Optimization method of LCL grid-connected inverter system based on fractional-order differential compensator

Abstract

The present invention belongs to the field of robustness control of new energy grid-connected inverter systems, and proposes an optimization method for an LCL-type grid-connected inverter system based on a fractional-order differential compensator. First, a mathematical model of an LCL-type grid-connected inverter system based on a fractional-order differential compensator is established; according to the system mathematical model, the relationship between the system reverse resonance peak frequency and the grid impedance is obtained; then, by analyzing the resonant zero poles of the inverter system open-loop transfer function, the parameter design conditions of the fractional-order differential compensator are obtained; then, the parameter design conditions are substituted into the fractional-order differential compensator expression to obtain the parameter design results of the fractional-order differential compensator; according to the frequency domain characteristics and fitting characteristics of the fractional-order differential, the fitting frequency band and fitting order design results of the fractional-order differential compensator are obtained. Finally, the system has sufficient phase margin to adapt to the changes in the weak power grid, which improves the robustness of the system in the weak power grid.

Description

Technical Field

[0001] The present invention belongs to the field of robustness control of new energy grid-connected inverter systems, and in particular relates to an optimization method for an LCL type grid-connected inverter system based on a fractional-order differential compensator. Background Art

[0002] With the depletion of conventional fossil energy and the worsening of environmental pollution, renewable energy such as photovoltaic and wind power generation has received widespread attention. The main way to develop and utilize renewable energy is distributed power generation. Grid-connected inverters, as the core device connecting the power generation system and the power grid, have received widespread attention.

[0003] In order to ensure that the grid-connected current meets the requirements of relevant standards, the inverter cascade L filter or LC filter is often used, but this method will cause the filter inductor to be bulky and expensive. At present, the common practice is to use LCL filter instead, which can effectively reduce the volume and obtain better performance. However, as a third-order system, the LCL filter has a resonant peak at a specific frequency, which will cause the grid current to oscillate and bring difficulties to control. To address this problem, there are currently three commonly used active damping methods: capacitor current and grid-connected current dual closed-loop control method, based on the series connection method of filter and current regulator, and system order reduction method. Among them, the system order reduction method can reduce the system order from third order to first order, greatly reducing the difficulty of system control. It has been widely used due to its simple and flexible parameter design and high control bandwidth.

[0004] The system order reduction method can achieve good control effects while ignoring the system delay. However, in actual digital control systems, delay is inevitable, which will greatly affect the robustness of the system and become sensitive to the grid impedance, making it difficult to apply. Therefore, based on the system order reduction method, how to compensate for the system delay can not only retain the advantages of the original method but also enhance the system stability, which has become an urgent problem to be solved. Summary of the invention

[0005] The object of the present invention is to provide an optimization method for an LCL type grid-connected inverter system based on a fractional-order differential compensator, aiming to compensate for the digital delay of the system and solve the problem of poor robustness of the grid-connected system in a digital control system.

[0006] Considering that the fractional-order controller has better control effect and wider application range, the present invention introduces a fractional-order differential compensator in the optimization problem of the LCL type grid-connected inverter system, and uses its unique fitting characteristics to optimize the control performance.

[0007] The technical solution adopted by the present invention is: to provide an LCL type grid-connected inverter system optimization method based on a fractional-order differential compensator, comprising the following steps:

[0008] Establish a mathematical model of LCL grid-connected inverter system based on fractional-order differential compensator;

[0009] According to the system mathematical model, the relationship between the system reverse resonance peak frequency and the grid impedance is obtained;

[0010] Analyze the resonant zero poles of the inverter system open-loop transfer function and obtain the parameter design conditions of the fractional-order differential compensator;

[0011] Substituting the parameter design conditions into the expression of fractional-order differential compensator, the parameter design results of fractional-order differential compensator are obtained.

[0012] According to the frequency domain characteristics and fitting characteristics of fractional-order differential, the fitting frequency band and fitting order design results of the fractional-order differential compensator are obtained.

