Low‐voltage ride‐through control strategy for flywheel energy storage system

Due to its high energy storage density, high instantaneous power, quick charging and discharging speeds, and high energy conversion efficiency, flywheel energy storage technology has emerged as a new player in the field of novel energy storage. With the wide application of flywheel energy storage system (FESS) in power systems, especially under changing grid conditions, the low‐voltage ride‐through (LVRT) problem has become an important challenge limiting their performance. In this paper, we propose a machine‐grid side coordinated control strategy based on model predictive current control (MPCC) for the insufficient LVRT capability of traditional FESS during grid faults. Excellent dynamic properties are demonstrated by the technique, which allows the grid‐side converter output current to swiftly follow the reference current instruction. The FESS's LVRT capability is increased when the grid‐side converter uses the MPCC current inner loop rather than the proportional–integral current inner loop during grid voltage dips. This greatly increases the reactive power response speed and efficiently supports the quick recovery of grid voltage. According to simulation verification carried out by Matlab/Simulink, the suggested control approach can assure the long‐term dependable operation of the FESS during voltage dips. This study can also be used as a reference for improving the FESS's LVRT capabilities in the future.


| INTRODUCTION 1.| Motivation
A good opportunity for the quick development of energy storage is created by the notion of a carbon-neutral aim.
To promote the accomplishment of the carbon peak carbon-neutral goal, accelerating the development of a new form of electricity system with a significant portion of renewable energy has emerged as a critical priority.The installed capacity of new energy storage projects that had been placed into service countrywide by the end of 2022 was 8.7 million kW, and the average period that energy was stored was 2.1 h, an increase of more than 110% from the end of 2021.Compared with other nations, flywheel energy storage is one of the innovative energy storage technologies.China started its research and development into flywheel energy storage later than other countries, but in recent years, the country's installed capacity has also expanded.In 2022, China's total installed capacity of flywheel energy storage climbed by 115.8% year over year.
With the massive expansion of China's new energy, "new energy + energy storage" has emerged as a key strategy for addressing the issue of consumption.Power grid enterprises now have strict testing requirements for access to "new energy + energy storage" systems, including requirements for power regulation and low-voltage ride-through (LVRT) capabilities.LVRT presents significant issues for flywheel energy storage system (FESS) as a low-voltage grid event might impair system performance or potentially cause the system to fail.Under LVRT situations, flywheel systems' output power quality and stability may be jeopardized, which raises additional concerns about their dependability in power systems.As a result, it is crucial to comprehend and deal with flywheel energy storage devices' behavior in LVRT circumstances.The LVRT of wind turbines linked to the grid has received a lot of attention from specialists and academics recently, whereas flywheel energy storage solutions have received less attention.

