider frequency range of disturbances. By configuring the appropriate observer structure parameters, the disturbance observation bandwidth under the nonlinear function gain variation is always higher than the expected bandwidth. The effectiveness of the proposed control strategy is verified by simulation results at last.


| INTRODUCTION
Due to the uncertainty and intermittency of renewable energy, the power system can hardly meet the load requirements in the future, when the power consumption is at peak; a large amount of renewable energy waste may occur when the power consumption is at a low point.Besides, the randomness of renewable energy can cause frequency fluctuation of the power system, which will lead to serious security issues in the power system.To solve these problems, energy storage systems have received more and more attention. 1lywheel Energy Storage System (FESS) is an electromechanical energy conversion energy storage device. 2 It uses a high-speed flywheel to store mechanical kinetic energy, and realizes the mutual conversion between electrical energy and mechanical kinetic energy by the reciprocal electric/generation two-way motor.As an energy storage system, it has a series of advantages such as long service life, high conversion efficiency, high energy density, and small impact on the environment.Therefore, FESS has been widely applied in the uninterruptable power supply system, 3 microgrid, 4,5 wind power generation, 6 rail transit, 7 electric vehicle charging, 8,9 and other fields.
Direct current (DC)-link voltage control of the FESS is a key point in the energy storage system to achieve stable grid-connection.The quality of control performance directly determines the power quality of gridconnection and the stability of DC-link voltage.At present, the most widely used DC-link voltage control algorithm in literature for the FESS adopts the double closed-loop structure based on proportional-integral (PI) regulation. 10However, the dynamic model of the FESS is a typical nonlinear system, 11 and the parameters of PI controllers are usually tuned near a steady operating point. 12Under the traditional PI control, when the FESS switches from the charging stage to other operating stages, the DC-link voltage cannot reach the set value quickly and stably, and the dynamic performance of the DC-link voltage is poor under the low-charged state.Therefore, the PI controllers tuned based on a certain steady state of the FESS can no longer meet the system operation requirements.
As for the DC-link voltage optimization control, a series of schemes based on feedback linearization, 13 sliding mode control (SMC), 14 and model predictive control (MPC) 15 are mainly studied to deal with nonlinear systems and improve the robustness of discharge control.In Jarzebowicz, 13 the feedback linearization has been used to deal with nonlinear problems of the system.In Biao et al., 14 the SMC has been combined with a nonlinear disturbance observer to improve transient tracking performance.In Bigarelli et al., 15 the direct power control based on MPC has been proposed to obtain fast dynamic performance.However, SMC can easily cause chatter and current harmonics in high-speed systems.For feedback linearization and MPC, the complex algorithms employed require sufficient computational power of the real-time system.Therefore, 16 proposed a scheme combining two-degree-of-freedom internal model control (TDOF-IMC) with a linear extend state observer to ensure industrial practicability with few parameters and easy adjustment.However, the proposed method is complex and faces the problem of model mismatch due to the introduction of internal models.Most literature use linear active disturbance rejection control (ADRC) or simplified second-order linear extended state observer (ESO) for DC-link voltage control.However, nonlinear ADRC obviously has better control performance, but it is rarely applied to the actual control process because of the difficulty of tuning multiple parameters.
This paper attempts to use nonlinear ADRC with better control performance for voltage control, and proposes a reasonable parameter tuning method.The DC-link voltage and its differential value are considered as the state variables in this strategy.Internal and external disturbances in the voltage control loop, such as load power, switching loss, and parameter uncertainty are regarded as an expanded state.The voltage error and observed disturbance are input into the nonlinear state error feedback (NLSEF) control law to form the control quantity.In addition, this paper uses the coefficient freezing method to analyze the influence of nonlinear gain and pole position changes on the disturbance observation bandwidth.A specific parameter configuration method applied to the nonlinear ESO structure is proposed to alleviate the difficulty of parameter configuration.The simulation results prove that the proposed voltage control strategy based on ADRC for the DC-link voltage of FESS can improve the stability of the DC-link voltage.
This study is organized in five sections.In Section 2, the structure of the FESS with back-to-back coupled pulse width modulation (PWM) converter is presented.In Section 3, according to the mathematical model of the motor side of FESS, the ADRC-based control strategy for DC-link voltage control of the FESS is proposed, and the ESO parameter optimization configuration method is designed.In Section 4, the performance of the proposed ADRC voltage control strategy is verified by the FESS simulations at different speeds.Finally, a conclusion is drawn in Section 5.