[0013] Preferably, the mathematical model of the LCL grid-connected inverter system based on the fractional-order differential compensator is the following open-loop transfer function, which is represented by the first expression:

[0014]

[0015] In the above formula, L 1 is the inverter side inductance, L 2 is the grid-side inductor, C is the filter capacitor, together they form the LCL inverter, R d is the damping resistor, and the grid impedance at the common coupling point PCC is a pure inductor L g , β and 1-β are current weighting coefficients, K PWM =v in / v tri Indicates the inverter voltage gain, v tri is the triangular carrier amplitude, v in Indicates the input DC bus voltage of the inverter, G f (s) is the PCC voltage feedforward function, G d (s) represents a digital delay link, and its transfer function is the second expression:

[0016]

[0017] Among them, T s represents the sampling time of the system;

[0018] G i (s) represents the PI current regulator, and the mathematical expression is the third expression;

[0019]

[0020] Among them, K p is the proportionality coefficient, K ris the integration time constant;

[0021] Take G f (s) and β satisfy the fourth expression and the fifth expression respectively:

[0022]

[0023]

[0024] G c (s) is a fractional-order differential compensator, and its mathematical expression is the sixth expression:

[0025] G c (s) = Ks μ ,μ∈(0,1)

[0026] Where K is the differential time constant and μ is the differential order.

[0027] Preferably, the step of obtaining the relationship between the system reverse resonance peak frequency and the grid impedance according to the system mathematical model comprises:

[0028] Substituting the fourth expression and the fifth expression into the first expression, the open-loop transfer function of the inverter system is obtained as the seventh expression:

[0029]

[0030] There is a pair of conjugate resonant zeros in the inverter open-loop transfer function, which causes the appearance of reverse resonance peaks in the amplitude-frequency characteristic.

[0031] Let the molecular resonance term of the seventh expression be zero, and we get the eighth expression:

[0032]

[0033] Can be obtained with L g The change of reverse resonance frequency is expressed as the ninth expression:

[0034]

[0035] It can be seen that the reverse resonance frequency f rx As the grid impedance changes, the robustness of the grid-connected system decreases as the grid impedance increases.

[0036] Preferably, the step of analyzing the resonant zero poles of the open-loop transfer function of the inverter system to obtain the parameter design conditions of the fractional-order differential compensator includes:

[0037] From the seventh expression, we can see that the root cause of the inability to eliminate the resonant zero pole is 1-G c (s)G d (s);

[0038] In order to make 1-G c (s)G d The amplitude of (s) is approximately equal to zero at the reverse resonant frequency, and the fractional-order differential compensator G c (s) in f rx-min The amplitude at f is 1, and the inverter open-loop transfer function is rx-min There is a phase jump at f. In order to maintain the stability of the grid-connected system, the fractional-order differential compensator is used at f rx-min The advanced phase angle provided at the digital delay link G can completely offset the delay d (s) the phase lag introduced;

[0039] Therefore, the parameter design condition of the fractional-order differential compensator is set to the tenth expression:

[0040]

[0041] Among them, f rx-min is the reverse resonant frequency corresponding to the maximum grid impedance.

[0042] Preferably, the step of substituting the parameter design conditions into the fractional-order differential compensator expression to obtain the parameter design result of the fractional-order differential compensator includes:

[0043] For the fractional-order differential compensator transfer function G c (s), let s = jω, then Substituting into the tenth expression we get the eleventh expression:

[0044]

[0045] Finally, the parameter design result of the fractional-order differential compensator is the twelfth expression:

[0046]

[0047] Where K is the differential time constant and μ is the differential order.

[0048] Preferably, the step of obtaining the fitting frequency band and fitting order design result of the fractional-order differential compensator according to the frequency domain characteristics and fitting characteristics of the fractional-order differential comprises:

[0049] According to the frequency domain characteristics and fitting characteristics of fractional-order differential, the fitting frequency band of the fractional-order differential compensator is set to [10 Hz, 100000 Hz], and the fitting order is selected as N=5.

