Plug-in second-order feed-forward dual-mode repetitive control method

Abstract

The invention relates to a plug-in type second-order feed-forward dual-mode repetitive control method. The method comprises the following steps: establishing a single-phase LCL type grid-connected inversion model based on a PP-SFDMRC controller; according to the single-phase LCL type grid-connected inversion model, a transfer function of a controlled object is obtained, a PP-SFDMRC controller structure is discretized, and a discrete transfer function of an internal model of the SFDMRC is obtained; the method comprises the following steps: acquiring an error transfer function of a PP-SFDMRC controller based on an SFDMRC internal model discrete transfer function by taking SFDMRC internal model stability as a target, converting the error transfer function into a characteristic polynomial, and determining a stability condition of the PP-SFDMRC controller; through stable conditions, corresponding parameters of the PP-SFDMRC controller are set, and odd and even harmonics are controlled to different degrees. The PP-SFDMRC strategy provided by the invention has excellent dynamic performance and super-strong adaptability to power grid frequency change.

Description

Technical Field

[0001] The present invention relates to the technical field of single-phase inverter control, and particularly to a plug-in second-order feedforward dual-mode repetitive control method. Background Art

[0002] Microgrids are widely adopted because they can improve the utilization rate of distributed renewable energy sources such as wind energy and photovoltaic systems. However, due to the low inertia of power electronic devices, frequency fluctuations will occur in microgrids powered by renewable energy sources. In addition, the non-linear characteristics of power electronic devices will also increase the harmonic level in the system. The grid-connected inverter is a key component connecting the power generation equipment and the microgrid, and is responsible for providing high-quality grid-connected current to ensure the stable operation of the system. Therefore, it is necessary to suppress the current harmonics of the grid-connected inverter when the microgrid frequency fluctuates.

[0003] RC is widely used in inverter control because it can achieve zero-static-error tracking of fundamental-period signals and disturbance elimination of double-frequency harmonic signals. The combination of common RC control and PI control can solve the problem of slow dynamic response of RC, and improve the steady-state response speed and enhance the steady-state performance of the control system. Although the repetitive series PI and repetitive control parallel PI composite controllers improve the dynamic performance of the system, there is coupling between the outputs of the two controllers and the parameter design is complex. The designs of the repetitive controller and the PI controller are independent of each other to ensure the fast performance of the PRC structure and effective suppression of current harmonics. DMRC has independent odd-mode and even-mode internal models, which can suppress odd and even harmonics to different degrees, and can accelerate the convergence speed of the tracking error without loss of accuracy. In practical applications, clock error drift, measurement noise, Hall sensor accuracy limitations, etc. all cause system frequency fluctuations, resulting in a significant decline in the performance of DMRC. Higher-order RC can be used to reduce the sensitivity of the processed disturbance to periodic fluctuations, but when the grid frequency changes, the control accuracy still needs to be improved. Summary of the Invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a plug-in second-order feedforward dual-mode repetitive control method, which adds a feedforward channel on the basis of the PP-SDMRC internal model to propose PP-SFDMRC. The introduction of the feedforward channel makes PP-SFDMRC exhibit higher gain and wider resonance bandwidth at harmonic frequencies. Therefore, the proposed PP-SFDMRC strategy has excellent dynamic performance and strong adaptability to grid frequency changes.

[0005] To achieve the above purpose, the present invention provides the following solution:

[0006] A plug-in second-order feedforward dual-mode repetitive control method, comprising:

[0007] Build a single-phase LCL grid-connected inverter model based on the PP-SFDMRC controller, where the PP-SFDMRC controller is a controller that introduces an inserted second-order feedforward dual-mode repetitive control strategy on the basis of the inserted proportional repetitive control;

[0008] According to the single-phase LCL grid-connected inverter model, obtain the transfer function of the controlled object, and discretize the structure of the PP-SFDMRC controller to obtain the discrete transfer function of the SFDMRC internal model;

[0009] Based on the discrete transfer function of the SFDMRC internal model, with the stability of the SFDMRC internal model as the goal, obtain the error transfer function of the PP-SFDMRC controller, convert it into a characteristic polynomial, and determine the stability condition of the PP-SFDMRC controller;

[0010] Through the stability condition, set the corresponding parameters of the PP-SFDMRC controller to control odd and even harmonics to different degrees; the corresponding parameters include: phase compensator parameters, proportional gain, active damping coefficient, internal model coefficient, filter parameters, phase lead link, weight factor, and gain.

