A control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system

Abstract

This invention discloses a control method for improving the damping of a fractional-order virtual synchronous machine (FSM) grid-connected system. This method introduces an angular frequency compensation stage based on angular frequency differential feedforward into the FSM control structure. By adjusting the filtering time constant and feedforward compensation coefficient of the first-order low-pass filter, the damping of the FSM grid-connected system and the dynamic response performance of active power and output frequency are optimized. This effectively suppresses the dynamic oscillations and overshoot of the active power and output frequency of the FSM grid-connected system under internal and external disturbances such as active power reference commands and grid frequency. Compared to a standard FSM, this method offers advantages such as higher control freedom, more flexible control parameter selection, and smaller output active power overshoot amplitude. It is applicable to the field of FSM grid-connected control in power electronics technology.

Description

Technical Field

[0001] This invention relates to the field of virtual synchronous machine control technology, and in particular to a control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system. It is applicable to the field of grid-connected control of fractional-order virtual synchronous machines in power electronics technology, as well as the field of microgrid integration into distribution networks containing such fractional-order virtual synchronous machines. Background Technology

[0002] Virtual Synchronous Generators (VSGs) introduce integer-order virtual inertia elements, providing voltage and virtual inertia support to the grid during grid-connected operation. However, this introduction transforms the system into a second-order oscillating system, causing dynamic oscillations and overshoot in the VSG's active power and output frequency under internal and external disturbances such as active power reference commands and grid frequency. Furthermore, Fractional Order VSGs (FOVSGs) introduce fractional-order virtual inertia into the fractional-order rotor motion equations, effectively suppressing the oscillations in the active power and output frequency of the VSG grid-connected system. However, there is still room for improvement in suppressing dynamic active power oscillations and output frequency response overshoot in FOVSG grid-connected systems.

[0003] To this end, various studies have been conducted, such as the article entitled "Small-signal modeling and characteristic comparative analysis for a single grid-connected grid-forming VSG with full-order and second-order", LIANG CF, Shi RL, JU CW, et al., *Engineering Science and Technology, an International Journal*, 2024, 59, 101879. This article proposes a VSG grid-connected control method based on angular frequency differential feedforward, which effectively reduces the dynamic oscillations of VSG grid-connected active power and output frequency under step disturbances such as active power reference command and grid frequency. However, it suffers from drawbacks such as limited increase in control freedom, increased system control order, and insufficient flexibility in parameter selection.

[0004] The article, titled "Frequency stability enhancement of an islanded microgrid: Afractional-order virtual synchronous generator," by LONG B, LI XY, RODRIGUEZ J, et al., *International Journal of Electrical Power and Energy Systems*, 2023, 147, 108896, describes a method to enhance the frequency stability of an islanded microgrid: a fractional-order virtual synchronous generator. This method replaces integer-order virtual inertia elements with fractional-order virtual inertia elements to form a FOVSG (Frequency Stability Enhancement Virtual Synchronous Generator). By adjusting the fractional-order virtual inertia parameters to balance the dynamic response and steady-state performance of the grid-connected active power, the control order of the system can be reduced, and the dynamic oscillation and overshoot of the grid-connected active power during disturbances can be mitigated. However, the FOVSG suffers from drawbacks such as having only one added degree of control freedom, insufficient flexibility in selecting control parameters, and large overshoot in the output frequency response.

[0005] The article, titled "Active Response Strategy for VSG Grid Connection Based on Active Fractional-Order Differential Correction," published in *Electric Power Automation Equipment*, Vol. 44, No. 2, 2024, pp. 204-210, proposes an optimized control strategy for the active response of VSG grid connection based on active fractional-order differential correction. This strategy achieves control performance comparable to FOVSG, effectively solving the problem of VSG grid connection struggling to maintain good dynamic and steady-state response performance under both active reference command and grid frequency disturbances. However, it also exhibits similar drawbacks to FOVSG.

[0006] The article, titled “Fractional-order virtual synchronous generator”, YU Y, GUAN YJ, KANG WF, et al., IEEE Transactions on Power Electronics, 2023, 38(6), 6874-6879, introduces a double fractional-order virtual inertia control loop into the rotor motion equation of the VSG. This can increase the system’s control degrees of freedom and the flexibility of control parameter selection, and effectively suppress the dynamic oscillation of the VSG’s grid-connected active power and output frequency under step disturbances such as active power reference command and grid frequency. However, its ability to suppress the overshoot of the VSG’s grid-connected active power and output frequency still needs to be further improved.

[0007] The article, titled "Improved Grid-Connected Control Strategy for VSG Based on Triple Fractional Inertia," published in *Electric Power Automation Equipment*, Vol. 45, No. 7, 2025, pp. 183-189+224, proposes an improved grid-connected control strategy for VSG based on triple fractional virtual inertia. This strategy can further increase the system's control degrees of freedom and the flexibility of control parameter selection, and can effectively suppress the dynamic oscillation and overshoot of VSG grid-connected active power and output frequency under step disturbances such as active power reference command and grid frequency. However, it has the disadvantages of high control structure complexity, parameter tuning dependence on experience, and large output frequency response overshoot.