[0050] According to another aspect of the present invention, the present invention also provides an electronic device, comprising a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, any one of the LCL type grid-connected inverter system optimization methods based on a fractional-order differential compensator is executed.

[0051] The technical solution provided by the present invention has the following beneficial effects:

[0052] 1. Improved the stability of LCL type grid-connected inverter system in digital system.

[0053] 2. The adaptability of the LCL grid-connected inverter system to grid impedance is improved, thereby enhancing the robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The specific effects of the present invention will be further described below in conjunction with the accompanying drawings and embodiments, in which:

[0055] Figure 1 is an execution flow chart of an LCL type grid-connected inverter system optimization method based on a fractional-order differential compensator provided by an embodiment of the present invention;

[0056] Figure 2 It is a topology structure of an LCL type grid-connected inverter system based on a fractional-order differential compensator in an embodiment of the present invention;

[0057] Figure 3 is a control block diagram of an LCL type grid-connected inverter system based on a fractional-order differential compensator in an embodiment of the present invention;

[0058] Figure 4 is a Bode diagram of a fractional-order differential compensator in an embodiment of the present invention;

[0059] Figure 5 is an open-loop Bode diagram of the LCL-type grid-connected inverter system based on the fractional-order differential compensator in the embodiment of the present invention when the grid impedance changes;

[0060] Figure 6 : is a closed-loop system root locus diagram of an LCL type grid-connected inverter system based on a fractional-order differential compensator in an embodiment of the present invention;

[0061] Figure 7 It is a grid-connected voltage and current waveform diagram of an LCL-type grid-connected inverter system based on a fractional-order differential compensator in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0063] refer to Figure 1 The LCL grid-connected inverter system optimization method based on the fractional-order differential compensator provided by the embodiment of the present invention comprises the following steps:

[0064] S10: Establish a mathematical model of LCL grid-connected inverter system based on fractional-order differential compensator;

[0065] S20: According to the system mathematical model, the relationship between the system reverse resonance peak frequency and the grid impedance is obtained;

[0066] S30: Analyze the resonant zero poles of the open-loop transfer function of the inverter system to obtain the parameter design conditions of the fractional-order differential compensator;

[0067] S40: Substituting the parameter design condition into the fractional-order differential compensator expression to obtain the parameter design result of the fractional-order differential compensator;

[0068] S50: According to the frequency domain characteristics and fitting characteristics of the fractional-order differential, a fitting frequency band and a fitting order design result of the fractional-order differential compensator are obtained.

[0069] like Figure 2 As shown, according to Figure 2 The system topology diagram establishes a mathematical model, and the system control structure diagram is as follows Figure 3 shown.

[0070] In one embodiment of the present invention, step S10 is implemented as follows:

[0071] The mathematical model of the LCL grid-connected inverter system based on fractional-order differential compensator is constructed, and its open-loop transfer function is:

[0072]

[0073] In the above formula, L 1 is the inverter side inductance, L 2 is the grid-side inductor, C is the filter capacitor, together they form an LCL filter, R d is the damping resistor, and the grid impedance at the point of common coupling (PCC) is a pure inductor L g β and 1-β are current weighting coefficients, K PWM =v in / v tri (v in Indicates the input DC bus voltage of the inverter, v tri is the triangular carrier amplitude) represents the inverter voltage gain. i (s) is the PI current regulator, G f (s) is the PCC voltage feedforward function. d (s) represents the digital delay link, where T srepresents the sampling time of the system, and its transfer function is:

[0074]

[0075] G i (s) represents the PI current regulator, K p is the proportionality coefficient, K r is the integration time constant.

[0076]

[0077] Take G f (s) and β satisfy the following design:

[0078]

[0079]

[0080] G c (s) is a fractional-order differential compensator, K is the differential time constant, and μ is the order.