[0011] Optionally, obtaining the transfer function of the controlled object includes:

[0012] According to the grid-side current control with the target cycle delay, the target cycle delay includes: sampling calculation delay and PWM delay, reduce the resonance peak of the LCL filter, and obtain the transfer function of the controlled object:

[0013]

[0014] where, L 1 is the filter inductor on the inverter side, L 2 is the filter inductor on the grid side, C is the filter capacitor, T s is the sampling period, H ic is the capacitor current feedback coefficient.

[0015] Optionally, obtaining the error transfer function of the PP-SFDMRC controller includes:

[0016]

[0017] where, Q(z) is the internal model filter, z is the discrete operator, z m is the phase lead link, S(z) is the low-pass filter, w is the weight factor, k o is the odd harmonic gain, k e is the even harmonic gain.

[0018] Optionally, obtaining the error transfer function of the PP-SFDMRC controller includes:

[0019] Taking the stability of the SFDMRC internal model as the goal, all poles of the discrete transfer function of the SFDMRC internal model should be set inside the unit circle, and |w| < 1, eliminating the case of w = 0, and further obtaining the error transfer function of the PP-SFDMRC controller:

[0020]

[0021] where i ref (z) is the reference current, d g (z) is the harmonic disturbance current, P(z) is the original controlled object, k p is the proportional link, and w is the weight factor.

[0022] Optionally, the conversion into the characteristic polynomial includes:

[0023] 1 + [1 + G c (z)]P(z)k p = [1 + P(z)k p [1 + P 1 (z)G c (z)]

[0024] where G c (z) is the discrete transfer function of the SFDMRC internal model.

[0025] Optionally, determining the stability conditions of the PP-SFDMRC controller includes:

[0026] The first stability condition includes: the roots of 1 + P(z)k p are inside the unit circle;

[0027] The second stability condition includes: |1 + P 1 (z)G c (z)| ≠ 0;

[0028] where P 1 (z) is the new controlled object, and G c (z) is the discrete transfer function of the SFDMRC internal model.

[0029] Optionally, after determining the stability conditions of the PP-SFDMRC controller, it includes:

[0030] Substituting the error transfer function of the PP-SFDMRC controller into the second stability condition, and letting obtain:

[0031]

[0032] If the frequencies of the reference signal and the disturbance signal are integer multiples of the fundamental frequency, then |z-N / 2 | = 1, and further obtain:

[0033]

[0034] where A(z) is the high-order compensator of the dual-mode repetitive control, z is the discrete operator, and N is the number of sampling points within a fundamental frequency period;

[0035] Obtain the amplitude-frequency and phase-frequency characteristics of the new controlled object and the low-pass filter, and let k r > 0, Obtain the new stability condition:

[0036]

[0037] where θ P is the phase of the controlled object, is the discrete operator, θ S is the phase of the low-pass filter S(z), m is the number of phase lead compensation beats, T s is the sampling period, and cosγ(ω) is the amplitude of the low-pass filter S(z), is the amplitude of the controlled object.

[0038] Optionally, setting the corresponding parameters of the PP-SFDMRC controller includes:

[0039] Setting the parameters of the phase compensator includes: selecting a phase compensator based on the new stability condition;

[0040] Setting the proportional gain and the active damping coefficient includes: performing a Bode plot analysis on the new controlled object according to the first stability condition, that is, the poles of the new controlled object are inside the unit circle in the z-plane, and selecting the proportional gain and the active damping coefficient;

[0041] Setting the internal model coefficient and the filter parameters includes: setting the internal model coefficient according to the change in the open-loop gain of the SFDMRC internal model, and selecting the cut-off frequency of the filter based on the low-frequency harmonic frequency of the PP-SFDMRC controller.

[0042] Optionally, setting the corresponding parameters of the PP-SFDMRC controller further includes:

[0043] Setting the phase lead link includes: according to the phase lag of the new controlled object and the low-pass filter, using a phase guiding compensator to make the phase closest to the target phase angle, thereby setting the phase lead link;

[0044] Setting the weight factor includes: according to w 2 and k o +k e Combining the positive correlation between and, and setting the weight factor in combination with the new stability condition; where w is the weight factor and k o is the odd-order gain and k e is the even-order gain;

[0045] Setting the gain includes: determining according to the new stability condition:

[0046]

[0047] wherein, is the discriminant of the second stability condition, and P 1 (z) is the new controlled object;

[0048] Judging whether the Nyquist curve of the discriminant of the second stability condition is within the unit circle. If it is within the unit circle, then further set the gain.