| PRELIMINARY KNOWLEDGE AND ISSUE DESCRIPTION
The FESS consists of a bidirectional PWM converter, a grid-side LCL filter, and a coaxial flywheel driven by a permanent magnet synchronous motor/generator (PMSM/G), 17 as shown in Figure 1.The back-to-back PWM converter consists of the grid-side converter, the motor-side converter, and the DC-link capacitor C. The LCL filter is composed of the grid-side inductor L g , the converter-side inductor L conv and, the filter capacitor C g .
FESS has three working stages: charging, holding, and discharging.The control systems consist of the FESS grid-side converter control and motor-side converter control, and adopt different control modes in different working stages.The converter control modes in each stage of the FESS are shown in Table 1.Converter control mode and PI controller parameters setting refer to Wenjun et al. 17 Space vector pulse width modulation (SVPWM) technology is used to control the conversion voltage of the converter circuit in the FESS. 18As shown in Figure 2, the space vector (SV) switching table will generate S 1 -S 12 PWM signals according to the target voltage values of the u* iα and u* iβ (i = g, m).To control the switching sequence and duty cycle of the three-phase inverter, the PWM control signals are output to 12 insulated gate bipolar transistors (IGBTs) on the grid-side and the motorside, respectively.
In the charging stage, the flywheel rotor accelerates to convert the input energy into mechanical energy, and PMSM/G works in the motor state.The grid-side converter adopts the uncontrolled rectification strategy.The motor-side converter adopts the double closed-loop PI control strategy consisting of the speed outer control loop and current inner control loop.The speed outer control loop adjusts the target qaxis current i* q m through the deviation of the reference speed ω* m and the feedback speed ω m .The current inner control loop uses the deviation between i* q m and the feedback q-axis current i q m to adjust the target qaxis voltage u* q m .In the holding stage, the grid-side converter still adopts the uncontrolled rectification strategy.The motor-side converter adopts the double closed-loop PI control strategy of the voltage outer control loop and current inner control loop.The DC-link voltage controlled by the voltage outer control loop is required at a fixed value during the holding stage.The fixed value should be greater than the voltage obtained by uncontrolled rectification on the grid-side for the pre-discharging purpose.In this case, the electric energy can flow from the motor-side to the grid-side.
In the discharge stage, the flywheel rotor speed reduces to release the mechanical energy of the FESS into electrical energy, and PMSM/G works in the generator state.The gridside converter adopts the direct power control strategy based on the grid-side current loop to control the grid-connected active power P. The motor-side converter still adopts the double closed-loop PI control strategy of the voltage outer loop and current inner loop to maintain the DC-link voltage at the set value.
The working stages of the FESS have been introduced, but the DC-link voltage cannot track its reference value quickly and smoothly using the above control strategies during the holding and discharging stages.The ADRC control is adopted during the two stages for the following reasons:

