Grid-connected inverter hybrid damping method based on LCL-LC filtering

Abstract

The invention relates to a grid-connected inverter hybrid damping method based on LCL-LC filtering. The invention combines the advantages of a passive damping method and an active damping method, and provides a grid-connected inverter hybrid damping method based on LCL-LC filtering. The problem that pure passive damping affects stable operation of the system is effectively solved; and pure active damping has a poor high-frequency resonance peak suppression effect. According to the invention, two positive resonance peaks are effectively suppressed without influencing resonance valleys; the method has the characteristics of strong adaptability, small delay influence, small resistance loss and the like. A current controller is designed by discussing a steady-state error, an amplitude margin and a phase margin, and the system stability and the dynamic operation capability are ensured.

Description

Technical Field

[0001] The invention relates to a hybrid damping control technology, and in particular to a hybrid damping method of a grid-connected inverter based on LCL-LC filtering. Background Art

[0002] With the development of new energy generation technologies such as photovoltaic and wind power, grid-connected inverters are key devices for integrating new energy into the grid, and their performance directly affects the power quality of the grid. As a key link in the inverter, the selection and design of the filter plays an important role in the performance of the inverter. There will be a large number of harmonics on the output side of conventional inverters, among which the harmonics at the switching frequency are particularly serious. Therefore, a filter is required at the output of the inverter to filter out the harmonics before it can be connected to the grid.

[0003] The new fifth-order filter LCL-LC filter not only has the advantage of LCL filter's strong ability to filter out switching harmonics, but can also suppress harmonics of specific frequencies. Although this filter further improves the quality of grid-connected current, the resonance problem of LCL and LLCL filters still exists, and effective damping methods are needed to suppress the resonance spikes.

[0004] Traditional damping methods include passive damping and active damping. The passive damping method can maintain good high-frequency attenuation characteristics of the system and effectively suppress resonant spikes without delay, but there is additional heat loss, and improper value selection will cause the fundamental gain to be too small, resulting in large amplitude errors and insufficient phase margin affecting filtering performance. The active damping control method solves the problem of additional heat loss caused by passive damping control, but there are problems such as control delay and poor suppression of high-frequency positive resonance spikes. Summary of the invention

[0005] Combining the advantages of passive damping method and active damping method, a hybrid damping method for grid-connected inverter based on LCL-LC filtering is invented. It effectively solves the problems that pure passive damping affects the stable operation of the system; pure active damping has poor effect on suppressing high-frequency resonance spikes.

[0006] The technical solution of the present invention is: a hybrid damping method for grid-connected inverters based on LCL-LC filtering. Combining the advantages of passive damping methods and active damping methods, a damping method is invented, and it is proposed to constrain and verify the hybrid damping parameters according to the Routh-Hurwitz stability criterion, and calculate the active damping and passive damping parameters by the idea of ​​taking values ​​separately. The controller parameters and active damping parameters are designed from the aspects of dynamic operation capability and stability; the passive damping parameters are determined by empirical value discussion. This method is more accurate than the traditional damping ratio empirical value method and can verify the correctness of the parameters.

[0007] The beneficial effects of the present invention are: effectively suppressing two positive resonance peaks without affecting the resonance valley; having the characteristics of strong adaptability, small delay influence, small resistance loss, etc. The current controller is designed by discussing the steady-state error, amplitude margin, and phase margin to ensure the system stability and dynamic operation capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 The present invention is a topological block diagram of the main circuit of a single-phase grid-connected inverter based on an LCL-LC filter.

[0009] Figure 2 The invention discloses a hybrid damping method based on an LCL-LC filter.

[0010] Figure 3 The figure is a flow chart for designing the mixed damping coefficient of the present invention.

[0011] Figure 4 This is an experimental operation diagram of the single-phase grid-connected inverter based on the LCL-LC filter of the present invention before and after hybrid damping is added. DETAILED DESCRIPTION

[0012] Firstly, the main circuit topology block diagram of the single-phase grid-connected inverter based on LCL-LC filter is designed, as shown in Figure 1 shown; U g is the grid voltage; I g is the grid-connected current; I c is the filter capacitor branch current; I ref is the reference current; U dc is the DC voltage; C f , L f are the capacitance and inductance of the series resonant branch respectively; C d is the filter capacitor; L 1 is the inverter side inductance; L 2 is the grid-side inductance; L g is the grid impedance; R d is the damping resistor; the dotted box is the control algorithm.

[0013] A hybrid damping method is designed based on the passive damping method and the active damping method. The control method block diagram is as follows: Figure 2 As shown, the transfer function is derived as shown in formula (1).

[0014] (1)

[0015] Where: ; ; ; ; .

[0016] The value of the hybrid damping parameter must ensure the stability of the system. If the value is inappropriate, the system will be unstable. Therefore, a reasonable value range must be determined before design. According to the Routh-Hurwitz stability criterion combined with the stability analysis of the system, the effective value range of the damping parameters K and A is obtained through the characteristic equation of the closed-loop transfer function of the LCL-LC filter. The correctness can be verified by substituting the obtained parameters into the Routh table.

