Modeling method of fractional order LC type three-phase inverter

Abstract

The invention discloses a modeling method of a fractional order LC type three-phase inverter, and relates to the technical field of modeling and control of power electronic converters. On the basis of a traditional integer order LC type three-phase inverter, an integer order LC type filter in the inverter is replaced by a fractional order LC type filter, so that a new fractional order inverter topology is constructed. On the basis of the topology, mathematical models under a three-phase static abc coordinate system and a two-phase rotating dq coordinate system are constructed. Based on the mathematical model, a voltage and current double-closed-loop decoupling control strategy of the fractional order LC type three-phase inverter is deduced. In addition, a traditional virtual synchronous generator control link is replaced by an FOVSG control link, and the stability of the FOVSG control link is analyzed through a small signal model. According to the invention, dynamic decoupling can be effectively realized according to the order of the fractional order LC filter. In addition, an adjustable order is introduced in the FOVSG control link, and the performance of the inverter is improved under different control requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of power system operation and control, and in particular to a modeling method of a fractional-order LC type three-phase inverter. Background Art

[0002] At present, almost all control systems described by differential equations consider their differentials to be integer orders. However, actual systems are usually fractional orders. When using fractional orders to describe objects that have fractional order characteristics, the essential characteristics and behaviors of the objects can be better revealed. With the development of science and technology and the deepening of human understanding of nature, fractional calculus has been widely used in many fields. Especially in the field of electrical engineering, more and more studies have shown that inductors and capacitors are essentially fractional orders, and the use of fractional calculus theory can establish more accurate fractional mathematical models. At the same time, scholars have continuously proposed analysis and design methods for fractional inductors and capacitors. The fractional order of inductors and capacitors has brought about changes in the research of power electronic converters in topology construction, mathematical modeling, working characteristics analysis, and controller design, forming a new development direction. Introducing fractional capacitors and fractional inductors into power electronic topologies can more accurately study their physical characteristics. Research on the topology and modeling of fractional-order power electronic converters has mainly focused on DC / DC converters, but in recent years, the modeling and analysis of power electronic converters such as fractional-order rectifiers, fractional-order inverters, and fractional-order static VAR generators have also gradually deepened. These studies have shown that the use of fractional-order models for scientific research can more realistically reflect the actual operation of the converter. In addition, fractional-order calculus is also widely used in controller design, introducing adjustable fractional orders into the controller to obtain better control effects. Currently, fractional-order PI is widely used in power systems. λ D μ Control, fractional-order sliding mode control, fractional-order active disturbance rejection control, etc. Studies have shown that the rational use of fractional-order controllers can achieve better control effects.

[0003] At present, the main way of distributed generation control structure is to connect the electric energy generated by renewable energy to the common connection point (PCC) of the power grid environment through the grid-connected inverter. Compared with the access scheme of traditional synchronous generators, it has obvious advantages in control form and response speed. However, due to the large number of distributed power sources connected to the power grid, its randomness and volatility are easy to affect the stability of the power grid, which puts higher requirements on the performance of the three-phase inverter as a core component. As for the traditional three-phase inverter, its research and analysis methods have gradually matured, and the introduction of fractional calculus has become a new way to improve the performance of the inverter. In this regard, the main research methods at present are to introduce fractional inductance and fractional capacitance into the topology of the inverter and use fractional controllers, that is, fractional model and fractional control. However, with the increase in the penetration rate of renewable energy generation, the low inertia and no damping characteristics of power electronic equipment have a negative impact on the stable operation of the power system. To this end, a virtual synchronous generator (VSG) control technology that can simulate the frequency and voltage control characteristics of a synchronous generator has been proposed. It can enable the three-phase inverter to obtain the external characteristics of a traditional synchronous generator, with a certain inertia and damping, and buffer the voltage and frequency fluctuations of the power grid. However, the traditional VSG control has poor capabilities under transient disturbances and overload operation, which will produce large power oscillations, cause current shocks, and even trigger the grid-connected inverter to shut down for protection. At the same time, the introduction of virtual inertia and damping also slows down the response speed of the system. Fractional-order control can introduce expanded degrees of freedom, improve inertial response, and achieve good damping power control.

[0004] In view of this, this paper proposes a modeling method for fractional-order LC three-phase inverter. Summary of the invention

[0005] In view of the problem that ignoring the fractional-order characteristics of the system in the prior art may lead to inconsistency between the results of research and simulation analysis and the results of actual engineering operation, the present invention provides a modeling method for a fractional-order LC three-phase inverter, which can introduce fractional-order capacitors and inductors that are closer to reality, and construct a fractional-order LC three-phase inverter circuit topology and mathematical model. In addition, in order to improve the performance of the inverter, a new type of fractional-order voltage and current dual closed-loop control is proposed in the control link, and FOVSG control is used in the power control link to improve the inertial response. The specific technical solution is as follows:

[0006] A fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control includes a main circuit topology part and a control part. The main circuit part replaces the LC filter in the traditional LC three-phase inverter with a fractional-order LC filter and connects the local load, and is connected to the infinite power grid through the PCC point and the equivalent line of the external power grid. The control link mainly includes FOVSG control and fractional-order voltage and current dual closed-loop control. FOVSG control includes active control and reactive control. Active control simulates the inertia and primary frequency modulation of the synchronous generator, and reactive control simulates the active voltage regulation of the synchronous machine; the voltage and current dual closed-loop control generates a voltage reference signal, and uses the space vector pulse width modulation method (Space Vector Pulse Width Modulation, SVPWM) to generate a drive signal to control each switch device.

