Inverter grid-connected synchronous optimization control method based on backstepping method

Abstract

The invention discloses an inverter grid-connected synchronous optimization control method based on a backstepping method, and belongs to the technical field of new energy grid-connected control, and the method comprises the steps: building a second-order nonlinear mathematical model of a phase-locked loop based on a grid-connected inverter phase-locked loop control structure, and deducing a state-space equation; decomposing the state space equation according to the state variable, and determining the virtual control quantity of each order of subsystem; defining an error variable by using the virtual control quantity, and recursively constructing a control law by using a backstepping method based on a Lyapunov asymptotic stability theory; and controlling the phase-locked loop by using the obtained control law to realize closed-loop control. According to the method, backstepping design is carried out on the phase-locked loop variable, on the premise that an original phase-locked loop structure is reserved, an additional control law is introduced, the robustness of the system under the condition that the power grid impedance is increased is remarkably improved due to the addition of the control law, the stability of voltage and current of a grid-connected point can be maintained, and the frequency hopping and instability risk can be effectively restrained.

Description

Technical Field

[0001] This invention relates to the field of new energy grid-connected control technology, specifically to an inverter grid-connected synchronization optimization control method based on the backstepping method. Background Technology

[0002] As global climate issues intensify and the energy crisis worsens, the replacement of non-renewable energy with clean energy and the large-scale integration of new energy sources into the power grid are inevitable trends. As a crucial component of new energy grid-connected systems, the stability of grid-connected inverters is paramount.

[0003] Grid-connected inverters typically employ grid-following control. Under strong grid conditions, traditional grid-following inverters exhibit strong stability. However, if grid impedance increases or grid strength weakens due to grid faults or other factors, the voltage amplitude and phase at the common coupling point will fluctuate drastically. This will severely affect the synchronous control performance of the inverter's phase-locked loop (PLL), which can easily lead to system synchronous instability, resulting in voltage and frequency oscillations. To address the instability problem of PLL synchronous control under weak grid conditions, common methods to improve inverter stability include: (1) Parameter adaptation and intelligent optimization: This method can estimate the resonant frequency in real time, measure the grid impedance online, and optimize the feedforward or filter parameters using the particle swarm optimization (PSO) algorithm. However, this method increases hardware costs and has poor real-time performance. (2) Impedance reshaping method: This method adjusts the inverter's output impedance by designing a specific impedance reshaping controller, enabling it to exhibit better impedance characteristics under weak grid conditions, thereby enhancing stability. However, this requires significant modifications to the inverter's control structure, increasing control complexity. (3) Transient reactive power overcompensation: When the system detects low-frequency oscillation, it outputs reactive power instantaneously, which can quickly suppress low-frequency oscillation and has good dynamic performance, but it will increase steady-state losses.

[0004] Backstepping control, also known as inverse control, is a method that decomposes a high-order system into multiple first-order systems. The state variables of the next-order system are treated as virtual inputs to control the previous-order system. A Lyapunov function is then established based on the previous-order system to achieve asymptotic stability, continuing until the last system is controlled, thus deriving the control law. When traditional backstepping is applied to inverter control, directly analyzing and designing the main circuit leads to a massive computational burden, significantly increasing design difficulty and system complexity. Furthermore, the control algorithm derived by this method is highly sensitive to LCL filter parameters; changes in inductor or capacitor parameters (including long-term component aging and losses) can easily trigger system instability. Therefore, specific control algorithms need to be customized for inverter systems with different parameters, lacking universality.

[0005] To improve inverter stability under conditions of increased impedance and to enhance system robustness by differentiating itself from the traditional backstepping method's reliance on the main circuit's mathematical model, this invention provides an inverter grid-connected synchronization optimization control method based on the backstepping method. Summary of the Invention

[0006] The technical problem to be solved by this invention is: how to improve the stability of the inverter when the inverter is under the condition of increased impedance, and to improve the robustness of the system by differentiating itself from the dependence of the traditional backstepping method on the mathematical model of the main circuit. This invention provides an inverter grid-connected synchronization optimization control method based on the backstepping method.