[0017] The LCL-LC filter is a fifth-order system. Let the denominator of the closed-loop transfer function of the system be equal to 0, and the characteristic equation shown in equation (2) is obtained.

[0018] (2)

[0019] The coefficients in formula (2) are the same as those in formula (1), namely: 0 = A ; a 1 = B ; a 2 = C ; a 3 = D ; a 4 = E ; a 5 =0.

[0020] Necessary and sufficient conditions for system stability: All coefficients of the closed-loop characteristic equation of the system are positive, that is, all elements in the first column of the Routh table are positive; the mixed damping parameters must meet this condition. The Routh table is listed according to the characteristic equation as shown below.

[0021] <![CDATA[ s 5 ]]> <![CDATA[a 0 ]]> <![CDATA[a 2 ]]> <![CDATA[a 4 ]]> <![CDATA[ s 4 ]]> <![CDATA[a 1 ]]> <![CDATA[a 3 ]]> <![CDATA[a 5 ]]> <![CDATA[ s 3 ]]> <![CDATA[b 1 ]]> <![CDATA[b 2 ]]> 0 <![CDATA[ s 2 ]]> <![CDATA[c 1 ]]> <![CDATA[c 2 ]]> 0 <![CDATA[ s 1 ]]> <![CDATA[d 1 ]]> 0 0 <![CDATA[e 1 ]]> 0 0

[0022] Parameters in the table: , ; , ; ; .

[0023] The selection of active damping parameters in the hybrid damping method of the present invention links the active damping feedback coefficient with the value range of the controller parameter. By analyzing the system loop gain, amplitude margin, phase margin and other characteristics, the final damping feedback coefficient is obtained after discussion from the aspects of dynamic performance and stability.

[0024] Firstly, the transfer function of the quasi-PR controller is designed.

[0025] (3) Where: K p is the proportional gain; K r is the integral gain; ω 0 is the fundamental angular frequency; ω c is the bandwidth corresponding to the cutoff frequency of the controller.

[0026] The system loop gain of the LCL-LC filter is defined as shown in equation (4).

[0027] (4)

[0028] Where: ; ; .

[0029] The grid current is split into the multiplication of the previous and next stages, as shown in formula (5): (5)

[0030] Under normal operation, the switching frequency A of the system must satisfy equation (6):

[0031] f c <0.1 f s < f 1 (6)

[0032] in f c is the cut-off frequency; f 1 is the low-frequency resonant frequency; f s is the switching frequency.

[0033] When analyzing the cutoff frequency band, the influence of the filter capacitor can be ignored, thereby further simplifying the expression of the system loop gain as shown in equation (7).

[0034] (7)

[0035] The steady-state error of the grid-connected inverter is divided into phase angle error θ and amplitude error e ; Due to the presence of a phase-locked loop in the control system, I g2 The phase lags behind I g1 90°, I g1 The phase of is the same as the grid voltage. The present invention adopts a quasi-PR controller, which can eliminate the dynamic error at the base frequency and minimize the phase angle error, so the phase angle error is no longer considered.

[0036] The loop gain of the system at the cutoff frequency is 1, and the loop gain at the fundamental frequency is much greater than 1, and considering , the expression of grid current at fundamental frequency can be rewritten as equation (8).

[0037] (8)

[0038] Amplitude error e The definition of is shown in formula (9).

[0039] (9) At the base frequency A, the expression of the quasi-PR controller can be rewritten as equation (10).

[0040] (10)

[0041] To ensure the dynamic performance of the system, when the system frequency is greater than the cutoff frequency, the amplitude of the quasi-PR controller is approximately equal to K p , so we can get A And A , the proportionality coefficient can be derived K p The expression of is shown in formula (11).

[0042] (11)

[0043] Since LCL-LC is a fifth-order filter with two resonance peaks, the phase will cross -180° at the second resonance peak; in order to make the amplitude margin positive, the high-frequency resonance frequency must be less than 0dB, and the influence of the filter capacitor here cannot be ignored. This paper effectively suppresses the high-frequency resonance peak by designing hybrid damping. In order to make the system run stably, the phase margin must be greater than 0dB, and f 2 The influence of the filter capacitor current at cannot be ignored.

[0044] Amplitude marginG M The definition is shown in Equation (12).

[0045] (12)

[0046] Phase margin P M The definition of... is shown in Equation (13).

[0047] (13)

[0048] The resonance coefficient can be derived from Equation (11). K r The expression of... is shown in Equation (14).

[0049] (14)

[0050] Let R p and R e be the limiting conditions determined by the phase margin P M and the amplitude error e The limited active damping coefficient can be obtained, as shown in Equation (17).

[0051] (15)

[0052] (16)

[0053] (17).

