The flywheel energy storage system (FESS) has been attracting the attention of national and international academicians gradually with its benefits such as high energy power density, high conversion productivity, and inexpensive pollution. For the mutual limitation problem of reaction speed and overshoot of the conventional PI controller, it is hard to satisfy the demand of high efficiency control. In this study, the Active Disturbance Rejection Controller (ADRC) is adopted to substitute the classical PI controller in the flywheel energy storage control system. The control system of an external loop of speed and an internal loop of current is adopted at the motor side. The standard ADRC is adopted by increasing the new nonlinear control function. The control system adopted the control strategy of the DC bus voltage external loop and the current internal loop on the grid side, as well as the second-order Linear Active Disturbance Rejection Controller (LADRC), to enhance the control ability of the DC bus voltage. In the charge/discharge control of the FESS, both the velocity external loop and current internal loop control strategies are utilized to simplify the system structure. The performance shows that the improved control system could effectively enhance the charging and discharging speed of the FESS and effectively suppress the DC bus voltage rise caused by flywheel state switching so that the system has better robustness.

## I. INTRODUCTION

As the new power system flourishes, the Flywheel Energy Storage System (FESS) is one of the early commercialized energy storage systems that has the benefits of high instantaneous power, fast responding speed, unlimited charging as well as discharging times, and the lowest cost of maintenance.^{1,2} In addition, it has been broadly applied in the domains of aerospace, new energy generation, uninterruptible power source and power grid peaking, and frequency regulation.^{3} With the research on the FESS, there are still some problems in the flywheel rotor, bearing support, vacuum and system cooling, and system control technology of composite materials.^{4,5} The future flywheel energy storage system will also focus on in-depth research from the perspectives of arraying, automation, intelligence, high performance, and high stability.

The FESS primarily involves a flywheel rotor, motor/generator, and power electronic converter. Direct-drive permanent magnet synchronous motors (PMSM) are broadly applied to flywheel energy storage motors owing to their simple structure, reliable operation, and high efficiency.^{6,7}

The FESS has three working states: charging, stand-by, and discharging. Through the power electronic conversion equipment, the operating state of the motor can be controlled, the flywheel can be driven to accelerate and decelerate, the charging and discharging of the system can be completed, and the mutual conversion between electrical energy and mechanical energy can be realized.^{8}

The literature^{9} simplified the charge or discharge model of the FESS and applied it to microgrids to verify the feasibility of the flywheel as a more efficient grid energy storage technology. In the literature,^{10} an adaptive PI vector control method with a dual neural network was proposed to regulate the flywheel speed based on an energy optimization perspective. In Ref. 11, an adaptive nonlinear controller was applied to the FESS to keep the DC bus voltage stable when switching the system load, but the system response was slow. Reference 12 used the immersion invariant manifold algorithm and the bus voltage square outer loop to effectively suppress the flywheel speed and DC side load changes, but this method requires more parameters to be tuned. The compensation link of load current and flywheel speed was introduced in Ref. 13 to inhibit the influence of load and speed changes, but this method ignores the loss power of the motor.

The active disturbance rejection control (ADRC) strategy is a nonlinear control method, which has the features of quick feedback, accurate control, and robust resistance to disturbances.^{14,15} As the modern control theory and motor control technology progress, in the last few years, various nonlinear control methodologies have been applied to the control of the PMSM.^{16,17}

Reference 18 applied the ADRC technique to the control strategy of a microgrid with hybrid energy storage to decrease the DC bus voltage swings and improve the grid connection capability of the system. Reference 19 proposed an ADRC speed control system without a speed sensor. The ADRC controller controls both the external speed loop and internal current loop. While it can decrease the over-tuning, many parameters are introduced, and the alignment process is more complicated. Reference 20 omitted the tracking differentiator module and used direct errors instead of nonlinear functions in the expansion stateful observer and nonlinear stateful feedback control method modules. There is a certain overshoot in the velocity. Reference 21 proposed an LADRC devise approach for the PMSM so that the motor does not overshoot at startup but still has some overshoot when a load is suddenly applied.

Position sensorless control is broadly used in motor control because of the advantages of reducing system cost and improving system reliability. Commonly used position sensorless control methods include the model reference adaptive system (MRAS), Extended Kalman Filter (EKF), and sliding mode observer (SMO).^{22}

In Ref. 23, an improved sliding mode observer (SMO) is designed to control the charging/discharging of the FESS. A closed-loop current control based on the analog angle is used for flywheel start-up and low-speed operation, and it switches to a sliding-mode variable structure control when the set speed is reached. In the literature,^{24} a new exponential convergence rate is proposed to reduce the shuttle frequency in the sliding process, but the system is weak against disturbances. In the literature,^{25} segmented composite functions were proposed to improve the observer accuracy, but the adaptive capability was poor.