[0081] G c (s) = Ks μ ,μ∈(0,1) (6)

[0082] It should be noted that the system grid impedance L g It is closely related to the degree of weak power grid of the system. In order to facilitate the subsequent explanation of the embodiment, the formula of short-circuit current ratio SCR is given here to characterize the strength of the power grid:

[0083]

[0084] Among them, I SC Indicates the effective value of the short-circuit current, I N Indicates the rated current value of the inverter output, P o is the system rated power, ω o is the fundamental angular frequency. The smaller the SCR value, the stronger the weak grid is. When the SCR value is greater than 25, it is called a strong grid, and when the SCR value is less than 10, it is called a weak grid. g It is linearly related to SCR and can be used to calculate the grid impedance L g The change of reflects the strength of the power grid. In this embodiment, the parameters are set as shown in Table 1. Let SCR = 25, and the critical power grid impedance of the strong power grid is L g-strong =1mH. Let SCR = 10, and the critical grid impedance of the weak grid is L g-weak =2.6mH.

[0085] Table 1 Parameters of the embodiments

[0086]

[0087]

[0088] In the above embodiment, according to the above system model, the change of system stability when the system works in a weak power grid can be compared by changing the power grid impedance.

[0089] In one embodiment of the present invention, the implementation method of analyzing the relationship between the system reverse resonance peak frequency and the grid impedance according to the system mathematical model in step S20 is specifically as follows:

[0090] Based on the design of formulas (4) and (5), substituting into formula (1), the open-loop transfer function of the system is:

[0091]

[0092] It can be seen from formula (8) that there is a pair of conjugate resonance zero points, which directly causes the appearance of the reverse resonance peak in the amplitude-frequency characteristic. To further study the frequency characteristics of the reverse resonance peak, let the amplitude of the molecular resonance term in formula (8) be zero, that is,

[0093]

[0094] Can be obtained with L g The reverse resonant frequency changes to:

[0095]

[0096] It can be seen that the reverse resonance frequency f rx In order to fully analyze the working state of the system under different conditions, in this embodiment, when the system short circuit ratio SCR = 5, the corresponding maximum value of the grid impedance is obtained according to formula (7) as L g-max =5.1mH, substitute into formula (10) to get the minimum value f of the reverse resonance peak frequency at this time rx-min =773.1Hz.

[0097] In the above embodiment, based on the analysis of S20, the relationship between the resonance peak frequency and the grid impedance is obtained.

[0098] In step S30, the resonant zero poles of the inverter system open-loop transfer function are analyzed according to the system mathematical model, and the implementation method of obtaining the parameter design conditions of the fractional-order differential compensator is specifically as follows:

[0099] From formula (8), we can see that the root cause of the failure of the resonant zero pole to cancel each other is 1-G c (s)G d(s), as long as this term is set to 0, the influence of digital delay on the system can be eliminated. Therefore, the compensator parameters can be analyzed from two aspects: amplitude-frequency characteristics and phase-frequency characteristics.

[0100] From the analysis in the previous step, it can be seen that the robustness of the grid-connected system decreases as the grid impedance increases. Therefore, in the parameter design of the embodiment, it is only necessary to set L as L for the case where the grid impedance is the largest. g-max =5.1mH, the reverse resonance frequency is f rx-min =773.1Hz.

[0101] In order to make 1-G c (s)G d The amplitude of (s) is approximately equal to 0 at the reverse resonant frequency, and the compensator G c (s) in f rx-min The magnitude at f should be 1. In addition, the inverter open-loop transfer function is rx-min There is a phase jump at f. In order to maintain the stability of the grid-connected system, the lead compensator is rx-min A sufficiently large leading phase angle should be provided to completely offset the delay link G d (s) The phase lag introduced, according to the above analysis, the following parameter design conditions can be obtained:

[0102]

[0103] In one embodiment of the present invention, in step S40, according to the derivation and conclusion of steps S20 and S30, the obtained parameter design conditions are substituted into the expression of the fractional-order differential compensator to obtain the implementation method of the parameter design result of the fractional-order differential compensator, and the specific implementation method is:

[0104] For the fractional-order differential compensator transfer function G c (s), let s = jω, then Substituting into formula (11) we have:

[0105]

[0106] Finally, the parameter design results of the fractional-order differential compensator are obtained:

[0107]

[0108] It should be noted that since fractional-order differential terms cannot be directly implemented, high-order integer polynomials are usually used in engineering to fit fractional-order differential terms, which can make their frequency domain response close to the original fractional-order model in a specific frequency band. Therefore, in the fractional-order implementation, it is necessary to explain the selection of the fitting frequency band and fitting order. Since there is some loss near the two ends of the fitting frequency band during fractional-order approximate fitting, the ideal setting value cannot be reached. In order not to affect the compensation effect, the fitting frequency band needs to be set larger.

