A method for optimizing parameters of a phase-locked loop of a grid-following converter under wide grid strength

Abstract

The present application relates to a kind of wide grid strength under the grid following converter phase-locked loop full working condition parameter optimization method, belong to power system parameter optimization field, comprising: the grid following converter small signal state space model is established, obtains system matrix;With system small signal stability as constraint condition, define line inductance stability interval, with stability interval maximization as objective function, construct phase-locked loop parameter optimization model;In single condition, with phase-locked loop parameter as optimization variable, based on constraint condition and maximization objective function, solve optimization model, obtain optimal phase-locked loop parameter;With apparent power and four-quadrant power factor angle construct full working condition operation set, under the satisfaction constraint condition, point by point solve optimization model with inductance stability interval maximization as target, solve phase-locked loop optimization result in full working condition range.The present application, significantly widen the stable operation range of converter under weak grid, guarantee the stable operation of converter under wide grid intensity and full working condition.

Description

Technical Field

[0001] This invention relates to a method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength, belonging to the field of power system parameter optimization technology. Background Technology

[0002] As the proportion of new energy sources in the power system continues to increase, power electronic devices, primarily converters, are largely replacing traditional synchronous generators, resulting in a significant decrease in the inertia level and voltage support capacity of the power system. As the mainstream grid-connected interface, grid-connected converters typically rely on phase-locked loops (PLLs) to track the voltage phase at the grid connection point in real time to achieve precise synchronization with the grid. Therefore, the PLL control parameters become a key factor affecting the grid-connected stability of the converter.

[0003] When the grid strength is weak, the coupling between the phase-locked loop (PLL) and the grid impedance is significantly enhanced. If the parameters are not properly tuned, it can easily induce system oscillations or even instability. Simultaneously, under the wide power variation range caused by source-load fluctuations, the converter's operating conditions shift significantly, and fixed PLL parameters often fail to meet the stability requirements of all operating conditions. Conventional PLL parameters are usually tuned based on experience or local operating conditions, lacking the systematic adaptability to changes in grid strength and large-scale power fluctuations. This results in a significant risk of insufficient stability domain in extremely weak grids or scenarios with sudden power changes.

[0004] Therefore, how to systematically extract and quantify the small-signal stability range of the converter, and effectively optimize the phase-locked loop control parameters with the goal of widening this stability range, so that it can maintain robust and stable operation under wide grid intensity and full power conditions, has become a key technical problem that urgently needs to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for optimizing the parameters of a phase-locked loop (PLL) converter under various operating conditions within a wide grid intensity range. This method uses system small-signal stability as a constraint and maximizes the inductor stability range as the objective function. Based on this objective function and constraint, a PLL parameter optimization model is constructed. The proportional and integral parameters of the PLL are used as optimization variables. The optimal PLL parameters that maximize the grid intensity adaptability range are obtained under a single operating condition. Furthermore, the optimal parameters are obtained by solving point by point within the entire operating range, significantly improving the converter's stable operation capability under all operating conditions.

[0006] The present invention adopts the following technical solution:

[0007] A method for optimizing the parameters of a grid-connected converter's phase-locked loop under all operating conditions under wide grid strength includes the following steps:

[0008] (1) Based on the main circuit topology and control system of the grid-connected converter, a small-signal state-space model of the grid-connected converter is established to obtain the system matrix;

[0009] (2) Taking the stability of the small signal of the system as a constraint, the line inductance stability range is defined as the difference between the maximum allowable inductance and the minimum allowable inductance. The phase-locked loop parameter optimization model is constructed with the maximization of this stability range as the objective function.

[0010] (3) Under a single operating condition, the proportional and integral parameters of the phase-locked loop are used as optimization variables. Based on the small-signal stability constraint and the objective function of maximizing the stability range of the inductor, the optimization model is solved to obtain the optimal phase-locked loop parameters.

[0011] (4) Construct a full-condition operating set using apparent power and four-quadrant power factor angles. Under the constraint conditions, solve the optimization model point by point with the goal of maximizing the inductance stability range, and solve the phase-locked loop optimization results in the full-condition range.