To address some of the problems of the above-mentioned system, an ADRC is used in this paper to improve the FESS in order to increase the system control, improve the system response, and enhance the system robustness. A new nonlinear function is designed with better smoothness and continuity at the origin than the conventional function in this article. In addition, a modified SMO is applied to monitor the rotor position angle and speed of the motor. In the grid-side converter control, a second-order LADRC is used to control the DC bus voltage to improve the system control effect. Results of the simulation demonstrate that the controller with the ADRC technique can stably maintain the charge/discharge of the FESS and can switch the charging/discharging state quickly and reliably, effectively reducing the impact on the electrical grid and voltage swings at the DC bus.

## II. FLYWHEEL ENERGY STORAGE SYSTEM

### A. Flywheel energy storage system structure

The main circuit topology of the FESS grid-connected system is given in Fig. 1. It consists primarily of a flywheel rotor, PMSM, machine side converter, DC bus capacitor, grid side converter, and grid.

The FESS mainly includes three working states: energy storage, storage, and energy emission. During energy storage, the motor works in the motor state, the electric energy is accelerated by the power electronic converter to drive the flywheel, and the energy is converted from electric energy to kinetic energy. When the speed increases to the set speed, the system works in the stand-by state and the speed remains unchanged. When the system receives the energy release signal, the motor works in the generator state and exports the required voltage and current through the power electronic converter, the rotor speed decreases, and the transformation of kinetic energy to electrical energy is completed. The working principle is shown in Fig. 2.

From Eq. (1), it can be seen that the rotational speed of the flywheel rotor accelerates during charging and decelerates during discharging. The flywheel is controlled to absorb and release energy by changing the speed within a certain period of time.

### B. Mathematical model of the permanent magnet synchronous motor

In this study, the PMSM is chosen as the motor for the FESS. Since the PMSM is a nonlinear system, for the purpose of reducing the complexity of the mathematical model of the PMSM, it is supposed that there is no reluctance winding in the rotor. The stator windings are symmetrically distributed in the three phases, and swirl currents, magnetic saturation, and hysteresis losses are ignored.^{26,27}

The vector control strategy of the PMSM mainly consists of i_{d}* = 0 control, maximum torque/current control, weak magnetic area control, and maximum output power control. In this paper, the method of i_{d}* = 0 vector control can simplify the mathematical model of the PMSM, make the control process simpler, and achieve the purpose of controlling the motor speed by controlling the stator current to control the electro-magnetic torque.

_{f}is the permanent magnet flux and ω is the electric angular velocity.

_{α}and ψ

_{β}are the flux linkage components in the α-β coordinate system.

_{L}is the load torque.

## III. DESIGN OF THE ACTIVE DISTURBANCE REJECTION CONTROLLER

### A. Active disturbance rejection controller

The ADRC primarily involves a Tracking Differentiator (TD), Extended State Observer (ESO), and Nonlinear State Error Feedback (NLSEF). The TD arranges the process of transition for the set import signal, obtains the differential import signal, and produces a filtering effect on the input signal to obtain a stable input response. The ESO can estimate the condition parameters in the system but also obtains an estimate of the disturbances inside and outside the system. The NLSEF exports the system control signal to improve the control effect.

The center ideology of the ADRC is to take the standard integral series type and consider the components of system dynamics varying from the standard type as the total perturbation. The ESO is used as a tool to provide real-time estimation of the total disturbance, and it is removed so that the controlled target full of disruption, indeterminacy, and irregularity is restored to the basic system of the standard integral series type and the control system design is changed from complex to easy.

Its basic structure is shown in Fig. 3.

### B. Nonlinear active disturbance rejection controller

The first-order nonlinear ADRC equations are as follows:

Because the function of nonlinearity is an essential part of the ADRC algorithm, and the traditional “fal” function is not differentiable at piecewise points and origin, the continuity and smoothness of this function are poor. Therefore, this paper improves and optimizes the traditional “fal” function, and the improved new nonlinear function is “nfal”

When |e| > δ, the tangent function of the hyperbolic tangent tan h will be used replacing the sine function.

The compared graphs of the sine and tan h curves are shown in Fig. 4.