[0109] In one embodiment of the present invention, in step S50, the fitting frequency band of the fractional-order differential compensator is set to [10 Hz, 100000 Hz], and the fitting order is selected as N=5, as follows: Figure 4 shown.

[0110] According to the parameters of the embodiment in Table 1, a bode diagram of the open-loop transfer function of the LCL grid-connected inverter system based on the fractional-order differential compensator is drawn when the grid impedance changes from 0mH to 5.1mH, as shown in FIG. Figure 5 As shown. It can be seen that after using the fractional-order differential compensator, the frequency characteristics of the inverter system open-loop transfer function still have a reverse resonance peak. This is due to the fact that the calculation error cannot be fully compensated. g The larger the difference from 5.1mH, the larger the resonance peak amplitude will be. However, the phase-frequency characteristics before the resonance peak have been greatly improved compared with the traditional WAC method, the phase margin of the system is greater than 0, the system is in a stable state, and the system robustness has been greatly improved.

[0111] according to Figure 3 It can be deduced that the system is 2 (s) to The closed-loop transfer function is expressed as:

[0112] When the grid impedance L g When changing from 0mH to 6mH, Figure 6 The root locus diagram of the closed-loop transfer function of the system with the fractional-order differential compensator added (only the dominant pole is shown in the figure, and the arrow direction is L g Increasing direction), it can be seen that all poles are located in the left half plane, the system remains stable, and the system has good robustness.

[0113] In order to further verify the effectiveness of the method of the present invention, an LCL grid-connected inverter system of the embodiment is established. The system parameters are shown in Table 1. The control method is implemented based on the NI PXIE-1071 hardware-in-the-loop experimental platform, and is connected to the power analyzer through an external interface board to display the waveform and measure the output grid-side current THD value.

[0114] like Figure 7 As shown, Figure 7 The experimental waveform diagram of the grid-connected inverter is shown in Figure 1 when the LCL grid-connected inverter system optimization method based on the fractional-order differential compensator proposed in the present invention is used under different grid impedance values. It can be seen from the figure that when the grid impedance changes from 0mH to 5.1mH, the grid-connected inverter can work stably and maintain a high grid-connected current quality, which verifies that the LCL grid-connected inverter system optimization method based on the fractional-order differential compensator can indeed improve the system robustness under weak grid conditions.

[0115] As a preferred embodiment of the present invention, the present invention also provides an electronic device, comprising a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the LCL type grid-connected inverter system optimization method based on the fractional-order differential compensator described in the above embodiment is executed, and the same technical effect can be achieved, which will not be repeated here.

[0116] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0117] The serial numbers of the embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In a unit claim that lists several means, several of these means may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words may be interpreted as identifiers.