[0008] As can be seen from the above, the existing technology can provide some technical support and research ideas for solving the dynamic oscillation and overshoot problems of VSG grid-connected active power and output frequency under disturbances such as active power reference command and grid frequency. However, there is still a lot of room for improvement in terms of control freedom, parameter selection flexibility and control effect. Specifically, the increased control freedom is limited, the parameter selection flexibility is insufficient, and the control effect of suppressing VSG grid-connected active power and output frequency overshoot still needs to be further improved. Summary of the Invention

[0009] To overcome the limitations of various technical solutions presented in the background art, this invention addresses the problem of dynamic oscillations and overshoot in the active power and output frequencies of fractional-order virtual synchronous machine (FSM) grid-connected systems under disturbances such as active power reference commands and grid frequencies. It provides a control method to improve the damping of FSM grid-connected systems. This method introduces an angular frequency compensation stage based on angular frequency differential feedforward into the FSM control structure. By adjusting the filtering time constant and feedforward compensation coefficient of the first-order low-pass filter, the damping and dynamic response performance of the FSM grid-connected system's active power and output frequencies are optimized. This effectively suppresses the dynamic oscillations and overshoot in the active power and output frequencies of the FSM grid-connected system under internal and external disturbances such as active power reference commands and grid frequencies. Compared to the FSM itself, this method offers advantages such as higher control freedom, more flexible control parameter selection, and smaller output active power overshoot amplitude.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0011] A control method for improving the damping of a grid-connected system using a fractional-order virtual synchronous machine includes the following steps:

[0012] Step 1, power calculation section: First, collect the three-phase grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and three-phase output voltage u a u b uc The dq component I of the three-phase grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through single-synchronous rotating coordinate transformation. d I q and the dq component U of the three-phase output voltage d U q Then, the grid-connected active power P of the fractional-order virtual synchronous machine is obtained through the power calculation equation. e And grid-connected reactive power Q e ;

[0013] Step 2, primary voltage regulation section, based on the grid-connected reactive power Q of the fractional-order virtual synchronous machine obtained in Step 1. e The reactive power reference instruction Q of the fractional-order virtual synchronous machine ref Primary voltage regulation coefficient k q The voltage reference command E0 is used to obtain the dq axis output voltage reference command E of the fractional-order virtual synchronizer through a voltage regulation equation. d E q ;

[0014] Step 3, Fractional Rotor Motion Equations: The active power reference command P of the fractional virtual synchronizer is used. ref Subtract the grid-connected active power P of the fractional-order virtual synchronous machine obtained in step 1. e The power difference ΔP is obtained. The power difference ΔP, the fractional integral coefficient μ, the virtual inertia coefficient J, the virtual damping coefficient D of the fractional-order virtual synchronizer, and the rated angular frequency ω0 are used to obtain the angular frequency deviation Δω of the fractional-order virtual synchronizer through the fractional-order rotor motion equation.

[0015] Step 4: Based on the angular frequency compensation part of the differential feedforward, according to the angular frequency deviation Δω of the fractional virtual synchronizer obtained in Step 3 and the filtering time constant τ of the first-order low-pass filter and the feedforward compensation coefficient k... a The angular frequency compensation amount Δω of the fractional-order virtual synchronizer is obtained through an angular frequency compensation stage based on angular frequency differential feedforward. a ;

[0016] Step 5: Output the phase angle generation part, and use the angular frequency compensation amount Δω of the fractional-order virtual synchronizer obtained in Step 4. a After adding the angular frequency deviation Δω of the fractional virtual synchronizer obtained in step 3, and adding the rated angular frequency ω0 of the fractional virtual synchronizer, the output angular frequency ω of the fractional virtual synchronizer is obtained. The output angular frequency ω is then integrated to obtain the output phase angle θ of the fractional virtual synchronizer.

[0017] Step 6: First, based on the fractional-order virtual synchronizer output phase angle θ obtained in Step 5, and the fractional-order virtual synchronizer dq-axis output voltage reference command E obtained in Step 2. dE q The three-phase bridge arm voltage modulation signal E of the fractional-order virtual synchronous machine is obtained by inverse transformation of the single-synchronous rotating coordinates. a E b E c Then, the three-phase bridge arm voltage modulation signal E a E b E c The SVPWM modulation stage generates the drive signals for the inverter bridge switching transistors of the fractional-order virtual synchronous machine.

[0018] Preferably, the grid-connected active power P in step 1 e The calculation formula used is:

[0019] P e =1.5(U d I d +U q I q ),

[0020] Grid-connected reactive power Q e The calculation formula used is:

[0021] Q e =1.5(U q I d -U d I q ).

[0022] Preferably, the output voltage reference command E in step 2 d The calculation formula used is:

[0023] E d =E0+(Q ref -Q e )k q ,

[0024] Output voltage reference command E q The calculation formula used is:

[0025] E q =0.

