Fractional order virtual synchronous machine grid-connected control method based on active differential feedback

Abstract

The invention discloses a fractional order virtual synchronous machine grid-connected control method based on active differential feedback, and the method introduces a power compensation link based on active differential feedback into a fractional order virtual synchronous machine control structure. The dynamic response performance of the active power and the output frequency of the fractional order virtual synchronous machine grid-connected system is optimized by adjusting the filtering time constant and the feedback compensation coefficient of the first-order low-pass filter; dynamic oscillation and overshoot of active and output frequencies of a fractional order virtual synchronous machine grid-connected system under internal and external disturbances such as an active reference instruction and a power grid frequency can be effectively suppressed, and compared with a fractional order virtual synchronous machine, the method has the advantages of more control freedom degrees, more flexible control parameter selection and smaller output active ultra-amplitude modulation value; the method can be applied to the field of fractional order virtual synchronous machine grid-connected control in the power electronic technology.

Description

Technical Field

[0001] This invention relates to the field of virtual synchronous machine control technology, and in particular to a grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback. 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 that include such fractional-order virtual synchronous machines. Background Technology

[0002] Virtual Synchronous Generators (VSGs) can provide a certain voltage and virtual inertia support to the connected power grid during grid-connected operation. However, the grid-connected active power and output frequency of VSGs exhibit dynamic oscillations and overshoot problems under internal and external disturbances such as active power reference commands and grid frequency. Furthermore, fractional-order virtual synchronous generators introduce fractional-order virtual inertia control into the rotor motion equations of the VSG, increasing the adjustable parameters of the VSG grid-connected system and significantly suppressing the dynamic oscillations of the grid-connected active power and output frequency. However, their ability to suppress overshoot in grid-connected active power and output frequency still needs further improvement.

[0003] To address this, various studies have been conducted, such as the article entitled "Suppression Strategy for Transient Power Oscillation of Virtual Synchronous Generator Considering Overshoot," published in Automation of Electric Power Systems, Vol. 46, No. 11, 2022, pp. 131-141. This article proposes a strategy for suppressing the dynamic oscillation of VSG grid-connected active power based on active power differential feedback, which can effectively improve the transient damping of the VSG grid-connected active power closed-loop control system, thereby reducing the dynamic oscillation and power overshoot of VSG grid-connected active power. However, the control freedom increased by the active power differential feedback link is limited and the selection of control parameters is not flexible enough. Furthermore, its ability to suppress VSG grid-connected active power and output frequency overshoot still needs further improvement.

[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, proposes a fractional-order VSG control method based on a single-stage fractional-order virtual inertia. This method transforms the integer-order virtual inertia element into a single-stage fractional-order virtual inertia element, resulting in a control system order lower than second-order. This method offers advantages such as simple system parameter design and effective suppression of grid-connected active power dynamic oscillations. However, the fractional-order VSG only increases the control degrees of freedom by one and does not consider the response overshoot problem that easily occurs in the VSG output frequency under grid-connected conditions.

[0005] The article titled “Fractional-order virtual synchronous generator”, YUY, GUAN YJ, KANG WF, et al., IEEE Transactions on Power Electronics, 2023, 38(6), 6874-6879 (“Fractional-order virtual synchronous generator”, IEEE Journal of Power Electronics, Vol. 38, No. 6, 2023, pp. 6874-6879); This article modifies the integer-order virtual inertia element of the traditional grid-type VSG to a double fractional-order virtual inertia element to form a fractional-order VSG, so that the order of the control system is lower than the second order. It has the advantages of effectively suppressing grid-connected active power dynamic oscillation and increasing control degrees of freedom, but there are problems such as limited adjustable range of fractional-order VSG control parameters and output frequency response overshoot.