| Mathematical model of motor-side of FESS
The basic equations of PMSG and motor-side converter model are shown in the following equation: where u i , , and L d q , are d-q axis voltage, current and equivalent inductance of the motor, ω r and ω m is the electrical and mechanical rotational angular velocity of the flywheel rotor, p is the polar logarithm, T e is the electromagnetic torque, T L is the load torque, B is the rotational damping coefficient of the flywheel rotor, J is the rotational inertia of the flywheel rotor around the axial spindle, R s is the stator resistance, i dc is the DC-link current, R g represents The controller of flywheel energy storage system (FESS) generates pulse width modulation (PWM) control signal of converter.PI, proportional integral; PWM, pulse width modulation; SVPWM, space vector pulse width modulation.
the equivalent load resistance on the grid-side, ψ m is the flux linkage of PMSG, and P switch is the converter power loss.
The instantaneous active power balance equation between the DC and AC sides of the converter is derived as From ( 2), the energy storage grid-connected converter is a strong coupling nonlinear system in the d-q rotational coordinate system.Therefore, the DC-link voltage control using the traditional PI control method is generally difficult to meet the actual requirements over the wide rotor speed range of the FESS.
(3) can be deduced by Define the state variable x u = 1 d c to construct the state space equation of the FESS bus voltage control.To conveniently acquire the system coefficient b of the ADRC control strategy, the voltage value u ¯dc of the steady-state operating point of the DC-link voltage is introduced.The multivariate function f x t ( , ) 0 1 can be defined as Substitute ( 4) into (3) to get (5), Taking the derivative of ( 5) and substituting the second formula in (1), ( 6) is derived, where . By defining the total disturbance as x f x t = ′ ( , ) , the DC-link voltage nonlinear control model can be extended to a third-order state-space equation, expressed as where , and the

| Construction and design of ADRC controller
The structure of ADRC controller is shown in Figure 3.The ADRC controller consists of three parts: tracking differentiator (TD), ESO and NLSEF.TD is a transition tracking process designed to prevent the adverse effects of sudden changes in the target value.ESO uses the control quantity u 1 and the controlled quantity y to observe the state variables, and the internal and external disturbances of the control system.NLSEF is a nonlinear control law introduced to improve the flaws of PID direct linear weighting, and it is suitable for nonlinear systems.The Plant is the controlled object model of FESS.The DC-link voltage output u dc is adjusted by inputting the control quantity u* q m .

| TD
The first-order differential tracker is shown in the following equation: WEI ET AL.
| 4145 where the DC-link voltage target value u* dc is the TD input, the TD output v 1 is a tracking value of u v * , dc 2 is the differential of v 1 , and e 0 is the error value of v 1 tracking u* dc .The climbing time of v 1 depends on the adjustment of fast-tracking factor r. With the increase of r v , 1 will get the set value faster, but it also brings the side effect of noise amplification.Since the input value of the TD u* dc is a constant value, the target value tracking process can be ignored, and

| ESO
The ESO is the core of ADRC, and its core idea is to observe each state and the total disturbance in the controlled plant.A new state is extended by combining internal and external disturbances.By selecting the observer parameters appropriately, the observed values of all states of the system can be obtained.The fal function is the core unit of ESO.The expression of the nonlinear function fal is shown as where e is the error, α is a nonlinear factor, δ is a linear interval, e sign( ) is a sign function, α determines the nonlinear shape of the fal function, and δ affects the size of the nonlinear interval.Function filter fal is a special nonlinear structure with the characteristics of "small gain in the large error, large gain of small error," and has a good filtering effect for noise.When   e δ > , the nonlinear feedback   e e sign( ) a can make the system state z 1 quickly approach the input signal v 1 , so that the error e approaches to δ.When   e δ  , the structure of ( 9) is actually a low-pass filter. 19ccording to the characteristics of fal nonlinear function, the implementation form of nonlinear ESO can be shown in the following equation: where z z , 1 2 , and z 3 are the feedback voltage, the differential value, and the total disturbance observed by ESO, respectively.It is worth noting that x 1 and y are the same value, which is the output value of the DC-link voltage u dc .ε is the observation error, the difference between the observed voltage and the actual voltage.β β β , , 01 02 03 are the observer structural parameters of ESO, and the parameter optimization configuration method will be mentioned later.b is the system coefficient, and the control quantity u 1 is the AC armature voltage set value u* q .

