Particle swarm fractional order power control method and system for flywheel energy storage system

Abstract

The application relates to the technical field of flywheel energy storage control, in particular to a particle swarm fractional order power control method and system of a flywheel energy storage system. λ The controller processes power tracking errors and continuously iteratively optimizes controller core parameters in combination with a particle swarm algorithm, can realize more accurate power tracking, meanwhile, feedforward decoupling control of the machine-side converter can eliminate the coupling interference of d-axis and q-axis currents, in cooperation with the stable DC bus voltage maintained by voltage-current double closed loop control of the grid-side converter, the smoothness of flywheel motor operation state adjustment and the stability of system grid-connected operation can be improved, the impact on the power grid during the grid-connected process is reduced, and the control process of the circulation iteration can make the system adaptively adjust the control strategy, always maintain the optimal operation state, reduce the power loss, improve the overall operation efficiency of the system, and guarantee that the flywheel energy storage system stably and efficiently completes power scheduling and grid-connected operation.

Description

Technical Field

[0001] This invention relates to the field of flywheel energy storage control technology, and in particular to a particle swarm fractional-order power control method and system for flywheel energy storage systems. Background Technology

[0002] Flywheel energy storage systems have been widely used in scenarios such as renewable energy grid integration and consumption, grid frequency and voltage regulation, user-side peak-valley arbitrage, and microgrid stability control due to their advantages such as fast response speed, high power density, long cycle life, and environmental friendliness. Their core topology generally adopts a back-to-back dual PWM converter architecture, which includes a generator-side converter and a grid-side converter. The generator-side converter is connected to the flywheel motor and is responsible for regulating the flywheel motor's operating state to achieve power charging and discharging. The grid-side converter is connected to the grid and is responsible for maintaining the DC bus voltage stability and achieving grid-connected interaction with the grid. The coordinated control of the two is the key to ensuring the overall performance of the flywheel energy storage system.

[0003] Currently, the power control of flywheel energy storage systems mainly adopts a closed-loop control architecture centered on traditional integer-order PI controllers. The generator-side power control often employs a dual-loop control logic of "power outer loop + current inner loop." The power outer loop receives the error between the preset power command and the actual power feedback value, outputting a current reference value through an integer-order PI controller. The current inner loop performs integer-order PI adjustment on the d / q-axis current error, supplemented by simple decoupling measures, ultimately outputting the generator-side voltage control quantity to drive the converter. Grid-side control generally adopts a "voltage-current dual-loop PI control mode," maintaining a stable DC bus voltage to provide a stable power environment for generator-side power control. This is also a mature technology for grid-connected control of power electronic converters. For PI controller parameter tuning, existing technologies mostly use traditional methods such as empirical trial-and-error and the Ziegler-Nichols method. A few schemes use a single optimization algorithm for local parameter tuning.

[0004] Although existing control schemes can achieve basic power control of flywheel energy storage systems, they still have many significant shortcomings due to the nonlinear and time-varying characteristics of flywheel energy storage systems, such as the rotational inertia of the flywheel motor and the switching nonlinearity of the converter. Furthermore, there are also disturbances on the grid side, such as voltage fluctuations and load disturbances. On the one hand, traditional integer-order PI controllers have fixed parameters, which can only achieve good control performance under specific operating conditions. Faced with the time-varying characteristics of flywheel systems and complex operating conditions such as dynamic power command tracking and load disturbances, they are prone to problems such as large power tracking errors, slow dynamic response, and high overshoot, failing to meet the requirements of high-precision power control. On the other hand, some research has attempted to use fractional-order PI controllers. λWhile controllers improve control performance, the numerical approximation methods for fractional-order integral operators are not yet perfect. Furthermore, the tuning of core parameters, including proportional coefficients, integral coefficients, and fractional-order integral orders, lacks efficient global optimization methods, relying heavily on experience or single algorithms, making it difficult to obtain optimal parameter combinations and thus failing to fully leverage the advantages of fractional-order controllers. In addition, permanent magnet synchronous motors, as the mainstream type of flywheel motors, exhibit natural coupling between their d / q-axis currents. Existing decoupling measures are mostly simplified compensations, failing to completely eliminate coupling interference, thereby affecting current tracking accuracy and ultimately reducing the reliability of power control. Simultaneously, existing solutions for optimizing power tracking accuracy on the generator side do not effectively coordinate with grid-side DC bus voltage stability control, easily leading to mutual constraints between power tracking and grid stability under complex operating conditions, further impacting overall system performance. In summary, existing power control methods for flywheel energy storage systems struggle to simultaneously meet the dual requirements of high-precision power tracking and system grid stability, necessitating a more efficient control method to address these technical issues. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a particle swarm optimization fractional power control method and system for flywheel energy storage systems, so as to solve the dual problems of grid connection stability and response speed of existing flywheel energy storage systems.