| Literature review
For the LVRT of double fed induction generator, Zhou et al. 1 and Lin and Wang 2 start from the perspective of the power imbalance between the machine-side, direct current (DC)-side, and grid-side when a fault occurs in the grid when an abnormally high voltage in the circuit is detected, the Crowbar circuit forms a low impedance path to conduct the excess energy away quickly and prevent overvoltage damage to the equipment.Compared with other overvoltage protection methods, Crowbar circuits are quicker to respond and less costly, but they can introduce high currents, the impact of which needs to be evaluated and current limits set appropriately.After taking into account the benefits of the supercapacitor's quick response time and good long-term cycling stability, Du et al., 3 Wang et al., 4 Liu et al., 5 and Zhang et al. 6 proposed to address the power imbalance issue by using the external supercapacitor energy storage system scheme at the DC bus capacitor to maintain the stability of the DC chain voltage.To increase the LVRT capabilities, it was suggested in Yang et al. 7 and Dang and Lin 8 to employ superconducting magnetic energy storage (SMES) in parallel at the DC bus capacitor.This was done to take advantage of SMES's high energy density and losslessness.According to Li et al., 9 Chen et al., 10 and Zheng et al., 11 the grid-side converter adjusts each of the active and reactive outputs under the magnitude of voltage dips while the machine-side converter controls the DC voltage to stabilize the system's stability and LVRT capability in the event of grid faults.
It is important to remember that the FESS's control strategy is essential to resolving the LVRT issue.In Jia et al., 12 the researcher proposes a speed-current double closed-loop control system for the wind farm frequency regulation charging phase.Flywheel speed is regulated using a proportional-integral (PI) regulator.A novel control approach for grid-connected flywheel energy storage devices operating in parallel was suggested by the researcher in Liu et al. 13 for the grid-connected operation phase.To be more precise, the grid-side converter uses a direct power control technique to efficiently manage the grid-connected active power, while the machine-side converter uses dual closed-loop control with a voltage outer loop and current inner loop.An artificial neural network technique is put forth in Abdel-Khalik et al. 14 to regulate the flywheel's charging and discharging.Fuzzy neural networks are suggested in Jian et al. 15 as a way to keep the FESS's DC bus voltage stable.Fuzzy control is used in Hamazaoui et al. 16 and Jerbi et al. 17 to regulate the flywheel's spinning speed.
Multivariable systems, or systems with numerous inputs and multiple outputs, may be handled using model predictive control (MPC).Because of this, it excels at managing intricate industrial processes and systems that may consider the interactions between several control variables.By reoptimizing the control inputs at each control step, MPC is an online optimum control approach that can adjust to changes in the system in realtime.Therefore, MPC is resilient to uncertainty and nonlinear, time-varying systems.MPC has a wide range of applications in energy systems, including power systems, wind and solar systems, and energy storage systems.The nonlinear relationship between generator speed and DC-side voltage in a turbine back-to-back converter has been explored in Nguyen et al., 18 and an MPC strategy has been employed for system regulation.In Ghanaatian and Lotfifard, 19 Zhang et al., 20 and Ramirez et al., 21 it is described how the MPC technique is used to manage the back-to-back converter to preserve the unit power factor while achieving regulation of the DC link voltage and permanent magnet synchronous motor (PMSM) speed.
On the basis of current research, this work presents a machine-grid side coordinated control technique based on model predictive current control (MPCC) to improve the LVRT capacity of the flywheel energy storage gridconnected system in the event of grid faults.To prevent the system from going off-grid in the event of symmetrical or asymmetrical faults, the control strategy seeks to stabilize the system's DC bus voltage.At the same time, it greatly increases the reactive power response speed, which can quickly supply reactive power support for the grid voltage recovery.This paper provides a practical coordinated control technique to increase the LVRT capacity of the flywheel energy storage grid-connected system.It does this by utilizing Matlab/Simulink simulation to evaluate the effectiveness of the recommended control strategy.

| Contributions of this paper
The main contributions and innovations of this paper are summarized in the following three areas.
(1) The LVRT criterion is elaborated, and the relationship of power flow and the variation of DC bus voltage of flywheel energy storage grid-connected system in the face of grid voltage dips are analyzed in detail.(2) The control concept of the model predictive current is explained.The MPCC is proposed based on the conventional machine-grid side coordinated control approach, which effectively removes the intricate nonlinear connection from the conventional system.The system design is simplified by the suggested control method, which does away with the grid-side converter's requirement for pulse width modulation technology.This not only cuts the cost and simplifies the hardware implementation, but it also increases the system's dependability.(3) By comparing the simulation results, we observe that the grid-side converter with MPCC current innerloop control shows a significant improvement in reactive current response speed during faults.By optimizing the control algorithm, we have successfully reduced the current harmonic content, thus improving the current quality of the system.This has a positive impact on improving the interaction between the FESS and the grid.

| Organization of this paper
The remainder of this article follows.Section 2 briefly introduces the structure of the flywheel energy storage gridconnected system and the LVRT criterion.Section 3 analyzes the impact of grid voltage dips on the flywheel energy storage grid-connected system, mathematically models the machine-side converter and the grid-side converter, and introduces the traditional LVRT control strategy for FESS.In Section 4, the MPCC concept is presented, and a coordinated control method based on MPCC for various drop circumstances is suggested for the FESS's LVRT.In Section 5, the symmetric and asymmetric faults with different drop levels are simulated and verified, and the MPCC controller is compared with the PI controller to verify the effectiveness of the proposed control strategy.Section 6 summarizes the research results of this paper and gives an outlook for the future.