[0006] The article, titled "Improved Grid-Connected Control Strategy for VSG Based on Triple Fractional Inertia," published in *Electric Power Automation Equipment*, Vol. 45, No. 07, 2025, pp. 1833-189+224, proposes an improved grid-connected control strategy for VSG based on triple fractional virtual inertia. This strategy can effectively suppress the dynamic oscillation and overshoot of VSG grid-connected active power and output frequency under step disturbances such as active power commands and grid frequency. It has the advantages of increasing the system's control degrees of freedom and the flexibility of control parameter selection. However, it also has problems such as high control structure complexity, parameter tuning dependence on experience, and output frequency response overshoot.

[0007] As can be seen from the above, the existing technology can provide some solutions and technical support for suppressing the dynamic oscillation of the grid-connected active power and output frequency of VSG under disturbances such as active power reference command and grid frequency. However, it has the disadvantages that the ability to suppress the grid-connected active power and output frequency overshoot of VSG still needs to be further improved, the increased control freedom is limited, the adjustable range of control parameters is limited, and the output frequency response overshoot is a problem. Summary of the Invention

[0008] To overcome the limitations of various technical solutions presented in the background art, this invention addresses the technical problem that the grid-connected active power and output frequency dynamic oscillation and overshoot suppression capabilities of fractional-order virtual synchronous machines still need further improvement. It provides a grid-connected control method for fractional-order virtual synchronous machines based on active power differential feedback. This control method introduces a power compensation link based on active power differential feedback into the control structure of the fractional-order virtual synchronous machine. By adjusting the filtering time constant and feedback compensation coefficient of the first-order low-pass filter, the dynamic response performance of the active power and output frequency of the grid-connected system of the fractional-order virtual synchronous machine is optimized. This effectively suppresses the dynamic oscillation and overshoot of the active power and output frequency of the grid-connected system of the fractional-order virtual synchronous machine under internal and external disturbances such as active power reference commands and grid frequency. Compared with the fractional-order virtual synchronous machine, it has the advantages of more control degrees of freedom, more flexible control parameter selection, and smaller output active power overshoot amplitude.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] A grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback includes the following steps:

[0011] Step 1, power calculation section: First, collect the grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and output voltage u a u b u c The dq component I of the grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through a single synchronous rotating coordinate transformation.d I q and the dq component of the output voltage U 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 ;

[0012] 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 ;

[0013] Step 3, based on the power compensation part using active power differential feedback, according to the grid-connected active power P of the fractional-order virtual synchronous machine obtained in Step 1. e The filtering time constant τ and feedback compensation coefficient k of a first-order low-pass filter a The power compensation amount P of the fractional-order virtual synchronous machine is obtained through a power compensation stage based on active power differential feedback. a ;

[0014] Step 4, 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 respectively e The power compensation amount P of the fractional-order virtual synchronizer obtained in step 3 a The power difference ΔP is obtained. The power difference ΔP, the virtual inertia coefficient J, the rated angular frequency ω0, the virtual damping coefficient D and the fractional coefficient μ of the fractional-order virtual synchronizer are used to obtain the angular frequency deviation Δω of the fractional-order virtual synchronizer through the fractional-order rotor motion equation.

[0015] Step 5, Output phase angle generation section: Add the rated angular frequency ω0 to the angular frequency deviation Δω of the fractional-order virtual synchronizer obtained in step 4 to obtain the output angular frequency ω of the fractional-order virtual synchronizer. Then, perform an integration operation on the output angular frequency ω to obtain the output phase angle θ of the fractional-order virtual synchronizer.

[0016] 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 is obtained through single synchronous rotating coordinate inverse transformation. a E bE 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.

[0017] Preferably, the grid-connected active power P in step 1 e The calculation formula used is:

[0018] P e =1.5(U d I d +U q I q ),

[0019] The formula for calculating the grid-connected reactive power Qe is:

[0020] Q e =1.5(U q I d -U d I q ).

[0021] Preferably, the output voltage reference command E in step 2 d The calculation formula used is:

[0022] E d =E0+(Q ref -Q e )k q ,

[0023] Output voltage reference command E q The calculation formula used is:

[0024] E q =0.