[0026] Preferably, the formula used to calculate the power difference ΔP in step 3 is:

[0027] ΔP=P ref - P e,

[0028] The formula for calculating the angular frequency deviation Δω is:

[0029]

[0030] In the formula, s is the Laplace operator.

[0031] Preferably, the angular frequency compensation amount Δω in step 4 a The calculation formula used is:

[0032]

[0033] In the formula, s is the Laplace operator.

[0034] Preferably, the formula used to calculate the output angular frequency ω of the fractional-order virtual synchronizer in step 5 is:

[0035] ω=Δω a +Δω+ω0,

[0036] The formula for calculating the output phase angle θ is:

[0037]

[0038] In the formula, s is the Laplace operator.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] This invention discloses a control method for improving the damping of a fractional-order virtual synchronous machine (FSM) grid-connected system. This method introduces an angular frequency compensation stage based on angular frequency differential feedforward into the FSM control structure. By adjusting the filtering time constant and feedforward compensation coefficient of the first-order low-pass filter, the damping of the FSM grid-connected system and the dynamic response performance of active power and output frequency are optimized. This effectively suppresses the dynamic oscillations and overshoot of the active power and output frequency of the FSM grid-connected system under internal and external disturbances such as active power reference commands and grid frequency. Compared to a standard FSM, this method offers advantages such as higher control freedom, more flexible control parameter selection, and smaller output active power overshoot amplitude. It is applicable to the field of FSM grid-connected control in power electronics technology. Attached Figure Description

[0041] Figure 1 This is a grid-connected control structure diagram of a fractional-order virtual synchronous machine according to an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram illustrating the calculation of angular frequency compensation based on angular frequency differential feedforward in an embodiment of the present invention.

[0043] Figure 3 This is an equivalent control structure diagram of the grid-connected active power closed loop of a fractional-order virtual synchronous machine according to an embodiment of the present invention.

[0044] Figure 4 This is a schematic diagram of coordinate transformation and modulation according to an embodiment of the present invention.

[0045] Figure 5This is a Bode plot comparing the virtual synchronizer before and after adopting this invention.

[0046] Figure 6 This is a comparison of the simulation waveforms of the virtual synchronizer before and after adopting this invention.

[0047] Figure 7 This is a comparison of experimental waveforms before and after the virtual synchronizer was implemented using this invention. Detailed Implementation

[0048] The following detailed embodiments will be further described in conjunction with the above-mentioned figures, as follows:

[0049] Please see Figure 1 The present invention proposes a control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system, comprising the following steps:

[0050] Step 1, power calculation section: First, collect the three-phase grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and three-phase output voltage u a u b u c The dq component I of the three-phase grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through single-synchronous rotating coordinate transformation. d I q and the dq component U of the three-phase output voltage d U q Then, the grid-connected active power P of the fractional-order virtual synchronous machine is obtained through the power calculation equation. e and grid-connected reactive power q e ;

[0051] Among them, grid-connected active power P e The calculation formula used is:

[0052] P e =1.5(U d I d +U q I q ),

[0053] Grid-connected reactive power Q e The calculation formula used is:

[0054] Q e =1.5(U q I d -U d I q ).

[0055] Step 2, primary voltage regulation section, based on the grid-connected reactive power Q of the fractional-order virtual synchronous machine obtained in Step 1.e The reactive power reference instruction Q of the fractional-order virtual synchronous machine ref Primary voltage regulation coefficient k q The voltage reference command E0 is used to obtain the dq axis output voltage reference command E of the fractional-order virtual synchronizer through a voltage regulation equation. d E q ;

[0056] Among them, the output voltage reference command E d The calculation formula used is:

[0057] E d =E0+(Q ref -Q e )k q ,

[0058] Output voltage reference command E q The calculation formula used is:

[0059] E q =0.

[0060] Step 3, Fractional Rotor Motion Equations: The active power reference command P of the fractional virtual synchronizer is used. ref Subtract the grid-connected active power P of the fractional-order virtual synchronous machine obtained in step 1. e The power difference ΔP is obtained. The power difference ΔP, the fractional integral coefficient μ, the virtual inertia coefficient J, the virtual damping coefficient D of the fractional-order virtual synchronizer, and the rated angular frequency ω0 are used to obtain the angular frequency deviation Δω of the fractional-order virtual synchronizer through the fractional-order rotor motion equation.

[0061] The formula used to calculate the power difference ΔP is as follows:

[0062] ΔP=P ref -P e ,

[0063] The formula for calculating the angular frequency deviation Δω is:

[0064]

[0065] In the formula, s is the Laplace operator.

[0066] Step 4, based on the angular frequency differential feedforward angular frequency compensation part, such as... Figure 2 As shown, based on the angular frequency deviation Δω of the fractional-order virtual synchronizer obtained in step 3 and the filtering time constant τ of the first-order low-pass filter and the feedforward compensation coefficient k a The angular frequency compensation amount Δω of the fractional-order virtual synchronizer is obtained through an angular frequency compensation stage based on angular frequency differential feedforward. a ;

[0067] Among them, the angular frequency compensation amount Δω a The calculation formula used is:

[0068]

[0069] In the formula, s is the Laplace operator.