| System components
Figure 1 depicts the physical layout of the flywheel energy storage grid-connected system.It is made up of a flywheel powered by a PMSM, a power grid, a DC bus capacitor, a filter inductor, an equivalent resistor, and machine-side and grid-side converters.The FESS works by storing energy using the inertia of a fast-rotating flywheel.When the battery is being charged, external Structural diagram of flywheel energy storage grid-connected system.PMSM, permanent magnet synchronous motor.
electrical energy is transformed into mechanical energy by a power electronic conversion device and stored in the flywheel.When the battery is discharged, the flywheel drives the generator to transform mechanical energy into electrical energy output, allowing for the realization of energy storage and release. 22he flywheel rotor is the most important component in the FESS, and the whole system relies on the rotation of the flywheel rotor to realize energy conversion. 23The kinetic energy when the flywheel rotates is where J and ω denote the rotational inertia and rotational speed of the flywheel, respectively.Through Equation (1), by attempting to raise the flywheel rotor's moment of inertia and the rate of rotation, it is possible to enhance the capacity for storing energy of the flywheel.

| LVRT
Countries around the world have developed standards for LVRT for wind turbines in the face of grid faults.LVRT refers to a situation in which a power system is allowed to temporarily drop the system voltage to a level lower than the normal minimum operating voltage during a fault, but not to the point of complete blackout.The research instead refers to connected to the grid LVRT technical requirements for wind farms as there is presently no defined LVRT standard for FESS. Figure 2 shows the flywheel's storing energy for the LVRT standard.
The LVRT requirements for wind farms are as follows: (a) When the voltage at the grid-connection point drops to 20% of the nominal voltage, the WTGs need to be guaranteed to operate continuously without going offgrid for at least 625 ms under these voltage conditions. 24(b) When the voltage at the grid-connection point can be restored to 90% of the nominal voltage within 2 s of the fault, the WTGs need to be guaranteed to operate continuously without going off-grid during the voltage restoration period. 24

| LVRT CONTROL STRATEGY FOR CONVENTIONAL FESS
As can be seen from Figure 1, the output power P e of the flywheel energy storage motor and the instantaneous active power P g output to the grid from the AC side of the grid-side converter satisfy the following relationship equation: 2 (2) The flywheel energy storage motor's powered output P e and the grid-side converter's total power P g achieve a condition of conservation when the FESS is operating steadily, and at this point the voltage of the DC bus is stable.
If the actual power P e output of the flywheel energy storage motor is left unchanged when a symmetrical fault in the grid occurs, it will result in the converter's overcurrent limitation on the grid side and a power imbalance on the DC-side.The active output must be appropriately adjusted to stabilize the DC voltage to prevent the system from going off-grid.This might cause symmetrical decreases in grid voltage to appear as unbalanced power at the bus that transports DC power.When the FESS is discharged at this time, the unbalanced power will cause the DC bus voltage to increase, and when the FESS is charged at this time, the DC bus voltage will decrease. 25The converter has overvoltage and undervoltage protection systems that disable the flywheel system's parallel connection to the grid when the DC voltage exceeds the upper and lower limits (e.g., 10% of the rated value).In the case of unforeseen voltage conditions, this protects the flywheel motor and converter.

| Machine-side converter control strategy
The power-current double closed-loop control approach is employed when the grid voltage begins to decrease because the imbalance between the machine-side power generated and the grid-side produces power resulting in oscillations in the DC bus capacitance.The fundamental concept behind this approach is to manage the electromagnetic power of the motor to regulate the DC-side voltage when the grid voltage is unstable.The control block diagram for this approach is depicted in Figure 3.
The deviation of the grid-side converter output power from the machine-side output power is given as the qaxis current, which can be written as The control in conventional vector control i = 0 d is used in the machine-side control scheme, and the reference value of the d q − -axis of the modulating voltage can be obtained by using a conventional PI regulator and combining it with a feed-forward decoupling control strategy, which can be written as