Figure 4 demonstrates that the tan h function is continuous in the real range and the value of the feature is zero at the zero point. It is distinct from the figure that the convexity of tanh(ax) is adapted by modifying the value of the parameter “a.” The larger the value of “a,” the steeper it is near the zero point. By considering the steepness of the function, the continuity, and the system simulation results, this paper selects “a = 1.”

^{2}is 0, the convergence of the new nonlinear function obtained after interpolation fitting is better.

The improved new nonlinear function “nfal” has better continuity and smoothness than the traditional “fal” function. Substituting the “fal” function in formula (10) with Eq. (18), a new ADRC can be obtained.

A comparison between the “fal” function and the improved “nfal” function is shown in Fig. 5. Combining noise and rectangular waves as perturbation inputs, the improved function has significantly improved anti-turbulence performance and filtering ability.

### C. Linear active disturbance rejection controller

Due to the nonlinear function in the nonlinear ADRC, the higher the rank of the system, the more adjustable parameters there are, which will complicate the system’s tuning process. Therefore, Professor Gao proposed an LADRC on this basis. The parameter gain is adjusted using the bandwidth method.

The core idea of converting a nonlinear ADRC to an LADRC is an Linear Extended State Observer (LESO) and correlates the parameters to be adjusted with the observer bandwidth using a simple PD control with scaling factors, derivative time constants, and the associated controller bandwidth, while simplifying the setup of controller parameters.

An ADRC is applied to the second-order mathematical model of a network-side converter. If a nonlinear ADRC controller is used, a third-order ESO needs to be designed, and the adjustment process is complicated. For the purpose of enhancing the control capability of the grid-connected inverter of the FESS on the DC bus voltage, a linear second-order ADRC system is used in this section. The tracking performance of the system is improved with Linear Tracking Differentiator (LTD). Adding system state variables to observe and compensate for disturbances through the LESO avoids system response speed and solves the problem of oscillations.

Meanwhile, the strategy of DC bus voltage external loop and current internal loop control can make the AC side export the sine current well so that the inverter can satisfy the demands of grid integration with the unit strength factor and maintain the DC bus voltage stability effectively.

The DC bus voltage is preserved by adapting the external loop control of the DC bus voltage to the difference between the given voltage and the feedback on the DC side. The outlet of the external loop is the given current of the D-axis of the internal loop, while the purpose of the internal loop current is to provide a fast follow-up of the given current.

Traditional PI controllers use an integrator to eliminate static errors, but adding an integrator causes output phase lag, increases response time, and reduces system stability.

_{0}is the output of the linear error feedback control law.

From the above-mentioned formula, it can be seen that when f ≈ z_{3}, this system can be streamlined and the controlled object can be simplified by the method of interference compensation.

_{p}and k

_{d}are controller parameters.

_{c},

_{c}is the controller bandwidth.

It can be seen that in the LTD and PD error feedback laws, the unique necessary parameter to be set is ω_{c}. As ω_{c} is larger, the response of the system output is quicker and the process of dynamics is shorter; However, in the meantime, the system’s ability to suppress noise may be reduced, which affects the reliability of the system.

^{28}the gain coefficient of the observer is

### D. Linear extended state observer band characteristics and filtering performance analysis

As the core part of the ADRC, the tracking and estimation ability of the extended state observer should be analyzed, and the effect of disturbed observed noise and control inputs on the third-order LESO should be considered.

_{1}, z

_{2}, and z

_{3}can be obtained by Laplace transform derivation and arrangement,

The frequency domain characteristic curves of ω_{0} = 10, 50, 100, 150, 200, and 250 are shown in Fig. 6.

ω_{0} mainly affects the tracking speed of the ESO. The tracking ability of the ESO becomes stronger as the value of ω_{0} increases. Therefore, the faster the system response speed, the smaller the system observation error. However, if ω_{0} is too large, the high frequency gain will increase. The more obvious the effect of noise amplification, the worse the observation performance.

Taking b_{0} = 100, ω_{0} = 10, 50, 100, 150, 200, and 250, the characteristics curves in the frequency range are shown in Fig. 7.

Unlike the frequency domain feature profile of the observed noise, the addition of the bandwidth of the observer reduces the phase lag of the tracking signal and essentially does not affect the gain in the higher frequency bands, and the third-order LESO has a better rejection of the interference at the input.