[0012] Preferably, the process of establishing the small-signal state-space model of the grid converter in step (1) is as follows:

[0013] (1.1) In the dq axis coordinate system, based on Kirchhoff's voltage law and Kirchhoff's current law, establish the nonlinear large-signal differential equation of the converter main circuit;

[0014] (1.2) Based on the principle of complete control link, the nonlinear large-signal differential equation of the converter control system is obtained;

[0015] (1.3) Based on the nonlinear large-signal differential equation of the converter main circuit and the nonlinear large-signal differential equation of the control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equation system.

[0016] (1.4) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter main circuit is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter main circuit.

[0017] (1.5) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter control system is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter control system.

[0018] (1.6) By combining the small-signal state-space equations of the main circuit and the control system, the complete small-signal state-space model of the converter is obtained, in the following standard form:

[0019] (5)

[0020] In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represents the input matrix;

[0021] The equations of the small-signal state-space model of the complete converter are rearranged into standard matrix form, and the small-signal state variables are extracted. The corresponding coefficient matrix is ​​the system matrix. .

[0022] Preferably, the implementation process of step (2) is as follows:

[0023] (2.1) Define constraints:

[0024] Under the condition of fixed system power, the small-signal stability of the converter is determined by the system matrix obtained in step (1). The decision was made regarding the system matrix of the grid converter. Subject to line inductance L s And the influence of phase-locked loop (PLL) parameters, including the proportional parameter k. pPLL and integration parameter k iPLL For any set of phase-locked loop parameters, the following small-signal stability constraints must be met:

[0025] (14)

[0026] in, For the system matrix The i-th eigenvalue is only the system matrix. The converter can only operate stably if all the real parts of its eigenvalues ​​are non-positive; n represents the system matrix. The order of;

[0027] (2.2) Define the stable range of the inductor:

[0028] In AC power systems, grid strength is typically measured by the short-circuit ratio (SCR); the short-circuit ratio (SCR) is related to the line inductance (L). s They exhibit an inverse proportional mapping relationship, expressed mathematically as follows:

[0029] (15)

[0030] In the formula, U2 represents the effective value of the grid phase voltage, ω represents the fundamental angular frequency of the grid, and S n Indicates the rated apparent power of the converter;

[0031] From the formula, under the operating conditions where the rated parameters of the converter system are determined, the line inductance L is... sThe larger the value, the smaller the short-circuit ratio, indicating a weaker grid strength. Therefore, the wide range of fluctuations in line inductance is physically equivalent to changes in grid strength. This invention defines the inductance stability range as a quantitative evaluation index. The larger the value of this range, the greater the range of line inductance variation that the converter can tolerate while maintaining small-signal stability, thus possessing stronger grid strength adaptability.

[0032] For any given set of phase-locked loop parameters, we obtain the set of all line inductances that satisfy the small-signal stability constraint. The upper and lower boundaries of the line inductance set are defined as the maximum allowable inductance L, respectively. smax With minimum allowable inductance L smin Define the inductor stability range ΔL s The difference between the two:

[0033] (16)

[0034] ΔL s The larger the value, the stronger the system's adaptability to a wide power grid intensity under this set of phase-locked loop parameters;

[0035] (2.3) Constructing a phase-locked loop parameter optimization model:

[0036] Select the proportional parameter k of the phase-locked loop pPLL With the integration parameter k iPLL As optimization variables, and with maximizing the inductor's stable range as the objective function, the following PLL parameter optimization model is obtained:

[0037] (17).