[0070] Step 5: Output the phase angle generation part, and use the angular frequency compensation amount Δω of the fractional-order virtual synchronizer obtained in Step 4. a After adding the angular frequency deviation Δω of the fractional virtual synchronizer obtained in step 3, and adding the rated angular frequency ω0 of the fractional virtual synchronizer, the output angular frequency ω of the fractional virtual synchronizer is obtained. The output angular frequency ω is then integrated to obtain the output phase angle θ of the fractional virtual synchronizer.

[0071] The formula for calculating the output angular frequency ω of the fractional-order virtual synchronizer is as follows:

[0072] ω=Δω a +Δω+ω0,

[0073] The formula for calculating the output phase angle θ is:

[0074]

[0075] In the formula, s is the Laplace operator.

[0076] Combination Figure 1 Based on the power transmission model and the above control, the equivalent control structure diagram of the grid-connected active power closed loop of the fractional-order virtual synchronous machine proposed in this invention can be obtained, as follows: Figure 3 As shown. Figure 3 In this context, δ represents the power factor angle of the fractional-order virtual synchronizer; K represents the synchronization voltage coefficient of the fractional-order virtual synchronizer.

[0077] The formula used to calculate the power factor angle δ of the fractional-order virtual synchronous machine is as follows:

[0078]

[0079] The formula for calculating the synchronization voltage coefficient K of a fractional-order virtual synchronizer is as follows:

[0080]

[0081] In the formula, ω g U is the angular frequency of the power grid. g Let X be the grid voltage amplitude, E be the output voltage amplitude of the fractional-order virtual synchronous machine, X be the line equivalent inductive reactance, and s be the Laplace operator.

[0082] Step 6, as follows Figure 4As shown, first, based on the fractional-order virtual synchronizer output phase angle θ obtained in step 5, and the fractional-order virtual synchronizer dq-axis output voltage reference command E obtained in step 2, d E q The three-phase bridge arm voltage modulation signal E of the fractional-order virtual synchronous machine is obtained by inverse transformation of the single-synchronous rotating coordinates. a E b E c Then, the three-phase bridge arm voltage modulation signal E a E b E c The SVPWM modulation stage generates the drive signals for the inverter bridge switching transistors of the fractional-order virtual synchronous machine.

[0083] Example

[0084] To verify the control effect of the proposed control method for improving the damping of a fractional-order virtual synchronous machine (AFF-FOVSG) grid-connected system, the proposed AFF-FOVSG control method was compared with the existing control method for a traditional virtual synchronous machine (VSG). (This VSG control method is mentioned in the background section as "Improved Grid-Connected Strategy Based on Triple Fractional-Order Grid-Connected Virtual Synchronous Machine," *Electric Power Automation Equipment*, 2025, Vol. 45, No. 07, pp. 183-189+224.) The existing control methods for fractional-order virtual synchronous machines (FOVSG) (the FOVSG control method is mentioned in the background section in the article entitled "Active Response Strategy for Energy Storage VSG Grid Connection Based on Active Fractional-Order Differential Correction", Vol. 44, No. 2, 2024, pp. 204-210) and the existing control methods for virtual synchronous machines based on angular frequency differential feedforward (AFFVSG) {the AFFVSG control method is mentioned in the background section in the article entitled "Small-signal The article "Small-signal modeling and characteristic comparative analysis for a single grid-connected grid-forming VSG with full-order and second-order models" by LIANG CF, Shi RL, JU CW, et al., *Engineering Science and Technology, an International Journal*, 2024, 59, 101879, provides simulation and experimental comparisons, primarily focusing on the differences in handling active power reference command (Pref) and grid frequency (f). g Grid-connected active power P under step disturbance conditions e And the dynamic response performance at the output frequency f. Specifically:

[0085] First, the relevant parameters are set. In this embodiment, the relevant parameter settings in the control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system of the present invention are as follows:

