Passiveness-based phase-locked loop parameter adaptive optimization method under weak power grid

Abstract

The invention discloses a passivity-based weak power grid phase-locked loop parameter adaptive optimization method, which comprises the following steps of: (1) establishing a dynamic coupling model of a phase-locked loop and a converter system under a weak power grid condition, and analyzing an influence mechanism of phase-locked loop parameters on system stability; (2) deriving a real-time calculation method of the equivalent short-circuit ratio of the system based on a passivity theory, and constructing a short-circuit ratio-parameter sensitivity relation matrix; and (3) adaptively adjusting the bandwidth coefficient and the damping ratio parameter of the phase-locked loop by dynamically sensing the change of the short-circuit ratio of the power grid, and eliminating the harmonic oscillation or instability risk caused by the fixed parameter. According to the method, stable operation of the system under the full working condition is ensured, and the dynamic stability and robustness of the wind turbine generator under the low-short-circuit-ratio weak-power-grid working condition can be remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of renewable energy power generation grid-connected control, and in particular relates to a passivity-based phase-locked loop parameter adaptive optimization method in a weak power grid. Background Art

[0002] When new energy units are connected to the grid through power electronic converters, although the control flexibility is better than that of traditional synchronous generators, since most new energy sites are located in remote areas at the end of the grid, long-distance transmission lines and multi-stage transformers cause the grid to present weak grid characteristics with high impedance and low short-circuit ratio (SCR<3). Under this operating condition, the dynamic interaction between the inverter equivalent output impedance and the grid impedance will destroy the system's passivity, causing wide-band harmonic oscillations in the 50Hz-1kHz frequency band (typical amplitude exceeds 5% of rated current), subsynchronous oscillations (SSO, 10-50Hz) and phase margin deterioration (less than 30° under extreme conditions). Traditional phase-locked loops use fixed parameter design (bandwidth 30-50Hz, damping ratio ξ =0.7-1.2). When the grid short-circuit ratio drops suddenly from 3.0 to 1.5, the probability of system instability increases by 80%. Existing adaptive methods rely on periodic measurements, with response delays exceeding 100ms, and there is a risk of misjudgment under sudden operating conditions such as symmetrical grid faults. Therefore, a dynamic phase-locked loop parameter tuning method based on real-time grid state perception is urgently needed. By adaptively adjusting the bandwidth coefficient and damping ratio, this method decouples the strong correlation between the phase-locked loop's dynamic characteristics and the grid impedance, ensuring stable system operation under all operating conditions. Summary of the Invention

[0003] The present invention is proposed to overcome the shortcomings of the prior art and aims to provide a method for adaptively optimizing phase-locked loop parameters in a weak power grid based on passivity.

[0004] The present invention is achieved through the following technical solutions: A passivity-based phase-locked loop parameter adaptive optimization method under weak power grid conditions includes the following steps: (I) Establish a dynamic coupling model between the phase-locked loop and the converter system under weak grid conditions and analyze the impact of the phase-locked loop parameters on system stability; (II) Establish the system passivity criterion and derive the real-time calculation method of the system equivalent short-circuit ratio based on the passivity theory, and construct the short-circuit ratio-parameter sensitivity relationship matrix and the stability margin sensitivity matrix; (III) When any one of the system parameters does not meet the passivity criterion, the phase-locked loop bandwidth coefficient and damping ratio parameters are adaptively adjusted by dynamically sensing the change in the grid short-circuit ratio.

[0005] In the above technical solution, the step (I) specifically includes the following steps: (Ⅰ-i) Establish the mathematical model of the grid-connected current of the inverter according to the mathematical model of the grid-connected inverter control system; The mathematical model expression of the grid-connected current is: … (1) In the formula: is the grid-connected current, with the unit of A; I ref is the command current, with the unit of A; is the grid-connected voltage at the PCC point, with the unit of V; G (s) is the current-loop transfer function of the double-closed-loop control; G pll (s) is the equivalent transfer function of the phase-locked loop; Y inv (s) is the equivalent admittance of the inverter; (Ⅰ-ii) Derive the output impedance of the inverter Z inv (s) and the equivalent impedance of the phase-locked loop Z pll (s) expressions; …… (6) In the formula: Z inv ( s ) is the output impedance of the inverter, with the unit of Ω; Y inv ( s ) is the equivalent admittance of the inverter, with the unit of S; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; s is the Laplace operator, with the unit of second -1 ; G i (s) is the current regulator; The equivalent impedance of the phase-locked loop Z pll (s) expression is: …… (7) In the formula: Z pll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ω; I ref is the command current, with the unit of A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G (s ) is the current loop transfer function of the double closed-loop control; L L1 is the inductor on the inverter side, with the unit of H; L L2 is the inductor on the grid side, with the unit of H; C C is the filter capacitor, with the unit of F; s is the Laplace operator, with the unit of second -1 ; G i ( s ) is the current regulator; (Ⅰ-ⅲ) Establish a dynamic coupling model of the phase-locked loop and the converter system after comprehensively considering the mutual influence of the phase-locked loop and the inverter control; The expression of the dynamic coupling model of the phase-locked loop and the converter system is: …… (8) In the formula: Z O Z(s) is the equivalent impedance after comprehensively considering the mutual influence of the phase-locked loop and the inverter, with the unit of Ω; u is the grid-connected voltage at the PCC point, with the unit of V; i g i(s) is the grid-connected current, with the unit of A; Z inv ( s ) is the output impedance of the inverter, with the unit of Ω; Z pll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ω; s is the Laplace operator, with the unit of second -1 ; L L1 is the inductor on the inverter side, with the unit of H; L L2 is the inductor on the grid side, with the unit of H; C C is the filter capacitor, with the unit of F; I ref i* is the command current, with the unit of A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G i ( s ) is the current regulator.