[0118] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for optimizing an LCL grid-connected inverter system based on a fractional-order differential compensator, characterized in that: The following steps are involved: Establish a mathematical model of LCL grid-connected inverter system based on fractional-order differential compensator; According to the system mathematical model, the relationship between the system reverse resonance peak frequency and the grid impedance is obtained; Analyze the resonant zero poles of the inverter system open-loop transfer function and obtain the parameter design conditions of the fractional-order differential compensator; Substitute the parameter design conditions into the fractional-order differential compensator expression to obtain the parameter design result of the fractional-order differential compensator; According to the frequency domain characteristics and fitting characteristics of fractional-order differential, the fitting frequency band and fitting order design results of the fractional-order differential compensator are obtained; The mathematical model of the LCL grid-connected inverter system based on fractional-order differential compensator is the following open-loop transfer function, which is expressed by the first expression: In the above formula, L1 is the inverter side inductor, L2 is the grid side inductor, C is the filter capacitor, together they constitute the LCL type inverter, R d is the damping resistor, and the grid impedance at the common coupling point PCC is a pure inductor L g , β and 1-β are current weighting coefficients, K PWM =v in / v tri Indicates the inverter voltage gain, v tri is the triangular carrier amplitude, v in Indicates the input DC bus voltage of the inverter, G f (s) is the PCC voltage feedforward function, G d (s) represents a digital delay link, and its transfer function is the second expression: Among them, T s represents the sampling time of the system; G i (s) represents the PI current regulator, and the mathematical expression is the third expression; Among them, K p is the proportionality coefficient, K r is the integration time constant; Take G f (s) and β satisfy the fourth expression and the fifth expression respectively: G c (s) is a fractional-order differential compensator, and its mathematical expression is the sixth expression: G c (s)=Ks μ ,μ∈(0,1) Where K is the differential time constant and μ is the differential order.

2. The LCL grid-connected inverter system optimization method based on fractional-order differential compensator according to claim 1 is characterized in that: The step of obtaining the relationship between the system reverse resonance peak frequency and the grid impedance according to the system mathematical model comprises: Substituting the fourth expression and the fifth expression into the first expression, the open-loop transfer function of the inverter system is obtained as the seventh expression: There is a pair of conjugate resonant zeros in the inverter open-loop transfer function, which causes the appearance of reverse resonance peaks in the amplitude-frequency characteristic. Let the molecular resonance term of the seventh expression be zero, and we get the eighth expression: Can be obtained with L g The change of reverse resonance frequency is expressed as the ninth expression: It can be seen that the reverse resonance frequency f rx As the grid impedance changes, the robustness of the grid-connected system decreases as the grid impedance increases.

3. The LCL grid-connected inverter system optimization method based on fractional-order differential compensator according to claim 2 is characterized in that: The step of analyzing the resonant zero poles of the open-loop transfer function of the inverter system to obtain the parameter design conditions of the fractional-order differential compensator includes: From the seventh expression, we can see that the root cause of the inability to eliminate the resonant zero pole is 1-G c (s)G d (s); In order to make 1-G c (s)G d The amplitude of (s) is approximately equal to zero at the reverse resonant frequency, and the fractional-order differential compensator G c (s) in f rx-min The amplitude at f is 1, and the inverter open-loop transfer function is rx-min There is a phase jump at f. In order to maintain the stability of the grid-connected system, the fractional-order differential compensator is used at f rx-min The advanced phase angle provided at the digital delay link G can completely offset the delay d (s) Phase lag introduced; Therefore, the parameter design condition of the fractional-order differential compensator is set to the tenth expression: Among them, f rx-min is the reverse resonant frequency corresponding to the maximum grid impedance.

4. The LCL grid-connected inverter system optimization method based on fractional-order differential compensator according to claim 3 is characterized in that: The step of substituting the parameter design conditions into the fractional-order differential compensator expression to obtain the parameter design result of the fractional-order differential compensator includes: For the fractional-order differential compensator transfer function G c (s), let s = jω, then Substituting into the tenth expression we get the eleventh expression: Finally, the parameter design result of the fractional-order differential compensator is the twelfth expression: Where K is the differential time constant and μ is the differential order.

5. The LCL grid-connected inverter system optimization method based on fractional-order differential compensator according to claim 4 is characterized in that: The step of obtaining the fitting frequency band and fitting order design result of the fractional-order differential compensator according to the frequency domain characteristics and fitting characteristics of the fractional-order differential comprises: According to the frequency domain characteristics and fitting characteristics of fractional-order differential, the fitting frequency band of the fractional-order differential compensator is set to [10 Hz, 100000 Hz], and the fitting order is selected as N=5.

6. An electronic device, characterized in that: The electronic device includes a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the LCL type grid-connected inverter system optimization method based on a fractional-order differential compensator as described in any one of claims 1-5 is executed.

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