[0086] The virtual synchronous machine has a rated capacity of 100kVA and an active power reference command P. ref The power supply is 20kW, the grid's rated angular frequency ω0 is 314.16 rad / s, and the virtual inertia coefficient J is 6 kg·m. 2The virtual damping coefficient D is 50.66 J / rad, and the grid voltage amplitude U g The voltage is 311V, and the primary voltage regulation coefficient is k. q 1.4×10 -4 The virtual synchronous machine output voltage amplitude E is 311V, the line equivalent inductive reactance X is 0.1Ω, and the synchronization voltage coefficient K = 1.5UgE / X is 1450815. It is worth noting that if the feedforward compensation coefficient k in AFF-FOVSG is set... a If μ = 0, then AFF-FOVSG will be equivalent to FOVSG, which shows that FOVSG is only a special case of AFF-FOVSG; if the fractional integral coefficient μ in AFF-FOVSG is set to 1, then AFF-FOVSG will be equivalent to AFFVSG, which shows that AFFVSG is only a special case of AFF-FOVSG; if the feedforward compensation coefficient k in AFF-FOVSG is set to 1... a If the integral coefficient u = 0 and the fractional integral coefficient u = 1, then AFF-FOVSG is equivalent to VSG, which shows that VSG is only a special case of AFF-FOVSG. Meanwhile, combining... Figure 3 Through a series of formula derivations, the active power reference command P of the VSG grid-connected system at this time can be obtained. ref To grid-connected active power P e The closed-loop transfer function is The damping ratio of the corresponding VSG grid-connected active power closed-loop control system That is, the VSG grid-connected active power closed-loop control system is an underdamped system, therefore the VSG grid-connected active power P e With output frequency f in active reference command P ref and grid frequency f g Under step disturbance conditions, dynamic oscillations and overshoot will inevitably occur. Furthermore, according to... Figure 3 Through a series of formula derivations, the active power reference command P of the FOVSG grid-connected system can be obtained. ref To grid-connected active power P e The closed-loop transfer function is The fractional-order coefficients in G1(s) are set to u = 0.6, and the virtual inertia coefficient is set to J = 6 kg·m. 2 The virtual damping coefficient is set to D = 50.66 J / rad to ensure that FOVSG and VSG have the same grid-connected active power steady-state response performance, while also suppressing the grid-connected active power P of FOVSG. e With output frequency f in active reference command P ref and grid frequency f g Dynamic oscillations exist under step disturbances. Then, based on... Figure 3Through a series of formula derivations, the active power reference command P of the AFFVSG grid-connected system can be obtained. ref Grid-connected active power P e The closed-loop transfer function is The filtering time constant in G2(s) is set to τ = 0.006s, and the feedforward compensation coefficient is set to k. a =6. The virtual inertia coefficient is set to J = 6 kg·m 2 The virtual damping coefficient is set to D = 50.66 J / rad to ensure that AFFVSG and VSG have the same grid-connected active power steady-state response performance, while also suppressing the grid-connected active power P of AFFVSG. e With output frequency f in active reference command P ref and grid frequency f g Dynamic oscillations existing under step disturbances.

[0087] In this embodiment, the fractional integral coefficient μ, the filtering time constant τ of the first-order low-pass filter, and the feedforward compensation coefficient K are set appropriately. a The value of [value] is selected to further optimize the grid-connected active power P of AFF-FOVSG. e With output frequency f in active reference command P ref and grid frequency f g Dynamic response performance under a step disturbance. Similarly, according to Figure 3 Through a series of formula derivations, the active power reference command P of the AFF-FOVSG grid-connected system can be obtained. ref To grid-connected active power P e The closed-loop transfer function is Therefore, the grid-connected active power dynamic response performance of VSG, FOVSG, AFFVSG, and AFF-FOVSG can be directly analyzed by comparing and contrasting the closed-loop transfer functions G(s), G1(s), G2(s), and G3(s). To further simplify the theoretical analysis process, the fractional-order coefficients in AFF-FOVSG are set to μ = 0.6, the filtering time constant of the first-order low-pass filter is set to τ = 0.006s, and the feedback compensation coefficient is set to k. a =6. The virtual inertia coefficient is J = 6 kg·m 2 The virtual damping coefficient is D = 50.66 J / rad. Substituting these parameters into the closed-loop transfer functions G3(s), G2(s), G1(s), and G(s) respectively, we can obtain the active power reference command step disturbance ΔP for the grid-connected active power closed-loop control systems of AFF-FOVSG, AFFVSG, FOVSG, and VSG. ref To the grid-connected active power response Δp e (ΔP e / ΔP re f ) For a comparison of the Bode plot, see [link / details]. Figure 5 (a). Similarly, the grid angular frequency step disturbance Δω of the grid-connected active power closed-loop control system of AFF-FOVSG, AFFVSG, FOVSG and VSG can be obtained respectively. g To the grid-connected active power response ΔP e (ΔP e / Δω g Active reference command step disturbance ΔP ref Output angular frequency response Δω(Δω / ΔP) ref ) and the step disturbance of the power grid angular frequency Δω g Output angular frequency response Δω(Δω / Δω) g For comparison with the Bode plot, please refer to the details below. Figure 5 (b) Figure 5 (c) and Figure 5 (d). Among them, Figure 5 In this paper, VSG represents the Bode plot of an existing traditional virtual synchronous machine control method, FOVSG represents the Bode plot of an existing fractional-order virtual synchronous machine control method, AFFVSG represents the Bode plot of an existing virtual synchronous machine control method based on angular frequency differential feedforward, and AFF-FOVSG represents the Bode plot of a control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system proposed in this invention. Specifically, the curve pointed to by VSG is the Bode plot before the application of this invention, specifically the Bode plot using an existing traditional virtual synchronous machine control method; the curve pointed to by FOVSG is the Bode plot before the application of this invention, specifically the Bode plot using an existing fractional-order virtual synchronous machine control method; the curve pointed to by AFFVSG is the Bode plot before the application of this invention, specifically the Bode plot using an existing virtual synchronous machine control method based on angular frequency differential feedforward; and the curve pointed to by AFF-FOVSG is the Bode plot after the application of this invention, specifically the Bode plot of a control method for improving the damping of a fractional-order virtual synchronous machine grid-connected system proposed in this invention.