[0054] According to the constraints of the phase margin P M , amplitude margin G M , and amplitude error e , it can be judged whether the operation effect of the selected proportional resonance coefficient is good; when the control system parameters meet the following constraints, the system has good dynamic performance.

[0055] 1) The phase margin is in the range of .

[0056] 2) The amplitude margin G M ≤ 6 dB.

[0057] 3) The amplitude error e ≤ 5%.

[0058] The controller parameters and active damping parameters can be derived therefrom.

[0059] The hybrid damping method of the present invention empirically determines the values ​​of the passive damping parameters and needs to comply with the following two rules.

[0060] (1) The value of A should not be too large, otherwise the loss of the passive damping method cannot be effectively reduced.

[0061] (2) The value of A needs to take into account the impact on the filter's high-frequency harmonic attenuation capability, taking into account both the dynamic performance and the damping effect of the system.

[0062] The derived passive damping parameters R d Active damping parameters K Substituting it into the Routh table for verification, we can find that all the elements in the first column of the Routh table are positive, which proves that the mixed parameters meet the stability requirements of the system and the values ​​are reasonable.

[0063] The hybrid damping control method for grid-connected inverter based on LCL-LC filter designed in the present invention effectively solves the problems that pure passive damping affects the stable operation of the system and pure active damping has poor suppression effect on high-frequency resonance peaks, and effectively suppresses the resonance peaks.

[0064] According to the above method, an example is implemented, but the protection scope of the present invention is not limited to the following embodiments; the experimental operation diagram of the single-phase grid-connected inverter based on the LCL-LC filter before and after adding hybrid damping is shown in FIG. Figure 4 As shown, the specific parameter settings of the embodiment are shown in the table below.

[0065] parameter Numeric parameter Numeric <![CDATA[Inductance on the Inverter Side L 1 / mH]]> 2 <![CDATA[DC bus voltage U dc / V > 750 <![CDATA[Filter capacitor C d / mF]]> 2 <![CDATA[Grid voltage U g / V]]> 380 <![CDATA[Grid-side inductor L 2 / mH]]> 0.4 Rated power P / kW 10 <![CDATA[Series resonance capacitance C f / mF]]> 2 <![CDATA[Switching frequency f s / kHz]]> 10 <![CDATA[Inductance L of the series resonance branch f / mH]]> 49.52 <![CDATA[Passive damping coefficient R d / Ω]]> 1 <![CDATA[Controller parameter K p > 0.5 <![CDATA[Controller parameter K r > 20

[0066] The above description is only the preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A hybrid damping method for grid-connected inverter based on LCL-LC filtering, characterized in that: The specific steps include: 1) Design the hybrid damping control block diagram of LCL-LC filtering and derive its mathematical formula; 2) List the Routh table for the mathematical formula derived in step 1) to obtain the effective range of the mixed damping parameters; 3) Design active damping parameters and controller parameters based on the system's dynamic operation capability and stability, and then discuss passive damping parameters based on the system's Bode diagram; 4) Substitute the mixed damping parameters derived in step 3) into step 2) to verify whether they are reasonable.

2. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The hybrid damping control method of the LCL-LC filter designed in step 1) is a combination of an active damping method and a passive damping method, wherein the active damping is based on capacitor current feedback and does not consider the delay term; Passive damping is connected in series with the filter capacitor branch.

3. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The current controller in the hybrid damping control method of the LCL-LC filter designed in step 1) adopts quasi-PR control. The present invention discusses the selection of controller parameters and active damping coefficient based on the quasi-PR current controller.

4. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The parameters in the Routh table designed in step 2) are determined by the hybrid damping control method of the LCL-LC filter designed in step 1); the necessary and sufficient condition for system stability: all coefficients of the closed-loop characteristic equation of the system are positive, that is, all elements in the first column of the Routh table are positive; if this condition is met, the correctness of the active damping parameters and the passive damping parameters can be judged.

5. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The selection of active damping parameters designed in step 3) links the active damping feedback coefficient with the value range of the controller parameters. By analyzing the system loop gain, amplitude margin, phase margin and other characteristics, the final damping feedback coefficient is obtained after discussion from the aspects of dynamic performance and stability.

6. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The active damping parameters and controller parameters designed in step 3) are calculated based on the phase margin. P M , Amplitude Margin G M , Amplitude Error e The constraints of can be used to determine whether the selected proportional resonance coefficient has a good operating effect; when the control system parameters meet the following constraints, the system has good dynamic performance; 1) Phase margin scope; 2) Amplitude margin G M ≤6dB; 3) Amplitude error e ≤5%.

7. The hybrid damping method for grid-connected inverter based on LCL-LC filtering according to claim 1, characterized in that: The selection of the passive damping parameters designed in step 3) needs to comply with the following two rules: 1) The value of the passive damping parameter should not be too large, otherwise the loss of the pure passive damping method cannot be effectively reduced; 2) The value of the passive damping parameters needs to take into account the impact on the filter's high-frequency harmonic attenuation capability, taking into account both the dynamic performance and the damping effect of the system.

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