[0038] Preferably, the implementation process of step (3) is as follows:

[0039] The apparent power and power factor angle of the fixed converter are used as optimization variables, with the phase-locked loop proportional and integral parameters as optimization variables. For each set of given phase-locked loop parameters (k... pPLL,j k iPLL,j ), where k pPLL,j Let k represent a given proportional parameter. iPLL,j This represents a given integral parameter, expressed in terms of line inductance L. s Using the rated value as the rated point and starting from there, the line inductance is gradually increased, and the system matrix is ​​updated in real time. And solve the system matrix. The maximum permissible inductance L under this parameter is calculated by analyzing all characteristic roots until the system is just critically stable. smax,j Similarly, starting from the rated point, gradually decrease the line inductance to find the minimum allowable inductance L at the critical stability point. smin,j And by formula ΔL s,j =L smax,j-L smin,j The inductor stability range ΔL corresponding to the calculated parameters is obtained. s,j ;

[0040] To maximize ΔL s,j With the objective of ensuring small-signal stability of the parameters, the objective function is optimized within the parameter candidate interval. The proportional and integral parameters that maximize the stability of the inductor are obtained, which are the optimal phase-locked loop parameters for this single operating condition.

[0041] Preferably, the parameter candidate interval in step (3) is obtained by scaling the parameters calculated by conventional second-order system theory in combination with engineering experience.

[0042] Preferably, in step (4), a full-condition operating set is constructed using the apparent power S and the four-quadrant power factor angle φ. For each operating point, the operating condition is fixed, and the proportional and integral parameters of the phase-locked loop are used as optimization variables. Under the constraint of small signal stability, the inductor stability range is maximized, and the phase-locked loop parameter optimization model is obtained point by point. Finally, the optimal phase-locked loop parameters covering the full operating condition range are obtained to guide the parameter design under the full operating condition.

[0043] For any details not covered in this invention, please refer to the prior art.

[0044] The beneficial effects of this invention are as follows:

[0045] The present invention provides a full-condition parameter optimization method for phase-locked loop (PLL) converters operating under wide grid strength conditions. Using system small-signal stability as a constraint, it defines an inductance stability interval formed by the difference between the maximum and minimum allowable inductance. Maximizing this interval is the objective function. The proportional and integral parameters of the PLL are used as optimization variables to establish a parameter optimization model. Solving this model yields the PLL optimization results across the entire operating condition range. This significantly broadens the stable operating range of the converter under weak grid conditions, enhances its robustness to grid strength fluctuations, and provides a systematic parameter optimization sequence for full-condition operation. Attached Figure Description

[0046] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0047] Figure 1 This is a flowchart illustrating the method for optimizing the parameters of the phase-locked loop of a grid-connected converter under all operating conditions under wide grid strength conditions, as described in this invention.

[0048] Figure 2 This is a schematic diagram of the main circuit and control system structure of the grid-connected converter of the present invention;

[0049] Figure 3A comparison chart of the inductance stability ranges for different phase-locked loop parameters under different apparent power and power factor angle conditions;

[0050] Figure 4 This is a two-dimensional cross-sectional comparison of the inductor's stable range as a function of the power factor angle when the apparent power S = 2.5 kVA.

[0051] Figure 5 A two-dimensional cross-sectional comparison of the inductor's stable range as a function of the power factor angle when the apparent power S = 10 kVA;

[0052] Figure 6 A comparison of active power response under different phase-locked loop parameters in an extremely weak power grid;

[0053] Figure 7 This is a comparison chart of the grid-connected current response under different phase-locked loop parameters in extremely weak power grids. Detailed Implementation

[0054] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. However, this is not the only description; all aspects not described in detail herein are based on conventional techniques in the art.

[0055] Example 1

[0056] A method for optimizing the parameters of a grid-connected converter's phase-locked loop under all operating conditions under wide grid strength, such as... Figure 1 As shown, it includes the following steps:

[0057] (1) Based on the main circuit topology and control system of the grid-connected converter, a small-signal state-space model of the grid-connected converter is established to obtain the system matrix;

[0058] (2) Taking the stability of the small signal of the system as a constraint, the line inductance stability range is defined as the difference between the maximum allowable inductance and the minimum allowable inductance. The phase-locked loop parameter optimization model is constructed with the maximization of this stability range as the objective function.

[0059] (3) Under a single operating condition, the proportional and integral parameters of the phase-locked loop are used as optimization variables. Based on the small-signal stability constraint and the objective function of maximizing the stability range of the inductor, the optimization model is solved to obtain the optimal phase-locked loop parameters.