| Grid-side converter control strategy
To provide smooth power delivery to the grid, the gridside converter must manage the AC-side output frequency as well as amplitude to match the grid while maintaining the DC bus voltage steady.The grid-side converter's job is to invert DC power into AC power and supply power to the grid.To stabilize the DC-side and provide a steady supply of power to the grid, the grid-side converter utilizes a grid voltage-directed vector control method.
According to Kirchhoff's law, the mathematical model of the grid-side converter in the ABC coordinate system is known as where L is the converter side filter inductance; R is the equivalent resistance; u inva , u invb , u invc are the components of the converter outlet voltage in the ABC coordinate system; i ga , i gb , i gc are the components of the converter outlet current in the ABC coordinate system; u ga , u gb , u gc are the components of the converter shunt point voltage in the ABC coordinate system.The instantaneous output voltage of the grid-side converter is expressed in the d q − coordinate system as The output power expression of the grid-side converter is given below: g g dg d g qg q g g dg q g qg d From Equation ( 6), it can be seen that the dq axial current component of the grid-side converter is not only affected by the control voltage of the grid-side converter but also by the cross-coupling voltage term and the grid voltage.Therefore, the dq axial voltage control equation can be obtained as follows: ) According to the latest LVRT guidelines in China, when the flywheel energy storage grid-connected system realizes LVRT, the grid-side converter should provide reactive power to the grid-side to maintain the stability of the grid and the control mode of the grid-side converter is shown in Figure 4.The magnitude of the reactive current input to the grid should be changed according to the variation of the grid-connected point voltage, 26,27 and Equation ( 9) is as follows: = 0 ( > 0.9), = 1.5 × (0.9 − ) × (0.9 0.2), = 1.05 × ( < 0.2).Where u t (pu) for the wind farm grid point voltage Missing Value and I n (A) for the rated current of the wind farm.
At this point, the active current output is limited by the capacity of the inverter: where i g max is the rated current that the grid-side converter can withstand.The DC bus voltage deviation is adjusted by PI to obtain the active current reference value i gdref 1 , calculate the active current limit value i gdref 2 , and take the smaller of the two values as the final active current output reference value i gdref of the grid-side converter.When i i < gdref gdref 1 2 , it indicates that the voltage stability can still be maintained by the outer-loop control, when i i > gdref gdref 1 2 , it indicates that the DC capacitor stability cannot be maintained only by the outer-loop control; at this time, it should start the coordinated control of the machine-grid side, the active power of the grid-side converter may be used to compute the machine-side derating active power command.The DC capacitor voltage can then be brought back within the allowable range by controlling both the machine-side produce activity power and the grid-side produce activated power.

| Control principle of model predicted current
Model prediction-based current control is an advanced strategy commonly used in power electronic systems and motor drives.The method predicts future current values by modeling the system and using a prediction algorithm to achieve effective control.The process includes building mathematical models of the inverter and load, current estimation using a prediction algorithm, constructing a value function g evaluating the control behavior, and implementing it through a discretized state space.The optimal control strategy is selected by considering the load current to ensure that the load demand is met.This strategy helps improve system responsiveness and efficiency and adapt to dynamic changes in power electronics and motor systems.
The ABC coordinate system is transformed to the αβ coordinate system and the transformation matrix is given in the following equation: Substituting Equation (11) into Equation ( 5), the following expression for the dynamic current equation of the grid-side converter in αβ the coordinate system can be obtained: The finite control set MPC algorithm is based on a discrete-time model of the system, and therefore the continuous-time equation (12) of the system needs to be discretized when designing the controller.Specifically, to predict the future values of the system, we use the forward Eulerian approximation method to approximate the derivative of the load current at discrete time.This approximation method helps simplify the mathematical model and takes into account the computational speed and computational effort of digital signal processors, as well as the differences between discrete and continuous models.One of the motivations for choosing the forward Eulerian approximation is that it is an effective substitute for the load current derivative di dt / when the system sampling period is sufficiently small and improves the computational efficiency of the controller in a simplified form.(15)   In this paper, the absolute value form is used as the value function to evaluate the eight voltage vectors of the three-phase inverter to select which voltage vector minimizes the value function value, and the corresponding switching state is applied to the inverter at the next sampling time.The value function g is denoted as + * ( + 1) − ( + 1) .
gα gα gβ gβ (16)   The MPCC process is shown in Figure 5.It includes the following four parts: (1) System modeling and discretization: A discretized prediction model is obtained based on the modeling of the grid-side inverter, and the current-voltage variables i k ( ) moment are sampled and the reference current is calculated.
(2) Prediction of current: At the beginning of each control cycle, the measured value at the current moment and the model are used to make a prediction, and the predicted value of current i k ( + 1) in the future period is obtained.(3) Optimizing control inputs: The MPC algorithm is used to optimize the control inputs so that the predicted current is as close as possible to the desired current.This usually involves solving an optimization problem that takes into account the dynamic response of the system, constraints, and so forth.(4) The search for optimization is completed in this sampling period and the process is repeated in the next sampling period.