[0025] Preferably, the power compensation amount P of the fractional-order virtual synchronizer in step 3 is... a The calculation formula used is:

[0026]

[0027] In the formula, s is the Laplace operator.

[0028] Preferably, the formula used to calculate the power difference ΔP in step 4 is:

[0029] ΔP=P ref -P e -P a ,

[0030] The formula for calculating the angular frequency deviation Δω is:

[0031]

[0032] In the formula, s is the Laplace operator.

[0033] Preferably, the formula used to calculate the angular frequency ω of the fractional-order virtual synchronizer output in step 5 is:

[0034] ω = Δω + ω0,

[0035] The formula for calculating the output phase angle θ is:

[0036]

[0037] In the formula, s is the Laplace operator.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention discloses a grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback. This control method introduces a power compensation link based on active power differential feedback into the control structure of the fractional-order virtual synchronous machine. By adjusting the filtering time constant and feedback compensation coefficient of the first-order low-pass filter, the dynamic response performance of the active power and output frequency of the grid-connected system of the fractional-order virtual synchronous machine is optimized. It can effectively suppress the dynamic oscillation and overshoot of the active power and output frequency of the grid-connected system of the fractional-order virtual synchronous machine under internal and external disturbances such as active power reference command and grid frequency. Compared with the fractional-order virtual synchronous machine, it has the advantages of more control degrees of freedom, more flexible selection of control parameters, and smaller output active power overshoot amplitude. It can be applied to the field of grid-connected control of fractional-order virtual synchronous machines in power electronics technology. Attached Figure Description

[0040] 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.

[0041] Figure 2 This is a schematic diagram illustrating the calculation of power compensation based on active differential feedback in this invention.

[0042] 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.

[0043] Figure 4 This is a schematic diagram of coordinate transformation and modulation according to an embodiment of the present invention.

[0044] Figure 5 This is a Bode plot comparing the virtual synchronizer before and after adopting this invention.

[0045] Figure 6 This is a comparison of the simulation waveforms of the virtual synchronizer before and after adopting this invention.

[0046] Figure 7 This is a comparison of experimental waveforms before and after the virtual synchronizer was implemented using this invention. Detailed Implementation

[0047] The following detailed embodiments will be further described in conjunction with the above-mentioned figures, as follows:

[0048] Please see Figure 1 The present invention proposes a grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback, comprising the following steps:

[0049] Step 1, power calculation section: First, collect the grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and output voltage u a u b u c The dq component I of the grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through a single synchronous rotating coordinate transformation. d I q and the dq component of the output voltage U 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 ;

[0050] Among them, grid-connected active power P e The calculation formula used is:

[0051] P e =1.5(U d I d +U q I q ),

[0052] Grid-connected reactive power Q e The calculation formula used is:

[0053] Q e =1.5(U q I d -U d I q ).

[0054] 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 ;

[0055] Among them, the output voltage reference command E d The calculation formula used is:

[0056] E d =E0+(Q ref -Q e )k q ,

[0057] Output voltage reference command E q The calculation formula used is:

[0058] E q =0.

[0059] Step 3, power compensation based on active power differential feedback, such as... Figure 2 As shown, based on the grid-connected active power P of the fractional-order virtual synchronous machine obtained in step 1... e The filtering time constant τ and feedback compensation coefficient k of a first-order low-pass filter a The power compensation amount P of the fractional-order virtual synchronous machine is obtained through a power compensation stage based on active power differential feedback. a ;

[0060] Among them, the power compensation P of the fractional-order virtual synchronous machine a The calculation formula used is:

[0061]

[0062] In the formula, s is the Laplace operator.

[0063] Step 4, 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 respectively e The power compensation amount P of the fractional-order virtual synchronizer obtained in step 3 a The power difference ΔP is obtained. The power difference ΔP, the virtual inertia coefficient J, the rated angular frequency ω0, the virtual damping coefficient D and the fractional coefficient μ of the fractional-order virtual synchronizer are used to obtain the angular frequency deviation Δω of the fractional-order virtual synchronizer through the fractional-order rotor motion equation.