[0049] The beneficial effects of the present invention are:

[0050] The present invention mainly solves the problem of how to suppress odd-order and even-order harmonic currents in the application of single-phase inverters. The specific advantages are as follows:

[0051] Excellent harmonic suppression ability: The present invention proposes SFDMRC, which makes PP-SFDMRC have a higher gain at harmonic frequencies, so it can effectively suppress odd-order harmonics. According to the different odd-order and even-order harmonic contents in the power grid, different odd-order and even-order control gains are set, so that PP-SFDMRC can control odd-order and even-order harmonics to different degrees.

[0052] Strong robustness: The present invention proposes SFDMRC, which makes PP-SFDMRC have a wider resonance bandwidth at harmonic frequencies, and can provide high-quality output current even under the condition of power grid frequency fluctuation, with strong robustness. Description of the Drawings

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0054] Figure 1 is the RC-PC control block diagram of the embodiment of the present invention;

[0055] Figure 2Block diagram of the PP-RC controller according to an embodiment of the present invention;

[0056] Figure 3 Block diagram of the internal model structure of SFDMRC according to an embodiment of the present invention;

[0057] Figure 4 Bode diagrams of SFDMRC, SDMRC and DMRC at the 5th harmonic frequency according to an embodiment of the present invention; wherein, Figure 4 (a) Amplitude-phase response curves of three algorithms within 1Khz; Figure 4 (b) Amplitude-frequency diagrams of three algorithms at the 5th harmonic;

[0058] Figure 5 Structure diagram of a single-phase three-level grid-connected inverter according to an embodiment of the present invention;

[0059] Figure 6 System structure diagram of PP-SFDMRC according to an embodiment of the present invention;

[0060] Figure 7 Schematic diagram of the output waveform of the inverter and the THD of the grid-connected current when the grid frequency is 50Hz in the PP-SFDMRC system according to an embodiment of the present invention; wherein, Figure 7 (a) Output waveform diagram of the inverter when the grid frequency is 50.Hz; Figure 7 (b) THD diagram of the grid-connected current;

[0061] Figure 8 Schematic diagram of the output waveform of the inverter and the THD of the grid-connected current when the grid frequency is 49.6Hz and 50.4Hz in the PP-SFDMRC system according to an embodiment of the present invention; wherein, Figure 8 (a) Schematic diagram of the output waveform of the inverter and the THD of the grid-connected current when the grid frequency is 49.6Hz; Figure 8 (b) Schematic diagram of the output waveform of the inverter and the THD of the grid-connected current when the grid frequency is 50.4Hz;

[0062] Figure 9 Output waveform of the inverter when the reference current changes from 5A to 10A in the PP-SFDMRC system according to an embodiment of the present invention. Detailed implementation manners

[0063] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0064] To make the above objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Regarding the problem that the odd and even harmonic contents in the output current harmonics of a single-phase inverter are different and relatively high, the plug-in dual-mode repetitive control (P-DMRC) control strategy has been widely used to suppress odd and even harmonics to varying degrees. However, due to the inherent delay of repetitive control (RC), the dynamic performance of P-DMRC is limited. Moreover, the change in the grid frequency will greatly reduce the control accuracy of P-DMRC. To solve the above problems, the present invention proposes a design method of plug-in proportional second order feedforward dual-mode RC (PP-SFDMRC). Compared with P-DMRC, the introduction of the feedforward channel enables PP-SFDMRC to exhibit higher gain and a wider resonance bandwidth at the fundamental frequency and odd harmonic frequencies, and can more effectively suppress current harmonics even when the grid frequency fluctuates. Therefore, the proposed PP-SFDMRC control strategy has excellent dynamic performance and strong adaptability to grid frequency changes. The present invention gives a complete parameter design scheme for the plug-in proportional second order feedforward dual-mode repetitive controller. Based on a single-phase grid-connected inverter simulation experiment platform, the effectiveness of the proposed controller is verified.

[0066] The present invention proposes a mathematical equivalence relationship between a plug-in proportional repetitive controller and a proportional integral multi-resonance controller (PIMR).

[0067] The design method of the plug-in second order feedforward odd harmonic controller for a single-phase inverter of the present invention.