[0060] (4) Construct a full-condition operating set using apparent power and four-quadrant power factor angles. Under the constraint conditions, solve the optimization model point by point with the goal of maximizing the inductance stability range, and solve the phase-locked loop optimization results in the full-condition range.

[0061] Example 2

[0062] A method for optimizing the parameters of a grid-connected converter under full operating conditions of a wide grid strength phase-locked loop is described in Example 1. The difference is that the process of establishing the small-signal state-space model of the grid-connected converter in step (1) is as follows:

[0063] (1.1) In the dq-axis coordinate system, based on Kirchhoff's voltage law and current law, the nonlinear large-signal differential equation of the converter main circuit is established as follows:

[0064] (1)

[0065] In the formula, Symbols representing differential calculations, Represents the d-axis component of the grid-connected current. Represents the q-axis component of the grid-connected current. This represents the d-axis voltage at the filter output. This represents the q-axis voltage at the filter output. This indicates the d-axis output current on the converter bridge arm side. This indicates the output q-axis current on the converter bridge arm side. Represents the d-axis voltage of the power grid. Represents the q-axis voltage of the power grid. Indicates the inductance of the output filter. This indicates the capacitance of the output filter. This represents the equivalent series resistance of the filter inductor. Indicates the line inductance on the power grid side. Represents the steady-state value of angular frequency. This represents the reference value for active power. This represents the reference value for reactive power. and These represent the state variables of the d-axis and q-axis voltage regulation integrators in the current loop control, respectively. and These represent the state variables of the integrators in the active and reactive power control loops, respectively. This represents the phase angle of the phase-locked loop. This represents the steady-state value of the filter output voltage on the d-axis. This represents the rated constant value of the filter output voltage on the d-axis. This represents the rated constant value of the filter output voltage on the q-axis; and This represents the ratio and integral coefficient of the active power outer loop. and This represents the proportional and integral coefficients of the reactive power outer loop. and This represents the proportional and integral coefficients of the inner current loop.

[0066] (1.2) Based on the complete control link principle, which includes power calculation, phase-locked loop, power outer loop, and current inner loop, the nonlinear large-signal differential equation of the converter control system is obtained as follows:

[0067] (2)

[0068] In the formula, This indicates the phase angle of the phase-locked loop output. This represents the state variable of the integrator in the phase-locked loop. and This represents the ratio and integral coefficient of the active power outer loop. and This represents the proportional and integral coefficients of the reactive power outer loop. and This represents the proportional and integral coefficients of the phase-locked loop.

[0069] (1.3) Based on the nonlinear large-signal differential equation of the converter main circuit and the nonlinear large-signal differential equation of the control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equation system.

[0070] (1.4) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter main circuit is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter main circuit, as follows:

[0071] (3)

[0072] In the formula, This represents the small-signal disturbance of the grid-connected current on the d-axis. This represents the steady-state value of the grid-connected current on the d-axis. This represents the small-signal disturbance of the grid-connected current on the q-axis. This represents the steady-state value of the grid-connected current on the q-axis. This represents the small-signal disturbance of the filter output voltage on the d-axis. This represents the steady-state value of the filter output voltage on the d-axis. This represents the small-signal disturbance of the filter output voltage on the q-axis. This represents the steady-state value of the filter output voltage on the q-axis. This represents the small-signal disturbance of the converter bridge arm output current on the d-axis. This represents the small-signal disturbance of the converter bridge arm output current on the q-axis. and These represent the steady-state settings of the active power and reactive power reference values, respectively. and These represent the steady-state values ​​of the integrator states in the active power and reactive power control loops, respectively. This represents the small-signal disturbance of the d-axis voltage of the power grid. This represents the small-signal disturbance of the q-axis voltage of the power grid. Small-signal disturbances representing the active power reference value. This represents the small-signal disturbance quantity indicating the state of the integrator in the reactive power control loop. Small-signal disturbances representing the reactive power reference value This represents the steady-state value of the q-axis voltage regulation integrator in the current inner loop control. This represents the steady-state value of the d-axis voltage regulation integrator in the current inner loop control.