[0006] To achieve the above objectives, the present invention provides a particle swarm optimization fractional-order power control method for a flywheel energy storage system, comprising the following steps:

[0007] Step S1: Real-time acquisition of operating data of the flywheel energy storage system. The flywheel energy storage system is built based on back-to-back dual PWM converters. The dual PWM converters include a machine-side converter and a grid-side converter. The machine-side converter is connected to the flywheel motor, and the grid-side converter is connected to the power grid. The two achieve power transmission through the DC bus.

[0008] Step S2: Calculate the actual power feedback value based on the operating data, compare the preset power command with the actual power feedback value to obtain the power tracking error, and use a fractional-order PI... λ The controller calculates the power tracking error and outputs a q-axis current reference value.

[0009] Step S3: Set the d-axis current reference value to 0, compare the d-axis current reference value with the actual d-axis current, and compare the q-axis current reference value output in step S2 with the actual q-axis current to obtain the d-axis and q-axis current errors respectively. Introduce a feedforward decoupling term and combine it with integer-order PI regulation to adjust the d-axis and q-axis current errors, and output the d / q-axis voltage control quantity on the machine side.

[0010] Step S4: Preset DC bus voltage reference value, adopt voltage-current dual closed-loop PI control mode, adjust based on the error between the DC bus voltage reference value and the actual DC bus voltage value, combine grid voltage angle locking and coordinate transformation to generate drive signal, control grid-side converter operation to maintain DC bus voltage stability;

[0011] Step S5: With optimal power point tracking accuracy as the optimization objective, the fractional-order PI is optimized using a particle swarm optimization algorithm. λ The controller's core parameters are iteratively optimized to output the optimal parameter combination and update the PI. λ Controller;

[0012] Step S6: Repeat steps S1-S5. Under the stable DC bus voltage maintained in step S4, generate a drive signal based on the machine-side voltage control quantity to control the operation of the machine-side converter, adjust the operating status of the flywheel motor, and achieve accurate power tracking and stable grid-connected operation of the system.

[0013] Preferably, fractional PI λ The fractional integral order of the controller has a range of 0 < λ < 1, and the fractional PI mentioned in step S5... λ The core parameters of the controller include the proportional coefficient, the integral coefficient, and the fractional integral order.

[0014] Preferably, in step S5, the optimization objective for achieving optimal power tracking accuracy is to minimize the integral of the product of time and the absolute value of the power tracking error.

[0015] Preferably, the operating parameters of the particle swarm optimization algorithm are: a total number of particles of 30, a maximum number of iterations of 50, an inertia weight of 0.7, and a learning factor of 2.

[0016] Preferably, the feedforward decoupling term is constructed based on the motor's mechanical angular velocity, d / q-axis inductance, and d / q-axis actual current.

[0017] Preferably, in step S4, the generation of the drive signal by combining grid voltage angle locking and coordinate transformation includes:

[0018] The grid voltage angle is locked by a phase-locked loop as the coordinate transformation reference. Both the outer voltage loop and the inner current loop use integer-order PI controllers. After adjustment, the driving signal is generated by inverse dq coordinate transformation.

[0019] Preferably, the DC bus voltage reference value is preset based on the rated operating parameters of the flywheel energy storage system, the grid voltage level, and the converter design requirements.

[0020] The present invention also provides a particle swarm optimization fractional-order power control system for a flywheel energy storage system, comprising:

[0021] Hardware module: It consists of a back-to-back dual PWM converter, a flywheel motor, a data acquisition module and a grid connection module. The back-to-back dual PWM converter includes a machine-side converter and a grid-side converter. The machine-side converter is connected to the flywheel motor and the grid-side converter is connected to the grid. The two realize power transmission through the DC bus.

[0022] Control module: Stores a computer program, which, when executed by a processor, implements the aforementioned particle swarm fractional power control method.