[0064] The formula used to calculate the power difference ΔP is as follows:

[0065] ΔP=P ref -P e -P a ,

[0066] The formula for calculating the angular frequency deviation Δω is:

[0067]

[0068] In the formula, s is the Laplace operator.

[0069] Step 5, Output Phase Angle Generation Section: The angular frequency deviation Δω of the fractional-order virtual synchronizer obtained in Step 4 is added to the rated angular frequency ω0 to obtain the output angular frequency ω of the fractional-order virtual synchronizer. The output angular frequency ω is then integrated to obtain the output phase angle θ of the fractional-order virtual synchronizer.

[0070] The formula used to calculate the output angular frequency ω of the fractional-order virtual synchronizer is as follows:

[0071] ω = Δω + ω0,

[0072] The formula for calculating the output phase angle θ is:

[0073]

[0074] In the formula, s is the Laplace operator.

[0075] 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 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.

[0076] The formula used to calculate the power factor angle δ of the fractional-order virtual synchronous machine is as follows:

[0077]

[0078] The formula for calculating the synchronization voltage coefficient K of a fractional-order virtual synchronizer is as follows:

[0079]

[0080] In the formula, ω g U is the grid angular frequency. 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.

[0081] Step 6, as follows Figure 4 As 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 is obtained through single synchronous rotating coordinate inverse transformation. a Eb 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.

[0082] Example

[0083] To verify the control effect of the proposed fractional-order virtual synchronous machine grid-connected control method based on active power differential feedback, the proposed APF-FOVSG control method was compared with the existing traditional virtual synchronous machine (VSG) control method (described in the background section as "Improved Grid-Connected Strategies Based on Triple Fractional-Order Virtual Synchronous Machine", Vol. 45, No. 07, pp. 183-189, *Electric Power Automation Equipment*, 2025) and the existing fractional-order virtual synchronous machine (FOVSG) control method (described in the background section as "Frequency stability enhancement of anislanded microgrid: A fractional-order virtual synchronous generator", LONG B, LI XY, RODRIGUEZ J, et al., *International Journal of Electrical Power and Energy*). The article "An Enhanced Frequency Stability Control Method for Independent Microgrids: Fractional-Order Virtual Synchronous Machine" (published in *International Journal of Power and Energy Systems*, Vol. 147, No. 108896, 2023) and the existing Active Differential Feedback-based Virtual Synchronous Machine (APFVSG) control method (mentioned in the background section, titled "Transient Power Oscillation Suppression Strategy for Virtual Synchronous Generators Considering Overshoot" (published in *Automation of Electric Power Systems*, Vol. 46, No. 11, pp. 131-141, 2022) are compared in simulation and experiments, mainly focusing on the performance in dealing with the active power reference command P. ref 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:

[0084] First, the relevant parameters are set. In this embodiment, the relevant parameters in the grid-connected control method of a fractional-order virtual synchronous machine based on active power differential feedback of the present invention are set as follows:

[0085] 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 8 kg·m. 2 The 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 Given a virtual synchronous machine output voltage amplitude E of 311V and an equivalent inductive reactance X of 0.15Ω, the synchronization voltage coefficient K = 1.5U. g The E / X ratio is 967210. It is worth noting that if the feedback compensation coefficient k in APF-FOVSG is set... a If μ = 0, then APF-FOVSG is equivalent to FOVSG, indicating that FOVSG is only a special case of APF-FOVSG; if the fractional order coefficient μ in APF-FOVSG is set to 1, then APF-FOVSG is equivalent to APFVSG, indicating that APFVSG is only a special case of APF-FOVSG; if the feedback compensation coefficient k in APF-FOVSG is set to 0... a If μ = 0 and the fractional coefficient μ = 1, then APF-FOVSG is equivalent to VSG, indicating that VSG is only a special case of APF-FOVSGG. 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 first-order fractional coefficient in G1(s) is set to μ = 0.6, and the virtual inertia coefficient is set to J = 8 kg·m. 2The 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 3 Through a series of formula derivations, the active power reference command P of the APFVSG grid-connected system can be obtained. ref To grid-connected active power P e The closed-loop transfer function is The filtering time constant of the first-order low-pass filter in G2(s) is set to τ = 0.007, and the feedback compensation coefficient is set to k. a =12. The virtual inertia coefficient is set to J = 8 kg·m 2 The virtual damping coefficient is set to D = 50.66 J / rad to ensure that the APFVSG and VSG have the same grid-connected active power steady-state response performance, while also suppressing the grid-connected active power P of the APFVSG. e With output frequency f in active reference command P ref and grid frequency f g Dynamic oscillations existing under step disturbances.