[0073] (1.5) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter control system is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter control system, as follows:

[0074] (4)

[0075] In the formula, Represents the steady-state value of angular frequency. This represents the small-signal change in the phase angle of the phase-locked loop output. Indicates the initial phase angle. This represents the small signal change in the state of the phase-locked loop integrator. and These represent the small-signal changes in the integrator state in the active power and reactive power control loops, respectively. and These represent the small signal changes in the d-axis and q-axis voltage regulation integrator states, respectively, in the current loop control.

[0076] (1.6) By combining the small-signal state-space equations of the main circuit and the control system, the complete small-signal state-space model of the converter is obtained, in the following standard form:

[0077] (5)

[0078] In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represents the input matrix;

[0079] In this embodiment:

[0080] (6)

[0081] Based on the mathematical models of the main circuit and control system of the converter, small-signal state variables are extracted. The coefficients are used to obtain the system matrix A; in this embodiment, due to the aforementioned state variables The system matrix in formula (5) contains 12 elements. Specifically, this translates to a 12th-order square matrix A. 12×12 Specifically:

[0082] (7)

[0083] in, , , All are for the 12th order system square matrix A 12×12 The intermediate submatrix introduced by the block simplification is expressed as follows:

[0084] (8)

[0085] (9)

[0086] (10)

[0087] The input matrix in formula (5) Specifically, this expands to a 12×4 matrix B. 12×4 Specifically:

[0088] (11)

[0089] In the formula, m1 to m 26 These represent the 12th-order system matrix A. 12×12 and the 12×4 matrix B 12×4 The intermediate submatrix introduced by the block simplification is expressed as follows: (12)

[0090] (13).

[0091] Example 3

[0092] A method for optimizing the parameters of a grid-connected converter phase-locked loop under full operating conditions under wide grid strength, as described in Example 2, differs in that the implementation process of step (2) is as follows:

[0093] (2.1) Define constraints:

[0094] Under the condition of fixed system power, the small-signal stability of the converter is determined by the system matrix obtained in step (1). The decision was made regarding the system matrix of the grid converter. Subject to line inductance Ls And the influence of phase-locked loop (PLL) parameters, including the proportional parameter k. pPLL and integration parameter k iPLL For any set of phase-locked loop parameters, the following small-signal stability constraints must be met:

[0095] (14)

[0096] in, For the system matrix The i-th eigenvalue is only the system matrix. The converter can only operate stably if all the real parts of its eigenvalues ​​are non-positive; n represents the system matrix. The order of;

[0097] (2.2) Define the stable range of the inductor:

[0098] In AC power systems, grid strength is typically measured by the short-circuit ratio (SCR); the short-circuit ratio (SCR) is related to the line inductance (L). s They exhibit an inverse proportional mapping relationship, expressed mathematically as follows:

[0099] (15)

[0100] In the formula, U2 represents the effective value of the grid phase voltage, ω represents the fundamental angular frequency of the grid, and S n Indicates the rated apparent power of the converter;

[0101] From the formula, under the operating conditions where the rated parameters of the converter system are determined, the line inductance L is... s The larger the value, the smaller the short-circuit ratio, indicating a weaker grid strength. Therefore, the wide range of fluctuations in line inductance is physically equivalent to changes in grid strength. This invention defines the inductance stability range as a quantitative evaluation index. The larger the value of this range, the greater the range of line inductance variation that the converter can tolerate while maintaining small-signal stability, thus possessing stronger grid strength adaptability.

[0102] For any given set of phase-locked loop parameters, we obtain the set of all line inductances that satisfy the small-signal stability constraint. The upper and lower boundaries of the line inductance set are defined as the maximum allowable inductance L, respectively. smax With minimum allowable inductance L smin Define the inductor stability range ΔL s The difference between the two:

[0103] (16)

[0104] ΔL s The larger the value, the stronger the system's adaptability to a wide power grid intensity under this set of phase-locked loop parameters;

[0105] (2.3) Constructing a phase-locked loop parameter optimization model:

[0106] Select the proportional parameter k of the phase-locked loop pPLL With the integration parameter k iPLL As optimization variables, and with maximizing the inductor's stable range as the objective function, the following PLL parameter optimization model is obtained:

[0107] (17).