[0023] The beneficial effects of this invention are:

[0024] The control method of this invention can effectively improve the operating performance of flywheel energy storage systems by collecting system operating data in real time and using fractional-order PI control. λ The controller processes power point tracking errors and continuously iterates and optimizes core controller parameters using a particle swarm optimization algorithm, enabling more accurate power point tracking and adapting to the power dispatching requirements of the power grid. Simultaneously, the feedforward decoupling control of the generator-side converter eliminates coupling interference between d-axis and q-axis currents. Combined with the voltage-current dual closed-loop control of the grid-side converter to maintain a stable DC bus voltage, this improves the smoothness of flywheel motor operation and the stability of grid-connected operation, reducing the impact on the power grid during grid connection. Furthermore, the iterative control process allows the system to adaptively adjust its control strategy, always maintaining optimal operating conditions, reducing energy loss, improving overall system efficiency, and ensuring the stable and efficient completion of power dispatching and grid-connected operation of the flywheel energy storage system. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a schematic flowchart of the power control method according to an embodiment of the present invention.

[0027] Figure 2 Fractional order in embodiments of the present invention Control structure block diagram;

[0028] Figure 3 This is a schematic diagram of the PSO parameter optimization process according to an embodiment of the present invention;

[0029] Figure 4 This is an embodiment of the invention based on the PSO algorithm. Control system block diagram;

[0030] Figure 5This is a simulation model diagram of the flywheel energy storage system according to an embodiment of the present invention;

[0031] Figure 6 This is a power control simulation diagram according to an embodiment of the present invention;

[0032] Figure 7 This is a simulation diagram of the speed control according to an embodiment of the present invention;

[0033] Figure 8 This is a charge / discharge PI power response curve diagram of an embodiment of the present invention;

[0034] Figure 9 This is a charge / discharge FOPI power response curve diagram of an embodiment of the present invention;

[0035] Figure 10 This is a graph showing the change in charging and discharging speed according to an embodiment of the present invention;

[0036] Figure 11 This is a diagram of the FOPI linear dynamic power response curve according to an embodiment of the present invention;

[0037] Figure 12 This is a PI linear dynamic power response curve diagram of an embodiment of the present invention;

[0038] Figure 13 This is a diagram of the FOPI sinusoidal dynamic power response curve according to an embodiment of the present invention;

[0039] Figure 14 This is a diagram of the PI sinusoidal dynamic power response curve according to an embodiment of the present invention;

[0040] Figure 15 This is a load disturbance FOPI power response curve diagram of an embodiment of the present invention;

[0041] Figure 16 This is a load disturbance PI power response curve diagram of an embodiment of the present invention;

[0042] Figure 17 This is a comparison chart of the power response of the particle swarm optimization parameters and conventional parameters in an embodiment of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0044] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0045] Example 1:

[0046] like Figures 1-5 As shown in the embodiments of this specification, a particle swarm fractional-order power control method for a flywheel energy storage system is provided. This method aims to solve the technical problems existing in the power control of existing flywheel energy storage systems, such as poor adaptability of integer-order PI controllers, low parameter tuning efficiency of fractional-order controllers, incomplete elimination of current coupling interference, and insufficient coordination between machine-side power control and grid-side grid connection stability. Ultimately, this method achieves accurate power tracking of the flywheel energy storage system and stable grid-connected operation.

[0047] The flywheel energy storage system addressed in this invention has a well-defined hardware structure. This system is built upon a back-to-back dual PWM converter architecture. The dual PWM converter comprises two core components: a machine-side converter and a grid-side converter. The machine-side converter is directly electrically connected to the flywheel motor, responsible for driving the motor's speed regulation and energy conversion. The grid-side converter connects to the public power grid via a grid connection module, undertaking the function of power exchange with the grid. Bidirectional power transmission between the machine-side and grid-side converters is achieved through a DC bus. The DC bus, as a core component for power buffering and transfer, directly affects the operating status of the entire system due to its voltage stability. Furthermore… The flywheel energy storage system is also equipped with a complete data acquisition module, including a current sensor (for acquiring the three-phase current and actual d / q axis current on the machine side and grid side), a voltage sensor (for acquiring the actual DC bus voltage, grid voltage, and machine side voltage), a speed / angular velocity sensor (for acquiring the mechanical angular velocity of the flywheel motor), and a phase detection module (for acquiring the grid voltage angle). It is also equipped with a control module based on a microprocessor or digital signal processor (DSP). The control module is connected to the power switching devices of the data acquisition module, the machine-side converter, and the grid-side converter to realize data reception, processing, and drive signal output.