| NLSEF
The nonlinear control law is a special nonlinear function.To obtain the control quantity, it uses the output result of TD and the observation value of the ESO by the following equation: where e 1 is the difference between the target voltage after transition and the observed voltage, e 2 is the difference between the target voltage differential value and the observed voltage differential value, β 1 and β 2 are the proportion and differential coefficient of NLSEF, u 0 is the control quantity of the NLSEF output, and u 1 is the total control quantity.The difference between u 1 and u 0 is that u 1 superimposes the total disturbance compensation of the system on u 0 .From the above analysis, the control structure of the second-order nonlinear ADRC application in the DC-link voltage control of the FESS is shown in Figure 4.

| ESO parameter optimization configuration method
The function e α δ fal( , , ) has the same sign with e, so nonlinear function gain F ε α δ ε = fal( , , )∕ can be defined.When ε F 0, > 0  , and ESO can be redescribed as The nonlinear feedback   e e sign( ) α with α 0 < < 1 is more efficient than linear feedback because the tracking error can reach zero faster in finite time. 19Therefore, to realize the stable control of the voltage, this paper adopts the nonlinear ESO with higher efficiency.
The Laplace transform of the continuous state expression of the ESO is Through deduction, the relationship between the observation state z 3 , the system state x 1 , and the control input u 1 can be obtained as is the total disturbance signal of the controlled object obtained by ESO.The closed-loop characteristic equation of the disturbance observer is shown in the following equation: When b is confirmed by (7), the observation performance of z 3 on the disturbance signal f 0 entirely depends on the characteristics of G s ( ) from (14).To get better observation performance, it is desired to have G s ( ) = 1 f within the bandwidth range of the disturbance signal f 0 . The is the gain coefficients that vary with ε.The stability and internal dynamics of nonlinear ESO are difficult to analyze.Due to the fal nonlinearity, frequency response analysis can hardly be done.In Wu and Chen, 19 the description function method is used to approximate and analyze the frequency response of nonlinear ESO, but this method is too complicated.Therefore, it is necessary to propose a simple and feasible method to analyze the influence of the nonlinear function gain F on the disturbance observation bandwidth of the nonlinear ESO.
F I G U R E 4 Third-order nonlinear ADRC in DC-link voltage control of the flywheel energy storage system.ESO, extended state observer; NLSEF, nonlinear state error feedback; PI, proportional integral; TD, tracking differentiator.

| Analysis of the effect of changes of pole position P and nonlinear gain F on disturbance observation bandwidth
To deal with this nonlinear characteristic, the coefficient freezing method is used for analysis.Firstly, analyze the influence of the pole position ρ on the disturbance observation bandwidth.Assume that the error ε is a certain value, then F is fixed.Therefore, G s ( ) f can be regarded as a linear system to configure the poles.According to the linear ESO parameter configuration method given in JingQing, 20 the three poles can be configured as the same value ρ, as follows: For the convenience of analysis, let 3 .For analyzing the influence of the pole position on the disturbance observation bandwidth, the Bode diagram of the closed-loop system is obtained when ρ increases from 10 to 100.From Figure 5, as the distance between the pole and the imaginary axis becomes larger, the disturbance observation bandwidth increases linearly.Therefore, the observer can obtain a larger disturbance observation bandwidth with increasing ρ.
Next, analyze the changing law of the disturbance observation bandwidth when the nonlinear gain F changes.According to the definition of the nonlinear function fal, nonlinear gain F can be obtained by equation (17), where δ α 0 < < 1, < 1.
Based on the mathematical properties of the nonlinear fal function, it can be known that it has following bounded properties, and the range of F is δ [0, ] α−1 .F changes monotonously with ε.When the observation error ε tends to infinity, F tends to 0. When the observation error ε gets smaller and less than ε F , increases and reaches F δ = α max −1 .From the definition of ε ε , tends to infinity only when the closed-loop system or the observer is unstable and divergent.But in actual system, the absolute value of the observation error   ε is always less than a given threshold ε max .So the variation range of Through literature review and analysis, [21][22][23] it can be found that for various linear and nonlinear fal functions, they all have the above bounded properties, as shown in Figure 6.
When F 1  , apply the Cardan formula in (15) to obtain the pole position formula When F nonlinearly changes with ε, the poles will inevitably change, accordingly leading to the changes in observation bandwidth.To facilitately analyze the influence of F on the disturbance observation bandwidth, the idea of the coefficient freezing method is again applied to the analysis.Fix the pole position on ρ = 100.The Bode diagram of the observer closed-loop system can be obtained when F increases from 0.1 to 20, as shown in Figure 7.