[0108] Example 4

[0109] A method for optimizing the parameters of a grid-connected converter phase-locked loop under full operating conditions under wide grid strength is described in Example 3, except that the implementation process of step (3) is as follows:

[0110] The apparent power and power factor angle of the fixed converter are used as optimization variables, with the phase-locked loop proportional and integral parameters as optimization variables. For each set of given phase-locked loop parameters (k... pPLL,j k iPLL,j ), where k pPLL,j Let k represent a given proportional parameter. iPLL,j This represents a given integral parameter, expressed in terms of line inductance L. s Using the rated value as the rated point and starting from there, the line inductance is gradually increased, and the system matrix is ​​updated in real time. And solve the system matrix. The maximum permissible inductance L under this parameter is calculated by analyzing all characteristic roots until the system is just critically stable. smax,j Similarly, starting from the rated point, gradually decrease the line inductance to find the minimum allowable inductance L at the critical stability point. smin,j And by formula ΔL s,j =L smax,j -L smin,j The inductor stability range ΔL corresponding to the calculated parameters is obtained. s,j ;

[0111] To maximize ΔL s,j With the objective of ensuring small-signal stability of the parameters, the objective function is optimized within the parameter candidate interval. The proportional and integral parameters that maximize the stability of the inductor are obtained, which are the optimal phase-locked loop parameters for this single operating condition.

[0112] The parameter candidate interval is obtained by scaling parameters calculated based on conventional second-order system theory and combined with engineering experience.

[0113] Example 5

[0114] A method for optimizing the parameters of a grid-connected converter phase-locked loop (PLL) under full operating conditions under wide grid strength is described in Example 4. The difference is that in step (4), a full operating condition set is constructed using the apparent power S and the four-quadrant power factor angle φ. For each operating point, the operating condition is fixed, and the proportional and integral parameters of the PLL are used as optimization variables. Under the constraint of small-signal stability, the inductor stability range is maximized, and the PLL parameter optimization model is obtained point by point. Finally, the optimal PLL parameters covering the full operating condition range are obtained to guide the parameter design under full operating conditions.

[0115] The specific parameters of the main circuit and control system of the grid-connected converter are shown in Table 1. The proportional and integral parameters of the conventional phase-locked loop in Table 1 are determined based on the theory of typical second-order systems in the existing technology.

[0116] Table 1 Parameters of Grid Converter

[0117]

[0118] Figure 2 This diagram illustrates the grid-connected converter system block diagram used in this embodiment. Its structure can be divided into two main parts: the converter and the power grid. The converter topology includes the main circuit, Park transformation, power calculation, power outer loop, current inner loop, and phase-locked loop. The converter is connected to the power grid via an inductor, forming the physical channel for power transmission. This block diagram clearly defines the complete control link from power command to the bridge arm modulation signal, which is the foundation for establishing the small-signal model and subsequent solution of optimal parameters. Based on the main circuit and... Figure 2 The control structure shown establishes a complete small-signal state-space model. Figure 2 In this context, SPWM stands for sinusoidal pulse width modulation; u1 represents the converter bridge arm output voltage; i L Indicates the filter inductor current; u s Indicates the voltage at the filter output terminal; i s Indicates the grid-connected current; This indicates the reference value of the d-axis current in the inner current loop; This indicates the reference value for the q-axis current of the inner current loop.

[0119] With the system parameters of the grid converter in Table 1, the optimal phase-locked loop parameters for each operating condition are solved by changing different combinations of apparent power and four-quadrant power factor angles, as shown in Table 2.

[0120] Table 2. Optimization results of PLL parameters under different apparent power and power factor angles.

