Method and device for improving stability of grid-connected inverter under weak grid

Abstract

The application discloses a method and device for improving stability of a grid-connected inverter under a weak power grid, and the method comprises the following steps: sampling a grid-side current, subtracting a given signal from the grid-side current to obtain an error signal; inputting the error signal into a repetitive controller to obtain an output signal; inputting the output signal into a power grid voltage resonance feedforward controller to obtain a modulation signal of the inverter; establishing a mathematical model of a control object according to parameters of the inverter; judging stability of the repetitive control, keeping current control under the stable condition, selecting a compensation coefficient under the unstable condition, adjusting the repetitive controller, thereby adjusting the modulation signal until the system control is stable; and the application has the advantages that the application is suitable for wide-range change of impedance of the power grid, and can guarantee stability of the grid-connected inverter under the weak power grid.

Description

Technical Field

[0001] This invention relates to the field of grid-connected inverter technology, and more specifically to a method and apparatus for improving the stability of grid-connected inverters under weak power grid conditions. Background Technology

[0002] In distributed generation systems, grid-connected inverters serve as a crucial interface between renewable energy sources and the power grid, and their current control has attracted considerable attention from experts and scholars. To obtain high-quality grid-connected current, repetitive control and grid voltage feedforward have been widely adopted. However, renewable energy sources are often located in remote areas, and long-distance transmission lines result in high grid impedance. Therefore, the stable operation of power equipment connected to the point of common coupling (PCC) faces challenges under varying grid conditions (widely varying grid impedance).

[0003] Proportional feedforward of grid voltage can significantly improve the output impedance of the inverter in the low-frequency band, which is beneficial to suppressing the influence of low-order harmonics of grid voltage on grid current. However, when the grid impedance is not zero, grid voltage feedforward will introduce a positive feedback loop, which will deteriorate the quality of the grid current and greatly reduce the stability of the system. Related studies have analyzed the formation mechanism of harmonic current and proposed a resonant feedforward strategy. For example, the literature "Xu Fei, Tang Yu, Gu Wei. Research on resonant feedforward control strategy of LCL grid-connected inverter under weak grid conditions [J]. Proceedings of the CSEE, 2016, 36(18): 4970-4979." sacrifices the suppression of low-frequency harmonics of grid voltage in exchange for the stable operation of the grid-connected inverter.

[0004] The repetitive controller based on the internal model principle is essentially equivalent to a parallel infinite-term resonant controller. Its equivalent inverter output impedance is high when it is an integer multiple of the fundamental frequency, which can be used to suppress low-order harmonics in the grid voltage. Repetitive control requires corresponding compensation based on the characteristics of the controlled object to ensure system stability. However, under weak grid conditions, the grid impedance varies over a wide range, and the amplitude and phase characteristics of the controlled object change significantly. The compensator designed for repetitive control cannot adapt to the controlled object under such wide impedance variations, posing a significant challenge to the stability of grid-connected inverters under weak grid conditions. Summary of the Invention

[0005] The technical problem to be solved by this invention is that existing repetitive controllers are difficult to adapt to a wide range of grid impedance variations and cannot guarantee the stability of grid-connected inverters under weak grid conditions.

[0006] This invention solves the above-mentioned technical problems through the following technical means: a method for improving the stability of grid-connected inverters under weak power grid conditions, the method comprising:

[0007] Step a: Sample the grid-side current, and subtract the grid-side current from the given signal to obtain the error signal;

[0008] Step b: Input the error signal into the repetitive controller G(z) to obtain the output signal;

[0009] Step c: Input the output signal into the grid voltage resonant feedforward controller G f (z) Obtain the modulation signal of the inverter;

[0010] Step d: Establish a mathematical model of the controlled object based on the inverter parameters;

[0011] Step e: Determine the stability of the repetitive control. If the system is stable, maintain the current control. If the system is unstable, select a compensation coefficient and adjust the repetitive controller G(z) to adjust the modulation signal until the system control is stable.

