Active damper resistance characteristic optimization method considering phase-locked loop influence
By optimizing the resistance characteristics of the active damper, the impedance phase offset problem caused by the phase locked loop is solved, the resonance suppression ability of the active damper is improved, and the grid connection stability and current quality of the inverter are improved.
Patent Information
- Application Number
- CN202510612772.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-13
- Publication Date
- 2025-08-22
AI Technical Summary
The phase-locked loop causes the phase shift of the active damper impedance, thereby reducing the resonance suppression capability of the active damper.
By establishing the main circuit topology and control structure of the active damper, the phase offset problem introduced by the phase locked loop is analyzed, and the impedance remodeling link Gc(s) is designed to optimize the resistance characteristics of the active damper. The three-phase LCL full-bridge converter structure, the notch filter GNA(s) and the current controller Gi(s) are adopted to suppress the influence of the phase locked loop.
The resonance suppression ability of the active damper is improved, the stability of the inverter under the weak grid is enhanced, and the total harmonic distortion rate of the grid-connected current is significantly improved, meeting the grid-connected requirements.
Smart Images
Figure CN120528003A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of smart grids, and in particular relates to a method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop. Background Art
[0002] As environmental pollution caused by traditional fossil fuels becomes increasingly prominent, new energy sources, such as wind power and photovoltaics, are gaining increasing attention. Grid-connected inverters, as the key interface between new energy power stations and the power grid, have been widely used. Due to factors such as the large number of power electronic devices and line impedance, the power grid is gradually exhibiting weak grid characteristics, which can easily lead to resonance problems and seriously affect the operational stability of grid-connected inverters. Active dampers, as independently configurable devices, can effectively suppress resonance without changing the control structure of other inverters in the system. They also provide reliable global resonance suppression in systems with multiple grid-connected inverters in parallel. However, the phase-locked loop (PLL) of the active damper can affect the simulated resistance characteristics of the active damper in weak grid conditions, significantly reducing the active damper's ability to improve resonance stability. Summary of the Invention
[0003] 1. Technical problems to be solved:
[0004] In the prior art, a phase-locked loop causes an impedance phase shift in the active damper, thereby reducing the resonance suppression capability of the active damper.
[0005] 2. Technical solution:
[0006] In order to solve the above problems, the present invention provides a method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop, which includes the following steps:
[0007] Step 1: Establish the main circuit topology and control structure of the active damper.
[0008] Step 2: Based on the equivalent transformation of the control block diagram of the active damper, the output impedance model of the active damper taking into account the influence of the phase-locked loop is obtained.
[0009] Step 3: Based on the established output impedance model, analyze the phase offset problem introduced by the phase-locked loop.
[0010] Step 4: Impedance Reshaping: Impedance Reshaping Step G c The expression of (s) is:
[0011]
[0012] Where: G PLL (s) is the adopted phase-locked loop transfer function; L 1B is the inductance of the active damper side; L 2B is the grid-side inductance; I *is the port current reference value; K p is the proportional coefficient of the current controller; R t is the resistivity; s is the Laplace variable.
[0013] Furthermore, in step 1, the main circuit topology of the active damper adopts a three-phase LCL full-bridge converter structure.
[0014] Furthermore, the control structure of the main circuit of the active damper includes an active damper function and a grid-connected function, and the specific control method is as follows:
[0015] Step 101: Use the notch filter G NA (s) Filter out the fundamental component and low-order harmonic components in the PCC voltage to obtain the target resonant component v that needs to be damped by the active damper pccr After filtering out the low-order harmonic components, the harmonic current reference value i absorbed by the active damper from the power grid is obtained. Bref .
[0016] Step 102: Detect the voltage v at the common connection point using a phase-locked loop. pcc , we get v pcc The phase information θ of the fundamental frequency component is obtained by dividing the phase cosine value cosθ with I * Multiply them to get the fundamental frequency current reference value I Bref ;
[0017] Step 103, then i Bref with I Bref Compare the difference between the signal obtained and the sampling value of the grid-connected current at the active damper port i B The difference is calculated and the generated error signal is then fed into the current controller G i (s) step for processing.