| ESO parameter configuration method
From Figures 6 and 7, F changes in the interval When the F min is close to zero, the disturbance observation bandwidth will be lower than the expected bandwidth 30rad s ∕ .This means that no matter where the pole is configured, the bandwidth may be lower than the expected value in this case.It is not expected.Therefore, F 0 is introduced, and the ESO parameter pole configuration is replaced by the following equation: The observer closed-loop transfer function is transformed into: After introducing To avoid the situation that the disturbance observation bandwidth is lower than the expected bandwidth 30rad s ∕ when the F min is close to zero, make . It is guaranteed that when F′ appears at the minimum value F F min 0 ∕ , the disturbance observation bandwidth is still during the high value 48.81 ~53.8 rad s ∕ .The following ESO parameter optimization configuration method is given to keep the disturbance observation bandwidth higher than the ESO expected disturbance observation bandwidth ω* b within the allowed range of F , of the fal function, determine F min and F max , and then get the variation range of Step 3: Select F 0 and ρ satisfying the following four conditions for pole configuration: 1.

| ESO and other parameter configuration
To make the TD tracking fast and avoid triggering oscillations, let the speed factor r = 100.The structure of the fal function shown in ( 10) is selected, and the parameters are selected as α = 0.5 0 .δ generally selected between 0.010 ˜. 1.The large value of δ will cause oscillations, therefore in this paper δ = 0.0025.
To build a third-order nonlinear ESO, the mathematical state space equations are shown in (10).Let the maximum observation error ε = 0.1 max , and then Assuming the disturbance observation bandwidth ω* = 30rad s b ∕ , using the method in this paper to configure ESO parameters, we can obtain that F ρ = 6.324, = 100.0 (22)   The ESO parameters obtained by (19) is The NLSEF parameters are α α β β , , , 1 2 1 2 , and δ, which are usually tuned after the ESO is configured.It should be guaranteed that α α 0 < < 1 < 1 2 .In this paper, we make α = 1.5 1 and α = 0.5 2 .Because β 1 and β 2 affect the control performance, we set β 1 and β 2 as 1, and then configure the ESO parameters.When the ESO reaches certain performance, i.e., repeatedly adjusting the ESO parameters does not improve the system performance, gradually increasing β 1 to a certain value to make the whole system reach better performance.