[0012] Beneficial effects: This invention designs a repetitive controller G(z) to determine the stability of repetitive control. Under stable conditions, it maintains the current control. Under unstable conditions, it selects a compensation coefficient and adjusts the repetitive controller G(z) to adjust the modulation signal until the system control is stable. It is applicable to a wide range of grid impedance variations and ensures the stability of grid-connected inverters under weak grid conditions.

[0013] Furthermore, the expression for the repetitive controller G(z) is:

[0014]

[0015] in, For the delay element, N is the number of sampling points within one power grid cycle, z -N Let N represent the delay in the discrete system. Since the sampling frequency of the device of this invention is 18000Hz, N is taken as 18000 / 50 = 360; Q is the compensation coefficient of the delay element; S(z) is the compensator element, which is used to compensate for the phase of the controlled object P(z), so that S(z)P(z) has approximately zero gain and zero phase shift in the low and medium frequency range. Its expression is:

[0016] S(z)=z k G LPF (z)G trap (z)

[0017] Among them, z k For advanced stages; G LPF (z) is a low-pass filter; G trap(z) is a notch filter used to suppress the high gain of S(z)P(z) near the fundamental frequency due to a weak power grid, while compensating for the phase margin of S(z)P(z) above the fundamental frequency range, achieving near-zero gain and zero phase shift of S(z)P(z) in the mid-to-low frequency range under weak power grid conditions. Notch filter G trap (z) by G trap (s) is obtained through a bilinear transformation, where G trap The expression for (s) is:

[0018]

[0019] Among them, G trap (s) is the expression for the notch filter in a continuous system, and its effect is equivalent to G. trap (z), where s is the Laplace operator; ω0 is the fundamental angular velocity; ξ2 is the optimal damping coefficient of the second-order system; and ξ1 is the compensation coefficient, with 0 < ξ1 < ξ2.

[0020] Furthermore, step d includes:

[0021] Mathematical model of the control object G LCL (z) by G LCL (s) is obtained by discretization using a zero-order hold, where G LCL The expression for (s) is

[0022] G LCL (s)=G PI (s)k pwm G d (s)(sCR+1) / {s 3 L1(L2+L g C+s 2 [(L1+L2+L g )CR-L g CRk pwm G d (s)G f (s)]+s[L1+L2+L g -L g k pwm G d (s)G f (s)]}

[0023] Among them, G LCL (s) represents the transfer function between the repetitive controller output and the grid-connected current, where L1 is the bridge-side inductance of the LCL filter; L2 is the grid-side inductance of the LCL filter; and C is the capacitance of the LCL filter. g R is the mains impedance; R is the passive damping of the LCL filter; G d (s) represents a 1.5-beat delay; kpwm For inverter gain, G PI (z) represents the proportional-integral element, G PI (s) represents the expression of the proportional-integral (PI) element in a continuous system. Since the tracking signal is a periodic signal, the effect of the integrator is not obvious. G PI (z) can be simplified to a proportional element to improve the dynamic performance of the first cycle. f (s) represents grid voltage resonant feedforward control, where the resonant feedforward is a second-order bandpass filter used to reduce the positive feedback path of grid impedance in the high-frequency band.

[0024] The expression for the grid impedance is as follows:

[0025]

[0026] In the formula, U0 is the grid voltage; P rate The inverter power rating is denoted by SCR, which indicates a weak grid level. An SCR less than 3 indicates that the grid is a weak grid.

[0027] Furthermore, the method for determining the stability of repetitive control in step e is as follows:

[0028] A sufficient condition for the stability of repetitive control is |QS(z)P(z)|<1, where P(z) is the compensation object and the expression for P(z) is:

[0029]

[0030] Among them G PI (z) represents the proportional integral element;

[0031] If the sufficient condition for the stability of repetitive control is met, it indicates that the repetitive control of the system is stable.

[0032] Furthermore, the steps e include:

[0033] Based on the stability criterion QS(z)P(z) of repetitive control, draw the Bode plot or Nyquist plot. Design the compensation coefficient ξ1 based on the Bode plot amplitude-frequency characteristic being less than 0 or the Nyquist trajectory being within the unit circle. Adjust the repetitive controller G(z) according to the designed compensation coefficient ξ1, thereby adjusting the modulation signal to make the system control stable.