[0048] The fractional-order power control method for particle swarm optimization includes the following steps:

[0049] Step S1: Real-time acquisition of operating data from the flywheel energy storage system, including the electromagnetic torque T of the flywheel motor. e Mechanical angular velocity m Actual value of DC bus voltage u dc , grid voltage angle θ and actual d / q axis current i d i q Key parameters, etc.

[0050] Step S2: Based on the electromagnetic torque T of the flywheel motor acquired in Step 1 e and mechanical angular velocity m According to formula P fb =T e ×ω m Calculate the actual power feedback value P fb Compare with the preset power command P ref and actual power feedback value P fb The power tracking error e is obtained. P =P ref -P fb e P Input fractional order PI λ The controller calculates and outputs the reference value of the q-axis current on the machine side. The PI λ The controller's transfer function is K p K is the proportionality coefficient. i The integral coefficient is... For fractional integrals of order (0 < <1), The fractional integral operator is used for numerical approximation via an Oustaloup recursive filter. Assume the frequency band to be approximated is... , The fractional integral operator is If we consider it as a continuous filter, then the transfer function of this continuous recursive filter is:

[0051]

[0052] In the formula, K represents the gain of the filter; N represents the order of the filter. and These are the zeros and poles of the filter.

[0053] , , .

[0054] In the formula , The fractional order is represented by N, which represents the order of the filter. N is typically an integer between 2 and 5. and These are the upper and lower limits of the fitted frequency, respectively. In this method, the fractional order... Control structure block diagram as follows Figure 2 As shown.

[0055] Step S3: Set the reference value for the machine-side d-axis current. =0, achieving maximum torque-to-current ratio control; compare respectively Actual d-axis current on the machine side The output of step S2 Actual q-axis current on the machine side The d-axis current error e is obtained. d = - q-axis current error e q = - To eliminate coupling interference between the d-axis and q-axis currents, a feedforward decoupling term is introduced, where the d-axis decoupling term F1 is... The q-axis decoupling term F2 is In the formula, ω is the electric angular velocity of the motor, and L d L q These are the d / q axis inductances, ψ f The flux linkage is a permanent magnet. The d / q axis current error and the corresponding feedforward decoupling term are input together into an integer-order PI regulator, which outputs the d / q axis voltage control quantity u on the machine side. d ∗ u q ∗ The adjustment formula is

[0056]

[0057] Among them, K pd K id K represents the proportional and integral coefficients of the inner loop of the d-axis current. pq K iq The ratio and integral coefficient of the inner loop of the q-axis current.

[0058] Step S4: Preset DC bus voltage reference value ,contrast Compared with the actual value of DC bus voltage collected in step S1 Calculate the voltage error e dc = - , will e dcInput an integer-order PI controller, output grid-side q-axis current reference value. , K pdc K is the voltage outer loop proportionality coefficient. idc This represents the voltage outer loop integral coefficient. Set the grid-side d-axis current reference value. Achieving a power factor of 0, unity power factor control is achieved. Combined with the grid voltage angle θ locked in step S1, the actual three-phase currents on the grid side are transformed using the abc / dq coordinate system to obtain the actual current i in the dq rotating coordinate system. dg i qg Calculate the d-axis current error e respectively. dg = -i dg e qg = - i qg The two current errors are input into an integer-order PI controller, which outputs a dq-axis voltage reference vector. , The voltage signal is converted into a three-phase stationary coordinate system through inverse dq / abc coordinate transformation. It is then input into the SVPWM module to generate PWM pulses, which control the switching on and off of the IGBTs in the grid-side converter to maintain the stability of the DC bus voltage.

[0059] Step S5: Optimize power point tracking accuracy as the objective, specifically by minimizing the integral of the product of time and the absolute value of power point tracking error. The objective function is:

[0060] ;

[0061] Fractional PI algorithms were applied using particle swarm optimization. λ The core parameters of the controller are iteratively optimized, and the algorithm's operating parameters are set as follows: total number of particles 30, maximum number of iterations 50, and inertia weight. The learning factors are c1=2 and c2=2. The iterative formula is:

[0062]

[0063]

[0064] Where x represents the particle's position, v represents the particle's velocity, and r1 and r2 represent generating two independent random numbers in the range [0, 1]. P represents the inertia weight, c1 and c2 represent the acceleration factor, also known as the learning factor. t G represents the best position the particle has found so far. t This represents the optimal position found so far in the entire particle swarm. The optimal parameter combination is output through iterative calculation, and the fractional-order PI is updated. λThe controller must be adapted to the system's operating characteristics. The particle swarm optimization process is as follows: Figure 3 As shown. Based on the PSO algorithm Control system block diagram as follows Figure 4 As shown.