[0007] The fractional-order inductor mathematical model is as follows:

[0008]

[0009] Among them, u L ,i L They represent fractional inductor voltage and fractional inductor current respectively. L is the inductance value and α is the fractional inductor order.

[0010] The fractional-order capacitor mathematical model is as follows:

[0011]

[0012] Among them, u C ,i C They represent the fractional capacitor voltage and fractional capacitor current respectively, C is the capacitance value, t is the time, and β is the fractional capacitor order.

[0013] Preferably, a mathematical model of a fractional-order LC three-phase inverter in a three-phase stationary coordinate system is established, specifically as follows:

[0014] A mathematical model of a fractional-order LC three-phase inverter in a three-phase stationary coordinate system is established. The mathematical model of the fractional-order LC three-phase inverter in the three-phase stationary coordinate system is:

[0015]

[0016] Where R is the inductor parasitic resistance, L f is the fractional-order filter inductance, in H / s 1-α , α is the fractional inductor order; C f Fractional filter capacitor, unit is F / s 1-β , β is the fractional capacitor order; i Labc is the current of the fractional-order filter inductor, which consists of three components iLa 、i Lb 、i Lc Composition, i Labc =[i La i Lb i Lc ] T ,i La 、i Lb 、i Lc is the current of phase a, phase b, and phase c of the fractional-order filter inductor; u abc is the converter output voltage, which consists of three components u a 、u b 、u c Composition, u abc =[u a u b u c ] T ,u a 、u b 、u c Output a-phase, b-phase, and c-phase voltages for the inverter bridge arm; u Cabc is the voltage of the fractional filter capacitor, which consists of three components u Ca 、u Cb 、u Cc Composition,u Cabc =[u Ca u Cb u Cc ] T ,u Ca 、u Cb 、u Cc is the voltage of phase a, phase b, and phase c of the fractional capacitor; i gabc is the line current, which consists of three components i ga 、i gb 、i gc Composition, i gabc =[i ga i gb i gc ] T ,i ga 、i gb 、i gc are the phase a, phase b and phase c currents of the fractional-order filter inductor.

[0017] In addition, the fractional-order LC filter can be obtained from the converter output voltage u abc To the filter output voltage u Cabc The transfer function is:

[0018]

[0019] Preferably, for ease of analysis, equation (3) is converted into a mathematical model of a fractional-order LC three-phase inverter in a two-phase rotating coordinate system, as follows:

[0020]

[0021] Performing Laplace transformation on the above equation, we get its mathematical model in the s domain:

[0022]

[0023] In the formula, i Ld (s), i Ld (s) is i Ld 、i Ld The quantity obtained by Laplace transformation; u d (s),u q (s) is u d 、u q The quantity obtained by Laplace transformation; u Cd (s),u Cq (s) is u Cd 、u Cq The quantity obtained by Laplace transformation; i gd (s), i gq (s) is i gd 、i gq The quantity obtained by Laplace transformation.

[0024] From equations (7) and (8), it can be seen that there is cross coupling between the d-axis and q-axis currents of the mathematical model of the fractional-order LC three-phase inverter in the synchronous rotating coordinate system, and measures need to be taken to decouple them.

[0025] Preferably, the decoupling design is performed by replacing the equivalent control variables. From formula (7), it can be seen that for the current inner loop, the variable e is defined as d (s), e q (s) are as follows:

[0026]

[0027] E d (s), e q When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes is eliminated, that is:

[0028]

[0029] Generally speaking, the equivalent control variable e d (s), e q (s) can be obtained by fractional PI λThe controller generates a PI controller, because it is a decoupling of the fractional-order inductor. λ The controller generates an equivalent control variable e d (s), e q (s).

[0030]

[0031] In the formula, K ip K is the current inner loop proportional coefficient, ii is the current inner loop integration coefficient, and γ is the current inner loop integration order.

[0032] By combining equations (9) and (11) and replacing the equivalent control variables, we can derive u d (s) and u q The equation for (s) is as follows:

[0033]

[0034] At this point, the current loop has been decoupled.

[0035] For the voltage loop, define the variable i vd (s), i vq (s) are as follows:

[0036]

[0037] will i vd (s), i vq When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes in equation (7) is eliminated, that is:

[0038]

[0039] The equivalent control variable i vd (s), i vq (s) can be obtained by fractional PI λ The controller generates the following equation:

[0040]

[0041] In the formula, K vp is the voltage outer loop proportional coefficient, K vi is the voltage outer loop integration coefficient, and μ is the voltage outer loop integration order.

[0042] By combining equations (13) and (15) and substituting the equivalent control variables, we can derive i Ld (s), i Lq (s) and use it as the given value i of the current inner loop Ld *(s), i Lq * (s), which is expressed as follows:

[0043]

[0044] At this time, the voltage outer loop has been decoupled.

[0045] Preferably, the power control part adopts FOVSG control, and an adjustable fractional order is introduced into the rotor motion equation of traditional VSG control. The control equation of FOVSG is as follows:

[0046]

[0047] Among them, P e and Q e are the output active power and reactive power respectively; P ref and Q ref are the reference active power and reactive power respectively; J and D are the moment of inertia and damping coefficient respectively; λ is the adjustable fractional order, ω0 and ω are the rated angular frequency and output angular frequency; k p and k q is the active power droop coefficient and reactive power droop coefficient; U m and U n is the reference voltage amplitude and the effective value of the terminal voltage.