| SIMULATION RESULTS
To verify the validity of the control strategy designed in this paper, the simulation model of FESS with bidirectional PWM converter is established.Parameters of the FESS are shown in Table 2.The FESS operating curves under traditional PI control are shown in Figure 8A-D for flywheel rotor speed, q-axis current, DC-link voltage, and FESS output power.The FESS is working in the charging stage during 03 ˜s, working in the  holding stage during 34 ˜s, and working in the discharging stage during 46 ˜s.
In the charging stage, the flywheel rotor speed increases from 9110 to 9200 rpm.The electric energy input from the grid is stored as the mechanical energy of the high-speed rotating rotor.i q is stable at 8 A, driving the rotor to accelerate.Since the control mode of the grid-side converter is uncontrolled rectification in this process, the uncontrolled DC-link voltage is stabilized at 910 V.
In the holding stage, the FESS neither stores energy nor releases energy, but the DC-link voltage is adjusted to 1000 V to satisfy the pre-discharging condition.During this time, the flywheel rotor speed is unchanged, the qaxis current i q fluctuates around 0 A, and the FESS power is close to 0 kW.
In the discharging stage, the grid active power command value is 15 kW.The flywheel rotor speed drops from 9200 to 9010 rpm.The flywheel rotor drives the generator that converts the stored mechanical energy into electrical energy that flows into the grid.The DClink voltage fluctuates at the initial moment of discharging but eventually stabilizes at 1000 V. From the above, it can be seen that the switching process of the FESS operating condition will cause the DC-link voltage fluctuations.
We simulate and analyze the dynamic response of the DC-link voltage at different flywheel rotor speeds under the same conditions as Figure 8. FESS working in the charging stage during 01 ˜s, working in the holding stage during 12 ˜s, and working in the discharging stage during 23 ˜s.As seen in Figure 9, the DC-link voltage fluctuates more at lower flywheel rotor speeds.To smooth the fluctuation of DC-link voltage in the switching process, ADRC replaces the traditional PI to control DC-link voltage.Its structural parameter values are shown in Table 3.
The performance of the proposed strategy and traditional PI strategy are compared at different flywheel rotor speeds of 6500, 8000, and 9500 rpm.Figures 10-12 present the results.The FESS switches from the charging stage to the holding stage at 1 s, and from the holding stage to the discharging stage at 2 s.The comparison of the overshoot and adjustment time of the result DC-link voltage curves under different control strategies are shown in Tables 4 and 5. Table 4 shows the responsing results from the charging stage to the holding stage.Table 5 shows the responsing results from the holding stage to the discharging stage.
From Figures 10-12A, when the DC-link voltage under PI control changes from the charging stage to the holding stage are 1 s, the voltage overshoots are 24.6,25.1, and 21.8 V, respectively.The adjustment times are 0.350, 0.378, and 0.334 s, respectively.However, when the FESS switches from charging to holding stage under the ADRC control strategy, the DC-link voltage rises rapidly and stabilizes at 1000 V at low or medium speeds without overshoot and static error.The adjustment times are 0.054, 0.068, and 0.070 s, respectively.This indicates that the voltage control under the ADRC strategy responds excellently at the low-speed state of the FESS.The voltage tracking effect is obviously better than the traditional PI control.
Furthermore, when the FESS switches from the holding stage to the discharging stage at 2 s, the DClink voltage will slip due to the sudden change in power requirement.The DC-link voltage under PI control changes from the holding stage to the discharging stage, and the voltage overshoots are − 33.5, − 25.1, and − 19.7 V, respectively.The adjustment times are 0.314, 0.232, and 0.210 s, respectively.And the voltage overshoots are -1.5, -1.1, and -0.6 V under ADRC control.The adjustment times are 0.052, 0.034, and 0.038 s, respectively.
Under the traditional PI control, the DC link voltage fluctuates larger when the FESS is switched from the holding stage to the discharging stage at the lower speed.
F G U R E 9 Output curve of voltage response under conventional proportional-integral control at different speeds.the ADRC control quantity u is 68.79 at the switching instant (t = 2 s) in Figure 13A, which is exactly equal to the change of the disturbance observation (67.08) shown in Figure 13B.This means that the ADRC can compensate the observed total internal and external disturbances into the control quantity at the switching instant, thus realizing good disturbance observation compensation performance.

| CONCLUSION
In this paper, an ADRC-based DC-link voltage control strategy is proposed for the operating stage switching process when the FESS is at different speeds.This strategy ensures fast-tracking performance and antiinterference capability for DC-link voltage control.Through the analysis of the experimental results, the following conclusions are obtained.
1. Aiming at the DC-link control strategy of FESS, the voltage control strategy based on ADRC can improve the power quality of grid-connected and the stability of DC-link voltage.2. The proposed parameter configuration method can ensure that when the observer is within the allowable range of the nonlinear gain F , the ESO disturbance observation bandwidth is always greater than the expected disturbance observation bandwidth, which

F
I G U R E 5 The effect of pole position on disturbance observation bandwidth: F = 1, when ρ increases from 10 to 100.(Left image) The Bode diagram curve of the transfer function of the closed-loop disturbance observer changes, (Right image) Disturbance observation bandwith ω* b changes when ρ increases.When the parameter F increases from 0.1 to 20, the disturbance observation bandwidth first increases and then decreases, and finally tends to stabilize at ρ 3 ∕ .The maximum bandwidth appears at F = 0.7.Suppose that the expected disturbance observation bandwidth ω* b is 30 rad/s.Thus, to ensure the global bandwidth ω

