Optimization Method of Electric Spring Circuit Based on Fractional Filter

Abstract

This invention discloses an optimization method for a power spring circuit based on a fractional-order filter, belonging to the field of power electronics and smart grid technology. The method includes sampling, constructing a power spring circuit based on a fractional-order filter using fractional-order inductors and capacitors, obtaining the optimal combination of α and β through a two-stage optimization method with the objectives of resonance suppression and minimizing output voltage ripple, and combining fuzzy fractional-order PI... λ D μ The control exhibits strong robustness under complex operating conditions. Simulations show that this method can avoid resonance spikes, reduce output voltage ripple, and demonstrate strong robustness. This invention effectively solves the key technical bottlenecks of electric spring systems, and is particularly suitable for high-requirement scenarios such as microgrids and precision instrument power supply, providing new technical support for smart grid construction.

Description

Technical Field

[0001] This invention relates to the fields of power electronics and smart grid technology, specifically to an optimization method for a power spring circuit based on a fractional-order filter. Background Technology

[0002] With the widespread and high-proportion integration of renewable energy generation into the grid, a mismatch between load demand and power generation may occur, leading to problems such as harmonic pollution, voltage fluctuations, and frequency flicker. Large power grids have a certain self-regulating capacity to withstand voltage fluctuations; however, small, isolated microgrids have weaker regulation capabilities, and voltage fluctuations can adversely affect electrical equipment, potentially damaging critical equipment in severe cases. To address these issues, Shu Yuen (Ron) Hui's team proposed the concept of an "Electric Spring (ES)."

[0003] Electric springs are a distributed voltage control technology. Their core idea is to maintain stable voltage at critical loads by adjusting non-critical loads in the power grid in response to fluctuations in intermittent renewable energy generation. This changes the traditional operating mode where power generation is constrained by electricity consumption, creating a new operating mode where power consumption automatically matches power generation.

[0004] Currently, the analysis and design of electric springs typically employ electric spring circuits based on integer-order LC filters, using integer-order controllers to stabilize critical load voltages. For example:

[0005] 1) Zhang Yun, Yang Gaoming, Zhang Guidong, et al., published an article entitled "Exploring the Evolution and Development of AC Electric Spring Topologies from the Perspective of Topological Function" in Volume 36, Issue 9 of Control Theory and Applications in 2019. This article summarizes existing AC electric spring topologies, explores the functional characteristics and shortcomings of electric springs with different topologies, and points out that all existing electric spring topologies use integer-order LC filters.

[0006] 2) Miao Degen, in his 2019 paper "Stability Analysis of LC Inverters and Research on Output Voltage Quality Improvement Strategies," proposed that the second-order resonance of integer-order LC filters affects system stability, and that nonlinear loads connected to LC inverters cause output voltage distortion problems.

[0007] 3) The paper “Chen, Z., Zhu, XQ, Hou, JT, Modeling and analysis of single-phase fractional-order Quasi-Z-Source Rectifier”, published at the 2nd International Power Electronics and Application Symposium in 2023, IEEE 2nd Int. Pow. Electron. App. Sym., 2023, points out that inductors and capacitors inherently possess fractional-order electrical characteristics. Fractional-order inductors (FOI) and fractional-order capacitors (FOC) can be either lossy components with an order less than 1 or active components with an order greater than 1. The order range extends to (0, 2), and the phase range covers the region of (-pi, pi).

[0008] In summary, the existing technology has the following problems:

[0009] 1) Traditional electric spring systems use integer-order LC filters, which have obvious resonance spikes.

[0010] 2) Traditional electric spring systems use integer-order LC filters. Connecting an LC filter to a nonlinear load will affect the output voltage quality. Summary of the Invention

[0011] The technical problem to be solved by this invention is that traditional electric spring systems using integer-order LC filters have obvious resonant spikes and the output voltage quality needs to be improved.