[0048] The inverter is connected to the grid, Z f is the equivalent impedance of the filter circuit, Z s is the line impedance, let Z = Z f +Z s =R+jX, δ is the phase difference between VSG output voltage and grid voltage δ=∫(ω-ω0)dt. U g is the grid voltage amplitude; E is the VSG output voltage.

[0049] Assuming that the impedance between the inverter and the grid is inductive (i.e. X>>R), the active and reactive power transmitted between the inverter and the grid is

[0050]

[0051] make The small signal model of the FOVSG output active increment and active reference value is obtained as follows:

[0052]

[0053] The small signal model of output frequency change and active power increment is:

[0054]

[0055] The stability of FOVSG when connected to the grid is analyzed by the zero-pole distribution and step response of formula (19), and the stability of FOVSG when operating on an isolated island is analyzed by the frequency response and step response of formula (20).

[0056] A modeling method for a fractional-order LC three-phase inverter is applied to a fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control as described above, and is characterized in that it comprises the following steps:

[0057] S1: Based on the definition of Caputo-type fractional calculus, mathematical models of fractional capacitors and fractional inductors are established;

[0058] S2: Considering the fractional-order characteristics of inductance and capacitance, the main circuit topology of the fractional-order LC three-phase inverter is constructed, and the mathematical model of the fractional-order LC three-phase inverter in the three-phase stationary coordinate system and the two-phase rotating coordinate system is obtained;

[0059] S3: Mathematical model and frequency domain characteristics of fractional-order LC filters, analyzing the influence of the order of fractional-order inductors and fractional-order capacitors on the frequency characteristics of fractional-order LC filters.

[0060] S4: Based on S1, the decoupling structure of the fractional-order current inner loop and the fractional-order voltage outer loop is derived according to the mathematical model of the fractional-order LC three-phase inverter in a two-phase rotating coordinate system;

[0061] S5: FOVSG control is used as power control, the small signal model of FOVSG control is derived, and the stability of FOVSG control under grid-connected and islanded operation is analyzed.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. The present invention considers the fractional-order characteristics of inductance and capacitance, establishes a mathematical model of a fractional-order LC three-phase inverter in a three-phase stationary (abc) coordinate system, and provides a mathematical model in a two-phase rotating (dq) coordinate system. The fractional-order model can replace the traditional integer-order LC three-phase inverter model, making it more in line with the complexity of the actual physical system. In addition, the fractional-order LC filter can achieve a more flexible frequency response by adjusting the fractional-order parameters, thereby more effectively suppressing harmonics. At the same time, the fractional-order LC filter can suppress the resonant characteristics of the system without introducing additional series resistance.

[0064] 2. The present invention proposes a voltage and current dual closed-loop control method based on fractional-order decoupling, which can more effectively perform dynamic decoupling according to the order of fractional inductance and capacitance. Fractional-order decoupling control can more flexibly adapt to the non-integer order characteristics of filter components, making the control of the inverter more accurate and stable in different frequency ranges.

[0065] 3. Compared with the traditional VSG control strategy, the FOVSG control strategy described in the present invention expands a new degree of freedom, which can speed up the response speed of the system, improve the inertial response of the system, achieve good damping power control, and enhance the dynamic performance of the inverter. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for the specific embodiments or the description of the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn according to the actual scale.

[0067] Figure 1 is the electrical symbol for fractional inductance and fractional capacitance;

[0068] Figure 2 This is the overall structural block diagram of a fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control proposed in this paper;

[0069] Figure 3 It is the frequency characteristic curve of the fractional-order LC filter after the fractional-order inductance and capacitance order change;

[0070] Figure 4 This is the structural block diagram of the fractional-order decoupling control of the current inner loop;

[0071] Figure 5 This is the structural block diagram of the fractional-order decoupling control of the voltage outer loop;

[0072] Figure 6 This is the control structure block diagram of the voltage and current dual loop based on fractional-order decoupling;

[0073] Figure 7 is the equivalent circuit diagram of the grid-connected inverter;

[0074] Figure 8 This is the block diagram of the active closed-loop small signal model of FOVSG;

[0075] Fig. 9 This is the analysis result diagram of FOVSG when it is connected to the grid;

[0076] Fig.10 This is the analysis result diagram of FOVSG island operation;

[0077] Fig.11 It is the A-phase grid-connected simulation waveform diagram of the change of inductance order and capacitance order under the open-loop operation state;

[0078] Fig.12It is a simulation waveform diagram of power frequency response of different rotor orders under grid-connected operation when the active reference value has a step;

[0079] Fig.13 It is a simulation waveform diagram of power-frequency response of different rotor orders under island operation state when load power steps occur; DETAILED DESCRIPTION

[0080] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0081] It should be understood that when used in this specification and the appended claims, the terms "include" and "comprises" indicate the presence of described features, integers, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof.

[0082] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0083] It should be further understood that the term "and / or" used in the present description and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0084] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which the present disclosure belongs. The terms used herein are only for the purpose of describing the embodiments of the present disclosure and are not intended to limit the present disclosure.