[0018] Step 104: the processed capacitor current signal i c Compare it with the output signal processed by the current controller link to generate a modulation wave voltage v M , the driving signal of the switching tube is generated through PWM modulation technology.
[0019] Furthermore, in the active damper control structure, a notch filter G is used. NA (s) and current controller G i (s) is used to suppress the influence of low-order harmonic components of background harmonics on the grid side. The expressions are:
[0020]
[0021] Where K p and K rare the proportional coefficient and resonance coefficient of the current controller respectively; ω i is the bandwidth of the resonance term, ω0 is the fundamental angular frequency; h is the harmonic order corresponding to the resonance term.
[0022] Furthermore, step 2 includes: step 201, based on the established main circuit topology and control structure of the active damper, a control block diagram of the active damper taking into account the influence of the phase-locked loop is obtained, and by performing equivalent transformation on the control block diagram, an equivalent current i of the active damper port is obtained. B (s) is expressed as:
[0023]
[0024] Where i sB (s) is the equivalent fundamental current of the active damper; R v is the virtual resistance of the active damper; G PLL (s) is the adopted phase-locked loop transfer function; T A (s) is the active damper loop gain; v pcc (s) is the voltage at the common coupling point; G NA (s) is a notch filter; G x (s) is v pcc (s) to i B The open-loop transfer functions of (s) are expressed as follows:
[0025]
[0026] Where G i (s) is the current regulator; K c is the capacitor current feedback coefficient; C B is the filter capacitor; G de (s) is the control delay link.
[0027] Step 202: Establish an output impedance model of the active damper according to the equivalent current expression of the active damper port.
[0028] Furthermore, the active damper output impedance Z op_c (s) is expressed as:
[0029]
[0030] G NA (s) is a notch filter.
[0031] Furthermore, in step 3, based on the output impedance model of the active damper, the original port impedance Z of the active damper is obtained. o (s), the impedance Z corresponding to the virtual resistance loop VR (s), equivalent impedance Z of the phase-locked loop feedback loopPLL The expressions of (s) are:
[0032]
[0033] Where R v is the virtual resistance of the active damper.
[0034] Furthermore, the original port impedance of the active damper and the impedance corresponding to the virtual resistor are considered as a whole, and the output impedance Z of the active damper before the influence of the phase-locked loop is taken into account. op (s), output impedance Z of the rear active damper op The expressions of ′(s) are:
[0035]
[0036] Furthermore, the output impedance of the active damper is reshaped into a resistor as the optimization goal, and the compensation link G is derived. c (s), let Z op_c (s)=R t , solve the problem to get G c (s) is expressed as:
[0037]
[0038] T A (s), G x Substitute (s) into G c (s), we get G c The specific expression of (s) is:
[0039]
[0040] After simplification, the impedance reshaping link G in step 4 is obtained c (s) expression.
[0041] Furthermore, the simplified method is: within the resonance damping frequency band, there is G NA (s)≈1,G i (s)≈K p ; The LCL filter of the active damper is L 1B +L 2B Single L filter; G de (s)≈1.
[0042] 3.Beneficial effects:
[0043] The present invention analyzes the impedance phase shift problem introduced by the phase-locked loop to the active damper, and improves the resonance suppression capability of the active damper by designing a method for optimizing the resistance characteristics of the active damper, thereby providing a reliable solution to the resonance problem of the inverter under weak power grid. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 The main circuit topology and control structure diagram of the active damper resistance characteristic optimization strategy taking into account the influence of the phase-locked loop provided by the present invention;
[0045] Figure 2 The control block diagram of the active damper taking into account the influence of the phase-locked loop.
[0046] Figure 3 The output impedance model diagram of the active damper taking into account the influence of the phase-locked loop.
[0047] Figure 4 Comparison of the Bode plots of the overall output impedance of the active damper before and after taking into account the influence of the phase-locked loop.
[0048] Figure 5 This is a control block diagram of the active damper resistance characteristic optimization strategy taking into account the influence of the phase-locked loop provided by the present invention.
[0049] Figure 6 Comparison of Bode diagrams of the overall output impedance of the active damper under different conditions.