[0034] The present invention also provides a device for improving the stability of grid-connected inverters under weak power grid conditions, the device comprising:

[0035] The signal processing module is used to sample the grid-side current and subtract the grid-side current from the given signal to obtain the error signal;

[0036] The signal output module is used to input the error signal into the repetitive controller G(z) to obtain the output signal;

[0037] The signal modulation module is used to input the output signal to the grid voltage resonant feedforward controller G. f (z) Obtain the modulation signal of the inverter;

[0038] The model building module is used to build a mathematical model of the control object based on the inverter parameters;

[0039] The stability control module is used to determine the stability of repetitive control. Under stable conditions, it maintains the current control. Under unstable conditions, it selects a compensation coefficient and adjusts the repetitive controller G(z) to adjust the modulation signal until the system control is stable.

[0040] Furthermore, the expression for the repetitive controller G(z) is:

[0041]

[0042] in, For the delay element, N is the number of sampling points within one power grid cycle, z -N Let N represent the delay in the discrete system. Since the sampling frequency of the device of this invention is 18000Hz, N is taken as 18000 / 50 = 360; Q is the compensation coefficient of the delay element; S(z) is the compensator element, which is used to compensate for the phase of the controlled object P(z), so that S(z)P(z) has approximately zero gain and zero phase shift in the low and medium frequency range. Its expression is:

[0043] S(z)=z k G LPF (z)G trap (z)

[0044] Among them, z k For advanced stages; G LPF (z) is a low-pass filter; G trap (z) is a notch filter used to suppress the high gain of S(z)P(z) near the fundamental frequency due to a weak power grid, while compensating for the phase margin of S(z)P(z) above the fundamental frequency range, achieving near-zero gain and zero phase shift of S(z)P(z) in the mid-to-low frequency range under weak power grid conditions. Notch filter G trap (z) by G trap (s) is obtained through a bilinear transformation, where G trap The expression for (s) is:

[0045]

[0046] Among them, G trap (s) is the expression for the notch filter in a continuous system, and its effect is equivalent to G.trap (z), where s is the Laplace operator; ω0 is the fundamental angular velocity; ξ2 is the optimal damping coefficient of the second-order system; and ξ1 is the compensation coefficient, with 0 < ξ1 < ξ2.

[0047] Furthermore, the model building module is also used for:

[0048] Mathematical model of the controlled object G LCL (z) by G LCL (s) is obtained by discretization using a zero-order hold, where G LCL The expression for (s) is

[0049] G LCL (s)=G PI (s)k pwm G d (s)(sCR+1) / {s 3 L1(L2+L g C+s 2 [(L1+L2+L g )CR-L g CRk pwm G d (s)G f (s)]+s[L1+L2+L g -L g k pwm G d (s)G f (s)]}

[0050] Among them, G LCL (s) represents the transfer function between the repetitive controller output and the grid-connected current, where L1 is the bridge-side inductance of the LCL filter; L2 is the grid-side inductance of the LCL filter; and C is the capacitance of the LCL filter. g R is the mains impedance; R is the passive damping of the LCL filter; G d (s) represents a 1.5-beat delay; k pwm For inverter gain, G PI (z) represents the proportional-integral element, G PI (s) represents the expression of the proportional-integral (PI) element in a continuous system. Since the tracking signal is a periodic signal, the effect of the integrator is not obvious. G PI (z) can be simplified to a proportional element to improve the dynamic performance of the first cycle. f (s) represents grid voltage resonant feedforward control, where the resonant feedforward is a second-order bandpass filter used to reduce the positive feedback path of grid impedance in the high-frequency band.

[0051] The expression for the grid impedance is as follows:

[0052]

[0053] In the formula, U0 is the grid voltage; P rate The inverter power rating is denoted by SCR, which indicates a weak grid level. An SCR less than 3 indicates that the grid is a weak grid.

[0054] Furthermore, the method for determining the stability of repetitive control in the stability control module is as follows:

[0055] A sufficient condition for the stability of repetitive control is |QS(z)P(z)|<1, where P(z) is the compensation object and the expression for P(z) is:

[0056]

[0057] Among them G PI (z) represents the proportional integral element;

[0058] If the sufficient condition for the stability of repetitive control is met, it indicates that the repetitive control of the system is stable.