[0086] In this embodiment, the fractional-order coefficient μ, the filtering time constant τ of the first-order low-pass filter, and the feedback compensation coefficient k are set appropriately. a The value of [value] is selected to further optimize the grid-connected active power P of APF-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 APF-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, APFVSG, and APF-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 APF-FOVSG are set to μ = 0.6, the filtering time constant of the first-order low-pass filter is set to τ = 0.0001, and the feedback compensation coefficient is set to k. a =85. The virtual inertia coefficient is set to J = 8 kg·m 2The virtual damping coefficient is set to D = 50.66 J / rad. Substituting these parameters into the closed-loop transfer functions G3(s), G2(s), G1(s), and G(s) respectively, the active power reference command step disturbance ΔP of the grid-connected active power closed-loop control systems of APF-FOVSG, APFVSG, FOVSG, and VSG can be obtained. ref To the grid-connected active power response ΔP e (ΔP e / ΔP ref For a comparison of the Bode plot, see [link / reference]. Figure 5 (a). Similarly, the grid frequency step disturbance Δω of the grid-connected active power closed-loop control system of APF-FOVSG, APFVSG, 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 grid frequency step disturbance 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, APFVSG represents the Bode plot of an existing virtual synchronous machine control method based on active power differential feedback compensation, and APF-FOVSG represents the Bode plot of a fractional-order virtual synchronous machine grid-connected control method based on active power differential feedback 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 APFVSG is the Bode plot before the application of this invention, specifically the Bode plot using an existing virtual synchronous machine control method based on active power differential feedback; and the curve pointed to by APF-FOVSG is the Bode plot after the application of this invention, specifically the Bode plot using the fractional-order virtual synchronous machine grid-connected control method based on active power differential feedback proposed in this invention.

[0087] 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... eWith 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 grid-connected active power closed-loop control system ΔP of APFVSG will also be affected. e / Δω g , Δω / ΔP ref , Δω / Δω g The presence of a resonance peak before the cutoff frequency indicates that the grid-connected active power P of the APFVSG is... e At the grid angular frequency ω g Under step disturbance conditions, overshoot will occur, and the output angular frequency ω will be related to the active reference command P. ref and the angular frequency ω of the power grid g Under step disturbance conditions, overshoot will occur; secondly, the ΔP of the APF-FOVSG grid-connected active power closed-loop control system proposed in this invention... e / ΔP ref ΔP e / Δω g , Δω / Δω g The absence of significant resonance peaks before the cutoff frequency indicates that the grid-connected active power P of the APF-FOVSG is... e In the active reference instruction 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 APF-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, both exhibit smaller resonance peaks. This phenomenon indicates that the grid-connected active power P corresponding to APF-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 smaller output frequency response overshoot; IV. ΔP of the APF-FOVSG grid-connected active power closed-loop control system e / Δω g , Δω / Δω g Compared to APFVSG, both exhibit smaller resonance peaks. This phenomenon indicates that the grid-connected active power closed-loop control system corresponding to APF-FOVSG has a smaller resonance peak at the grid angular frequency ω. gUnder step disturbance conditions, it exhibits lower grid-connected active power and output frequency oscillations or overshoot. It is worth noting that the APF-FOVSG also offers advantages such as more control parameters and greater flexibility in parameter selection. For example, by selecting appropriate fractional-order coefficients μ, the filtering time constant τ of the first-order low-pass filter, and the feedback compensation coefficient k... a The value of P is selected to flexibly optimize the grid-connected active power P of APF-FOVSG. e The dynamic response performance with respect to the output angular frequency ω will not be listed in detail due to space limitations.