[0012] The technical solution of the present invention is as follows:

[0013] An optimization method for a power spring circuit based on a fractional-order filter is disclosed. The optimization method involves power system topologies including single-phase power springs, non-critical loads, critical loads, line impedance, and renewable energy microgrids. The single-phase power spring topology includes a DC-side power supply, a main inverter, and a fractional-order filter. The fractional filter includes a fractional-order filter inductor and a fractional-order filter capacitor. The optimization method optimizes the order α of the fractional-order filter inductor and the order β of the fractional-order filter capacitor. The specific steps are as follows:

[0014] Step 1, sample the following parameters: DC side voltage V dcThe impedance Z of non-critical loads NC The impedance Z of the critical load CL The voltage across the critical load is denoted as the critical load voltage V. S Line impedance Z g Renewable energy generation grid connection voltage V g The inductance value L of the fractional-order filter inductor α Fractional-order filter inductor current i Lα The capacitance value C of the fractional-order filter capacitor β The voltage across the fractional-order filter capacitor is denoted as the fractional-order filter capacitor voltage v. ES , where α is the order of the fractional-order filter inductor and satisfies 0 < α < 2, and β is the order of the fractional-order filter capacitor and satisfies 0 < β < 2;

[0015] Step 2: Based on fractional calculus theory and Kirchhoff's voltage and current laws, establish a fractional mathematical model of a single-phase electric spring.

[0016] Step 3: Based on the fractional-order mathematical model of a single-phase electric spring, perform two rounds of optimization on the order α of the fractional-order filter inductor and the order β of the fractional-order filter capacitor: the first round aims at resonance suppression, and the second round aims at the output ripple voltage Δv of the fractional-order electric spring. ES With minimization as the objective, the configuration range of the optimal order combination is ultimately obtained;

[0017] Step 4: Based on the optimal order combination, use fuzzy fractional PI. λ D μ Controlling and improving the adaptability of the power system under complex operating conditions is crucial for stabilizing the voltage of critical loads under such conditions.

[0018] Preferably, the expression for the fractional-order mathematical model of the single-phase electric spring described in step 2 is:

[0019]

[0020] In the formula, d α i Lα / dt α For the fractional-order filter inductor current i Lα Take the fractional differential form of the order of the fractional filter inductor α, d β v ES / dt β For fractional-order filter capacitor voltage v ES Take the fractional derivative of the order of the fractional-order filter capacitor β, where σ is the switching function of the power switch in the main inverter, when 0 < t < dT. s When σ = 1, when dT s <t<T sWhen σ = 0, T S t is the switching cycle, d is the running time, and d is the duty cycle.

[0021] Preferably, step 3 is implemented as follows:

[0022] Step 3.1: Based on fractional calculus theory, establish the frequency domain mathematical model of the fractional filter, whose expression is:

[0023]

[0024] In the formula, j represents the imaginary unit, satisfying j 2 =-1, ω is the angular frequency, This is the frequency domain function of a fractional-order filter;

[0025] Step 3.2: Based on the frequency domain mathematical model of the fractional filter, plot the phase frequency characteristic curve and amplitude frequency characteristic curve of the fractional filter under various order combinations with system frequency as the abscissa and phase and amplitude as the ordinate. Obtain the resonance peak that only exists when the order combination α+β=2. Perform the initial configuration of the order α of the fractional filter inductor and the order β of the fractional filter capacitor to make the order combination α+β≠2, so as to avoid the resonance peak.

[0026] Step 3.3: Based on the frequency domain mathematical model of the fractional-order filter, obtain the corner frequency ω of the fractional-order filter. t Its expression is:

[0027]

[0028] ω < ω t and ω>ω t The frequency ranges are defined as low frequency and high frequency bands, respectively. The asymptote attenuation slope of the logarithmic amplitude-frequency characteristic in the low frequency band varies from (0 to -20αdB / deg), and the asymptote attenuation slope of the logarithmic amplitude-frequency characteristic in the high frequency band varies from (0 to -20(α+β)dB / deg). The higher the fractional order, the greater the asymptote attenuation slope, and the stronger the filter's ability to attenuate harmonics. However, it may also introduce additional phase delay. Taking into account the harmonic attenuation capability, phase delay, and avoidance of resonance spikes of the fractional filter, the order combination configuration range for the first round of optimization is determined.

[0029] Step 3.4: Perform Laplace transform and inverse Laplace transform on the fractional-order mathematical model of the single-phase electric spring established in Step 2 to calculate the output ripple voltage Δv of the fractional-order electric spring. ES The formula for its calculation is:

[0030]

[0031] In the formula, D k Let Γ(.) be the duty cycle of the k-th switching cycle, and let Γ(.) be the Gamma function.