[0059] Furthermore, the stability control module is also used for:

[0060] Based on the stability criterion QS(z)P(z) of repetitive control, draw the Bode plot or Nyquist plot. Design the compensation coefficient ξ1 based on the Bode plot amplitude-frequency characteristic being less than 0 or the Nyquist trajectory being within the unit circle. Adjust the repetitive controller G(z) according to the designed compensation coefficient ξ1, thereby adjusting the modulation signal to make the system control stable.

[0061] The advantages of this invention are:

[0062] (1) The present invention designs a repetitive controller G(z) to determine the stability of the repetitive control. Under stable conditions, the current control is maintained. Under unstable conditions, a compensation coefficient is selected and the repetitive controller G(z) is adjusted to adjust the modulation signal until the system control is stable. It is applicable to a wide range of grid impedance changes and ensures the stability of grid-connected inverters under weak grid conditions.

[0063] (2) This invention discovers that the instability of grid-connected inverters under weak power grids is due to the wide range of variations in grid impedance. When the grid impedance is large, the grid impedance and the inverter's equivalent impedance intersect in the low-frequency band, and the phase margin at the intersection point is less than 0, resulting in low-frequency oscillations in the inverter's output current. This invention utilizes the characteristic that a notch filter can attenuate the amplitude-frequency gain of the compensation object P(z) Bode plot while improving the phase-frequency margin in the low-frequency band, and designs a repetitive controller to solve the problem of low-frequency oscillations in the grid-connected current of grid-connected inverters under weak power grids. This increases the stability margin of grid-connected inverters under weak power grids, promotes the widespread and reliable application of LCL filter grid-connected inverters, and helps to promote the development of distributed grid-connected power generation technology. It has important theoretical significance and practical value. Attached Figure Description

[0064] Figure 1 This is a flowchart of a method for improving the stability of a grid-connected inverter under a weak power grid, as disclosed in Embodiment 1 of the present invention.

[0065] Figure 2 The stability criterion Bode plot is used in the method for improving the stability of grid-connected inverters under weak power grid conditions disclosed in Embodiment 1 of the present invention.

[0066] Figure 3 The stability criterion Nyquist plot is used in the method for improving the stability of grid-connected inverters under weak power grid conditions disclosed in Embodiment 1 of the present invention.

[0067] Figure 4 This is a control principle block diagram of a method for improving the stability of a grid-connected inverter under a weak power grid, as disclosed in Embodiment 1 of the present invention.

[0068] Figure 5 The waveform of the inverter current before the implementation of the method for improving the stability of a grid-connected inverter under a weak power grid disclosed in Embodiment 1 of the present invention is shown.

[0069] Figure 6 The waveform of the inverter current after implementing the method for improving the stability of a grid-connected inverter under a weak power grid disclosed in Embodiment 1 of the present invention. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] Example 1

[0072] like Figure 1As shown, this invention provides a method for improving the stability of grid-connected inverters under weak power grid conditions, comprising the following steps:

[0073] (1) Design of a proportional-to-repetitive control loop, wherein the proportional-to-repetitive control loop includes a proportional controller, a repetitive controller and an adder;

[0074] (2) The compensation coefficient selection process includes establishing a mathematical model of the controlled object, determining the stability of repeated control, and selecting the compensation coefficient.

[0075] The construction process of the proportion plus repetition control link includes:

[0076] Step a: Sample the grid-side current, and subtract the grid-side current from the given signal to obtain the error signal;

[0077] Step b: Input the error signal into the repetitive controller G(z) to obtain the output signal; wherein, the expression of the repetitive controller G(z) is:

[0078]

[0079] in, For the delay element, N is the number of sampling points within one power grid cycle, z -N Let N represent the delay in the discrete system. Since the sampling frequency of the device of this invention is 18000Hz, N is taken as 18000 / 50 = 360; Q is the compensation coefficient of the delay element; S(z) is the compensator element, which is used to compensate for the phase of the controlled object P(z), so that S(z)P(z) has approximately zero gain and zero phase shift in the low and medium frequency range. Its expression is:

[0080] S(z)=z k G LPF (z)G trap (z)

[0081] Among them, z k For advanced stages; G LPF (z) is a low-pass filter; G trap (z) is a phase compensator, also known as a notch filter, designed to address insufficient stability margin in control systems. It suppresses the high gain of S(z)P(z) near the fundamental frequency due to a weak power grid, while compensating for the phase margin of S(z)P(z) above the fundamental frequency range. Under weak power grid conditions, it achieves near-zero gain and zero phase shift of S(z)P(z) in the mid-to-low frequency range. Notch filter G trap (z) by G trap (s) is obtained through a bilinear transformation, where G trap The expression for (s) is:

[0082]

[0083] Among them, G trap (s) is the expression for the notch filter in a continuous system, and its effect is equivalent to G. trap (z), where s is the Laplace operator; ω0 is the fundamental angular velocity; and ξ2 is the optimal damping coefficient of the second-order system. In this embodiment, ξ2 takes the value of It is the compensation coefficient and 0 < ξ1 < ξ2.

[0084] Step c: Input the output signal into the grid voltage resonant feedforward controller G f (z) Obtain the modulation signal of the inverter.

[0085] The process of constructing the compensation coefficient selection step includes:

[0086] Step d: Establish a mathematical model of the controlled object based on the inverter parameters; specifically, the mathematical model of the controlled object G LCL (z) by G LCL (s) is obtained by discretization using a zero-order hold, where G LCL The expression for (s) is

[0087] G LCL (s)=G PI (s)k pwm G d (s)(sCR+1) / {s 3 L1(L2+L g C+s 2 [(L1+L2+L g )CR-L g CRk pwm G d (s)G f (s)]+s[L1+L2+L g -L g k pwm G d (s)G f (s)]}

[0088] Among them, G LCL (s) represents the transfer function between the repetitive controller output and the grid-connected current, where L1 is the bridge-side inductance of the LCL filter; L2 is the grid-side inductance of the LCL filter; and C is the capacitance of the LCL filter. g R is the mains impedance; R is the passive damping of the LCL filter; G d (s) represents a 1.5-beat delay; k pwm For inverter gain, G PI (z) represents the proportional-integral element, G PI(s) represents the expression of the proportional-integral (PI) element in a continuous system. Since the tracking signal is a periodic signal, the effect of the integrator is not significant. G PI (z) can be simplified to a proportional element to improve the dynamic performance of the first cycle. f (s) represents grid voltage resonant feedforward control, where the resonant feedforward is a second-order bandpass filter used to reduce the positive feedback path of grid impedance in the high-frequency band.

[0089] The expression for the grid impedance is as follows:

[0090]

[0091] In the formula, U0 is the grid voltage; P rate The inverter power rating is denoted by SCR, which indicates a weak grid level. An SCR less than 3 indicates that the grid is a weak grid.

[0092] Step e: Determine the stability of the repetitive control. If stable, maintain the current control. If unstable, select a compensation coefficient and adjust the repetitive controller G(z) to adjust the modulation signal until the system control stabilizes. The method for determining the stability of the repetitive control is as follows:

[0093] A sufficient condition for the stability of repetitive control is |QS(z)P(z)|<1, where P(z) is the compensation object and the expression for P(z) is:

[0094]

[0095] Among them G PI (z) represents the proportional-integral (PI) element; if the sufficient condition for the stability of repetitive control is met, it indicates that the system is stable under repetitive control. According to the sufficient condition for the stability of a repetitive control system, |QS(z)P(z)| < 1, and based on relevant knowledge of automatic control principles, the stability of this system is equivalent to ω from 0 to the Nyquist frequency, with the endpoints of the QS(z)P(z) vectors all within a unit circle with a radius of 1. Furthermore, based on the equivalence relationship between Bode plots and Nyquist plots, the stability of this system is also equivalent to ω from 0 to the Nyquist frequency, with the Bode plots of QS(z)P(z) all below 0 dB.