## IV. DESIGN OF THE SLIDING MODE OBSERVER

### A. Traditional sliding mode observer

In the PMSM without sensor control, the SMO is applied to observe the state of change of the motor. A traditional SMO is designed from the error of the given current and the feedback current, and from this error, the back Extended Electromotive Force (EMF) signals and rotor speed of the motor are estimated.^{29,30} To begin with, a slipform surface is selected, the state variables to move along the slipform surface are controlled, and the state equation is built.

The SMO program diagram is displayed in Fig. 8.

_{c}is the low-pass filter crossover frequency.

### B. Improved sliding mode observer

The traditional SMO control function adopts the symbolic function as a nonlinear control system, and the system state point will switch back and forth near the slide surface, which will generate system jitter and affect system stability and estimation accuracy.^{31} To solve the chattering issues, tan h is used instead of “sgn” in this paper, which reduces the chattering to a large extent.

### C. Stability analysis of the improved sliding mode observer

_{α}|,|e

_{β}|} is guaranteed. In this paper, we combine the formula and simulation results and finally determine K = 280.

## V. SIMULATION AND ANALYSIS

To verify the possibility and usefulness of the improved ADRC and SMO, a flywheel energy storage control model was established in MATLAB/Simulink for simulation. The model consists of two parts: the motor side and grid side. The performance of the two control strategies based on the ADRC and PI controller is compared to demonstrate the effectiveness and superiority of the proposed control strategy. The system and controller parameters are presented in Tables I–III.

Parameters of the PMSM/G . | System parameters . |
---|---|

Poles (P_{n}) | 2 |

Stator resistance (R/mΩ) | 8.17 |

Stator inductance (L/μH) | 91.3 |

Inertia (J/kg∙m^{2}) | 0.115 |

Friction coefficient (B) | 0 |

Parameters of the PMSM/G . | System parameters . |
---|---|

Poles (P_{n}) | 2 |

Stator resistance (R/mΩ) | 8.17 |

Stator inductance (L/μH) | 91.3 |

Inertia (J/kg∙m^{2}) | 0.115 |

Friction coefficient (B) | 0 |

Parameters of the system . | System parameters . |
---|---|

Grid side line voltage (V) | 690 |

DC bus voltage (V) | 1100 |

DC bus capacitance (F) | 0.05 |

Filter inductor (L/H) | 0.002 |

Grid frequency (Hz) | 50 |

Parameters of the system . | System parameters . |
---|---|

Grid side line voltage (V) | 690 |

DC bus voltage (V) | 1100 |

DC bus capacitance (F) | 0.05 |

Filter inductor (L/H) | 0.002 |

Grid frequency (Hz) | 50 |

Parameters of the LADRC . | System parameters . |
---|---|

Controller bandwidth, ω_{c} | 750 |

Observer bandwidth, ω_{0} | 200 |

Control gain, b_{0} | 15 000 |

Parameters of the LADRC . | System parameters . |
---|---|

Controller bandwidth, ω_{c} | 750 |

Observer bandwidth, ω_{0} | 200 |

Control gain, b_{0} | 15 000 |

Parameters of the ADRC . | System parameters . |
---|---|

Correction gain, β_{1} | 3500 |

Correction gain, β_{2} | 1000 |

Compensation factor, b | 1000 |

Parameters of the ADRC . | System parameters . |
---|---|

Correction gain, β_{1} | 3500 |

Correction gain, β_{2} | 1000 |

Compensation factor, b | 1000 |

The motor side consists of a PMSM, a Pulse Width Modulation (PWM) converter, and a control policy. An improved nonlinear ADRC is used to substitute the conventional PI controller. The rotor position information is obtained through an SMO containing a tan(h) function. Vector control with i_{d}* = 0 is also applied.

The control strategy on the motor side is the speed external loop and the current internal loop. The PI controller is replaced with the ADRC controller. Considering the high real-time requirements of the system for the current internal loop, the PI controller is still used for the current internal loop. The estimated speed of the motor of the flywheel energy storage system is obtained by the SMO; a difference is made with the given speed of the system and input to the ADRC controller to obtain the q-axis current reference value, and then the q-axis voltage reference value is obtained by the internal PI controller. The schematic block diagram of the system is illustrated in Fig. 9.

The electrical grid side comprises the grid, the PWM converter, the phase locked loop (PLL), and the control strategy. The DC bus voltage external loop and current internal loop are taken as the network side control strategy. A second-order LADRC is implemented instead of the conventional PI controller. The control strategy of the DC bus voltage outer loop and current inner loop is adopted; the second-order LADRC is used instead of the traditional PI controller in the DC bus voltage outer loop, the LADRC is input to get the q-axis reference current after the difference between the DC bus voltage and the system reference voltage, and the q-axis voltage is obtained after the PI controller in the current inner loop. The use of a second-order LADRC can provide more effective stabilization of the bus voltage. The diagram of the system is shown in Fig. 10.