[0085] The present invention provides an embodiment of a modeling method for a fractional-order LC three-phase inverter. The modeling method for a fractional-order LC three-phase inverter specifically includes the following contents:

[0086] In one embodiment of the present invention, a fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control is constructed as follows:

[0087] S1: Based on the definition of Caputo-type fractional calculus, mathematical models of fractional capacitors and fractional inductors are established;

[0088] The mathematical model of fractional inductance and fractional capacitance is shown in formula (1), which is the basis of fractional circuit analysis. Fractional inductance and fractional capacitance are the basic components of fractional circuits. Their circuit symbols are as follows: Figure 1 As shown. Where L and C represent the fractional capacitance and inductance values ​​respectively; α and β represent the order of fractional inductance and fractional capacitance; u L and u C Represent the voltage of fractional inductance and fractional capacitance respectively; i L and i C Represent the current of fractional inductance and fractional capacitance respectively.

[0089]

[0090] S2: Construct the main circuit topology of the fractional-order LC three-phase inverter and obtain the mathematical model of the fractional-order LC three-phase inverter in the three-phase stationary coordinate system and the two-phase rotating coordinate system;

[0091] Figure 2 This is the system structure of the three-phase inverter based on the fractional-order LC filter and fractional-order virtual inertia control proposed by the present invention. In the main circuit part of the figure, V is IGBT, D is freewheeling diode, U dc is the DC side voltage, R is the inductor parasitic resistance, L f is the fractional-order filter inductance, in H / s 1-α , α is the fractional inductor order; C f Fractional filter capacitor, unit is F / s 1-β , β is the fractional capacitor order; i Labc is the current of the fractional-order filter inductor, which consists of three components i La 、i Lb 、i Lc Composition, i Labc =[i La i Lb i Lc ] T ,i La 、i Lb 、i Lc is the current of phase a, phase b, and phase c of the fractional-order filter inductor; u abc is the converter output voltage, which consists of three components u a 、u b 、u c Composition, u abc =[u a u b u c ] T ,u a 、u b 、uc Output a-phase, b-phase, and c-phase voltages for the inverter bridge arm; u Cabc is the voltage of the fractional filter capacitor, which consists of three components u Ca 、u Cb 、u Cc Composition,u Cabc =[u Ca u Cb u Cc ] T ,u Ca 、u Cb 、u Cc is the voltage of phase a, phase b, and phase c of the fractional capacitor; i gabc is the line current, which consists of three components i ga 、i gb 、i gc Composition, i gabc =[i ga i gb i gc ] T ,i ga 、i gb 、i gc are the phase a, phase b and phase c currents of the fractional-order filter inductor.

[0092] exist Figure 2 In the main circuit shown in the figure, the mathematical model of the fractional-order LC three-phase inverter in the three-phase stationary coordinate system is obtained by KCL and KVL:

[0093]

[0094] Preferably, for the convenience of analysis, a mathematical model of a fractional-order LC three-phase inverter in a two-phase rotating coordinate system is established, as follows:

[0095]

[0096] Performing Laplace transformation on the above equation, we get its mathematical model in the s domain:

[0097]

[0098] It can be seen from equations (5) and (6) that there is cross coupling between the d-axis and q-axis currents in the synchronous rotating coordinate system, and measures need to be taken to decouple them.

[0099] S3: Mathematical model and frequency domain characteristics of fractional-order LC filters, analyzing the influence of the order of fractional-order inductors and fractional-order capacitors on the frequency characteristics of fractional-order LC filters.

[0100] Depend on Figure 2 It can be seen that the converter output voltage u abcTo the filter output voltage u Cabc The transfer function is

[0101]

[0102] The frequency characteristics and resonance characteristics of the fractional-order LC filter are analyzed by formula (7). If R = 1Ω, L f =3.5mH / s 1 -α , C f =350μF / s 1-β , the frequency characteristics of the fractional-order LC filter are obtained as Figure 3 shown.

[0103] Figure 3 (a) is the frequency response characteristics of the fractional-order LC filter when the fractional-order capacitor order β is fixed to 1 and the fractional-order inductor order α increases from 0.75 to 1. As α increases, the corner frequency of the system gradually decreases, reflecting the significant influence of the fractional-order inductor on the dynamic response of the system. When α = 1, β = 1, a resonance peak appears in the amplitude-frequency characteristic of the filter, and as α decreases, the resonance effect becomes weaker and weaker. Taking the resonant frequency as the dividing line, before resonance, the curves almost overlap, indicating that the frequency characteristics of the fractional-order LC filter in this frequency band are not affected by the change of α; after the resonant frequency, the slope of the amplitude-frequency characteristic and the decrease amplitude of the phase-frequency characteristic increase significantly with the increase of α. Figure 3 (b) is the frequency characteristic of the fractional-order LC filter when the fractional-order inductor order α is fixed to 1 and the fractional-order capacitor order β increases from 0.75 to 1. The analysis method when β changes is similar to that when α changes. The difference is that as β decreases, the resonance effect of the fractional-order LC filter gradually weakens, but the degree of weakening is far less rapid than the rate of changing α, which shows that the order of the inductor has a greater impact on the performance of the fractional-order LC filter.

[0104] The results show that fractional-order LC filters can achieve a more flexible frequency response by adjusting the fractional-order parameters, thereby more effectively suppressing high-order harmonics. At the same time, the resonant characteristics of the system can be suppressed without introducing additional series resistance. The fractional-order LC filter is designed with more realistic fractional-order characteristics in mind, making the filter's operating performance more in line with expectations, improving the system's robustness and fault tolerance, and reducing design errors caused by the non-ideality of physical components. In short, fractional-order LC filters provide greater design freedom, and the performance of the filter can be optimized by reasonably configuring the fractional order, which can also reduce the errors caused by ideal component modeling.