[0007] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0008] S1: Based on the phase-locked loop control structure of the grid-connected inverter, a second-order nonlinear mathematical model of the phase-locked loop is established, and the state-space equation is derived; the state-space equation is decomposed according to the state variables, and the virtual control quantities of each subsystem are determined.

[0009] S2: Define error variables using virtual control quantities, and recursively construct control laws based on Lyapunov asymptotic stability theory using the backstepping method;

[0010] S3: Use the obtained control law to control the phase-locked loop to achieve closed-loop control.

[0011] Furthermore, in step S1, the second-order nonlinear mathematical model of the phase-locked loop is as follows:

[0012]

[0013] Where, k p,pll k i,pll These are the proportional and integral coefficients of the PI controller inside the phase-locked loop, respectively. g V represents the grid impedance, δ represents the difference between the phase angle of the phase-locked loop output and the grid phase angle, and α represents the output of the integral element of the phase-locked PI controller; g P0 is the grid voltage value, P0 is the mechanical power of the prime mover, P0 = ω g L g I sd ω g I is the angular velocity of the grid voltage. sd This is a reference value for grid-connected current.

[0014] Furthermore, in step S1, let δ be x1 and α be x2 in the second-order nonlinear mathematical model, and derive the state-space equations as follows:

[0015]

[0016] Here, x1 and x2 are state variables.

[0017] Furthermore, in step S1, based on the state-space equations, the nonlinearity of the phase-locked loop is decomposed into two subsystems, and virtual control variables are set for each subsystem. From the state-space equations, it can be seen that α is the input variable of the first-order subsystem and also acts on the second-order subsystem. By adjusting α as an external input, the state-space equations are transformed into:

[0018]

[0019] Based on the above equation, let the virtual control quantity of x2 be x. 2d The virtual control quantity of x1 is itself.

[0020] Furthermore, in step S2, the specific processing procedure is as follows:

[0021] S21: Let:

[0022] ;

[0023] Where Z1 and Z2 are error variables, and their derivatives are taken:

[0024] ;

[0025] S22: Let the Lyapunov function be:

[0026] ;

[0027] Differentiate it:

[0028] ;

[0029] S23: According to the Lyapunov asymptotic stability condition, let Ż1 = -C1x1, where C1 is any real number greater than 0. Then the derivative of V1 is negative definite. Let Z1 = x1, and we can obtain:

[0030] ;

[0031] ;

[0032] For x 2d Differentiation yields:

[0033] ;

[0034] S24: From Lyapunov's asymptotic stability theorem, we get:

[0035] ;

[0036] Differentiate it:

[0037] ;

[0038] Substituting the error variable Z2, we get:

[0039] ;

[0040] Similarly, to make If the condition is negative definite, then:

[0041] ;

[0042] Where C2 is any real number greater than 0;

[0043] S25: Then we can solve for x2, which is α, and thus obtain the control law as follows:

[0044] .

[0045] Furthermore, in step S3, δ in the control law is used as the only variable. An integral term is added after the output of the phase-locked loop PI controller. The output of the integral term is introduced into the control law as the independent variable. Finally, the output of the control law is superimposed on the proportional term output of the PI controller to achieve closed-loop control.