[0068] The PP-SFDMRC design method proposed by the present invention is applicable to all industrial facilities that require the ability to process periodic signals, including but not limited to devices such as inverters, servo motors, and steering gears. Any equivalent replacement or modification based on the method scheme and inventive concept of the present invention should be covered within the protection scope of the present invention.

[0069] RC is widely used in inverter control to achieve static-free tracking of fundamental periodic signals and eliminate the interference of double-frequency harmonic signals. It is usually combined with proportional integral (PI) control to improve its dynamic response. In addition, repetitive controllers usually adopt a parallel structure or an insertion structure. However, parallel repetitive controllers also face some challenges, such as complex parameter design and controller output coupling problems. Therefore, the present invention selects the plug-in RC (PRC). For the convenience of parameter design, in the process of selecting the parameters of the PI controller, only the proportional controller is selected, so the present invention proposes the plug-in proportional RC (PP-RC).

[0070] Dual-Mode Repetitive Control (DMRC) has independent odd-order and even-order internal models, which can suppress odd and even harmonics to different degrees, and can accelerate the convergence rate of tracking errors without loss of accuracy. In practical applications, clock error drift, measurement noise, Hall sensor accuracy limitations, etc. all cause system frequency fluctuations, resulting in a significant decline in the performance of DMRC. High-order RC can be used to reduce the sensitivity of the processed disturbances to periodic fluctuations. The present invention adds a feedforward channel to the internal model of the plug-in proportional DMRC (PP-DMRC) and proposes PP-SFDMRC.

[0071] First, analyze the proposed PP-RC:

[0072] The common repetitive controller (CRC) internal model transfer function G r (z) that includes the repetitive control gain k m , the phase lead link z a and the low-pass filter S(z) is as follows. The discrete expression is shown below.

[0073]

[0074] Where Q(z) is the internal model filter, N is the number of delay beats per cycle, and N = f s / f g , where f s is the sampling frequency and f g is the grid frequency.

[0075] The block diagrams of the repetitive control parallel proportional control (RC-PC) and the new PP-RC are respectively asFigure 1 , Figure 2 as shown

[0076] Figure 1 is the RC-PC control block diagram. k p is the proportional link. In this embodiment, the transfer function from the error E(z) to the inverter output voltage U(z) can be obtained as follows:

[0077]

[0078] where Q(z) is the internal model filter, z is the discrete operator, and z m is the phase lead link, and S(z) is the low-pass filter.

[0079] Figure 2 is the PP-RC control block diagram. The transfer function from the error E(z) to the inverter output voltage U(z) is as follows:

[0080]

[0081] where k p1 is the proportional link of the plug-in repetitive control, and k r1 is the plug-in repetitive control gain.

[0082] Combining equations (2) and (3) gives:

[0083]

[0084] From this, it can be concluded that the proposed PP-RC and RC-PC are completely equivalent. The proposed control structure has the same advantages as PIMR, with fewer parameter designs and is convenient for analysis and calculation.

[0085] Next, the second-order feedforward DMRC (second order feedforward dual-mode repetitive control, SFDMRC) is analyzed;

[0086] To further improve the internal model gain of the repetitive control, based on the proposed plug-in proportional repetitive control in this embodiment, a plug-in second-order feedforward dual-mode repetitive control strategy is proposed. A feedforward link is added to the odd and even internal models of the second-order dual-mode repetitive control (second order dual-mode repetitive control, SDMRC) to form SFDMRC. The internal model structure diagram is as shown in Figure 3 as shown. Its discrete transfer function is:

[0087]

[0088] where ko is the odd - order gain, k e is the even - order gain. For the convenience of analysis, let Q(z)=1, k o =k e =1 is substituted into formula (5), and the ideal internal - model transfer function of SFDMRC is as follows:

[0089]

[0090] where w is the weight factor. N(z) is the numerator of the ideal internal - model G ISFDMRC (z) of SFDMRC, and 1 - W(z) is the denominator of the ideal internal - model G ISFDMRC (z) of SFDMRC, where W(z)=(1 + w)z -N -wz -2N . Definition:

[0091]

[0092] The form of W(z) obtained in this embodiment conforms to the form of second - order RC. Therefore, the proposed scheme is second - order RC. In addition, as Figure 3 shown, the internal model of the ideal internal - model transfer function of SFDMRC can consider a two - mode structure RC with a high - order compensator Gho(z).