[0032] Step 3.5, output ripple voltage Δv using a fractional-order electric spring. ES With minimization as the optimization objective, a particle swarm optimization-based program that MATLAB can recognize is used to calculate the configuration range of the first round of optimization order combinations to obtain the configuration range of the optimal order combination.

[0033] Preferably, step 4 is implemented as follows:

[0034] Step 4.1: Design the optimal fractional PI based on the numerical optimization algorithm. λ D μ Controller parameters, where fractional-order PI λ D μ controller function G v The expression for (s) is:

[0035] G v (s)=K p +K i s -λ +K d s μ

[0036] In the formula, K p K is the proportionality coefficient. i K is the integral coefficient. d s is the differential coefficient; -λ For fractional integral operators, s μ For fractional differential operators, λ is the order of integration, and μ is the order of differentiation;

[0037] Step 4.2, the optimal fractional order PI obtained in step 4.1 is... λ D μ Controller parameters as fuzzy fractional-order PI λ D μ The initial value of the controller, combined with the S-function established based on the fuzzy inference rule table, realizes the fuzzy fractional-order pI. λ D μ Control measures are implemented to stabilize critical load voltages under complex operating conditions.

[0038] Preferably, the input terminal of the main inverter is connected in parallel with the DC power supply, the positive terminal of the main inverter output is connected in series with the fractional-order filter inductor, the other end of the fractional-order filter inductor is connected to the positive terminal of the fractional-order filter capacitor, the positive terminal of the critical load, and the line impedance, and the other end of the line impedance is connected to the positive terminal of the renewable energy microgrid; the negative terminal of the main inverter output is connected to the negative terminal of the fractional-order filter capacitor and the positive terminal of the non-critical load, and the negative terminal of the non-critical load is connected to the negative terminal of the critical load and the negative terminal of the renewable energy microgrid.

[0039] Preferably, the non-critical load refers to a dissipative load, and the critical load refers to a load that requires precise voltage at the opposite end.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] 1. Traditional electric spring systems use integer-order LC filters, which suffer from significant resonance spikes. This invention employs a fractional-order filter, adjusting the order α and β to change the filter's frequency response characteristics, fundamentally avoiding resonance problems and improving system robustness.

[0042] 2. This invention focuses on minimizing output voltage ripple by meticulously designing circuit parameters, thereby improving output voltage quality and ensuring the high performance of the power spring in low-ripple scenarios.

[0043] 3. This invention combines fuzzy fractional order pI λ D μ The controller is highly adaptable to complex operating conditions;

[0044] 4. This method is applicable to scenarios with strict voltage quality requirements, such as new energy microgrids and power supply for precision instruments, and fills the technical gap in high-frequency resonance and ripple suppression of traditional electric springs. Attached Figure Description

[0045] Figure 1 This is a main circuit diagram of the single-phase electric spring with fractional-order characteristics used in this invention.

[0046] Figure 2 Fractional filters under different order combinations The Bode plot.

[0047] Figure 3 For fuzzy fractional order PI λ D μ Adaptive control structure diagram.

[0048] Figure 4 The equivalent circuit model structure diagram is shown for a 0.8th order fractional inductor and a fractional capacitor.

[0049] Figure 5The equivalent circuit model structure diagram is shown for a 1.2 order fractional inductor and a fractional capacitor.

[0050] Figure 6 The simulation outputs key load voltage waveforms for electric spring systems under different order combinations.

[0051] Figure 7 The simulation output of the key load voltage RMS trend chart is provided for the electric spring system under different order combinations.

[0052] Figure 8 Simulate the output of electric spring voltage ripple for electric spring systems under different order combinations.

[0053] Figure 9 This simulates the output grid voltage waveform when the grid voltage changes abruptly.

[0054] Figure 10 The simulation outputs the key load voltage waveform when the grid voltage changes abruptly.

[0055] Figure 11 This is a trend chart of the effective value of the key load voltage during a sudden change in grid voltage.

[0056] Figure 12 The simulation outputs the key load voltage waveform when the grid impedance changes.

[0057] Figure 13 This is a trend chart of the RMS value of the key load voltage in the simulation output when the grid impedance changes. Detailed Implementation

[0058] The technical solution of the present invention will now be clearly and completely described in conjunction with the accompanying drawings.