[0096] Based on the stability criterion QS(z)P(z) for repetitive control, a Bode plot or Nyquist plot is drawn. A compensation coefficient ξ1 is designed based on the Bode plot's amplitude-frequency characteristic being less than 0 or the Nyquist trajectory being within the unit circle. The repetitive controller G(z) is then adjusted according to the designed compensation coefficient ξ1, thereby adjusting the modulation signal and stabilizing the system control. Specifically, as follows... Figure 2The Bode plot shows the stability criterion for grid-connected inverters under weak grid conditions. Adjusting the ξ1 parameter and observing that the amplitude-frequency curve of the QS(z)P(z) Bode plot is below 0 dB indicates that the system satisfies the repetitive control stability criterion. Alternatively, as... Figure 3 The Nyquist plot of the stability criterion for a grid-connected inverter in a weak power grid is shown. Adjusting the parameter ξ1 and observing that the Nyquist curve of QS(z)P(z) lies within the unit circle indicates that the system satisfies the repetitive control stability criterion.

[0097] It should be noted that the repetitive controller S(z), the delay element compensation coefficient Q, and the resonant feedforward controller G are related to these parameters. f (z) and proportional-integral controller G PI (z) The selection of relevant parameters only needs to ensure the stability of the system under strong power grid conditions. These parameters can be preset according to the actual application situation, and the adjustment of these parameters is not within the scope of the improvement of this invention, and will not be elaborated on here.

[0098] like Figure 4 The diagram shown is a control block diagram of a method for improving the stability of grid-connected inverters under weak power grid conditions provided by the present invention. Figure 5 Figure 6 Simulation waveforms of the inverter current before and after implementation of the repetitive controller proposed in this invention under weak power grid conditions. Figure 5 When no compensator is added to the weak power grid shown, the grid-connected current exhibits low-frequency oscillations, such as... Figure 6 When a compensator is added to a weak power grid, the grid-connected current exhibits excellent sinusoidal characteristics, resulting in stable system operation. Simulations demonstrate that this invention solves the problem of low-frequency oscillation of the grid-connected current in grid-connected inverters under weak power grid conditions.

[0099] Through the above technical solutions, this invention suppresses resonance caused by wide-range variations in grid impedance by adding a notch filter to the repetitive controller of the grid-connected inverter, thereby achieving near-zero gain and zero phase shift of S(z)P(z) in the low-frequency band, and solving the problem of low-frequency oscillation of grid-connected current in grid-connected inverters under weak grid conditions.

[0100] Example 2

[0101] Based on Embodiment 1, Embodiment 2 of the present invention also provides a device for improving the stability of grid-connected inverters under weak power grid conditions, the device comprising:

[0102] The signal processing module is used to sample the grid-side current and subtract the grid-side current from the given signal to obtain the error signal;

[0103] The signal output module is used to input the error signal into the repetitive controller G(z) to obtain the output signal;

[0104] The signal modulation module is used to input the output signal into the grid voltage resonant feedforward controller G. f (z) Obtain the modulation signal of the inverter;

[0105] The model building module is used to build a mathematical model of the control object based on the inverter parameters;

[0106] The stability control module is used to determine the stability of repetitive control. Under stable conditions, it maintains the current control. Under unstable conditions, it selects a compensation coefficient and adjusts the repetitive controller G(z) to adjust the modulation signal until the system control is stable.

[0107] Specifically, the expression for the repetitive controller G(z) is:

[0108]

[0109] in, For the delay element, N is the number of sampling points within one power grid cycle, z -N Let N represent the delay in the discrete system. Since the sampling frequency of the device of this invention is 18000Hz, N is taken as 18000 / 50 = 360; Q is the compensation coefficient of the delay element; S(z) is the compensator element, which is used to compensate for the phase of the controlled object P(z), so that S(z)P(z) has approximately zero gain and zero phase shift in the low and medium frequency range. Its expression is:

[0110] S(z)=z k G LPF (z)G trap (z)

[0111] Among them, z k For advanced stages; G LPF (z) is a low-pass filter; G trap (z) is a notch filter used to suppress the high gain of S(z)P(z) near the fundamental frequency due to a weak power grid, while compensating for the phase margin of S(z)P(z) above the fundamental frequency range, achieving near-zero gain and zero phase shift of S(z)P(z) in the mid-to-low frequency range under weak power grid conditions. Notch filter G trap (z) by G trap (s) is obtained through a bilinear transformation, where G trap The expression for (s) is:

[0112]

[0113] Among them, G trap (s) is the expression for the notch filter in a continuous system, and its effect is equivalent to G. trap (z), where s is the Laplace operator; ω0 is the fundamental angular velocity; ξ2 is the optimal damping coefficient of the second-order system; and ξ1 is the compensation coefficient, with 0 < ξ1 < ξ2.