[0105] S4: Based on the mathematical model of S2, the decoupling structure of the fractional-order current inner loop and the fractional-order voltage outer loop is derived according to the mathematical model of the fractional-order LC three-phase inverter in a two-phase rotating coordinate system;

[0106] Preferably, the decoupling design is performed by replacing equivalent control variables. From formula (6), it can be seen that for the current inner loop, the variable e is defined as d (s), e q (s) are as follows:

[0107]

[0108] E d (s), e q When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes is eliminated, that is:

[0109]

[0110] Generally speaking, the equivalent control variable e d (s), e q (s) can be generated by a PI regulator. Since the fractional-order inductor is decoupled, FOPI is selected here to generate the equivalent control variable e d (s), e q (s).

[0111]

[0112] In the formula, K ip K is the current inner loop proportional coefficient, ii is the current inner loop integration coefficient, and γ is the current inner loop integration order.

[0113] By combining equations (8) and (10) and replacing the equivalent control variables, we can derive u d (s) and u q The equation for (s) is as follows:

[0114]

[0115] At this point, the current loop has been decoupled. The structure of the current loop decoupling is as follows: Figure 4 shown.

[0116] For the voltage loop, define the variable i vd (s), i vq (s) are as follows:

[0117]

[0118] will i vd (s), i vq When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes in equation (7) is eliminated, that is:

[0119]

[0120] The equivalent control variable i vd (s), i vq (s) can be generated by a PI controller as shown below:

[0121]

[0122] In the formula, K vp is the voltage outer loop proportional coefficient, K vi is the voltage outer loop integration coefficient, and μ is the voltage outer loop integration order.

[0123] By combining equations (12) and (14) and substituting the equivalent control variables, we can derive i Ld (s), i Lq (s) and use it as the given value i of the current inner loop Ld * (s), i Lq * (s), which is expressed as follows:

[0124]

[0125] At this point, the voltage loop has been decoupled, and the structure of the current loop decoupling is as follows: Figure 5 As shown in the figure. i (s) is the transfer function of the current inner loop, which can be obtained from the control link of the current inner loop. The final fractional-order voltage-current double closed-loop structure is as follows: Figure 6 shown.

[0126] S5: FOVSG control is used as power control, the small signal model of FOVSG control is derived, and the stability of FOVSG control under grid-connected and islanded conditions is analyzed.

[0127] The control equation of the FOVSG is as follows:

[0128]

[0129] Among them, P e and Q e are the output active power and reactive power respectively; P ref and Q ref are the reference active power and reactive power respectively; J and D are the moment of inertia and damping coefficient respectively; λ is the adjustable fractional order, ω0 and ω are the rated angular frequency and output angular frequency; k p and k q is the active power droop coefficient and reactive power droop coefficient; U m and U n is the reference voltage amplitude and the effective value of the terminal voltage.

[0130] The equivalent circuit of the grid-connected inverter is as follows Figure 7 As shown, Z f is the equivalent impedance of the filter circuit, Z s is the line impedance, let Z = Z f +Z s =R+jX, δ is the phase difference between VSG output voltage and grid voltage δ=∫(ω-ω0)dt. U g is the grid voltage amplitude; E is the VSG output voltage.

[0131] Assuming that the impedance between the inverter and the grid is inductive (X>>R), the active and reactive power transmitted between the inverter and the grid is

[0132]

[0133] make The active closed-loop small signal model of FOVSG can be obtained as follows: Figure 8 shown.

[0134] have Figure 8 The small signal model of the FOVSG output active increment and active reference value is obtained as follows:

[0135]

[0136] The small signal model of output frequency change and active power increment is:

[0137]

[0138] When connected to the grid, the main task of the inverter is to output active power according to the change of the active power command value. The zero-pole distribution and step response of formula (18) are used to evaluate the operating performance when connected to the grid. Taking the parameters in Table 1, the analysis results are as follows: Fig. 9 shown.

[0139] Table 1 FOVSG theoretical analysis parameters

[0140] parameter value E 311V <![CDATA[U g ]]> 311V <![CDATA[k p ]]> 300 <![CDATA[ω0]]> 100πrad / s X 1.8Ω J <![CDATA[3kg·m 2 ]]> D 15 <![CDATA[ΔP ref ]]> 5kW ΔP 5kW

[0141] Fig. 9 (a) Describes the G corresponding to different fractional rotor orders p (s) Change of pole position, the arrow indicates the increase of fractional rotor order. Fig. 9 (b) shows the active power reference value has a step change (ΔP ref=5kW), the output active power response curve of the inverter under different fractional rotor orders. Adding fractional orders to the rotor equation of the traditional VSG will significantly change the pole distribution and dynamic behavior of the system. As the fractional rotor order increases, the two complex poles of the system get closer and closer to the imaginary axis. Their real components initially deviate from the real axis and then move closer to the real axis. The change in the pole trajectory illustrates the complex influence of the fractional order on the basic oscillation characteristics and attenuation rate of the system. The approach of the complex poles to the imaginary axis means a decrease in the natural frequency of the system, resulting in more intense oscillations. The change in the real component means that the attenuation rate of the system initially decreases and then increases. The nonlinear pole movement indicates the dual effect of the fractional order on the stability of the system, which may amplify the oscillation and affect the convergence speed. When the power reference value undergoes a step change, the overshoot and oscillation amplitude of the inverter output active power will increase significantly with the increase of the fractional order. This shows that the addition of fractional orders affects both the pole distribution and the transient response of the system, resulting in more obvious overshoot and oscillation, which puts higher requirements on control stability.