[0059] Figure 1 This is a main circuit diagram of the single-phase electric spring with fractional-order characteristics used in this invention. Figure 1 As can be seen, the power system topology involved in the optimization method of the present invention includes single-phase power spring, non-critical load, critical load, line impedance and renewable energy microgrid. The topology of the single-phase power spring includes DC power supply, main inverter and fractional-order filter. The fractional filter includes fractional-order filter inductor and fractional-order filter capacitor.

[0060] In this embodiment, the input terminal of the main inverter is connected in parallel with the DC power supply, and the positive terminal of the main inverter output terminal is connected in series with the fractional-order filter inductor. The other end of the fractional-order filter inductor is connected to the positive terminal of the fractional-order filter capacitor, the positive terminal of the critical load, and the line impedance. The other end of the line impedance is connected to the positive terminal of the renewable energy microgrid. The negative terminal of the main inverter output terminal is connected to the negative terminal of the fractional-order filter capacitor and the positive terminal of the non-critical load. The negative terminal of the non-critical load is connected to the negative terminal of the critical load and the negative terminal of the renewable energy microgrid.

[0061] In this embodiment, the non-critical load refers to a dissipative load, and the critical load refers to a load that requires precise voltage at the opposite end.

[0062] The dissipative loads include electric kettles, electric stoves, lighting systems, etc. The critical loads include vital sign monitoring medical equipment, data centers, and monitoring and ventilation equipment in coal mines, etc.

[0063] In addition Figure 1 Up, v in V is the output port voltage of the inverter. NC The voltage across a non-critical load, i NC For the current flowing through non-critical loads, i CL For the current flowing through the critical load, i g This is the grid-connected current.

[0064] In this embodiment of the invention, V is taken. dc =480V, L α =3mH, C β =50uF.

[0065] The optimization method described in this invention optimizes the order α of the fractional-order filter inductor and the order β of the fractional-order filter capacitor. The specific steps are as follows:

[0066] Step 1, sample the following parameters: DC side voltage V dc The impedance Z of non-critical loads NC The impedance Z of the critical load CL The voltage across the critical load is denoted as the critical load voltage V. S Line impedance Z g Renewable energy generation grid connection voltage V g The inductance value L of the fractional-order filter inductor α Fractional-order filter inductor current i Lα The capacitance value C of the fractional-order filter capacitor β The voltage across the fractional-order filter capacitor is denoted as the fractional-order filter capacitor voltage v. ES , where α is the order of the fractional-order filter inductor and satisfies 0 < α < 2, and β is the order of the fractional-order filter capacitor and satisfies 0 < β < 2.

[0067] Step 2: Based on fractional calculus theory and Kirchhoff's voltage and current laws, establish a fractional mathematical model of a single-phase electric spring.

[0068] In this embodiment, the expression for the fractional-order mathematical model of the single-phase electric spring is:

[0069]

[0070] In the formula, d α i Lα / dt α For the fractional-order filter inductor current i Lα Take the fractional differential form of the order of the fractional filter inductor α, d β v ES / dt β For fractional-order filter capacitor voltage v ES Take the fractional derivative of the order of the fractional-order filter capacitor β, where σ is the switching function of the power switch in the main inverter, when 0 < t < dT. s When σ = 1, when dT s <t<T s When σ = 0, T S t is the switching cycle, d is the running time, and d is the duty cycle.

[0071] Step 3: Based on the fractional-order mathematical model of a single-phase electric spring, perform two rounds of optimization on the order α of the fractional-order filter inductor and the order β of the fractional-order filter capacitor: the first round aims at resonance suppression, and the second round aims at the output ripple voltage Δv of the fractional-order electric spring. ES With minimization as the objective, the configuration range of the optimal order combination is ultimately obtained.

[0072] In this embodiment, step 3 is implemented as follows:

[0073] Step 3.1: Based on fractional calculus theory, establish the frequency domain mathematical model of the fractional filter, whose expression is:

[0074]

[0075] In the formula, j represents the imaginary unit, satisfying j 2 =-1, ω is the angular frequency, This is the frequency domain function of a fractional-order filter;

[0076] Step 3.2: Based on the frequency domain mathematical model of the fractional filter, plot the phase frequency characteristic curve and amplitude frequency characteristic curve of the fractional filter under various order combinations with system frequency as the abscissa and phase and amplitude as the ordinate. Obtain the resonance peak that only exists when the order combination α+β=2. Perform the initial configuration of the order α of the fractional filter inductor and the order β of the fractional filter capacitor to make the order combination α+β≠2, so as to avoid the resonance peak.