Step 1 :
According to the dynamic characteristics of the total disturbance set the expected disturbance observation bandwidth of ESO to be ω* b .Step 2: When ESO is working, give ε max of the tracking error ε.According to the structural characteristics F I G U R E 6 The characteristic curve of the nonlinear gain F = ε α δ ε fal ( , , ) .F I G U R E 7 The effect of nonlinear gain F on the disturbance observation bandwidth: p = 100, when F increases from 0.1 to 20. (Left image) The Bode diagram curve of the transfer function of the closed-loop disturbance observer changes, (Right image) Disturbance observation bandwith ω* b changes when ρ increases.

F
I G U R E 8 The output curves energy storage working in working stages.Flywheel speed change curve.(B) q-axis current change curve.(C) DC-link voltage change curve.(D) FESS output power change curve.

T A B L E 3 FFF
Parameter design of ADRC controller.As the flywheel rotor speed changes continuously, the disadvantages of PI control based on fixed parameters are gradually manifested, and the advantages of nonlinear convergence of ADRC are manifested.The DC-link voltage control strategy based on ADRC can effectively track the voltage value and overcome the disturbance caused by the change power requirement in the switching process.As shown in Figures10-12B,C, the trends of the flywheel rotor speed and output power curves are basically same when the FESS is under the ADRC control strategy.The proposed strategy does not affect the other operating quantities of the FESS, but has a qualitative leap in the DC-link voltage control performance.As shown in Figure13, during the operation stage switching process, the change of the disturbance observation z 3 of ADRC is the main factor for the change of the voltage control quantity.It can be seen that the change of I G U R E 10 Curve outputs of DC-link voltage, rotor speed, and output power under ADRC and Traditional proportional-integral strategies, respectively, at 6500 r/min operating condition.I G U R E 11 Curve outputs under ADRC and Traditional proportional-integral respectively, at 8000 r/min operating condition.(A) DC-link voltage change curve.(B) Flywheel change (C) power curve.I G U R E Curve outputs under ADRC and Traditional proportional-integral strategies, respectively, at 9500 r/min operating condition.DC-link change curve.(B) Flywheel rotor speed change curve.(C) FESS output power curve.

1
Structure diagram of FESS with back-to-back coupled Pulse Width Modulation converter.PMSM/G, permanent magnet synchronous motor/generator.
variable.And a special feedback mechanism is used to compensate the extend state quantities (the disturbances) into the control quantity.It is wellsuitable for the FESS that requires a certain antiinterference ability.
Comparison of the overshoot and adjustment time of the DC-link voltage under different control strategies during the transition process from the holding stage to the discharging stage.Comparison of the overshoot and adjustment time of the DC-link voltage under different control strategies during the transition process from the charging stage to the holding stage.Comparison of ADRC and PI control performance.(A)Control quantity output of ADRC controller compared to PI controller.(B)Output curves of state variables z z z , , 1 2 3 of ADRC observer.improvesthe ability of ADRC to suppress disturbances of different frequencies.3. When the FESS is switched from the charging stage to the holding stage, the DC-link voltage of the PI control strategy is overregulated by 21.82 ˜5.1 V, and the adjustment time is 0.3340 ˜. 354 s, in terms of the voltage tracking response.Compared with traditional PI control, ADRC control can achieve a low overshoot and millisecond response speed following.4) When the FESS is switched from the holding stage to the discharging stage, the power requirement suddenly changes.At the low speed of the flywheel rotor, the DC-link voltage is more inclined to fluctuate considerably.Compared to traditional PI control, the ADRC-based voltage control strategy reduces the voltage fluctuation range by 89.25-96.9%and the adjustment time by 79.05-84.5% in the different flywheel rotor speeds.The voltage anti-interference capability under the ADRC control strategy is significantly better than the conventional PI control.
T A B L E 4 F I G U R E 13