[0114] More specifically, the model building module is also used for:

[0115] Mathematical model of the control object G LCL (z) by G LCL (s) is obtained by discretization using a zero-order hold, where G LCL The expression for (s) is

[0116] G LCL (s)=G PI (s)k pwm G d (s)(sCR+1) / {s 3 L1(L2+L g C+s 2 [(L1+L2+L g )CR-L g CRk pwm G d (s)G f (s)]+s[L1+L2+L g -L g k pwm G d (s)G f (s)]}

[0117] Among them, G LCL (s) represents the transfer function between the repetitive controller output and the grid-connected current, where L1 is the bridge-side inductance of the LCL filter; L2 is the grid-side inductance of the LCL filter; and C is the capacitance of the LCL filter. g R is the mains impedance; R is the passive damping of the LCL filter; G d (s) represents a 1.5-beat delay; k pwm For inverter gain, G PI (z) represents the proportional-integral element, G PI (s) represents the expression of the proportional-integral (PI) element in a continuous system. Since the tracking signal is a periodic signal, the effect of the integrator is not significant. G PI (z) can be simplified to a proportional element to improve the dynamic performance of the first cycle. f (s) represents grid voltage resonant feedforward control, where the resonant feedforward is a second-order bandpass filter used to reduce the positive feedback path of grid impedance in the high-frequency band.

[0118] The expression for the grid impedance is as follows:

[0119]

[0120] In the formula, U0 is the grid voltage; P rate The inverter power rating is denoted by SCR, which indicates a weak grid level. An SCR less than 3 indicates that the grid is a weak grid.

[0121] More specifically, the method for determining the stability of repetitive control in the stability control module is as follows:

[0122] A sufficient condition for the stability of repetitive control is |QS(z)P(z)|<1, where P(z) is the compensation object and the expression for P(z) is:

[0123]

[0124] Among them G PI (z) represents the proportional integral element;

[0125] If the sufficient condition for the stability of repetitive control is met, it indicates that the repetitive control of the system is stable.

[0126] More specifically, the stability control module is also used for:

[0127] Based on the stability criterion QS(z)P(z) of repetitive control, draw the Bode plot or Nyquist plot. Design the compensation coefficient ξ1 based on the Bode plot amplitude-frequency characteristic being less than 0 or the Nyquist trajectory being within the unit circle. Adjust the repetitive controller G(z) according to the designed compensation coefficient ξ1, thereby adjusting the modulation signal to make the system control stable.

[0128] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for improving the stability of grid-connected inverters under weak power grid conditions, characterized in that, The method includes: Step a: Sample the grid-side current, and subtract the grid-side current from the given signal to obtain the error signal; Step b: Input the error signal into the repetitive controller Obtain the output signal; repetitive controller The expression is: ,in, For the delay element, N is the number of sampling points within one power grid cycle. This represents a delay of N time steps in a discrete system; This is the compensation coefficient for the delay stage; For the compensator element, its expression is: ,in, This is an advanced stage; It is a low-pass filter; Notch filter, notch filter Depend on It is obtained through bilinear transformation, where The expression is: ,in, Let be the expression for a notch filter in a continuous system, and s be the Laplace operator; The fundamental angular velocity; The optimal damping coefficient for a second-order system; For the compensation coefficient and ; Step c: Input the output signal into the grid voltage resonant feedforward controller Obtain the modulation signal of the inverter; Step d: Establish a mathematical model of the controlled object based on the inverter parameters. ; Step e: Determine the stability of the repetitive control. If stable, maintain the current control. If unstable, select a compensation coefficient and adjust the repetitive controller. This adjusts the modulation signal until the system control stabilizes; the method for determining the stability of repetitive control is as follows: a sufficient condition for the stability of repetitive control is... ,in, For the compensation object and The expression is ,in This is a proportional-integral (PI) element; if the sufficient condition for the stability of repetitive control is met, it indicates that the system is stable under repetitive control; step e also includes: according to the repetitive control stability criterion. Draw the Bode plot or Nyquist plot, and design the compensation coefficient based on the Bode plot's amplitude-frequency response being less than 0 or the Nyquist trajectory being within the unit circle. According to the designed compensation coefficient Adjusting the repeat controller This allows for adjustment of the modulation signal, thereby stabilizing system control.