[0050] Figure 7 This is the experimental waveform and current FFT analysis when inverter A is connected to the grid alone with a grid impedance of 5mH.
[0051] Figure 8 Experimental waveform and current FFT analysis of inverter A when active damper B without optimization strategy is connected in parallel with grid impedance of 5mH.
[0052] Figure 9 Experimental waveform and current FFT analysis of inverter A when active damper B with optimization strategy is connected in parallel with grid impedance of 5mH. DETAILED DESCRIPTION
[0053] The present invention is described in detail below with reference to the accompanying drawings and embodiments.
[0054] A method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop comprises the following steps:
[0055] Step 1: Establish the main circuit topology and control structure of the active damper.
[0056] Step 2: Based on the equivalent transformation of the control block diagram of the active damper, the output impedance model of the active damper taking into account the influence of the phase-locked loop is obtained.
[0057] Step 3: Based on the established output impedance model, analyze the phase offset problem introduced by the phase-locked loop.
[0058] Step 4: Impedance Reshaping: Impedance Reshaping Step Gc The expression of (s) is:
[0059]
[0060] Where: G PLL (s) is the adopted phase-locked loop transfer function; L 1B is the inductance of the active damper side; L 2B is the grid-side inductance; I * is the port current reference value; K p is the proportional coefficient of the current controller; R t is the resistivity; s is the Laplace variable.
[0061] Example 1:
[0062] The embodiment of the present invention provides an optimization strategy for the resistance characteristics of an active damper taking into account the influence of a phase-locked loop. Taking a grid-connected system consisting of a grid-connected inverter and an active damper as an example, the stability of the entire grid-connected system is improved by improving the resonance suppression capability of the active damper. Figure 1 As shown, Figure 1 The main circuit topology of the active damper adopts the structure of three-phase LCL full-bridge converter, V dc is the DC side voltage; i c_abc is the capacitor current; i B_abc is the port current; v pcc_abc is the PCC voltage; Z g is the grid impedance; v g is the grid voltage; the inductance L on the active damper side 1B , filter capacitor C B , grid-side inductance L 2B Constitutes LCL filter; PLL means phase-locked loop; G NA (s) is the notch filter; v pccr v pcc_abc The target damped resonance component is obtained after removing the fundamental wave and low-order harmonics through the notch filter; R V is a virtual resistor; I * is the port current reference value; cosθ is the v obtained by the phase-locked loop pcc_abc Phase cosine; I Bref is the product of the current reference value and the cosine value; i Bref is the harmonic current reference value; G i (s) is the current regulator; K c is the capacitor current feedback coefficient; v M_abc is the modulation wave voltage.
[0063] In one embodiment, in step 1, the control structure includes an active damper function and a grid-connected function. The specific control method is as follows: Step 101, using the notch filter GNA (s) Filter out the fundamental component and main low-order harmonic components in the PCC voltage to obtain the target resonant component v that needs to be damped by the active damper pccr After filtering out the low-order harmonic components, the harmonic current reference value i absorbed by the active damper from the power grid is obtained. Bref .
[0064] Step 102: Use a phase-locked loop to detect the voltage v at the common connection point. pcc , we get v pcc The phase information θ of the fundamental frequency component is obtained by dividing the phase cosine value cosθ with I * Multiply them to get the fundamental frequency current reference value I Bref .
[0065] Step 103: i Bref with I Bref Compare the difference between the signal obtained and the sampling value of the grid-connected current at the active damper port i B The difference is calculated and the generated error signal is then fed into the current controller G i (s) step for processing.
[0066] In order to suppress the resonant peak of the LCL filter, the capacitor current feedback method is used.
[0067] Step 104: The processed capacitor current signal i c Compare it with the output signal processed by the current controller link to generate a modulation wave voltage v M , the driving signal of the switching tube is generated through PWM modulation technology.