[0065] Step S6: Repeat steps S1 to S5. Under the stable DC bus voltage maintained in step S4, input the machine-side d / q axis voltage control quantity output in step S3 into the SVPWM module to generate a PWM drive signal to control the on / off state of the machine-side converter IGBT, thereby adjusting the speed, torque, and other operating states of the flywheel motor. Through the coordinated control of all the above steps, the flywheel energy storage system achieves the technical effects of precise power tracking and stable grid-connected operation, adapting to various operating conditions such as constant power charging and discharging, dynamic power command tracking, and load disturbances.

[0066] Example 2:

[0067] This embodiment uses the Matlab / Simulink platform to simulate and verify the method of Embodiment 1.

[0068] MATLAB / Simulink is an engineering simulation platform launched by MathWorks that integrates modeling, simulation, analysis and code generation. Its core is used for the visualization modeling and performance verification of dynamic systems (such as motor control, power electronics, automation, etc.).

[0069] The flywheel energy storage system, the grid-side control strategy model, the fractional-order controller model, and the particle swarm optimization algorithm in this embodiment all rely on this platform. By dragging modules such as motors, controllers, and converters, a dual closed-loop control model is built. Combined with parameter tuning and simulation analysis, the effectiveness of the control strategy is verified.

[0070] Establish a comprehensive simulation model of the flywheel energy storage system in MATLAB / Simulink, such as Figure 5 As shown.

[0071] The model strictly follows the typical structure of a flywheel energy storage system, and is mainly composed of three parts: the generator-side converter control unit, the grid-side converter control unit, and the flywheel body and grid unit, forming a complete simulation test model that can operate in a closed loop.

[0072] When the system receives a negative power command, the grid-side converter acts as a rectifier, absorbing electrical energy from the grid to supply power to the DC bus; the generator-side converter acts as an inverter, driving the flywheel motor to accelerate and converting electrical energy into the kinetic energy of the flywheel for storage. When the system receives a positive power command, the flywheel motor operates as a generator, and the generator-side converter converts the mechanical energy released by the flywheel's deceleration into electrical energy, which is then supplied to the DC bus; the grid-side converter inverts the DC power into AC power that is in phase and frequency with the grid, feeding it back into the grid. The core control task of the model is to ensure the efficiency, speed, and stability of the above energy conversion process, with the generator-side converter responsible for accurate power tracking and the grid-side converter responsible for stabilizing the DC bus voltage.

[0073] The design of a fractional-order controller first requires the implementation of a fractional-order differential operator simulation module. This module uses the Oustaloup filter approximation method and Simulink to write the initialization function of the encapsulated module based on the filter transfer function.

[0074] Based on the classic PSO algorithm, the simulation of its optimized fractional-order PI parameter tuning control algorithm is programmed using the m-language of Matlab software. The core logic of the simulation lies in establishing a closed-loop interaction between the algorithm and the control system. First, the optimization objective is defined, with minimizing the ITAE performance index as the criterion. The algorithm then searches for the optimal fractional-order PI parameter tuning control. Controller parameter combination (K) p K i , To ensure the effectiveness and rationality of the search, the physical constraints of each parameter must be set in advance to avoid the parameters exceeding the actual feasible range of the project.

[0075] Given a total number of particles N=30, a maximum number of iterations M=50, an inertia weight ω=0.7, and learning factors c1=2 and c2=2, write a Matlab program based on the steps of the particle swarm optimization algorithm to implement the fractional-order tuning of the particle swarm optimization algorithm. The controller parameters. The ITAE index is obtained by integrating the product of time and the absolute value of error.

[0076] A simulation model of the flywheel energy storage system was built in Matlab / Simulink. A three-phase motor was selected, and the motor parameters are shown in Table 1 below.

[0077] Table 1 Motor Parameter Table

[0078]

[0079] To clearly reveal the performance differences and engineering applicability of power control and speed control in flywheel energy storage systems, this embodiment designs a set of comparative simulation experiments. Under the same system parameters, the experiment employs both power control and speed control strategies to achieve similar final energy storage states, and conducts a systematic evaluation by comparing their dynamic processes and system responses.

[0080] Machine-side outer loop PI controller parameter K p K is 2.3. i The value is 33, and the inner current loop K is... p It is 48.5, K i The value is 2226; the outer loop PI controller parameter K of the grid-side voltage is... p For 10, K i The value is 20, and the inner current loop K is... p For 30, K i It is 20.