[0077] Step 3.3: Based on the frequency domain mathematical model of the fractional-order filter, obtain the corner frequency ω of the fractional-order filter. t Its expression is:

[0078]

[0079] ω < ω t and ω>ω t The frequency ranges are defined as low-frequency band and high-frequency band, respectively. The asymptote attenuation slope of the logarithmic amplitude-frequency characteristic in the low-frequency band varies from (0 to -20αdB / deg), and the asymptote attenuation slope of the logarithmic amplitude-frequency characteristic in the high-frequency band varies from (0 to -20(α+β)dB / deg). The higher the fractional order, the greater the asymptote attenuation slope, and the stronger the filter's ability to attenuate harmonics. However, it may also introduce additional phase delay. Taking into account the harmonic attenuation capability, phase delay, and avoidance of resonance spikes of the fractional filter, the order combination configuration range for the first round of optimization is determined.

[0080] In this embodiment, the order combination configuration range for the first round of optimization is: α∈[0.8, 1.2], β∈[0.8, 1.2].

[0081] Step 3.4: Perform Laplace transform and inverse Laplace transform on the fractional-order mathematical model of the single-phase electric spring established in Step 2 to calculate the output ripple voltage Δv of the fractional-order electric spring. ES The formula for its calculation is:

[0082]

[0083] In the formula, D k Let Γ(.) be the duty cycle of the k-th switching cycle, and let Γ(.) be the Gamma function.

[0084] Step 3.5, output ripple voltage Δv using a fractional-order electric spring. ES With minimization as the optimization objective, a particle swarm optimization-based program that MATLAB can recognize is used to calculate the configuration range of the first round of optimization order combinations to obtain the configuration range of the optimal order combination.

[0085] In this embodiment, the optimal order combination is α = 1.2 and β = 1.2.

[0086] Step 4: Based on the optimal order combination, use fuzzy fractional PI. λ D μ Controlling and improving the adaptability of the power system under complex operating conditions is crucial for stabilizing the voltage of critical loads under such conditions.

[0087] In this embodiment, step 4 is implemented as follows:

[0088] Step 4.1: Design the optimal fractional PI based on the numerical optimization algorithm. λ D μ Controller parameters, where fractional-order PI λ D μ controller function G v The expression for (s) is:

[0089] G v (s)=K p +K i s -λ +K d s μ

[0090] In the formula, K p K is the proportionality coefficient. i K is the integral coefficient. d s is the differential coefficient; -λ For fractional integral operators, s μ λ is a fractional differential operator, where λ is the integral order and μ is the differential order.

[0091] In this embodiment, K p =0.0031, K i =18.0002, K d =0.0001, λ=0.9842, μ=1.0117.

[0092] Step 4.2, the optimal fractional order PI obtained in step 4.1 is... λ D μ Controller parameters as fuzzy fractional-order PI λ D μ The initial value of the controller, combined with the S-function established based on the fuzzy inference rule table, realizes a fuzzy fractional-order PI controller. λ Dμ control is used to stabilize critical load voltages under complex operating conditions.

[0093] Figure 2 Fractional filters under different order combinations The Bode plot is shown. This plot analyzes the resonance characteristics of the fractional-order filter, verifying that the traditional integer-order LC filter has a resonance spike problem. The filter curve constructed within the configuration range of α and β is smooth, suppressing the resonance spike.

[0094] Figure 3 For fuzzy fractional order PI λ D μ The adaptive control structure diagram first uses the optimal fractional-order PI... λ D μ Controller parameters as fuzzy fractional-order PI λ The initial value of the Dμ controller is obtained, and then the fuzzy inference system file "Fractional-order controller object" established according to the fuzzy inference rule table is read into the MATLAB environment. Then, the parameter variable K is completed using S-functions. p K i K d The updates of λ and μ ultimately achieve fuzzy fractional-order PI. λ D μ Adaptive control.