[0068] In one embodiment, Figure 2 middle To calculate the 1.5 beat delay caused by the delay and modulation delay, T s =1 / f s is the sampling period, f s is the sampling frequency; the current controller G i (s), phase-locked loop G PLL (s), notch filter G NA The expressions of (s) are:
[0069]
[0070] Where K p and K r are the proportional coefficient and resonance coefficient of the current controller respectively; ω i is the bandwidth of the resonance term, ω0 is the fundamental angular frequency; k pp and k ip is the controller parameter of the phase-locked loop; h is the harmonic order corresponding to the resonance term.
[0071] according to Figure 2 , the open-loop transfer function of the system is:
[0072]
[0073] At the same time, we can get v pcc (s) to i B The open-loop transfer function of (s) is:
[0074]
[0075] At this time, the grid-connected current expression of the active damper port is:
[0076]
[0077] Where i sB (s) is the equivalent fundamental current of the active damper; R v is the virtual resistance of the active damper; G PLL (s) is the adopted phase-locked loop transfer function; T A (s) is the active damper loop gain; v pcc (s) is the voltage at the common coupling point; G NA (s) is a notch filter; G x (s) is v pcc (s) to i B The open-loop transfer function of (s),
[0078] In one embodiment, Figure 3 in,i sA (s) and Z eq (s) are the equivalent current source and equivalent output impedance of the grid-connected inverter respectively. sB (s) is the equivalent fundamental current of the active damper; Z o (s) is the original port impedance of the active damper; Z VR (s) is the impedance corresponding to the virtual resistance loop; Z PLL (s) is the equivalent impedance of the phase-locked loop feedback circuit. Z o (s), Z VR (s), Z PLL The expressions of (s) are:
[0079]
[0080] In one embodiment, the original port impedance of the active damper and the impedance corresponding to the virtual resistor are considered as a whole and used as the output impedance of the active damper before the phase-locked loop is considered. The output impedance Z of the active damper before and after the phase-locked loop is considered op (s), Zop The expressions of ′(s) are:
[0081]
[0082] like Figure 4 As shown, according to Z op (s), Z op The expression of ′(s) is used to draw the respective impedance Bode diagrams in Matlab. As can be seen from the figure, in the target resonant damping frequency band, the output impedance Z of the active damper without the influence of the phase-locked loop is op (s) can approach the resistance characteristic in a short period, but as the frequency increases, the phase angle gradually deviates from 0°. At 2000Hz, the phase shift reaches 70.4°. After taking into account the influence of the phase-locked loop, the output impedance Z of the active damper is op The phase angle of ′(s) further shifts, reaching 38.1° at 1000Hz. op (s), the phase angle further shifts by 32.1°; at 2000Hz, the phase angle shifts by 98.8°, which is significantly different from Z op (s), the phase angle further shifts by 28.4°. This shows that active dampers often fail to exhibit resistance characteristics well. In particular, the phase angle shift problem is further aggravated by the influence of the phase-locked loop (PLL). This results in the active damper failing to achieve ideal resonance suppression and even exacerbating the resonance stability problem of the grid-connected inverter in weak grid conditions.
[0083] like Figure 5 As shown, an impedance reshaping link G is added before the virtual resistance loop of the active damper. c (s), the added impedance reshaping link exists independently of the grid-connected function, so it will not affect the stability of the active damper and will not change the structure of the phase-locked loop.
[0084] In one embodiment, the output impedance expression of the active damper after adopting the proposed optimization strategy is:
[0085]
[0086] Taking the output impedance of the active damper as a resistor as the optimization goal, the compensation link G is derived. c (s), let Z op_c (s)=R t , we can solve G c (s) is expressed as:
[0087]
[0088] T A (s), G x Substitute (s) into G c(s), we get G c The specific expression of (s) is:
[0089]
[0090] Since it is too complex and not conducive to implementation, it is simplified.
[0091] The simplified method is:
[0092] 1) The notch filter and current controller only work on the fundamental wave and low-order harmonics. It can be considered that there is G in the resonance damping frequency band. NA (s)≈1,G i (s)≈K p .
[0093] 2) The control bandwidth of the active damper is often designed to be lower than the resonant frequency of the grid-connected inverter. In the resonant damping frequency band, the filter capacitor branch can be considered as an open circuit. In this way, the LCL filter of the active damper can be regarded as L 1B +L 2B Single L filter.