[0142] Under the condition of island operation, the focus of the study is the dynamic response performance of the angular frequency of the virtual synchronous generator after the load power changes. Assuming that the line loss can be ignored, that is, the inverter output power is equal to the load power, the core of the study is the dynamic relationship between the angular frequency and the output power. The frequency response and step response of formula (18) are used to evaluate the operating characteristics of the island. The analysis results are shown in Fig.10 shown.

[0143] Fig.10 (a) shows that as the fractional order λ increases, the slope of the amplitude-frequency curve increases, indicating that the fractional-order virtual inertial elements can provide a more gradual response compared to integer-order elements. This change highlights the advantage of fractional order in enhancing the stability of the system frequency response. In the phase-frequency response, as λ increases, the loss of phase angle also increases, indicating that the phase margin is steadily decreasing. This decrease indicates that the instability of the system is exacerbated when the frequency is interrupted. Fig.10 In (b), when a power step change of 5kW is implemented, the rate of change of frequency during the transient process gradually decreases with increasing λ. For smaller λ, the angular frequency decreases faster, indicating that the system inertia decreases. As λ increases, the rate of change of frequency decreases, the curve becomes more uniform, and the system inertia increases. In the steady-state frequency response, as λ increases, the final angular frequency decreases more, indicating that although the system frequency changes more smoothly, the steady-state frequency deviation becomes larger. This pattern emphasizes the adverse effect of virtual inertia on frequency recovery, indicating that increased inertia prolongs the frequency adjustment duration and leads to an increase in steady-state frequency error.

[0144] Based on the MATLAB / SIMULINK simulation platform, a three-phase inverter simulation model based on fractional-order LC filter and fractional-order virtual inertia control was built. The ideal DC voltage source module in Simulink is used on the DC side to simulate the energy storage battery, and the ideal controlled AC voltage source is used on the AC side to simulate the characteristics of the infinite power grid. The main circuit parameters are shown in Table 2.

[0145] Table 2 Main circuit parameters

[0146]

[0147] In order to analyze the impact of fractional-order inductance and capacitance orders on the performance of the inverter, the system is simulated in an open-loop, no-load state. First, while keeping the fractional-order capacitance order unchanged, the impact of different fractional-order inductance orders on system performance is studied. Then, the fractional-order inductance order is fixed, and the impact of the change of fractional-order capacitance order on the dynamic characteristics of the system is analyzed. The simulation results of the A-phase grid-connected current are shown in Figure 2. Fig.11 As shown in the figure, (a) shows the grid-connected situation when α is gradually increased from 0.75 to 1 when β is fixed at 1; (b) shows the grid-connected situation when α is gradually increased from 0.75 to 1 when α is fixed at 1. In this process, I a is the effective value of the grid-connected current of phase A, i a is the instantaneous value of the A-phase grid-connected current, is the phase angle difference between the voltage and current of phase A. For further analysis, specific simulation data are listed in Table 3. The initial time in the total harmonic distortion (THD) value is the first 0.1s, that is, the first 5 cycles, and the steady-state time is 0.1s-0.2s, that is, the last 5 cycles.

[0148] Depend on Fig.11 It can be seen from Table 3 that when the order of fractional capacitors remains unchanged and the order of inductance gradually increases from 0.75 to 1, the steady-state effective value of the grid-connected current of phase A decreases significantly, from 582.68A to 183.87A, indicating that higher-order fractional inductance can effectively suppress the current amplitude. At the same time, the steady-state phase difference increases from 26.57° to 64.26°, indicating that the increase in the order of inductance leads to an increase in the phase lag between voltage and current. The THD value at the initial moment increases from 5.32% to 13.12% with the increase in the order of inductance, but in steady state, the THD value decreases from 1.31% to 0.59%, indicating that the system's ability to suppress harmonic distortion in steady state increases with the increase in the order of inductance.

[0149] Table 3 Performance indicators when the inductance and capacitance order change

[0150]

[0151] When the inductor order is fixed at 1 and the capacitor order gradually increases from 0.75 to 1, the steady-state effective value of the A-phase grid-connected current changes slightly, and the range remains between 201.24A and 183.87A, indicating that the capacitor order has a limited effect on the current amplitude. The steady-state phase difference fluctuates from 64.26° to 65.86°, indicating that the capacitor order has little effect on the system phase difference. The THD at the initial moment increases slightly with the increase of the capacitor order, but the THD in the steady state always remains at a low level.

[0152] In summary, the order of fractional-order inductance significantly affects the current amplitude, phase difference and harmonic distortion of the grid-connected inverter. Higher-order inductance effectively suppresses the current amplitude, but improves harmonic control. While meeting the harmonic distortion rate requirements, other performance indicators such as power factor and system dynamic response can be given priority. Lower inductance orders can reduce current phase lag, thereby improving system efficiency and power output. Although the capacitor order has a smaller impact on the current amplitude and phase difference, it still plays an important role in steady-state harmonic control, and the capacitor order should not be too low. Therefore, the order of inductance and capacitance should be comprehensively considered in system design to achieve the best overall performance.