[0121]

[0122] To verify the effectiveness and reliability of the method proposed in this invention, based on Figure 2The detailed topology of the main circuit and control system of the grid converter shown is simulated and verified. Figure 3 The paper presents a comparison of the inductance stability range between the optimized phase-locked loop (PLL) parameters of this invention and those of conventional PLL parameters under different apparent power and four-quadrant power factor angles. It can be seen that, compared with conventional parameters, the optimized parameters of this invention significantly broaden the inductance stability range, especially under certain operating conditions, effectively enhancing the robustness of the converter to a wide range of grid strength variations. This verifies the superiority of the proposed method based on maximizing the stability domain width.

[0123] To further illustrate the optimization details at specific power levels, Figure 4 and Figure 5 Two-dimensional cross-sectional comparisons of the inductor stability range as a function of the power factor angle are presented for apparent power S=2.5kVA and S=10 kVA, respectively. It is clearly observed from the figures that within the power factor angle range of 0 to 2π, the inductor stability range corresponding to the optimized PLL parameters is consistently greater than or encompasses the stability range of the conventional parameters, with a particularly significant improvement at specific power factor angles. This result fully demonstrates that the proposed method is not only effective under a single operating condition but also maximizes the stable operation of the converter under wide grid strength during wide power range migrations, verifying the global superiority of the inductor stability range maximization optimization strategy.

[0124] Set the line inductance L under the parameters shown in Table 1. s =20 mH, apparent power is set to 10 kVA, power factor angle is 0°, and SCR is approximately 2.31, which is a typical characteristic of an extremely weak power grid. Figure 6 The diagram shows a comparison of active power response under different phase-locked loop (PLL) parameters in an extremely weak power grid. From 0 to 0.8 s, using the optimized PLL parameters of this invention, the active power can track the rated command without steady-state error, and the system maintains high-quality steady-state operation. At t=0.8 s, when the PLL control parameters are switched to conventional parameters online, the active power immediately fluctuates significantly, and the system eventually becomes unstable. Figure 7 The diagram shows a comparison of the output current response of the phase-a converter bridge arm side under different phase-locked loop (PLL) parameters in an extremely weak power grid. During the optimal parameter operation phase from 0 to 0.8 s, the output current waveform on the converter bridge arm side exhibits good sinusoidal characteristics, without distortion or low-frequency oscillations. However, after switching to conventional parameters at t=0.8 s, the output current on the converter bridge arm side immediately oscillates and diverges, with severely distorted waveforms, leading to complete system instability. This result demonstrates that the PLL parameter optimization method of this invention can effectively improve system stability, enabling the converter to maintain stable operation in an extremely weak power grid environment.

[0125] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the parameters of a grid-connected converter's phase-locked loop under all operating conditions under wide grid strength, characterized in that... Includes the following steps: (1) Based on the main circuit topology and control system of the grid-connected converter, a small-signal state-space model of the grid-connected converter is established to obtain the system matrix; (2) Taking the stability of the small signal of the system as a constraint, the line inductance stability range is defined as the difference between the maximum allowable inductance and the minimum allowable inductance. The phase-locked loop parameter optimization model is constructed with the maximization of this stability range as the objective function. (3) Under a single operating condition, the proportional and integral parameters of the phase-locked loop are used as optimization variables. Based on the small-signal stability constraint and the objective function of maximizing the stability range of the inductor, the optimization model is solved to obtain the optimal phase-locked loop parameters. (4) Construct a full-condition operating set using apparent power and four-quadrant power factor angles. Under the constraint conditions, solve the optimization model point by point with the goal of maximizing the inductance stability range, and solve the phase-locked loop optimization results in the full-condition range.

2. The method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength as described in claim 1, is characterized in that... The process of establishing the small-signal state-space model of the grid-connected converter in step (1) is as follows: (1.1) In the dq axis coordinate system, based on Kirchhoff's voltage law and Kirchhoff's current law, establish the nonlinear large-signal differential equation of the converter main circuit; (1.2) Based on the principle of complete control link, the nonlinear large-signal differential equation of the converter control system is obtained; (1.3) Based on the nonlinear large-signal differential equation of the converter main circuit and the nonlinear large-signal differential equation of the control system, the derivative terms of each state variable are set to zero to construct a steady-state algebraic equation system, and the steady-state equilibrium point of the system is determined by solving the equation system. (1.4) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter main circuit is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter main circuit. (1.5) At the steady-state equilibrium point, the nonlinear large-signal differential equation of the converter control system is linearized based on the first-order Taylor expansion, thereby obtaining the small-signal state-space equation of the converter control system. (1.6) By combining the small-signal state-space equations of the main circuit and the control system, the complete small-signal state-space model of the converter is obtained, in the following standard form: （5） In the formula, Represents the small-signal state variable at time t. This represents the small-signal input variable at time t. Represents the system matrix. Represents the input matrix; The equations of the small-signal state-space model of the complete converter are rearranged into standard matrix form, and the small-signal state variables are extracted. The corresponding coefficient matrix is ​​the system matrix. .