[0093] When Q(z)=0.95, the repetitive - control gain k o =k e =1, and the sampling frequency is 10 kHz, the Bode plots of SFDMRC, SDMRC, and DMRC at the 5th - harmonic frequency are shown in Figure 4 (a)-(b). SFDMRC provides a higher open - loop gain at the harmonic frequency than SDMRC and DMRC. Therefore, the proposed SFDMRC has better harmonic - suppression ability.

[0094] This embodiment discloses an insertion - type second - order feed - forward dual - mode repetitive control method, including: establishing a single - phase LCL - type grid - connected inverter model based on a PP - SFDMRC controller, where the PP - SFDMRC controller is a controller that introduces an insertion - type second - order feed - forward dual - mode repetitive control strategy on the basis of insertion - type proportional repetitive control; according to the single - phase LCL - type grid - connected inverter model, obtaining the transfer function of the controlled object, and discretizing the structure of the PP - SFDMRC controller to obtain the discrete transfer function of the SFDMRC internal model; based on the discrete transfer function of the SFDMRC internal model, with the stability of the SFDMRC internal model as the goal, obtaining the error transfer function of the PP - SFDMRC controller and converting it into a characteristic polynomial to determine the stability condition of the PP - SFDMRC controller; through the stability condition, setting the corresponding parameters of the PP - SFDMRC controller to control odd - and even - order harmonics to different degrees; the corresponding parameters include: phase compensator parameters, proportional gain, active damping coefficient, internal model coefficient, filter parameters, phase - lead link, weight factor, and gain.

[0095] Further, obtaining the transfer function of the controlled object includes: according to the grid - side current control with target - period delay, where the target - period delay includes sampling calculation delay and PWM delay, reducing the resonance peak of the LCL filter to obtain the transfer function of the controlled object.

[0096] Specifically:

[0097] Step 1: Obtain the transfer function of the controlled object according to the inverter model.

[0098] The model of the single - phase LCL - type grid - connected inverter is as Figure 5 shown, where U dc represents the DC - bus voltage, i g represents the grid - connected current, and u g is the grid voltage. The phase - locked loop (PLL) is a device that collects the phase of the point - of - common - coupling (PCC) voltage and generates a reference current i ref , and the amplitude of the reference current is I ref . The current controller is a PP - SFDMRC controller, denoted as G i (z).

[0099] Compared with the analog control system, the digital control delay of 1.5 periods (including 1 - period sampling calculation delay and 0.5 - period PWM delay) will change the characteristics of the closed - loop system. Therefore, considering the grid - side current control block diagram with 1.5 - period delay is as Figure 8 shown. In the figure, T s is the sampling period, and H icis the capacitance current feedback coefficient, aiming to reduce the resonance peak brought by the LCL filter. The transfer function of the controlled object can be obtained for precise control. P(s) is the transfer function of the controlled object, and the expression of the transfer function of the controlled object is:

[0100]

[0101] Among them, the system parameters are shown in Table 1:

[0102] Table 1

[0103]

[0104] Furthermore, obtaining the error transfer function of the PP-SFDMRC controller includes:

[0105] Taking the SFDMRC internal model stability as the goal, all poles of the SFDMRC internal model discrete transfer function should be set inside the unit circle, and |w| < 1, eliminating the case of w = 0, and further obtaining the error transfer function of the PP-SFDMRC controller.

[0106] Furthermore, determining the stability conditions of the PP-SFDMRC controller includes:

[0107] The first stability condition includes: the roots of 1 + P(z)k p are inside the unit circle;

[0108] The second stability condition includes: |1 + P 1 (z)G c (z)| ≠ 0;

[0109] Among them, P 1 (z) is the new controlled object, and G c (z) is the SFDMRC internal model discrete transfer function.

[0110] Furthermore, after determining the stability conditions of the PP-SFDMRC controller:

[0111] Substitute the error transfer function of the PP-SFDMRC controller into the second stability condition, and let and Obtain:

[0112]

[0113] If the frequencies of the reference signal and the disturbance signal are integer multiples of the fundamental frequency, then |z -N / 2 | = 1, and further obtain:

[0114]

[0115] Obtain the amplitude-frequency and phase-frequency characteristics of the new controlled object and the low-pass filter, and let k r > 0, Obtain the new stability condition:

[0116]

[0117] Specifically:

[0118] Step 2: Conduct a stability analysis on the plug-in feedforward odd-order repetitive control system:

[0119] The structure of the discrete PP-SFDMRC system is as Figure 6 shown, where S(z) is a low-pass filter used to attenuate high-order harmonics, z m is a phase lead compensator, and d g (z) is the disturbance signal. The SFDMRC internal model discrete transfer function including k r , z m , and S(z) is as follows:

[0120]

[0121] For stability, all poles of G c (z) should be set inside the unit circle and it is also required that |w| < 1 at the same time. Therefore, the value range of w is restricted to: -1 < w < 0 or 0 < w < 1, eliminating the case of w = 0, because the SFDMRC with w = 0 is simplified to the feedforward dual-mode repetitive control (FDMRC).