| Control strategy under symmetric drop
Distinguished from the traditional machine-grid side coordinated control strategy, to improve the reactive power response capability, the coordinated control strategy based on model current prediction proposed in this paper changes the PI current inner loop of the gridside converter of the traditional control idea into the MPC current inner loop, and the control idea of the machine-side converter remains unchanged, and the control block diagram of the grid-side converter under symmetrical drop is shown in Figure 6.When the grid is normal, the goal of the system is to minimize the error between the predicted current and the given current to ensure that the current output from the inverter meets the expectation, and in the link of controlling the switching tube conduction and shutdown, the switching state is optimized to minimize the selected value function.When a dip in the grid voltage occurs, the inverter prioritizes the adjustment of its output to support the reactive power demand of the system to help maintain the voltage and support the recovery of the grid, while the active current output should also be limited to ensure that the inverter mainly provides reactive power support during voltage dips without overly affecting the active currents, which helps maintain the stability of the system.

| Control strategy under the asymmetric drop
Voltage asymmetry and negative-sequence components may be brought on by grid failures, such as single-phase grounding. 28,29A three-phase voltage imbalance brought on by the negative-sequence component will be shown in the FESS at the gridconnected location.1][32] These voltage and power pulsations are not conducive to the stable output of the FESS.
When the grid voltage is asymmetrical and contains positive-dfnj and negative-sequence components u gabc , i gabc can be expressed as The final active and reactive power is found to be 33 Disregarding the fluctuating components of active power and reactive power, combined with Equation ( 9), it can be seen that the current command under asymmetrical fault is referred to as

| Delayed signal cancellation (DSC)
The delayed phase elimination method is a method to realize positive-and negative-sequence separation by using phase sensitivity, which is widely used in the fields of power system protection and power quality improvement, so this paper adopts the delayed phase elimination method for positive-and negative-sequence separation.Using a time-delay unit, one phase of the three-phase voltage or current is delayed, and the original three phases are superimposed with the delayed three phases, and the positive-sequence components can cancel each other after superposition due to symmetry. 34Negative-sequence components cannot be canceled due to the phase difference, thus realizing the separation of positive and negative sequences.This method is simple to implement but requires the calculation of additional phase delays and has high requirements for parameter accuracy.
In the case of asymmetrical grid voltage, the grid voltage vector in the αβ coordinate system is expressed as follows: Grid voltage dips change the phase angle, and to eliminate the phase difference caused by the dips, it is necessary to introduce an all-pass filter (APF). 35The APF can preset the phase locking angle of the grid at the moment of the fault, to realize the function of realizing the phase shift concerning the grid voltage.
The transfer function of the first-order APF is where ω 0 is the fundamental angular frequency.The Bird's plot of the first-order APF is shown in Figure 8.The phase shift is after processing through the firstorder APF: In Figure 8, the phase shift θ versus frequency ω characterizes the phase shift function of the system.At the frequency point ω ω = 0 , it is ahead of the input signal ∘ 270 ( ∘ −90 ).As the frequency increases, it is ahead of the input signal ∘ 180 ( ∘ −90 ), so for the signal of the input fundamental frequency ω 0 , the first-order APF can realize the phase shift ∘ 90 and the first-order APF can make the signal of this frequency realize the rated phase shift.

| Control program
In contrast to the traditional control strategy, the flywheel energy storage coordinated control strategy with MPCC eliminates the positive-and negative-sequence component extraction step of the grid-side current when an unbalanced dip in grid voltage occurs.This reduces system delay and error and allows it to simultaneously control the current's positive-and negative-sequence components.Figure 9 depicts the block diagram of MPCC-based grid-side converter control under asymmetrical drop fault.It consists of four sections: the voltage outer loop, the current inner loop, the MPCC, and the extraction and phase locking of the positive-and negative-sequence components of the grid-side voltage at the grid point.Using the model current prediction algorithm, the current of the system is predicted for a while in the future, and the optimal switching state is selected by optimizing the constructed value function to realize the effective control of the system under the asymmetrical dips in the grid-side voltage.During asymmetrical dips, control strategies are adopted to limit active current output and provide appropriate reactive power support to help maintain system stability.
When the grid voltage is unbalanced, it causes a secondary ripple in the DC bus voltage. 36The secondary ripple appears in the reference current of the energy storage device after PI regulation, so the energy storage device current also contains a secondary ripple component, which will affect the service life of the energy storage device and reduce the system efficiency. 36Therefore grid imbalance is one of the reasons for the reduced efficiency of FESS and measures need to be taken to eliminate the effect of grid imbalance on the system.To suppress the effect of a 2× frequency ripple on the DC bus, a 2× frequency trap is added to the voltage outer loop of the grid-side converter with the transfer function: ZHENG ET AL.
| 1495 where ω n is the natural frequency (ω πf = 2 n n ) and ζ is the damping ratio.