3. The method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength as described in claim 2, is characterized in that... The implementation process of step (2) is as follows: (2.1) Define constraints: Under the condition of fixed system power, the small-signal stability of the converter is determined by the system matrix obtained in step (1). The decision was made regarding the system matrix of the grid converter. Subject to line inductance L s And the influence of phase-locked loop (PLL) parameters, including the proportional parameter k. pPLL and integration parameter k iPLL For any set of phase-locked loop parameters, the following small-signal stability constraints must be met: （14） in, For the system matrix The i-th eigenvalue is only the system matrix. The converter can only operate stably if all the real parts of its eigenvalues ​​are non-positive; n represents the system matrix. The order of; (2.2) Define the stable range of the inductor: For any given set of phase-locked loop parameters, we obtain the set of all line inductances that satisfy the small-signal stability constraint. The upper and lower boundaries of the line inductance set are defined as the maximum allowable inductance L, respectively. smax With minimum allowable inductance L smin Define the inductor stability range ΔL s The difference between the two: （16） ΔL s The larger the value, the stronger the system's adaptability to a wide power grid intensity under this set of phase-locked loop parameters; (2.3) Constructing a phase-locked loop parameter optimization model: Select the proportional parameter k of the phase-locked loop pPLL With the integration parameter k iPLL As optimization variables, and with maximizing the inductor's stable range as the objective function, the following PLL parameter optimization model is obtained: （17）。 4. The method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength as described in claim 3, is characterized in that... The implementation process of step (3) is as follows: The apparent power and power factor angle of the fixed converter are used as optimization variables, with the phase-locked loop proportional and integral parameters as optimization variables. For each set of given phase-locked loop parameters (k... pPLL,j k iPLL,j ), where k pPLL,j Let k represent a given proportional parameter. iPLL,j This represents a given integral parameter, expressed in terms of line inductance L. s Using the rated value as the rated point and starting from there, the line inductance is gradually increased, and the system matrix is ​​updated in real time. And solve the system matrix. The maximum allowable inductance L under this parameter is calculated by analyzing all characteristic roots until the system is just critically stable. smax,j Similarly, starting from the rated point, gradually decrease the line inductance to find the minimum allowable inductance L at the critical stability point. smin,j And by formula ΔL s,j =L smax,j -L smin,j The inductor stability range ΔL corresponding to the calculated parameters is obtained. s,j ; To maximize ΔL s,j With the objective of ensuring small-signal stability of the parameters, the objective function is optimized within the parameter candidate interval. The proportional and integral parameters that maximize the stability of the inductor are obtained, which are the optimal phase-locked loop parameters for this single operating condition.

5. The method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength as described in claim 4, is characterized in that... The parameter candidate interval in step (3) is obtained by scaling the parameters calculated based on conventional second-order system theory.

6. The method for optimizing the parameters of a grid-connected converter phase-locked loop under all operating conditions under wide grid strength as described in claim 5, is characterized in that... In step (4), a full-condition operating set is constructed using the apparent power S and the four-quadrant power factor angle φ. For each operating point, the operating condition is fixed, and the proportional and integral parameters of the phase-locked loop are used as optimization variables. Under the constraint of small signal stability, the inductor stability range is maximized, and the phase-locked loop parameter optimization model is obtained point by point. Finally, the optimal phase-locked loop parameters covering the full operating condition range are obtained to guide the parameter design under the full operating condition.

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