[0122] The error transfer function of the system is:

[0123]

[0124] The system characteristic polynomial is:

[0125] 1 + [1 + G c (z)]P(z)k p = [1 + P(z)k p [1 + P 1 (z)G c (z)] (11)

[0126] Among them, the new controlled object:

[0127] The system stability condition is obtained through the characteristic equation as follows:

[0128] 1. The roots of 1 + P(z)k p are inside the unit circle;

[0129] 2. |1 + P 1 (z)G c (z)| ≠ 0.

[0130] Substitute formula (10) into condition 2:

[0131]

[0132] Let The above inequality becomes:

[0133]

[0134] If the frequencies of the reference signal and the disturbance signal are integer multiples of the fundamental frequency, then |z -N / 2 | = 1, and we can get:

[0135]

[0136] Assume P 1 (z) and S(z) have the following amplitude-frequency and phase-frequency characteristics:

[0137]

[0138] Because the phase of Q(z) is 0, Expanded by Euler's formula, k r > 0, The stability condition of formula (13) becomes:

[0139]

[0140]

[0141] Select an appropriate phase compensator z according to (16) m , and then select parameters k r and w according to (17). This can ensure the stability of the PP - SFDMRC system.

[0142] Furthermore, setting the corresponding parameters of the PP - SFDMRC controller includes:

[0143] Setting the phase compensator parameters includes: Based on the new stability condition, select the phase compensator.

[0144] Setting the proportional gain and the active damping coefficient includes: According to the first stability condition, that is, the poles of the new controlled object are inside the unit circle in the z - plane, perform Bode plot analysis on the new controlled object and select the proportional gain and the active damping coefficient; Setting the internal model coefficient and the filter parameters includes: According to the change of the open - loop gain of the SFDMRC internal model, set the internal model coefficient, and based on the low - frequency harmonic frequency of the PP - SFDMRC controller, select the cut - off frequency of the filter.

[0145] Furthermore, setting the corresponding parameters of the PP-SFDMRC controller also includes: setting the phase lead link, including: according to the phase lag of the new controlled object and the low-pass filter, using the phase guiding compensator to make have the phase closest to the target phase angle, so as to set the phase lead link;

[0146] Setting the weight factor includes: according to the positive correlation between w 2 and k o +k e and combining the new stability condition, setting the weight factor; where w is the weight factor, k o is the odd-order gain, and k e is the even-order gain;

[0147] Setting the gain includes: determining according to the new stability condition:

[0148]

[0149] Judge whether the Nyquist curve of is inside the unit circle. If it is inside the unit circle, then further set the gain.

[0150] Specifically:

[0151] Step 3: Design the parameters of each part of the plug-in feedforward odd-order repetitive control

[0152] (1) Design the proportional gain k p , the active damping coefficient H ic :

[0153] In order to make the stability condition 1 hold, an appropriate value of k p needs to be selected so that the roots of 1 + k p P(z) = 0 are inside the unit circle, that is, the poles of the new controlled object P 1 (z) are inside the unit circle of the z-plane. At the same time, k p plays an important role in improving the dynamic performance of the system, and it is necessary to analyze the value of k p . By selecting different values of k p , through the Bode plot analysis of P 1 (z), make P 1 (z) satisfy zero phase and zero gain as much as possible. In contrast, since the 0dB line provides a reference, the selection of k p is simpler than that of PRC. Finally, select H ic = 10, k p = 14, and the discrete expression of P 1 (z) is as follows:

[0154]

[0155] (2) Design the internal model coefficient Q(z) and the filter S(z):

[0156] The open-loop gain of the SFDMRC internal model decreases with the decrease of Q, while the bandwidth near the resonant frequency increases significantly. Therefore, Q(z) = 0.95 is selected. Since the main low-frequency harmonic frequency of the system is below the 20th harmonic frequency, the cut-off frequency of the filter is selected as 1 kHz. The transition band of the Butterworth low-pass filter is narrower than that of the second-order low-pass filter. Therefore, a 4th-order Butterworth low-pass filter with a cut-off frequency of 1 kHz is selected, and its transfer function is:

[0157]

[0158] (3) Design the phase lead link z m :

[0159] To solve the phase lag problem caused by P 1 (z) and the low-pass filter S(z), a phase lead compensator m is needed. According to different values of m, when m = 8, the phase is closest to the 0°dB line. Therefore, m = 8 is selected.