| SIMULATION ANALYSIS
In this study, Matlab/Simulink is employed to create a simulation model of a grid-connected FESS, set up two types of faults, verify the LVRT capability under symmetrical faults through three-phase drop, and verify the ridethrough capability under asymmetrical faults through single-phase drop, and systematically verify the validity of the proposed control strategy in a simulative environment.The relevant parameters of the flywheel energy storage grid-connected system are listed in Table 1: In Matlab/Simulink, set 0.5-1.0s as the symmetric drop and asymmetric drop intervals, and set the A-phase voltage drop 0.2 pu during the asymmetric drop, and the two-phase voltages of the grid BC are fault-free; and set the three-phase voltages of ABC drop 0.5 pu during the symmetric drop.

| Symmetrical fall
As shown in Figure 10A, a 50% symmetrical dip in the grid voltage occurs at 0.5 s with a duration of 0.5 s, and returns to the rated value at 1.0 s.The current waveform of a three-phase symmetrical grid voltage drop is depicted in Figure 10B.In the symmetrical drop simulation, the grid-side converter output current will be transiently impacted for 0.5 s along with the grid voltage drop, with the highest peak value of 675.156A for the current peak.After 91 ms, the three-phase current tends to a steady state, with no overcurrent.The DC bus voltage fluctuation effect of Figure 10C  1420.01V, the rise of about 9.2% did not exceed the overvoltage protection critical range of the grid-side converter, at this time the flywheel energy storage gridconnected system can be practiced in the LVRT, do not need to be cut out of the power grid.The waveforms of the reactive, as well as the active power output from the grid-side converter employing the aforementioned control technique, are shown in Figure 10D,E, respectively, and the active power output from the machine-side is shown in Figure 10F.The coordinated control of the machine-grid side is activated when the voltage drops to control the active output of the machine-side and to support the grid voltage recovery.The reactive power output is kept within a safe range to ensure the system's safe and reliable operation, which fully ensures that the FESS realizes the LVRT during the fault period.

| Asymmetric fall
Figure 11A shows the voltage waveform of the A-phase dip that occurs at 0.5 s, it can be seen that the 20% fault duration of the A-phase voltage dip on the grid is 0.625 s, and it returns to the rated value at 1.125 s.From Figure 11B, it can be seen that when an asymmetrical fault occurs on the grid side, the grid-side AC briefly rises to 684.629A at the moment of the drop, but does not show large fluctuations, and the three-phase current tends to a steady state after 51 ms. Figure 11C shows the DC bus voltage waveform, in the asymmetrical drop control strategy analysis, due to the influence of the negative-sequence component will cause the DC-side active imbalance of the 2× frequency fluctuations, the DC bus voltage fluctuation range is only 3.2% of the steady-state value when the machine-grid side coordinated control technique is applied, achieving the goal of eliminating the voltage 2× frequency fluctuations.The grid-side active power waveform is shown in Figure 11D, whereas the grid-side reactive power waveform is shown in Figure 11E.In the case of a grid fault, the FESS must inject positive-sequence reactive current into the grid to facilitate voltage restoration.Striking the appropriate equilibrium between the support for reactive power and the active output is required since doing so decreases the active power output and consumes converter capacity.The FESS is rectified when the voltage dips within 0.5-1.125 s, according to the flywheel energy storage motor output power waveform depicted in Figure 11F.As a result of this, to keep the voltage across the DC bus stable, the active power output from the machine-side must be reduced.