[0081] First, speed outer-loop control is used, with the given speed set based on engineering experience to achieve a peak flywheel power absorption of 20kW. Then, power control is used, with the given power set at 20kW. All conditions except the outer loop control are the same for both methods. Simulation results are as follows: Figure 6 As shown in Figure 7. (Through) Figure 6 Figure 7 shows that using the power outer loop control, the actual power reached the given 20kW at approximately 0.58s; while using the speed loop, the peak 20kW was reached at approximately 0.586s. The power loop directly controls the target quantity (power), which is direct and precise; the speed loop uses indirect control, which is indirect and crude, requiring changes in speed to affect the power, thus limiting the dynamic response speed.

[0082] This comparison clearly reveals that, at the most basic PI controller level, power control strategies have a structural advantage in response speed for grid-connected flywheel energy storage applications, providing a sound theoretical basis for this study. While speed control can also achieve instantaneous power, its difficulty in controlling power and slow response are drawbacks for grid connection. Based on engineering experience, the integer-order generator-side power outer-loop PI controller parameter K is set. p K is 2.3. i The value is 33, and the inner current loop K is... p It is 48.5, K i The value is 2226; the outer loop PI controller parameter K of the grid-side voltage is... p For 10, K i The value is 20, and the inner current loop K is... p For 30, K i The value is 20. The parameter K of the fractional-order machine-side power PI controller is... p K is 0.1 i The value is 1, and λ is 0.69; the network-side parameters are the same as above.

[0083] The power command is set to step to 20kW (charging state) at t=0s and step to -20kW (discharging state) at t=0.7s. The simulation time is set to 1s. The power response curve on the machine side is as follows: Figure 8 , Figure 9 As shown.

[0084] As shown by the power response curves, the FOPI power response curve rapidly approaches 20kW after the t=0s command is triggered, reaching 20kW in approximately 0.03~0.1s with no significant lag, exhibiting fast dynamic response and a smooth transition process. In contrast, the PI curve shows a lag of approximately 0.15~0.2s, and only reaches 20kW in 0.5~0.6s, indicating a significantly slower charging response speed compared to FOPI.

[0085] The FOPI controller introduces an integral order λ, resulting in a smoother transition between proportional and integral action. Compared to the fixed order of PI controllers, FOPI controllers can more precisely balance the dynamic response and stability of the system by adjusting λ. FOPI controllers exhibit a stronger proportional action in the initial stage of response, thereby quickly suppressing errors and accelerating the response speed; while PI controllers, due to the "inertia" of integral action, have a slower response in the initial stage and are prone to hysteresis.

[0086] The speed changes of the two control strategies are as follows: Figure 10 As shown.

[0087] FOPI control achieved a speed of 19290 r / min at the end of a 0.7s charging cycle, while PI control only reached 15080 r / min. Simulation results show that, under the same constant power charging command and charging duration, the flywheel system based on FOPI control achieves a significantly higher final speed than the traditional PI control. This phenomenon demonstrates the advantage of fractional-order control strategy in energy conversion efficiency. Traditional PI controllers, due to overshoot and oscillations in their dynamic response, result in an average effective output power lower than the command value, with some energy being consumed during dynamic adjustment. In contrast, the fractional-order controller, with its smooth, overshoot-free dynamic characteristics, achieves precise tracking of the power command, ensuring that more energy is efficiently stored in the flywheel per unit time, thus resulting in a higher speed increase.

[0088] The simulation results above verify that the FOPI controller achieves a synergistic effect of "strong proportional + weak integral" through the integral order λ (value 0~1). The proportional term rapidly amplifies the error, and the driving power responds quickly. At the same time, the non-integer characteristic of λ avoids the defect of "slow accumulation" of the integral term of integer order PI (λ=1), and reduces response lag.

[0089] The following is a simulation of dynamic power command tracking.

[0090] (1) Set the power command to increase linearly at a slope of 25kW at t=0s and to remain constant at 20kW at t=0.8s.

[0091] After t=1s, it decreases linearly with a slope of -75kW. The simulation time is set to 1.5s. The mathematical expression is as follows.

[0092]

[0093] The machine-side power response curve is as follows Figure 11 , Figure 12 As shown.

[0094] The core requirement of the linear tracking stage is to keep up with the linearly changing instructions in real time and minimize the tracking error. The error in this stage directly reflects the controller's ability to respond to "continuous dynamic instructions".