[0160] (4) Design the weight factor w:

[0161] The parameter w affects the robustness of the system, while k o +k e is related to the dynamic performance of the system. It should be noted that w 2 and k o +k e are approximately positively correlated. To balance these factors, we select w = 0.4.

[0162] (5) Design the gain k r :

[0163] When m = 8, the angle of γ(ω) is between 0° and 12.2°, so the minimum value of cosγ(ω) is 0.977, m = 8, z m S(z)P 0 (z) has a maximum gain of 0.355 dB, the maximum value of r is 1.04. Through formula (17), the maximum value of k

[0164] According to the stability condition 2, let:

[0165]

[0166] If If the Nyquist curve is inside the unit circle, it indicates that the system is stable. Finally, k is selected r = 0.28, the system is stable and the Nyquist curve of is closer to the center of the circle, that is, the system has better signal tracking ability. Since the content of odd harmonics in the power grid is greater than that of even harmonics, k is selected o = 0.186, k e = 0.093.

[0167] Step 4: Establish a simulation model to verify the controller:

[0168] A simulation model of a 1.5-kW single-phase three-level grid-connected inverter is established, and the proposed control strategy is verified by simulation experiments. The parameters of the inverter are shown in Table 1. To simulate the real power grid environment, grid background harmonics with a THD of 5.7% are added to the power grid, and its spectrum is shown in Table 2.

[0169] Table 2

[0170]

[0171] Simulation results:

[0172] (1) When the grid frequency becomes 50 Hz, the inverter output waveform and grid-connected current THD analysis of the control system based on PP-SDMRC are as Figure 6 shown. The results show that when the grid background harmonics are 5.7%, the proposed PP-SFDMRC can still output high-quality grid-connected current.

[0173] (2) When the grid frequency fluctuates between 49.6 Hz and 50.4 Hz, the output waveform and current THD analysis of the PP-SFDMRC system are as Figure 7-8 shown. Obviously, the proposed PP-SFDMRC based on the new design method can still have good control performance when the frequency fluctuates;

[0174] Among them, Figure 7 (a) is the inverter output waveform diagram when the grid frequency is 50. Hz; Figure 7 (b) is the grid-connected current THD diagram; Figure 8 (a) is the schematic diagram of the inverter output waveform and grid-connected current THD when the grid frequency is 49.6 Hz; Figure 8 (b) is the schematic diagram of the inverter output waveform and grid-connected current THD when the grid frequency is 50.4 Hz.

[0175] (3) When the reference current suddenly changes from 5 A to 10 A, the output waveform of the PP-SFDMRC system is as Figure 9 shown. i gThe waveform tends to be stable within about 2 cycles (40 milliseconds), and the PP-SFDMRC system has a relatively fast response speed.

[0176] The above embodiments are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An insertion-type second-order feedforward dual-mode repetitive control method, characterized in that: include: A single-phase LCL grid-connected inverter model based on a PP-SFDMRC controller is established. The PP-SFDMRC controller is a controller that introduces an inserted second-order feedforward dual-mode repetitive control strategy based on an inserted proportional repetitive control. According to the single-phase LCL grid-connected inverter model, the controlled object transfer function is obtained, and the PP-SFDMRC controller structure is discretized to obtain the SFDMRC inner model discrete transfer function; Based on the SFDMRC internal model discrete transfer function and with the SFDMRC internal model stability as the goal, the error transfer function of the PP-SFDMRC controller is obtained and converted into a characteristic polynomial to determine the stability condition of the PP-SFDMRC controller; According to the stability condition, the corresponding parameters of the PP-SFDMRC controller are set to control the odd and even harmonics to different degrees; the corresponding parameters include: phase compensator parameters, proportional gain, active damping coefficient, internal model coefficient, filter parameters, phase advance link, weight factor and gain.