[0153] The selected fractional-order LC filter inductor order α is 0.90, and the capacitor order β is 0.95. In order to verify the influence of the inverter power command on the output power and frequency response during the grid connection process, the following working conditions are set: at the initial moment, the grid frequency is maintained at 50Hz, and the inverter operates at the rated working state. According to the set active power reference value P ref , the inverter outputs 5kW of active power to the grid. 1s later, P ref A step change occurs, jumping to 10kW.

[0154] Fig.12 It describes the P under the grid-connected setting with different fractional rotor orders λ of FOVSG. ref The power frequency response curve for a step change from 5 kW to 10 kW. Fig.12 (a) shows that as λ increases, the active power response will have greater overshoot and oscillation. The smaller λ is, the more stable the power response is, the faster the adjustment is, and the less overshoot is. As λ increases, the more obvious inertial effect will lead to greater overshoot, oscillation, and reduced response speed. Fig.12(b) shows that the smaller λ is, the faster the system responds to the step change, resulting in a more obvious frequency increase and larger fluctuations. As λ increases, the frequency response becomes smoother. When λ increases, the frequency curve shows obvious oscillation. The simulation results verify the impact of λ on the grid control performance. Reducing the value of λ can improve the dynamic response speed but affect the instantaneous frequency stability, while increasing the value of λ will produce a smoother response but increase the possibility of oscillation. These findings show that the selection of λ must take into account both the response speed and the system stability.

[0155] In order to verify the influence of load power change on system frequency response under island operation, the following simulation settings are made: at the initial moment, the active power reference value P output by the inverter is ref Set to 5kW, the load power is also 5kW at this time, and the system is in a power balance state. After 1s, the load power changes stepwise and increases to 10kW to simulate the impact of a sudden load increase on the dynamic response of the system frequency.

[0156] Fig.13 When the order λ of FOVSG changes during islanding, the power-frequency response curve of the inverter. Fig.13 As can be seen from (a), as λ increases, the impact on the system's active power response curve is small. Fig.13 From the response analysis results in (b), when the step load disturbance of ΔP=5kW is set, as λ increases, the transient response of the system frequency becomes smoother and the frequency change rate gradually decreases. This verifies the results of the theoretical analysis, that is, the increase in fractional order will enhance the virtual inertia of the system and reduce the frequency change rate. However, in the steady-state frequency response, the system with a larger λ value exhibits a larger frequency deviation, which further supports the theoretical prediction of the negative impact on the frequency recovery capability. In summary, the experimental results show that although increasing the fractional order can significantly improve the dynamic frequency response characteristics of the system, its impact on the steady-state frequency deviation cannot be ignored and needs to be weighed in practical applications.

[0157] The present invention proposes a three-phase inverter topology of a fractional-order LC filter based on the fractional-order characteristics of inductance and capacitance, and derives the mathematical model of the fractional-order LC type three-phase inverter under the three-phase stationary coordinate system (a, b, c) and the mathematical model in the two-phase rotating coordinate system (dq). Based on the mathematical model, a voltage and current double closed-loop control method with fractional-order decoupling is designed, and a fractional-order virtual synchronous generator (FOVSG) control strategy is adopted in the power control link. The present invention takes into account the influence of the order of inductance and capacitance on the performance of the inverter, and finds that the order of inductance has a greater influence on it. In addition, the FOVSG control adopted by the present invention adds one degree of freedom compared to the traditional VSG control. When connected to the grid, the FOVSG rotor order can be appropriately reduced to reduce the overshoot and oscillation of power. When operating in an isolated island, the FOVSG rotor order can be appropriately increased to obtain greater inertia, which can be reasonably set according to design needs. It can be seen that the technical solution proposed by the present invention solves the problems raised in the background technology.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A modeling method for a fractional-order LC three-phase inverter, characterized in that: The following steps are involved: Based on the definition of Caputo-type fractional calculus, mathematical models of fractional capacitors and fractional inductors are established; Based on the fractional-order capacitor and fractional-order inductor mathematical models established in step S1, a main circuit topology of a fractional-order LC three-phase inverter is constructed to obtain a mathematical model of the fractional-order LC three-phase inverter in a three-phase stationary coordinate system and a two-phase rotating coordinate system; Based on the main circuit topology of the fractional-order LC three-phase inverter, the mathematical model of the fractional-order LC filter is obtained; Based on the mathematical model of the fractional-order LC three-phase inverter in a two-phase rotating coordinate system, the decoupling control structure of the fractional-order current inner loop and the fractional-order voltage outer loop is derived. Taking FOVSG control as power control, the small signal model of FOVSG control is derived, and the stability of FOVSG control under grid-connected and islanded operation is analyzed.

2. A fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control according to claim 1, characterized in that: It includes a main circuit topology part and a control part, wherein the main circuit part replaces the LC filter in the traditional LC three-phase inverter with a fractional-order LC filter and then connects to the local load, and is connected to the infinite power grid through the external power grid via the PCC point. The control link includes FOVSG control and voltage and current dual closed-loop control. The FOVSG control includes active control and reactive control. Active control simulates the inertia and primary frequency modulation of the synchronous generator, and reactive control simulates the active voltage regulation of the synchronous machine. The voltage and current dual closed-loop control generates a voltage reference signal, and uses the space vector pulse width modulation method to generate a drive signal to control each switch device. The fractional-order inductor mathematical model is as follows: In the formula, u L ,i L They represent fractional inductor voltage and fractional inductor current respectively, L is the inductance value, and α is the fractional inductor order; The fractional-order capacitor mathematical model is as follows: In the formula, u C ,i C They represent the fractional capacitor voltage and fractional capacitor current respectively, C is the capacitance value, t is the time, and β is the fractional capacitor order.