[0095] Figure 11 After t=0.1s, the actual power curve and the power command curve (slope 25kW) almost completely overlap, with no visible lag. Figure 12 The actual power curve almost completely overlaps with the command curve after about 0.4~0.5s; before t=0.4s, it lags completely behind the command curve. This fully verifies that the FOPI control strategy is superior to PI control. After t=1s, there is no significant difference between the two phases, which may be because the nonlinear characteristics of the system or the parameter settings of the controller during the discharge process make the performance of the two controllers similar.

[0096] The fractional-order characteristic of the FOPI controller makes it more adaptable when tracking continuously changing signals. In the linear growth phase, the system needs a continuous proportional action to track the slope change. The configuration of λ=0.69 makes it exhibit stronger proportional characteristics in the early stage and can respond quickly to slope changes. The fixed integral order λ=1 results in slow integral accumulation, which cannot keep up with the rate of change of the linear command in time.

[0097] (2) Set the power command to a pure wave command with ±4kW and 10Hz sinusoidal fluctuation as the base at t=0s and -20kW as the base at t=0.7s. Set the simulation time to 1s.

[0098] Mathematical expression:

[0099]

[0100] The machine-side power response curve is as follows Figure 13 , Figure 14The core verification controller's ability to track high-frequency periodic fluctuations is demonstrated by a 10Hz sine wave with a period of 0.1s, which places extremely high demands on the controller's dynamic response speed, phase synchronization, and fluctuation stability.

[0101] Figure 13 The fluctuation amplitude of the actual FOPI power is relatively fast and almost perfectly matches the command amplitude (±4kW). In contrast, the PI power does not track the command power well even after 0.7s. Furthermore, the graph shows that the FOPI power fluctuates around the actual power ±0.01kW, while the PI fluctuates around ±0.02kW; indicating that the FOPI curve is smoother than the PI curve.

[0102] The integral term of a PI converter has a "residual error accumulation" at high frequencies. When the command changes from a positive slope to a negative slope (such as from a rising segment to a falling segment), the "early accumulated amount" of the integral term cannot be quickly adjusted in the opposite direction, resulting in secondary oscillations of "overshoot and pullback" in the output. This oscillation intensifies as the command frequency increases, forming a superposition of "command fluctuation + secondary oscillation", which disrupts the stability of the power curve.

[0103] Verification using pure wave commands showed that, under the operating condition of "±4kW, 10Hz pure sinusoidal high-frequency wave", the fractional-order... The overall performance of the controller is superior to that of an integer-order PI controller. The "memory" and "non-locality" of the fractional integral term enable it to better understand and respond to periodically changing instructions, a unique advantage that integer-order controllers lack. This further validates the enormous potential of fractional-order control in improving the dynamic performance of flywheel energy storage systems.

[0104] The following is a load disturbance charging simulation:

[0105] Under constant power charging and discharging conditions, a load torque of 40 Nm is applied to the motor at t = 0.6 s. The simulation time is set to 1 s. The real-time power response is as follows. Figure 15 , Figure 16 As shown.

[0106] In the load disturbance charging simulation, the FOPI controller showed better disturbance rejection performance when a 40Nm load torque was suddenly applied at t=0.6s, with smaller power fluctuation amplitude and faster recovery speed, and the actual power could quickly return to the command value; while the IOPI controller showed larger power fluctuation and longer recovery time under load disturbance, and the system dynamic performance was significantly worse.

[0107] The fractional-order characteristic of the FOPI controller gives it better robustness and disturbance rejection capability. The "memory effect" of the fractional integral term can handle the dynamic process caused by load changes more smoothly. The optimized configuration of parameter λ=0.69 achieves a better balance between dynamic response and stability. On the other hand, the fixed order of the PI controller limits its flexibility in dealing with sudden disturbances. The rapid accumulation of the integral term causes the system to generate large overshoot and oscillations when the load changes, and the recovery process is slow.

[0108] The following is a system simulation based on the optimized controller parameters using particle swarm optimization:

[0109] The fractional order is determined using the particle swarm optimization algorithm. The controller obtains the power outer loop parameters, K. p =0.015, K i =0.86, =0.74, while other controller parameters remain unchanged. Figure 17 To compare the power response curve after parameter optimization under constant power charge and discharge conditions with the power response curve of engineering experience parameters.