[0095] A 0.8th order fractional filter inductor L was constructed using standard RC passive synthesis based on the Oustaloup approximation principle. 0.8 and fractional-order filter capacitor C 0.8 The equivalent circuit model is as follows Figure 4 As shown, the 1.2 order fractional filter inductor L 1.2 and fractional-order filter capacitor C 1.2 The equivalent circuit model is as follows Figure 5 As shown, it includes equivalent resistances R0, R1, R2, R3, R4, R5, R6, and R7; equivalent inductances L1, L2, L3, L4, L5, L6, and L7; and equivalent capacitances C1, C2, C3, C4, C5, C6, and C7.

[0096] In this embodiment of the invention, dynamic response simulation was also performed to demonstrate the beneficial effects of the invention.

[0097] Take v g =250V, three fractional-order electric spring circuits with orders α and β of (1.2, 1.2), (1.2, 0.8), and (0.8, 0.8) respectively all employ fuzzy fractional-order PI. λ D μ Control, at this time, the system outputs the simulated waveform of the key load voltage as follows: Figure 6As shown, the effective value of the output key load voltage amplitude is as follows: Figure 7 As shown, the output power spring voltage ripple is as follows: Figure 8 As shown. From Figure 6-8 It can be seen that in the fuzzy fractional order PI λ D μ Under the control of the controller, the output critical load voltage is a sine wave under different order combinations, and the effective value of the output critical load voltage can be stabilized at the expected value of 220V. By comparing the output voltage ripple under different order combinations, it can be found that the output power spring voltage ripple is the smallest when the combination of order α and β is (1.2, 1.2).

[0098] Grid voltage sudden change scenario: During the period (0-0.15)s, v g =219.33sqrt(2), (0.15-0.3)s period v g =255.89sqrt(2), during the period (0.3-0.45)s, v g =231.52sqrt(2). Figure 9 The simulation outputs the grid voltage waveform when the grid voltage changes abruptly. Figure 10 The simulation outputs the key load voltage waveform when the grid voltage changes abruptly. Figure 11 This simulates the output of key load voltage amplitudes during sudden changes in grid voltage. Figure 9-11 It can be seen that using fuzzy fractional PI λ D μ Controlling electric springs can stabilize the voltage of critical loads in the event of sudden changes in grid voltage. Figure 12 The simulation outputs the key load voltage waveform when the grid impedance changes. Figure 13 This simulates the effective value of the key load voltage when the grid impedance changes. Figure 12-13 It can be seen that using fuzzy fractional PI λ D μ Controlling an electric spring can stabilize the voltage of critical loads under varying grid impedance conditions. In summary, a fuzzy fractional-order PI... λ D μ The control system exhibits better robustness and strong adaptability to external disturbances and complex operating conditions with varying parameters.