[0088] according to Figure 5 It can be observed that, firstly, both the grid-connected active power closed-loop control systems of VSG and FOVSG exhibit significant resonance peaks before the cutoff frequency. This phenomenon indicates that the grid-connected active power P of VSG and FOVSG... e With the output angular frequency ω in the active reference command P ref and the angular frequency ω of the power grid g Dynamic oscillations or overshoot will occur under step disturbance conditions. The AFFVSG grid-connected active power closed-loop control system ΔP... e / ΔP ref ΔP e / Δω g , Δω / ΔP refThe presence of a resonance peak before the cutoff frequency indicates that the output angular frequency ω of the AFFVSG is at the active reference command P. ref Under step disturbance conditions, overshoot will occur, and the grid-connected active power P e In the active reference instruction P ref and the angular frequency ω of the power grid g Overshoot will occur under step disturbance conditions; secondly, the ΔP of the AFF-FOVSG grid-connected active power closed-loop control system proposed in this invention... e / ΔP ref ΔP e / Δω g , Δω / Δω g No obvious resonance peak exists before the cutoff frequency. This phenomenon indicates that the grid-connected active power Pe of the proposed AFF-FOVSG is within the active power reference command P. ref and the angular frequency ω of the power grid g There is no dynamic oscillation problem under step disturbance conditions, and the output angular frequency ω is at the grid angular frequency ω. g There is no dynamic oscillation problem under step disturbance conditions; III. ΔP of the proposed AFF-FOVSG grid-connected active power closed-loop control system e / ΔP ref ΔP e / Δω g , Δω / ΔP ref , Δω / Δω g Compared to FOVSG, AFF-FOVSG exhibits a smaller resonance peak, indicating that the grid-connected active power P corresponding to AFF-FOVSG is smaller. e With the output angular frequency ω in the active reference command P ref and the angular frequency ω of the power grid g Under step disturbance conditions, it exhibits smaller grid-connected active power oscillations and overshoot, as well as lower output frequency response overshoot amplitude; IV. ΔP of the proposed AFF-FOVSG grid-connected active power closed-loop control system. e / Δω g ΔP e / Δω g , Δω / Δω g Compared to ΔFFVSG, both exhibit smaller resonance peaks. This phenomenon indicates that the grid-connected active power closed-loop control system corresponding to the proposed AFF-FOVSG has a smaller resonance peak at the grid angular frequency ω. g Under step disturbance conditions, it exhibits lower grid-connected active power and output frequency oscillations or overshoot. It is worth noting that AFF-FOVSG also offers the advantages of more control parameters and more flexible parameter selection. For example, by selecting appropriate fractional integral coefficient μ, the filtering time constant τ of the first-order low-pass filter, and the feedforward compensation coefficient k... a The value of is selected to flexibly optimize the grid-connected active power P of AFF-FOVSG.e The dynamic response performance with respect to the output angular frequency ω will not be listed in detail due to space limitations.

[0089] Based on the above parameter settings, simulation and experimental comparisons were conducted for verification, as detailed below:

[0090] The simulation and experimental verification conditions are set as follows: at the initial moment, the virtual synchronous machine stably outputs 20kW of grid-connected active power, and the grid frequency f g Maintaining a constant 50Hz, the active power reference command P is available at 4.0s. ref The power output jumps from 20kW to 60kW; initially, the virtual synchronous machine stably outputs 20kW of grid-connected active power, with the grid frequency f. g Keeping the frequency constant at 50Hz, the grid frequency f at 4.0s g It suddenly dropped from 50Hz to 49.95Hz.

[0091] Based on the above working conditions, the following results were obtained: Figure 6 and Figure 7 The simulation and experimental verification comparison chart shown below, in which, Figure 6 and Figure 7 In this paper, VSG represents an existing traditional virtual synchronous machine control method, FOVSG represents an existing fractional-order virtual synchronous machine control method, AFFVSG represents an existing virtual synchronous machine control method based on angular frequency differential feedforward, and AFF-FOVSG represents a control method proposed in this invention to improve the damping of a grid-connected system using a fractional-order virtual synchronous machine. Specifically, the curve pointed to by VSG is the verification waveform before the application of this invention, specifically the dynamic response verification waveform using the existing traditional virtual synchronous machine control method; the curve pointed to by FOVSG is the verification waveform before the application of this invention, specifically the dynamic response verification waveform using the existing fractional-order virtual synchronous machine control method; the curve pointed to by AFFVSG is the verification waveform before the application of this invention, specifically the dynamic response verification waveform using the existing virtual synchronous machine control method based on angular frequency differential feedforward; and the curve pointed to by AFF-FOVSG is the verification waveform after the application of this invention, specifically the dynamic response verification waveform using the control method proposed in this invention to improve the damping of a grid-connected system using a fractional-order virtual synchronous machine.