[0110] Figure 17 Comparison of particle swarm optimization parameters (K) p =0.015, K i =0.86, =0.74) and engineering experience parameter (K) p =0.1, K i =1, =0.69) Power response performance under constant power charge and discharge conditions. The optimized power response curve is more stable during charge and discharge switching, and the overall response curve is also smoother. K p From 0.1 to 0.015, the proportional gain is significantly reduced, decreasing overshoot and oscillations; K i The integral coefficient is appropriately reduced from 1 to 0.86 to balance response speed and stability. The order of integration was increased from 0.69 to 0.74, enhancing the integral effect. This comparison demonstrates that optimizing parameters through particle swarm optimization can effectively improve system performance.

[0111] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0112] In the embodiments provided in this application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0113] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0114] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0115] The implementation of all or part of the processes in the methods of the above embodiments can also be accomplished by a computer program product. When the computer program product is run on a terminal device, the terminal device can implement the steps in the various method embodiments described above.

[0116] The embodiments described above are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A particle swarm optimization fractional-order power control method for a flywheel energy storage system, characterized in that, Includes the following steps: Step S1: Real-time acquisition of operating data of the flywheel energy storage system. The flywheel energy storage system is built based on back-to-back dual PWM converters. The dual PWM converters include a machine-side converter and a grid-side converter. The machine-side converter is connected to the flywheel motor, and the grid-side converter is connected to the power grid. The two achieve power transmission through the DC bus. Step S2, calculating an actual power feedback value based on the operation data, obtaining a power tracking error by comparing a preset power instruction with the actual power feedback value, and adopting a fractional order PI λ The controller performs operation on the power tracking error and outputs a q-axis current reference value. Step S3: Set the d-axis current reference value to 0, compare the d-axis current reference value with the actual d-axis current, and compare the q-axis current reference value output in step S2 with the actual q-axis current to obtain the d-axis and q-axis current errors respectively. Introduce a feedforward decoupling term and combine it with integer-order PI regulation to adjust the d-axis and q-axis current errors, and output the d / q-axis voltage control quantity on the machine side. Step S4: Preset DC bus voltage reference value, adopt voltage-current dual closed-loop PI control mode, adjust based on the error between the DC bus voltage reference value and the actual DC bus voltage value, combine grid voltage angle locking and coordinate transformation to generate drive signal, control grid-side converter operation to maintain DC bus voltage stability; Step S5: With optimal power point tracking accuracy as the optimization objective, the fractional-order PI is optimized using a particle swarm optimization algorithm. λ The controller's core parameters are iteratively optimized to output the optimal parameter combination and update the PI. λ Controller; Step S6: Repeat steps S1-S5. Under the stable DC bus voltage maintained in step S4, generate a drive signal based on the machine-side voltage control quantity to control the operation of the machine-side converter, adjust the operating status of the flywheel motor, and achieve accurate power tracking and stable grid-connected operation of the system.

2. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, The fractional order PI λ The fractional integral order of the controller has a range of 0 < λ < 1, and the fractional PI mentioned in step S5... λ The core parameters of the controller include the proportional coefficient, the integral coefficient, and the fractional integral order.

3. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, In step S5, the optimization objective for achieving optimal power tracking accuracy is to minimize the integral of the product of time and the absolute value of the power tracking error.

4. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, The operating parameters of the particle swarm optimization algorithm are: total number of particles 30, maximum number of iterations 50, inertia weight of 0.7, and learning factor of 2.

5. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, The feedforward decoupling term is constructed based on the motor's mechanical angular velocity, d / q-axis inductance, and actual d / q-axis current.

6. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, In step S4, the generation of the drive signal by combining grid voltage angle locking and coordinate transformation includes: The grid voltage angle is locked by a phase-locked loop as the coordinate transformation reference. Both the outer voltage loop and the inner current loop use integer-order PI controllers. After adjustment, the driving signal is generated by inverse dq coordinate transformation.

7. The particle swarm optimization fractional-order power control method for a flywheel energy storage system according to claim 1, characterized in that, The DC bus voltage reference value is preset based on the rated operating parameters of the flywheel energy storage system, the grid voltage level, and the converter design requirements.

8. A particle swarm optimization fractional-order power control system for a flywheel energy storage system, characterized in that, include: Hardware module: It consists of a back-to-back dual PWM converter, a flywheel motor, a data acquisition module and a grid connection module. The back-to-back dual PWM converter includes a machine-side converter and a grid-side converter. The machine-side converter is connected to the flywheel motor and the grid-side converter is connected to the grid. The two realize power transmission through the DC bus. Control module: stores a computer program, which, when executed by a processor, implements the particle swarm fractional power control method according to any one of claims 1-7.

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