[0094] 3) The delay link has a phase advance, which cannot be physically realized. In actual implementation, it can be considered that: G de (s)≈1.
[0095] After simplification, the impedance reshaping link G c The expression of (s) is finally expressed as:
[0096]
[0097] Where: G PLL (s) is the adopted phase-locked loop transfer function; L 1B is the inductance of the active damper side; L 2B is the grid-side inductance; I * is the port current reference value; K p is the proportional coefficient of the current controller; R t is the resistivity; s is the Laplace variable.
[0098] At this time, the output impedance expression of the active damper is:
[0099]
[0100] like Figure 6 As shown, according to Z op (s), Z op ′(s), Z op_c The expression of (s) is used to draw the respective impedance Bode diagrams in matlab. It can be seen from the figure that after adopting the optimization method proposed by the present invention, the output impedance Z of the active damper isop_c (s) can be very close to the resistance characteristics in the resonant damping frequency band. At 1000Hz, Z op_c The phase angle shift of (s) is 1.4°, which is compared with the output impedance Z of the active damper when the phase-locked loop is taken into account. op ′(s), the phase angle accuracy is improved by 36.8°; at 2000Hz Z op_c (s) The phase angle shift is only 15.6°, compared to Z op ′(s), the phase angle accuracy is greatly improved, and the improvement effect is significant.
[0101] In order to verify the effectiveness of the active damper resistance characteristic optimization strategy proposed in this invention, physical prototypes of inverter A and active damper B were built.
[0102] Figure 7 is the grid inductance L g =5mH, the experimental waveforms and grid current FFT analysis results for inverter A when operating alone on the grid. As can be seen from the figure, inverter A's grid current waveform is significantly distorted. FFT analysis of the grid current shows a high total harmonic distortion (THD) value of 40.67%, indicating poor system power quality and severe operational instability.
[0103] Figure 8 is the grid inductance L g The experimental waveforms and FFT analysis results of the grid-connected current of inverter A are shown when active damper B, which does not employ the optimization strategy, is connected in parallel at a voltage of 5mH. As can be seen from the figure, active damper B, which does not employ the optimization strategy, can somewhat improve the resonance phenomenon of inverter A, reducing the THD value of the grid-connected current to 19.42%. However, the resonance suppression effect of active damper B is not ideal, and the THD value of the grid-connected current of inverter A remains high, failing to meet the grid-connected current requirements.
[0104] Figure 9 is the grid inductance L g=5mH, when the active damper B using the resistance characteristic optimization strategy proposed in the present invention is connected in parallel, the experimental waveform and grid-connected current FFT analysis results of inverter A. As can be seen from the figure, the active damper B after the optimization strategy is adopted greatly improves the resonance phenomenon of inverter A, and the grid-connected current THD value at this time is 1.82%, which is 17.6% lower than before optimization, and the resonance suppression effect is significantly improved. This shows that the active damper B without the optimization strategy has a phase shift problem due to the influence of the phase-locked loop, and its output impedance characteristics are difficult to maintain resistance characteristics within the resonance damping frequency band, resulting in insufficient resonance suppression capability. In contrast, the active damper B using the optimization strategy proposed in the present invention can effectively compensate for the adverse effects of the phase-locked loop and significantly improve the resonance suppression capability of the active damper.
Claims
1. A method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop, characterized by: The following steps are involved: Step 1: Establish the main circuit topology and control structure of the active damper; Step 2: Based on the equivalent transformation of the control block diagram of the active damper, the output impedance model of the active damper taking into account the influence of the phase-locked loop is obtained; Step 3: Based on the established output impedance model, analyze the phase offset problem introduced by the phase-locked loop; Step 4: Impedance Reshaping: Impedance Reshaping Step G c The expression of (s) is: Where: G PLL (s) is the adopted phase-locked loop transfer function; L 1B is the inductance of the active damper side; L 2B is the grid-side inductance; I * is the port current reference value; K p is the proportional coefficient of the current controller; R t is the resistivity; s is the Laplace variable.
2. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 1, wherein: In step 1, the main circuit topology of the active damper adopts a three-phase LCL full-bridge converter structure.
3. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop as claimed in claim 2, wherein: The control structure of the main circuit of the active damper includes the active damper function and the grid connection function. The specific control method is as follows: Step 101: Use the notch filter G NA (s) Filter out the fundamental component and low-order harmonic components in the PCC voltage to obtain the target resonant component v that needs to be damped by the active damper pccr After filtering out the low-order harmonic components, the harmonic current reference value i absorbed by the active damper from the power grid is obtained. Bref ; Step 102: Detect the voltage v at the common connection point using a phase-locked loop. pcc , we get v pcc The phase information θ of the fundamental frequency component is obtained by dividing the phase cosine value cosθ with I * Multiply them to get the fundamental frequency current reference value I Bref ; Step 103, then i Bref with I Bref Compare the difference between the signal obtained and the sampling value of the grid-connected current at the active damper port i B The difference is calculated and the generated error signal is then fed into the current controller G i (s) step for processing; Step 104: The processed capacitor current signal i c Compare it with the output signal processed by the current controller link to generate a modulation wave voltage v M , the driving signal of the switching tube is generated through PWM modulation technology.
4. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop as claimed in claim 3, wherein: In the active damper control structure, a notch filter G is used. NA (s) and current controller G i (s) is used to suppress the influence of low-order harmonic components of background harmonics on the network side. The expressions are: Where K p and K r are the proportional coefficient and resonance coefficient of the current controller respectively; ω i is the bandwidth of the resonance term, ω0 is the fundamental angular frequency; h is the harmonic order corresponding to the resonance term.
5. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop as claimed in claim 4, wherein: Step 2 includes: Step 201: Based on the established main circuit topology and control structure of the active damper, a control block diagram of the active damper taking into account the influence of the phase-locked loop is obtained. By performing equivalent transformation on the control block diagram, the equivalent current i of the active damper port is obtained. B (s) is expressed as: Where i sB (s) is the equivalent fundamental current of the active damper; R v is the virtual resistance of the active damper; G PLL (s) is the adopted phase-locked loop transfer function; T A (s) is the active damper loop gain; v pcc (s) is the voltage at the common coupling point; G NA (s) is a notch filter; G x (s) is v pcc (s) to i B The open-loop transfer functions of (s) are expressed as follows: Where G i (s) is the current regulator; K c is the capacitor current feedback coefficient; C B is the filter capacitor; G de (s) is the control delay link; Step 202: Establish an output impedance model of the active damper according to the equivalent current expression of the active damper port.
6. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 5, wherein: Active damper output impedance Z op_c (s) is expressed as: T A (s)G NA (s)[s(L 1B +L 2B )+K p -R t +R t K p I * G PLL (s)], G NA (s) is a notch filter.
7. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 6, wherein: In step 3, based on the output impedance model of the active damper, the original port impedance Z of the active damper is obtained. o (s), the impedance Z corresponding to the virtual resistance loop VR (s), equivalent impedance Z of the phase-locked loop feedback loop PLL The expressions of (s) are: Where R V is the virtual resistance of the active damper.
8. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 7, wherein: Considering the original port impedance of the active damper and the impedance corresponding to the virtual resistor as a whole, the output impedance Z of the active damper before taking into account the influence of the phase-locked loop is op (s), output impedance Z of the rear active damper op The expressions of ′(s) are:
9. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 8, wherein: Taking the output impedance of the active damper as a resistor as the optimization goal, the compensation link G is derived. c (s), let Z op_c (s)=R t , solve the problem to get G c (s) is expressed as: T A (s), G x Substitute (s) into G c (s), we get G c The specific expression of (s) is: After simplification, the impedance reshaping link G in step 4 is obtained c (s) expression.
10. The method for optimizing the resistance characteristics of an active damper taking into account the influence of a phase-locked loop according to claim 9, wherein: The simplified method is: there is G in the resonance damping frequency band NA (s)≈1,G i (s)≈K p ; The LCL filter of the active damper is L 1B +L 2B Single L filter; G de (s)≈1.