[0046] Compared with existing technologies, this invention has the following advantages: The inverter grid-connected synchronous optimization control method based on backstepping incorporates an improved backstepping design, introducing a phase-locked loop (PLL) mathematical model into the design process. Based on Lyapunov's asymptotic stability theorem, a control law for variable α is derived without altering the original inverter topology and control structure; only the control law output needs to be superimposed on the original output, significantly improving system stability. The control law derivation is based on the PLL nonlinear signal, exhibiting robustness to changes in LCL filter parameters, avoiding instability risks caused by parameter drift (including long-term operating losses). The design method is simple and easy to implement, does not increase additional hardware costs, and does not affect the system's steady-state performance. Attached Figure Description

[0047] Figure 1 This is a diagram of the inverter phase-locked loop structure in an embodiment of the present invention;

[0048] Figure 2 This is a diagram of the phase-locked loop structure after adding a control law in an embodiment of the present invention;

[0049] Figure 3 This is a voltage and current waveform diagram at the grid connection point under the condition of high grid impedance without adding a control law in an embodiment of the present invention;

[0050] Figure 4 This is a voltage and current waveform diagram at the grid connection point under the condition of adding a control law to the grid with high impedance in an embodiment of the present invention.

[0051] Figure 5 This is a system frequency diagram in an embodiment of the present invention under the condition of high grid impedance without adding a control law;

[0052] Figure 6 This is a system frequency diagram for a high-impedance power grid with an added control law in an embodiment of the present invention.

[0053] Figure 7 A diagram showing the three-phase voltage distortion rate at the grid connection point after adding the control law;

[0054] Figure 8 The diagram shows the three-phase current distortion rate at the grid connection point after adding the control law. Detailed Implementation

[0055] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0056] Example 1

[0057] This embodiment provides a technical solution: an inverter grid-connected synchronization optimization control method based on backstepping, comprising the following steps:

[0058] S1: Based on the phase-locked loop control structure of the grid-connected inverter, a second-order nonlinear mathematical model of the phase-locked loop is established, and the state-space equation is derived; according to the state variable decomposition equation, the virtual control quantities of each subsystem are determined.

[0059] In this embodiment, the second-order nonlinear model of the phase-locked loop is established as follows:

[0060] (1)

[0061] Where, k p,pll ,k i,pll These are the proportional and integral coefficients of the PI controller inside the phase-locked loop, respectively. g Let represent the grid impedance, ignoring resistance in the worst-case scenario; δ represent the difference between the phase angle of the phase-locked loop output and the grid phase angle; and α represent the output of the integral element of the phase-locked PI controller. g P0 is the grid voltage value, P0 is the mechanical power of the prime mover, P0 = ω g L g I sd ω g I is the angular velocity of the grid voltage. sd This is a reference value for grid-connected current.

[0062] In this embodiment, let δ be x1 and α be x2 in the second-order nonlinear mathematical model, and derive the state-space equation:

[0063] (2)

[0064] For the above state-space equations, the nonlinearity of the system (phase-locked loop) is decomposed into two subsystems, and virtual control quantities are set for each subsystem (since δ is x1, which is the difference between the phase angle of the phase-locked loop output and the phase angle of the power grid, no additional virtual control quantity is needed as an error signal; the virtual control quantity of x1 is itself). From the state-space equations, α is the input variable of the first-order subsystem and also acts on the second-order subsystem. By adjusting α as an external input, the strict feedback form of the state-space system is written. The state-space equations are then transformed into:

[0065]

[0066] Based on the above equation, let the virtual control quantity of x2 be x. 2d .

[0067] S2: Using virtual control variables to define error variables, and based on Lyapunov asymptotic stability theory, the control law is recursively constructed using the backstepping method to ensure the asymptotic stability of the closed-loop system.

[0068] In this embodiment, the specific process of step S2 is as follows:

[0069] set up:

[0070] (3)

[0071] Then, taking the derivatives of Z1 and Z2 with respect to the error variables:

[0072] (4)

[0073] Let the Lyapunov function be:

[0074] (5)

[0075] Differentiate it:

[0076] (6)

[0077] According to the Lyapunov asymptotic stability condition, V1 > 0. Since V1 is a quadratic function, it must be greater than 0, satisfying the condition. Furthermore, the derivative of V1 must be negative definite. To satisfy this condition, let Ż1 = -C1x1, where C1 is any real number greater than 0. Then the derivative of V1 will be negative definite. Let Z1 = x1, then we get:

[0078] (7)

[0079] (8)

[0080] Among them, L g Given a specific impedance magnitude, it is a constant for x. 2d Differentiation yields:

[0081] (9)

[0082] make:

[0083] (10)

[0084] Define the error Z2 = x2 - x 2d Similarly, we can derive from Lyapunov's asymptotic stability theorem:

[0085] (11)

[0086] Differentiate it:

[0087] (12)

[0088] Substituting the error Z2 into (12), we have:

[0089] (13)

[0090] Similarly, to make If the condition is negative definite, then:

[0091] (14)

[0092] Substituting formulas (2), (9), and (10) into (14), we can solve for x2, which is α, and thus obtain the control law as follows:

[0093] (15)

[0094] Where, k p,pll k i,pll These are the proportional and integral coefficients of the PI controller inside the phase-locked loop, respectively. g V represents the grid impedance, δ represents the difference between the phase angle of the phase-locked loop output and the grid phase angle, and α represents the output of the integral element of the phase-locked PI controller; g P0 is the grid voltage value, P0 is the mechanical power of the prime mover, P0 = ω g L g I sd ω g I is the angular velocity of the grid voltage. sd This is a reference value for grid-connected current. 2d As given above, x 2d1 For x 2d The derivative has been given above.

[0095] S3: Use the obtained control law to control the phase-locked loop and establish a closed-loop control system.

[0096] In this embodiment, δ in the control law is used as the only variable. An integral term is added after the output of the phase-locked loop PI controller. The output of the integral term is introduced into the control law as the independent variable. Finally, the output of the control law is superimposed on the proportional term output of the PI controller to achieve closed-loop control.

[0097] Example 2

[0098] Considering that the derivation of the formula is too complex and lengthy, some parameters in the formula are given to simplify the derivation process.

[0099] Table 1 Inverter PLL System Parameter Table

[0100]

[0101] Figure 1 The diagram shows the structure of a phase-locked loop (PLL). Based on the diagram, a second-order nonlinear model of the PLL is established:

[0102] (1)

[0103] The state-space equations are derived by substituting the data from Table 1:

[0104] (2)

[0105] Design virtual control quantity x 2d Let Z1 = x1, and let the Lyapunov function be:

[0106] (3)

[0107] Differentiate it:

[0108] (4)

[0109] According to the Lyapunov asymptotic stability condition, V1 > 0. Since V1 is a quadratic function, it must be greater than 0, satisfying the condition. Furthermore, the derivative of V1 must be negative definite. To satisfy this condition, let Ż1 = x1, and C1 be any real number greater than 0. Then the derivative of V1 will be negative definite. Let Z1 = x1, we can obtain:

[0110] (5)

[0111] Where C1 is any real number greater than 0. We can obtain:

[0112] (6)

[0113] Differentiate equation (6):

[0114] (7)

[0115] make:

[0116] (8)

[0117] Define the error Z2 = x2 - x 2d By Lyapunov's asymptotic stability theorem, we have:

[0118] (9)

[0119] Differentiate it:

[0120] (10)

[0121] Substituting Z2 into (10), we have:

[0122] (11)

[0123] Similarly, to satisfy the condition of negative definiteness, we have:

[0124] (12)

[0125] (13)

[0126] Solve That is, α:

[0127] (14)

[0128] The control law is derived, and the location where the control law is added is as follows: Figure 2 As shown, the output of the PI controller is integratored to obtain the variable δ, which is then used as the input variable for the control law. The grid impedance is set to 18mH. Figure 3 It can be seen that, under this impedance, without a control law, the voltage and current at the grid connection point are already completely unstable, and due to... Figure 5 It can be seen that the system frequency fluctuates widely around 130Hz, which fails to meet the grid connection requirements. After adding a control law to the system, the voltage and current at the grid connection point are as follows: Figure 4 As shown, the waveform has stabilized, and the voltage and current are in phase. The system frequency is as follows. Figure 6 The frequency shown is 50Hz, and the system is operating stably. Figure 7 This is the grid-connected voltage distortion rate, which is 1.34%. Figure 8 The current distortion rate is 0.40%, which meets the grid connection requirements.