[0088] Based on the above parameter settings, simulation and experimental comparison tests were conducted, as follows:

[0089] The simulation and experimental test conditions were 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 From the initial moment of the jump from 20kW to 60kW, 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 The frequency jumps from 50Hz to 49.95Hz.

[0090] Based on the above working conditions, the following results were obtained: Figure 6 and Figure 7 The simulation and experimental test 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, APFVSG represents an existing virtual synchronous machine control method based on active power differential feedback, and APF-FOVSG represents a grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback proposed in this invention. Specifically, the curve pointed to by VSG is the test waveform before the application of this invention, specifically the dynamic response test waveform of the existing traditional virtual synchronous machine control method; the curve pointed to by FOVSG is the test waveform before the application of this invention, specifically the dynamic response test waveform of the existing fractional-order virtual synchronous machine control method; the curve pointed to by APFVSG is the test waveform before the application of this invention, specifically the dynamic response test waveform of the existing virtual synchronous machine control method based on active power differential feedback; and the curve pointed to by APF-FOVSG is the test waveform after the application of this invention, specifically the test waveform of the grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback proposed in this invention.

[0091] according to Figure 6(a) It can be seen that: 1. The grid-connected active power and output frequency of the APF-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 have power overshoots and large output frequency overshoots, and the grid-connected active power and output frequency of the existing APFVSG have no dynamic oscillations; 2. The output frequency overshoot of the APF-FOVSG proposed in this invention is 0.051Hz, which is smaller than that of the VSG (0.111Hz), FOVSG (0.141Hz), and APFVSG (0.052Hz). Therefore, it can be concluded that the APF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and APFVSG, has better performance in terms of active power reference command P. ref During the jump from 20kW to 60kW, the grid-connected active power and output frequency are oscillating and have smaller frequency overshoot.

[0092] And according to Figure 6 (b) It can be seen that: 1. The grid-connected active power and output frequency corresponding to the APF-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 APFVSG both have significant overshoots; 2. The grid-connected active power overshoot corresponding to the APF-FOVSG proposed in this invention is 3.36%, which is much smaller than the 46.64% corresponding to the existing VSG, 15.54% corresponding to the existing FOVSG, and 10.52% corresponding to the existing APFVSG. Therefore, it can be concluded that the APF-FOVSG proposed in this invention, compared with the existing VSG, FOVSG, and APFVSG, has no dynamic oscillations and smaller overshoots in the process of the grid frequency fg stepping from 50Hz to 49.95Hz.

[0093] according to Figure 7 (a) It can be seen that: 1. The grid-connected active power and output frequency of the APF-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 overshoot, the grid-connected active power and output frequency of the existing FOVSG have power overshoot and large output frequency overshoot amplitude, and the grid-connected active power and output frequency of the existing APFVSG have no dynamic oscillations; 2. The output frequency overshoot amplitude of the APF-FOVSG proposed in this invention is 0.061Hz, which is smaller than that of VSG (0.123Hz), FOVSG (0.151Hz), and APFVSG (0.064Hz). Therefore, it can be concluded that the APF-FOVSG proposed in this invention, compared to the existing VSG, FOVSG, and APFVSG, has better performance in terms of active power reference command P. refDuring the jump from 20kW to 60kW, the grid-connected active power and output frequency are oscillating and have smaller frequency overshoot.

[0094] And according to Figure 7 (b) It can be seen that: 1. The grid-connected active power and output frequency corresponding to the APF-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 APFVSG both have significant overshoots; 2. The grid-connected active power overshoot corresponding to the APF-FOVSG proposed in this invention is 4.36%, which is much smaller than the 55.81% corresponding to the existing VSG, 21.41% corresponding to the existing FOVSG, and 16.32% corresponding to the existing APFVSG. Therefore, it can be concluded that the FOD-APFVSG proposed in this invention, compared to the existing VSG, FOVSG, and APFVSG, has a higher grid frequency f... g During the step transition from 50Hz to 49.95Hz, both the grid-connected active power and the output frequency exhibit no dynamic oscillations and have a smaller overshoot.