[0092] according to Figure 6(a) It can be seen that: 1. The grid-connected active power and output frequency of the AFF-FOVSG proposed in this invention have no dynamic oscillations, while the grid-connected active power and output frequency of the existing VSG have large dynamic oscillations and overshoots; the grid-connected active power and output frequency of the existing FOVSG both have overshoots and large output frequency response overshoot values; and the grid-connected active power of the existing AFFVSG has large dynamic oscillations and small output frequency response overshoot values. 2. The output frequency response overshoot value of the AFF-FOVSG proposed in this invention is 0.091Hz, while that of the existing VSG is 0.097Hz, the existing FOVSG is 0.143Hz, and the existing AFFVSG is 0.061Hz. Therefore, it can be seen that the AFF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and AFFVSG, has better performance in terms of active power reference command P. ref During the jump from 20kW to 60kW, there was no oscillation in the grid-connected active power and output frequency, and it had a smaller output frequency response overshoot amplitude compared to the existing FOVSG.

[0093] According to Figure 6 (b) It can be seen that: 1. The grid-connected active power and output frequency corresponding to the AFF-FOVSG proposed in this invention have no dynamic oscillations, while the grid-connected active power and output frequency corresponding to the existing VSG have large dynamic oscillations and overshoots, and the grid-connected active power and output frequency corresponding to the existing FOVSG and existing AFFVSG both have significant overshoots; 2. The grid-connected active power overshoot corresponding to the AFF-FOVSG proposed in this invention is 0.35%, which is much smaller than the 41.1% corresponding to the existing VSG, 8.29% corresponding to the existing FOVSG, and 11.4% corresponding to the existing AFFVSG. Therefore, it can be concluded that the AFF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and AFFVSG, has a better performance at the grid frequency f. g During the sudden drop from 50Hz to 49.95Hz, there was no dynamic oscillation in either the grid-connected active power or the output frequency, and it also had a smaller overshoot.

[0094] according to Figure 7(a) It can be seen that: 1. The grid-connected active power corresponding to the AFF-FOVSG proposed in this invention has no dynamic oscillation, while the grid-connected active power and output frequency corresponding to the existing VSG have large dynamic oscillations and overshoot, the grid-connected active power and output frequency corresponding to the existing FOVSG both have overshoot and large output frequency response overshoot, and the grid-connected active power and output frequency corresponding to the existing AFFVSG both have dynamic oscillations; 2. The output frequency response overshoot of the AFF-FOVSG proposed in this invention is 0.257Hz, while that of the existing VSG is 0.121Hz, the existing FOVSG is 0.293Hz, and the existing AFFVSG is 0.224Hz. Therefore, it can be concluded that the AFF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and AFFVSG, has a higher active power reference command P... ref During the jump from 20kW to 60kW, there was no oscillation in the grid-connected active power and output frequency, and it had a smaller output frequency response overshoot amplitude compared to the existing FOVSG.

[0095] According to Figure 7 (b) It can be seen that: 1. The grid-connected active power and output frequency corresponding to the AFF-FOVSG proposed in this invention have no dynamic oscillations, while the grid-connected active power and output frequency corresponding to the existing VSG have large dynamic oscillations and overshoots, and the grid-connected active power and output frequency corresponding to the existing FOVSG and existing AFFVSG both have significant overshoots; 2. The grid-connected active power overshoot corresponding to the AFF-FOVSG proposed in this invention is 0.97%, which is much smaller than the 49.6% corresponding to the existing VSG, 5.21% corresponding to the existing FOVSG, and 8.5% corresponding to the existing AFFVSG. Therefore, it can be concluded that the AFF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and AFFVSG, has a higher grid frequency f... g During the sudden drop from 50Hz to 49.95Hz, there was no dynamic oscillation in either the grid-connected active power or the output frequency, and it also had a smaller overshoot.

[0096] Will Figure 7 (a) and Figure 6 Comparing the results of (a), it is not difficult to see that this implementation method Figure 7 The experimental verification comparison results in (a) are consistent with... Figure 6 The simulation verification comparison results in (a) maintain a one-to-one correspondence, both of which fully demonstrate that the AFF-FOVSG proposed in this invention, compared with existing VSGs, and existing FOVSGs and existing AFFVSGs, has advantages in active power reference command P. ref It exhibits faster response speed under step disturbances, smaller grid-connected active power overshoot, and no dynamic oscillations. Furthermore, it has a smaller output frequency response overshoot amplitude compared to existing FOVSGs. Therefore, the AFF-FOVSG proposed in this invention provides better control performance compared to existing VSGs, FOVSGs, and AFFVSGs.