[0129] In summary, the inverter grid-connected synchronization optimization control method based on backstepping in the above embodiments improves the stability of the power grid under high impedance by adding a control law to the traditional phase-locked loop. It does not require extensive modification to the original control structure, is simple to implement, and improves the stability of the inverter and the phase-locked loop. It is a safe, stable method that is worth promoting.

[0130] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A grid-connected synchronization optimization control method for inverters based on backstepping, characterized in that, Includes the following steps: S1: Based on the phase-locked loop control structure of the grid-connected inverter, a second-order nonlinear mathematical model of the phase-locked loop is established, and the state-space equations are derived. Decompose the state-space equations based on the state variables and determine the virtual control quantities of each subsystem. S2: Define error variables using virtual control quantities, and recursively construct control laws based on Lyapunov asymptotic stability theory using the backstepping method; S3: Use the obtained control law to control the phase-locked loop to achieve closed-loop control.

2. The inverter grid-connected synchronization optimization control method based on backstepping as described in claim 1, characterized in that, In step S1, the second-order nonlinear mathematical model of the phase-locked loop is as follows: ； Where, k p,pll k i,pll These are the proportional and integral coefficients of the PI controller inside the phase-locked loop, respectively. g V represents the grid impedance, δ represents the difference between the phase angle of the phase-locked loop output and the grid phase angle, and α represents the output of the integral element of the phase-locked PI controller; g P0 is the grid voltage value, P0 is the mechanical power of the prime mover, P0 = ω g L g I sd ω g I is the angular velocity of the grid voltage. sd This is a reference value for grid-connected current.

3. The inverter grid-connected synchronization optimization control method based on backstepping method according to claim 2, characterized in that, In step S1, let δ be x1 and α be x2 in the second-order nonlinear mathematical model, and derive the state-space equation as follows: ； Here, x1 and x2 are state variables.

4. The inverter grid-connected synchronization optimization control method based on backstepping method according to claim 3, characterized in that, In step S1, based on the state-space equations, the nonlinearity of the phase-locked loop is decomposed into two subsystems, and virtual control variables are set for each subsystem. From the state-space equations, α is the input variable of the first-order subsystem and also acts on the second-order subsystem. By adjusting α as an external input, the state-space equations are transformed into: ； Based on the above equation, let the virtual control quantity of x2 be x. 2d The virtual control quantity of x1 is itself.

5. The inverter grid-connected synchronization optimization control method based on backstepping method according to claim 4, characterized in that, In step S2, the specific processing procedure is as follows: S21: Let: ； Where Z1 and Z2 are error variables, and their derivatives are taken: ； S22: Let the Lyapunov function be: ； Differentiate it: ； S23: According to the Lyapunov asymptotic stability condition, let Ż1 = -C1x1, where C1 is any real number greater than 0. Then the derivative of V1 is negative definite. Let Z1 = x1, and we can obtain: ； ； For x 2d Differentiation yields: ； S24: From Lyapunov's asymptotic stability theorem, we get: ； Differentiate it: ； Substituting the error variable Z2, we get: ； Similarly, to make If the condition is negative definite, then: ； Where C2 is any real number greater than 0; S25: Then we can solve for x2, which is α, and thus obtain the control law as follows: 。 6. The inverter grid-connected synchronization optimization control method based on backstepping method according to claim 5, characterized in that, In step S3, δ in the control law is used as the only variable. An integral term is added after the output of the phase-locked loop PI controller. The output of the integral term is used as the independent variable in the control law. Finally, the output of the control law is superimposed on the proportional term output of the PI controller to achieve closed-loop control.

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