When the system starts up, as illustrated in Figs. 11 and 12, the system with the PI controller would have a major effect on the DC bus voltage, and the time for charging is prolonged. The charging can be completed in 1.1 s and enter the stand-by state, and the system enters the discharge state in 1.5 s, where the completion of the whole discharge process takes 0.9 s, and enters the charging state again in 2.5 s. The improved ADRC control system has significantly reduced the overshoot and fluctuation of the DC bus voltage during startup and improved the charging and discharging speed of the system compared with the conventional ADRC control system. Moreover, the fluctuation in the DC bus voltage can be reduced to less than 10 V in the charging and discharging switching state. The system boot took 0.8 s to complete charging, 1.5 s to enter the stand-by mode, and 0.7 s to complete discharge after discharge. Compared with PI control, it can effectively shorten the charging and discharging time and more effectively reflect the fast charging and discharging performance of the FESS.

As can be observed from Fig. 13, the FESS first enters the charging mode when it starts up. During startup, the DC bus voltage overflows a little but returns immediately to the reference DC bus voltage of 1100 V. After the motor speed is accelerated to the set speed of 10000r/min, the system enters the stand-by state.

When the FESS receives a signal to release power, the system is in the discharge mode, and the speed gradually decreases from 10000r/min. The DC bus voltage has a small amplitude fluctuation, and the fluctuation range is less than 10 V. When the speed decreases to the minimum speed, the system enters the stand-by state.

When the system receives the charging signal again, the FESS accelerates to the set velocity of 10000r/min, and the DC bus voltage fluctuates slightly.

When the FESS is switching between charging and discharging, although the DC bus voltage fluctuates slightly, it can be rapidly returned to a voltage reference of 1100 V.

As displayed in Fig. 14, the estimated motor speed of the control system can follow the actual motor speed in real time. The error between the two is small, and the steady-state effect is achieved.

As can be observed from Figs. 15 and 16, the rotor position estimates obtained by the SMO and the actual position errors during motor operation are both very small and stable at around −0.78 after the system is running stably. This demonstrates that the rotor location exported by the SMO has a high accuracy.

As evidenced by the power curves in Figs. 17 and 18, when the FESS is charging, the active power is positive and the FESS absorbs energy. While the FESS discharges, the active power is negative and the FESS releases energy, and the reactive power is stable around the zero value.

To further highlight the effectiveness of the improved ADRC and SMO proposed in this paper, the load is changed abruptly during the system operation, as shown in Fig. 19. Compared with the PI controller and the conventional ADRC and SMO control systems, the improved control system has a stronger ability to suppress the DC bus voltage fluctuations and can return to the stable value in just 0.1 s.

## VI. CONCLUSION

In this article, the ADRC is applied to optimize the FESS. The motor side control adopts the improved nonlinear ADRC and introduces an improved SMO based on the hyperbolic tangent function to reduce the chattering phenomenon. The second-order LADRC is required to maintain the voltage reliability of the DC bus. The simulation results demonstrate that the modified FESS can effectively improve the charging/discharging speed. The DC bus voltage rise induced by switching between charging and discharging states of the system is suppressed, and the speed and rotor position angle are estimated with a higher accuracy, which makes the system more robust. At the same time, it is verified that the DC bus voltage fluctuation can be effectively suppressed when the system load changes suddenly, which is of great significance to improve the control accuracy and system stability.

## ACKNOWLEDGMENTS

This work was supported by the Major Science and Technology Project of the Inner Mongolia Autonomous Region of China (Grant No. 2020ZD0016).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

Y.L., K.M., J.Z., J.G., and K.L. contributed equally to this work.

**Yujia Liu**: Conceptualization (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). **Keqilao Meng**: Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). **Jiangong Zhang**: Supervision (equal); Writing – review & editing (equal). **Junfeng Gao**: Supervision (equal); Writing – review & editing (equal). **Kaibiao Liang**: Supervision (equal); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## REFERENCES

*Introduction to Active Disturbance Rejection Control*

*Active Disturbance Rejection Control Technique-The Technique for Estimating and Compensation the Uncertainties*

*Sensorless Control of Permanent Magnet Synchronous Motor Based on Improved Sliding Mode Observer*