[0097] And again Figure 7 (b) and Figure 6 (b) Comparing the results, it is not difficult to see that this implementation method Figure 7 The experimental verification comparison results in (b) are consistent with... Figure 6 The simulation verification comparison results in (b) maintain a one-to-one correspondence, both of which fully demonstrate that the AFF-FOVSG proposed in this invention, compared with existing VSGs, and existing FOVSGs, and existing AFFVSGs, are superior at the grid frequency f. g Under step disturbances, the proposed AFF-FOVSG exhibits advantages such as no dynamic oscillations in grid-connected active power and output frequency, and smaller overshoot. Therefore, compared with existing VSGs, FOVSGs, and AFFVSGs, the proposed AFF-FOVSG demonstrates superior control performance.

[0098] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A control method for improving the damping of a grid-connected system using a fractional-order virtual synchronous machine, characterized in that, Includes the following steps: Step 1, power calculation section: First, collect the three-phase grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and three-phase output voltage u a u b u c The dq component I of the three-phase grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through single-synchronous rotating coordinate transformation. d I q and the dq component U of the three-phase output voltage d U q Then, the grid-connected active power P of the fractional-order virtual synchronous machine is obtained through the power calculation equation. e And grid-connected reactive power Q e ; Step 2, primary voltage regulation section, based on the grid-connected reactive power Q of the fractional-order virtual synchronous machine obtained in Step 1. e The reactive power reference instruction Q of the fractional-order virtual synchronous machine ref Primary voltage regulation coefficient k q The voltage reference command E0 is used to obtain the dq axis output voltage reference command E of the fractional-order virtual synchronizer through a voltage regulation equation. d E q ; Step 3, Fractional Rotor Motion Equations: The active power reference command P of the fractional virtual synchronizer is used. ref Subtract the grid-connected active power P of the fractional-order virtual synchronous machine obtained in step 1. e The power difference ΔP is obtained. Then, the power difference ΔP, the fractional integral coefficient μ, the virtual inertia coefficient J, the virtual damping coefficient D of the fractional-order virtual synchronizer, and the rated angular frequency ω0 are used to obtain the angular frequency deviation Δ of the fractional-order virtual synchronizer through the fractional-order rotor motion equation. ω ; Step 4: Based on the angular frequency compensation part of the differential feedforward, according to the angular frequency deviation Δω of the fractional virtual synchronizer obtained in Step 3 and the filtering time constant τ of the first-order low-pass filter and the feedforward compensation coefficient k... a The angular frequency compensation amount Δω of the fractional-order virtual synchronizer is obtained through an angular frequency compensation stage based on angular frequency differential feedforward. a ; Step 5: Output the phase angle generation part, and use the angular frequency compensation amount Δω of the fractional-order virtual synchronizer obtained in Step 4. a After adding the angular frequency deviation Δω of the fractional virtual synchronizer obtained in step 3, and adding the rated angular frequency ω0 of the fractional virtual synchronizer, the output angular frequency ω of the fractional virtual synchronizer is obtained. The output angular frequency ω is then integrated to obtain the output phase angle θ of the fractional virtual synchronizer. Step 6: First, based on the fractional-order virtual synchronizer output phase angle θ obtained in Step 5, and the fractional-order virtual synchronizer dq-axis output voltage reference command E obtained in Step 2. d E q The three-phase bridge arm voltage modulation signal E of the fractional-order virtual synchronous machine is obtained by inverse transformation of the single-synchronous rotating coordinates. a E b E c Then, the three-phase bridge arm voltage modulation signal E a E b E c The SVPWM modulation stage generates the drive signals for the inverter bridge switching transistors of the fractional-order virtual synchronous machine.

2. The control method for improving the damping of a grid-connected system with a fractional-order virtual synchronous machine according to claim 1, characterized in that, The grid-connected active power P in step 1 e The calculation formula used is: P e =1.5(U d AND d +U q AND q ), Grid-connected reactive power Q e The calculation formula used is: Q e =1.5(U q I d -U d I q )。 3. The control method for improving the damping of a grid-connected system with a fractional-order virtual synchronous machine according to claim 1, characterized in that, Output voltage reference command E in step 2 d The calculation formula used is: E d <E0+(Q ref -Q e )k q , Output voltage reference command E q The calculation formula used is: E q ＝0。 4. The control method for improving the damping of a grid-connected system using a fractional-order virtual synchronous machine according to claim 1, characterized in that, The formula used to calculate the power difference ΔP in step 3 is: ΔP=P ref -P e , The formula for calculating the angular frequency deviation Δω is: In the formula, s is the Laplace operator.

5. The fractional-order virtual synchronous machine control method based on fractional-order differential feedforward of angular frequency according to claim 1, characterized in that, Angular frequency compensation amount Δω in step 4 a The calculation formula used is: In the formula, s is the Laplace operator.

6. The control method for improving damping in a grid-connected system using a fractional-order virtual synchronous machine according to claim 1, characterized in that, The formula used to calculate the output angular frequency ω of the fractional-order virtual synchronizer in step 5 is: oh = I see a +Dω+ω0, The formula for calculating the output phase angle θ is: In the formula, s is the Laplace operator.

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