| Comparative analysis with conventional controllers
The grid-side reactive power waveforms of the two control modes in the symmetrical drop case are shown in Figure 12, and the reactive power under MPCC control is faster than that under PI control in terms of both response speed and withdrawal speed.From the local zoomed-in graph of the reactive power withdrawal speed, it can be seen that the regulation time under PI control is 90 ms, the regulation time under MPCC control is 53 ms, which improves the withdrawal speed by 59%, and the overshooting amount is slightly reduced compared with that under PI control.The grid-side reactive power waveforms of the two control modes for a 20% drop in grid voltage phase A are shown in Figure 13, and it can be clearly seen from the locally enlarged diagrams of the reactive power withdrawal speeds that the regulation time under PI control is 50 ms and that under MPCC control is 25 ms, which is a 50% improvement in the withdrawal speeds compared with the former.
The total harmonic distortion (THD) histograms of the current under PI control of the grid-side converter during the symmetrical drop and the current under MPCC control of the grid-side converter during the symmetrical drop are displayed in Figure 14A,B, respectively.The analysis focuses on the A-phase current among the three-phase currents during the 0.75 s grid-side fault.The MPCC current inner loop introduced in the grid-side converter control scheme significantly reduces the harmonic content of the current compared with the traditional PI control current, with the fundamental frequency amplitude decreasing from 559.3 to 555 A, and the harmonic content decreasing from the original 0.5% to 0.14%.The current THD under PI control for the grid-side converter during the asymmetrical drop is shown in Figure 15A, and the current THD under MPCC control for the grid-side converter during the asymmetrical drop is shown in Figure 15B.From these figures, it is clear that the MPCC control significantly reduces the current's harmonic content when compared with the traditional PI control, with the harmonic content falling from 0.72% to 0.16% and the fundamental frequency amplitude increasing from 562 to 562.2 A. It is determined that the system's power quality can be enhanced and the harmonic content created when the grid collapses may be considerably suppressed by the existing inner-loop control employing MPCC.

| CONCLUSIONS
The realization of LVRT by the flywheel energy storage grid-connected system will be significantly impacted by issues with DC bus power imbalance and considerable voltage fluctuation while encountering grid voltage dips, it has been discovered.As a result, a machine-grid side coordinated control method based on MPCC is proposed.This method can quickly provide reactive current support under the LVRT criterion during grid voltage dips, as well as track the output current of the grid-side converter by substituting the MPCC current inner loop for the PI current inner loop.The MPCC can more flexibly adapt the system response during LVRT, lowering the danger of overcurrent and overvoltage, according to simulation data.MPCC improves the system's low-voltage features, including resilience and rapid reaction times.The coordinated control strategy based on MPCC proposed in this paper realizes the stabilization of DC bus voltage very quickly, and it can pass through the voltage dips more safely reliably, and smoothly, which guarantees the grid-connected longtime and reliable operation of the FESS, and proves the effectiveness of the control scheme, which is of great significance for the improvement of the LVRT capability of the FESS.At present, due to the lack of experimental conditions, the improved LVRT control strategy for FESS proposed in this paper has not been experimentally verified, and it is hoped that the experimental conditions will be available in the future to improve this part of the content.In the next task, our research team will continue to improve the proposed control strategy, which includes the parameter identification of the motor itself in the flywheel operation and the optimization of the machine-side converter control.These subsequent studies will be presented in other articles.

NOMENCLATURE
Block diagram of grid-side converter control during grid voltage faults.

Number of pole pairs p n 4
Abbreviations: DC, direct current; RMS, root mean square.

F I G U R E 13 FF I G U R E 15
Comparison of reactive power waveforms under asymmetric dips.MPCC, model predictive current control; PI, proportional-integral.I G U R E 14 Comparison of harmonic content under symmetrical drop.(A) Current harmonic content under PI control; (B) Current harmonic content under MPCC control.MPCC, model predictive current control; PI, proportional-integral; THD, total harmonic distortion.Comparison of harmonic content under asymmetrical drop.(A) Current harmonic content under PI control; (B) Current harmonic content under MPCC control.MPCC, model predictive current control; PI, proportional-integral; THD, total harmonic distortion. )).
Block diagram of MPCC-based grid-side converter control under symmetrical faults.MPCC, model predictive current control.
10 Simulated waveforms of LVRT for FESS based on MPCC under grid voltage symmetrical faults.(A) Grid voltage waveform, (B) grid current waveform, (C) DC bus voltage waveform, (D) grid-side active power waveform, (E) grid-side reactive power waveform, and (F) machine-side active power waveform.DC, direct current; FESS, flywheel energy storage system; LVRT, low-voltage ride-through; MPCC, model predictive current control.