[0095] 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 test results in (a) can be compared with those in (a) Figure 6 The simulation test results in (a) maintain a one-to-one correspondence, both fully demonstrating that the APF-FOVSG proposed in this invention, compared with existing VSGs, existing FOVSGs, and existing APFVSGs, performs better in terms of active power reference instruction P. ref Under step disturbances, it has the advantages of no dynamic oscillation in grid-connected active power and output frequency, and smaller frequency overshoot. Therefore, compared with existing VSG, existing FOVSG and existing APFVSG, the APF-FOVSG proposed in this invention has better control performance.

[0096] 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 test results in (b) can be compared with those in [the other two] Figure 6 The simulation test results in (b) maintain a one-to-one correspondence, both fully demonstrating that the APF-FOVSG proposed in this invention, compared with existing VSGs, existing FOVSGs, and existing APFVSGs, exhibits superior performance at grid frequency f. g Under step disturbances, it exhibits the advantages of no dynamic oscillations in both grid-connected active power and output frequency, and has smaller overshoot. Therefore, compared with existing VSG, existing FOVSG, and existing APFVSG, the APF-FOVSG proposed in this invention has better control performance.

[0097] 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 grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback, characterized in that, Includes the following steps: Step 1, power calculation section: First, collect the grid-connected current i of the fractional-order virtual synchronous machine. a i b i c and output voltage u a u b u c The dq component I of the grid-connected current, oriented by the output phase angle θ of the fractional-order virtual synchronous machine, is obtained through a single synchronous rotating coordinate transformation. d I q and the dq component of the output voltage U 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, based on the power compensation part using active power differential feedback, according to the grid-connected active power P of the fractional-order virtual synchronous machine obtained in Step 1. e The filtering time constant τ and feedback compensation coefficient k of a first-order low-pass filter a The power compensation amount P of the fractional-order virtual synchronous machine is obtained through a power compensation stage based on active power differential feedback. a ; Step 4, 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 respectively e The power compensation amount P of the fractional-order virtual synchronizer obtained in step 3 a The power difference ΔP is obtained. The power difference ΔP, the virtual inertia coefficient J, the rated angular frequency ω0, the virtual damping coefficient D and the fractional coefficient μ of the fractional-order virtual synchronizer are used to obtain the angular frequency deviation Δω of the fractional-order virtual synchronizer through the fractional-order rotor motion equation. Step 5, Output phase angle generation section: Add the rated angular frequency ω0 to the angular frequency deviation Δω of the fractional-order virtual synchronizer obtained in step 4 to obtain the output angular frequency ω of the fractional-order virtual synchronizer. Then, perform an integration operation on the output angular frequency ω to obtain the output phase angle θ of the fractional-order 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 is obtained through single synchronous rotating coordinate inverse transformation. a E b E c Then, the three-phase bridge arm voltage modulated 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 grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback 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 grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback 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 grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback according to claim 1, characterized in that, The power compensation amount P of the fractional-order virtual synchronizer in step 3 a The calculation formula used is: In the formula, s is the Laplace operator.

5. The grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback according to claim 1, characterized in that, The formula used to calculate the power difference ΔP in step 4 is: ΔP=P ref -P e -P a , The formula for calculating the angular frequency deviation Δω is: In the formula, s is the Laplace operator.

6. The grid-connected control method for a fractional-order virtual synchronous machine based on active power differential feedback according to claim 1, characterized in that, The formula used to calculate the angular frequency ω of the fractional-order virtual synchronizer output in step 5 is: ω = Δω + ω0, The formula for calculating the output phase angle θ is: In the formula, s is the Laplace operator.

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