Claims

1. An optimization method for a power spring circuit based on a fractional-order filter, wherein the optimization method involves power system topologies including single-phase power springs, non-critical loads, critical loads, line impedance, and renewable energy microgrids, wherein, The topology of the single-phase electric spring includes a DC power supply, a main inverter, and a fractional-order filter, wherein the fractional-order filter includes a fractional-order filter inductor and a fractional-order filter capacitor; characterized in that the optimization method is to optimize the order of the fractional-order filter inductor. and the order of the fractional-order filter capacitor The optimization process involves the following steps: Step 1: Sample the following parameters: DC side voltage impedance of non-critical loads impedance of critical load The voltage across the critical load is recorded as the critical load voltage. Line impedance Voltage at the grid connection point of renewable energy generation The inductance value of the fractional-order filter inductor Fractional-order filter inductor current The capacitance value of the fractional-order filter capacitor The voltage across the fractional-order filter capacitor is denoted as the fractional-order filter capacitor voltage. ,in, Let the order of the fractional-order filter inductor be such that it satisfies the following conditions: , The order of the fractional-order filter capacitor and satisfying ; Step 2: Based on fractional calculus theory and Kirchhoff's voltage and current laws, establish a fractional mathematical model of a single-phase electric spring. In the formula, Fractional order filter inductor current Take the order as the fractional order of the filter inductor. The fractional differential form, Fractional order filter capacitor voltage The order is taken as the order of the fractional-order filter capacitor. The fractional differential form, The switching function of the power switching transistors in the main inverter, when At that time, take ,when At that time, take ,in, For the switching cycle, For runtime, Duty cycle; Step 3: Based on the fractional-order mathematical model of a single-phase electric spring, determine the order of the fractional-order filter inductor. and the order of the fractional-order filter capacitor Two rounds of optimization were performed: the first round aimed at suppressing resonance, and the second round aimed at reducing the output ripple voltage Δ of a fractional-order electric spring. With minimization as the objective, the configuration range of the optimal order combination is ultimately obtained; The implementation process of step 3 is as follows: Step 3.1: Based on fractional calculus theory, establish the frequency domain mathematical model of the fractional filter, whose expression is: In the formula, Represents the imaginary unit, satisfying , Angular frequency, This is the frequency domain function of a fractional-order filter; Step 3.2: Based on the frequency domain mathematical model of the fractional-order filter, plot the phase-frequency response curves and amplitude-frequency response curves of the fractional-order filter under various order combinations, with system frequency as the abscissa and phase and amplitude as the ordinates, to obtain the order combinations. + The resonant spike that only exists when =2; the order of the fractional-order filter inductor. and the order of the fractional-order filter capacitor The initial configuration makes the order combination + ≠2, to avoid resonance spikes; Step 3.3: Based on the frequency domain mathematical model of the fractional-order filter, obtain the corner frequency of the fractional-order filter. Its expression is: Will < and > The frequency ranges are defined as low-frequency band and high-frequency band, respectively; the range of the attenuation slope of the asymptote of the logarithmic amplitude-frequency characteristic in the low-frequency band is... The range of the asymptotic attenuation slope of the logarithmic amplitude-frequency characteristic in the high-frequency band is as follows: The higher the fractional order, the greater the asymptote attenuation slope, and the stronger the filter's ability to attenuate harmonics. However, it may also introduce additional phase delay. Taking into account the harmonic attenuation capability, phase delay, and avoidance of resonance spikes of the fractional filter, the range of order combination configurations for the first round of optimization is determined. Step 3.4, perform a fractional-order mathematical model of the single-phase electric spring established in Step 2. Laplace Transformation and Inverse Laplace The fractional-order electric spring output ripple voltage Δ is obtained by transformation and calculation. The formula for its calculation is: In the formula, D k For the first k Duty cycle of each switching cycle for Gamma function; Step 3.5, output ripple voltage Δ using a fractional-order electric spring. Minimization is the optimization objective, through MATLAB The program, which is capable of recognizing particle swarm optimization algorithms, calculates the configuration range of the first round of optimization order combination to obtain the configuration range of the optimal order combination. Step 4: Based on the optimal order combination, adopt fuzzy fractional order. PI λ D μ Control and improve the adaptability of the power system under complex operating conditions, so as to stabilize the voltage of critical loads under complex operating conditions; The implementation process of step 4 is as follows: Step 4.1: Design the optimal fractional order based on the numerical optimization algorithm. PI λ D μ Controller parameters, where fractional order PI λ D μ controller function G v ( s The expression for ) is: In the formula, This is the proportionality coefficient. The integral coefficient is... These are the differential coefficients; For fractional integral operators, For fractional differential operators, For the order of integration, The order of the differential; Step 4.2, the optimal fractional order obtained in Step 4.1 PI λ D μ Controller parameters as fuzzy fractional order PI λ D μ The initial value of the controller, combined with the value established based on the fuzzy inference rule table. S - Function to implement fuzzy fractional order PI λ D μ Control measures are implemented to stabilize critical load voltages under complex operating conditions.

2. The optimization method for a power spring circuit based on a fractional-order filter according to claim 1, characterized in that, The main inverter input is connected in parallel with a DC power supply. The positive terminal of the main inverter output is connected in series with a fractional-order filter inductor. The other end of the fractional-order filter inductor is connected to the positive terminal of a fractional-order filter capacitor, the positive terminal of a critical load, and the line impedance. The other end of the line impedance is connected to the positive terminal of the renewable energy microgrid. The negative terminal of the main inverter output is connected to the negative terminal of the fractional-order filter capacitor and the positive terminal of a non-critical load. The negative terminal of the non-critical load is connected to the negative terminal of the critical load and the negative terminal of the renewable energy microgrid.

3. The optimization method for a power spring circuit based on a fractional-order filter according to claim 1, characterized in that, The non-critical loads refer to dissipative loads, while the critical loads refer to loads that require precise voltage at the receiving end.

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