2. The method for improving the stability of a grid-connected inverter under weak power grid conditions according to claim 1, characterized in that, Step d includes: Mathematical model of control object Depend on It is derived from the discretization of the zero-order hold, where The expression is in, This represents the transfer function between the repetitive controller output and the grid-connected current. For the bridge-side inductance of an LCL-type filter; For the grid-side inductance of an LCL-type filter; The capacitor is for an LCL-type filter; The impedance of the power grid; Passive damping for LCL type filters; This is a 1.5-beat delay segment; For inverter gain, This represents the expression for the proportional-integral element in a continuous system. This indicates grid voltage resonance feedforward control; The expression for the grid impedance is as follows: In the formula, This refers to the grid voltage. Inverter power; For weak power grids, an SCR of less than 3 indicates that the power grid is a weak power grid.

3. A device for improving the stability of grid-connected inverters under weak power grid conditions, characterized in that, The device includes: The signal processing module is used to sample the grid-side current and subtract the grid-side current from the given signal to obtain the error signal; The signal output module is used to input the error signal into the repetitive controller. Obtain the output signal; repetitive controller The expression is: ,in, For the delay element, N is the number of sampling points within one power grid cycle. This represents a delay of N time steps in a discrete system; This is the compensation coefficient for the delay stage; For the compensator element, its expression is: ,in, This is an advanced stage; It is a low-pass filter; Notch filter, notch filter Depend on It is obtained through bilinear transformation, where The expression is: ,in, Let be the expression for a notch filter in a continuous system, and s be the Laplace operator; The fundamental angular velocity; The optimal damping coefficient for a second-order system; For the compensation coefficient and ; The signal modulation module is used to input the output signal into the grid voltage resonant feedforward controller. Obtain the modulation signal of the inverter; The model building module is used to build a mathematical model of the controlled object based on the inverter parameters. ; The stability control module is used to determine the stability of the repetitive control. Under stable conditions, it maintains the current control; under unstable conditions, it selects a compensation coefficient and adjusts the repetitive controller. This adjusts the modulation signal until the system control stabilizes; the method for determining the stability of repetitive control is as follows: a sufficient condition for the stability of repetitive control is... ,in, For the compensation object and The expression is ,in This is a proportional-integral (PI) element; if the sufficient condition for the stability of repetitive control is met, it indicates that the system is stable under repetitive control; the stability control module is also used to: [based on the repetitive control stability criterion] Draw the Bode plot or Nyquist plot, and design the compensation coefficient based on the Bode plot's amplitude-frequency response being less than 0 or the Nyquist trajectory being within the unit circle. According to the designed compensation coefficient Adjusting the repeat controller This allows for adjustment of the modulation signal, thereby stabilizing system control.

4. The device for improving the stability of a grid-connected inverter under weak power grid conditions according to claim 3, characterized in that, The model building module is also used for: Mathematical model of control object Depend on It is derived from the discretization of the zero-order hold, where The expression is in, This represents the transfer function between the repetitive controller output and the grid-connected current. For the bridge-side inductance of an LCL-type filter; For the grid-side inductance of an LCL-type filter; The capacitor is for an LCL-type filter; The impedance of the power grid; Passive damping for LCL type filters; This is a 1.5-beat delay segment; For inverter gain, This represents the proportional-integral stage. Represents the expression of the proportional-integral element in a continuous system; The expression for the grid impedance is as follows: In the formula, This refers to the grid voltage. Inverter power; For weak power grids, an SCR of less than 3 indicates that the power grid is a weak power grid.

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