2. The plug-in second-order feedforward dual-mode repetitive control method according to claim 1, characterized in that: Obtaining the transfer function of the controlled object includes: According to the grid-side current control with target cycle delay, the target cycle delay includes: sampling calculation delay and PWM delay, reducing the resonance peak of the LCL filter, and obtaining the transfer function of the controlled object: Among them, L1 is the inverter side filter inductor, L2 is the grid side filter inductor, C is the filter capacitor, T s is the sampling period, H ic is the capacitor current feedback coefficient.

3. The plug-in second-order feedforward dual-mode repetitive control method according to claim 1, characterized in that: Obtaining the error transfer function of the PP-SFDMRC controller includes: Among them, Q(z) is the internal model filter, z is the discrete operator, z m is the phase advance link, S(z) is the low-pass filter, w is the weight factor, k o is an odd gain, k e Even gain.

4. The plug-in second-order feedforward dual-mode repetitive control method according to claim 1, characterized in that: Obtaining the error transfer function of the PP-SFDMRC controller includes: With the goal of SFDMRC internal model stability, all poles of the SFDMRC internal model discrete transfer function should be set within the unit circle, and |w| < 1, eliminating the case of w = 0, and further obtaining the error transfer function of the PP-SFDMRC controller: Among them, i ref (z) is the reference current, d g (z) is the harmonic disturbance current, P(z) is the original controlled object, k p is the proportional link, and w is the weight factor.

5. The plug-in second-order feedforward dual-mode repetitive control method according to claim 1, characterized in that: The conversion into the characteristic polynomial includes: 1+[1+G c (z)]P(z)k p =[1+P(z)k p ][1+P1(z)G c (with)] Among them, G c (z) is the discrete transfer function of the SFDMRC internal model.

6. The plug-in second-order feedforward dual-mode repetitive control method according to claim 1, characterized in that: Determining the stability conditions of the PP-SFDMRC controller includes: The first stability condition includes: 1+P(z)k p The roots of are inside the unit circle; The second stability condition includes: |1+P1(z)G c (z)|≠0; Among them, P1(z) is the new controlled object, G c (z) is the discrete transfer function of the SFDMRC internal model.

7. The plug-in second-order feedforward dual-mode repetitive control method according to claim 6, characterized in that: Determining the stability condition of the PP-SFDMRC controller includes: Substitute the error transfer function of the PP-SFDMRC controller into the second stability condition and let and get: If the frequencies of the reference signal and the disturbance signal are integer multiples of the fundamental frequency, then |z -N / 2 |=1, further obtain: Where A(z) is a high-order compensator for dual-mode repetitive control, z is a discrete operator, and N is the number of sampling points within a fundamental frequency period; Get the amplitude-frequency and phase-frequency characteristics of the new controlled object and the low-pass filter, let k r >0, Get new stable conditions: Among them, θ P is the phase of the controlled object, is a discrete operator, θ S is the phase of the low-pass filter S(z), m is the number of phase advance compensation beats, T s is the sampling period, cosγ(ω) is is the amplitude of the low-pass filter S(z), is the amplitude of the controlled object.

8. The plug-in second-order feedforward dual-mode repetitive control method according to claim 7, characterized in that: The corresponding parameters of the PP-SFDMRC controller are set as follows: Setting the phase compensator parameters includes: selecting a phase compensator based on the new stability condition; Setting the proportional gain and the active damping coefficient comprises: performing a Bode diagram analysis on the new controlled object according to the first stability condition, that is, the pole of the new controlled object is within the unit circle of the z plane, and selecting the proportional gain and the active damping coefficient; Setting the internal model coefficients and the filter parameters includes: setting the internal model coefficients according to the change of the open-loop gain of the SFDMRC internal model, and selecting the cutoff frequency of the filter based on the low-frequency harmonic frequency of the PP-SFDMRC controller.

9. The plug-in second-order feedforward dual-mode repetitive control method according to claim 7, characterized in that: Setting the corresponding parameters of the PP-SFDMRC controller also includes: Setting the phase advance link includes: according to the phase lag of the new controlled object and the low-pass filter, using a phase guidance compensator, The phase angle is closest to the target phase angle, thereby setting the phase advance link; Setting the weight factor includes: 2 and k o +k e The positive correlation between them is combined with the new stable condition to set the weight factor; where w is the weight factor, k o is an odd gain, k e is an even gain; Setting the gain includes: determining according to the new stability condition: in, is the discriminant of the second stable condition, P1(z) is the new controlled object; The discriminant for judging the second stability condition Whether the Nyquist curve of is within the unit circle, if it is within the unit circle, further setting the gain.

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