3. The modeling method of a fractional-order LC three-phase inverter according to claim 2, characterized in that: The mathematical model of the modeling method of the fractional-order LC three-phase inverter in the three-phase stationary coordinate system is as follows: Where R is the inductor parasitic resistance, L f is the fractional-order filter inductance, in H / s 1-α , α is the fractional inductor order; C f Fractional filter capacitor, unit is F / s 1-β , β is the fractional capacitor order; i Labc is the current of the fractional-order filter inductor, which consists of three components i La 、i Lb 、i Lc Composition, i Labc =[i La i Lb i Lc ] T ,i La 、i Lb 、i Lc is the current of phase a, phase b, and phase c of the fractional-order filter inductor; u abc is the converter output voltage, which consists of three components u a 、u b 、u c Composition, u abc =[u a u b u c ] T ,u a 、u b 、u c Output a-phase, b-phase, and c-phase voltages for the inverter bridge arm; u Cabc is the voltage of the fractional filter capacitor, which consists of three components u Ca 、u Cb 、u Cc Composition,u Cabc =[u Ca u Cb u Cc ] T ,u Ca 、u Cb 、u Cc is the voltage of phase a, phase b, and phase c of the fractional capacitor; i gabc is the line current, which consists of three components i ga 、i gb 、i gc Composition, i gabc =[i ga i gb i gc ] T ,i ga 、i gb 、i gc is the current of phase a, phase b and phase c of fractional order filter inductor; The mathematical model in the two-phase rotating coordinate system is as follows: In the formula, i Ld 、i Ld for i Labc The d-axis component and q-axis component obtained by dq transformation; u d 、u q for u abc The d-axis component and q-axis component obtained by dq transformation; u Cd 、u Cq for u Cabc The d-axis component and q-axis component obtained by dq transformation; i gd 、i gq for i gabc The d-axis component and q-axis component obtained by dq transformation; ω is the inverter output angular frequency; Performing Laplace transformation on the model in dq coordinates yields: In the formula, i Ld (s), i Ld (s) is i Ld 、i Ld The quantity obtained by Laplace transformation; u d (s),u q (s) is u d 、u q The quantity obtained by Laplace transformation; u Cd (s),u Cq (s) is u Cd 、u Cq The quantity obtained by Laplace transformation; i gd (s), i gq (s) is i gd 、i gq The quantity obtained by Laplace transformation.

4. A fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control according to claim 2, characterized in that The fractional-order LC filter outputs a voltage u from the converter abc To the filter output voltage u Cabc The transfer function is:

5. According to the mathematical model of the fractional-order LC three-phase inverter based on fractional-order virtual synchronous generator control in three-phase stationary coordinate system and two-phase stationary coordinate system, the decoupling control structure of the fractional-order current inner loop and the fractional-order voltage outer loop is derived as follows: The decoupling design is carried out by replacing equivalent control variables. For the current inner loop, the variable e is defined. d (s), e q (s) are as follows: E d (s), e q When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes is eliminated, that is: Select PI λ Generate equivalent control variable e d (s), e q (s): In the formula, K ip K is the current inner loop proportional coefficient, ii is the current inner loop integration coefficient, γ is the current inner loop integration order; After replacing the equivalent control variables, u can be derived d (s) and u q The equation for (s) is as follows: At this point, the current loop has been decoupled; For the voltage loop, define the variable i vd (s), i vq (s) are as follows: will i vd (s), i vq When (s) is used as an equivalent control variable, the mutual coupling relationship between the dq axes in the formula is eliminated, that is: The equivalent control variable i vd (s), i vq (s) can be obtained by fractional PI λ The controller generates the following equation: In the formula, K vp is the voltage outer loop proportional coefficient, K vi is the voltage outer loop integration coefficient, μ is the voltage outer loop integration order; After replacing the equivalent control variables, we can derive i Ld (s), i Lq (s) and use it as the given value i of the current inner loop Ld * (s), i Lq * (s), which is expressed as follows:

6. The modeling method of a fractional-order LC three-phase inverter according to claim 1, characterized in that: The FOVSG control equation in step S5 is as follows: Where P e and Q e are the output active power and reactive power respectively; P ref and Q ref are the reference active power and reactive power respectively; J and D are the moment of inertia and damping coefficient respectively; λ is the adjustable fractional order, ω0 and ω are the rated angular frequency and output angular frequency; k p and k q is the active power droop coefficient and reactive power droop coefficient; U m and U n is the reference voltage amplitude and the effective value of the terminal voltage.

7. The modeling method of a fractional-order LC three-phase inverter according to claim 6, characterized in that: The FOVSG control small signal model is as follows: The small signal model of the output active power increment and active power reference value is: In the formula, Where X is the reactance between the inverter and the grid; U g is the grid voltage amplitude; E is the VSG output voltage; The small signal model of output frequency change and active power increment is:

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein when the program is executed, the device where the computer-readable storage medium is located is controlled to execute the fractional-order LC type three-phase inverter based on fractional-order virtual synchronous generator control as described in any one of claims 1 to 7.

9. A processor, characterized in that: The processor is used to run a program, wherein the program, when running, executes a modeling method for a fractional-order LC three-phase inverter as claimed in any one of claims 1 to 7.

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