[0006] In the above technical solution, the current loop transfer function of the double closed-loop control G G(s) has the expression: …… (2) In the formula: G i (s) G(s) is the current regulator; L 1is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; s is the Laplace operator, representing the complex frequency domain variable, with the unit of second -1 ; The equivalent transfer function of the phase-locked loop G pll (s) is expressed as: ……(3) In the formula: k p is the proportionality of the PI controller of the phase-locked loop, dimensionless; k i is the integral coefficient of the PI controller of the phase-locked loop, with the unit of second -1 ; V d is d the steady-state value of the axis voltage, with the unit of V; s is the Laplace operator, with the unit of second -1 ; j is the imaginary unit, dimensionless; is the center frequency, with the unit of rad / s; The equivalent admittance of the inverter Y inv (s) are respectively expressed as: ……(4) In the formula: s is the Laplace operator, with the unit of second -1 ; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; G i (s) is the current regulator.

[0007] The current regulator G i (s) is expressed as: ……(5) In the formula: K p represents the proportional gain, dimensionless; K i represents the integral gain, with the unit of second -1 ; s is the Laplace operator, with the unit of second -1 。

[0008] In the above technical solution, step (II) specifically includes the following steps: (II-i) Establish a strict passivity criterion for the system The strict passivity criterion for the system includes: (a) …… (11) Where: ω min = 2π×10 rad / s, ω max = 2π×1000 rad / s; is the real part of the time-domain expression of Y sys ([[]] jω ) in the equivalent admittance matrix of the inverter and grid interaction system; (b) …… (12) Where: Ω = [10 rad / s, 1000 rad / s] is the sub / super-synchronous frequency band; Y sys ([[]] jω ) is the system equivalent admittance matrix, with the unit of S; is Y sys ([[]] jω )'s conjugate transpose matrix, with the unit of S; det is the determinant calculation of the matrix, dimensionless; (c) The positive-sequence admittance passivity index 's real-time value is lower than the positive-sequence admittance passivity index dynamic threshold for less than 3 consecutive times (the positive-sequence admittance passivity index 's real-time value is lower than the positive-sequence admittance passivity index dynamic threshold three times in a row, triggering the adjustment of the PLL parameters); (II-ii) Online estimate the grid impedance Inject a small current perturbation Δ i at the PCC point, measure the voltage response Δ v , and calculate the grid impedance value; The calculation formula for the grid impedance value is: …… (17) Where: Z grid (jω k ） is the grid impedance value, with the unit of Ω; Δ v is the voltage response, with the unit of V; Δ i is the current perturbation, with the unit of A; jIt is an imaginary unit and dimensionless; ω k is the frequency at the PCC point, in rad / s; ω k Covering 10Hz~1kHz; the small current disturbance Δ i It is a white noise signal of 0.5% rated current; (II-III) Take the impedance value at the fundamental frequency , calculate the equivalent short-circuit ratio; The calculation formula of the equivalent short-circuit ratio is: …… (18) Where: ESCR is the equivalent short-circuit ratio, dimensionless; is the impedance value at the fundamental frequency, in Ω, calculated according to formula (17); S base is the system base capacity, in VA; (II-IV) Construct the short-circuit ratio-sensitivity relationship matrix and the stability margin-sensitivity matrix; The expression of the stability margin-sensitivity matrix is: …… (19) The expression of the short circuit ratio-sensitivity relationship matrix is: …… (20) Where: A m is the amplitude margin, in dB; is the phase margin, in degrees; ξ is the damping ratio, dimensionless; ω n is the bandwidth, in rad / s, S ξ (ESCR) is the damping ratio ξ Sensitivity coefficient to equivalent short circuit ratio ESCR, dimensionless; ξ* To make the system meet the requirements under a specific ESCR Optimal damping ratio ≥45°, dimensionless; is the bandwidth ω n Sensitivity coefficient to equivalent short circuit ratio ESCR, dimensionless; The optimal bandwidth for the system to meet Am ≥ 6dB under a specific ESCR, expressed in rad / s.

[0009] In the above technical solution, the positive sequence admittance passivity index The calculation formula is: …… (13) Where: To separate the positive-sequence component from the admittance matrix; The real part of the time-domain expression of the positive-sequence admittance component; and are the off-diagonal elements of the admittance matrix, characterizing the dq-axis coupling; are discrete frequency points taken logarithmically uniformly distributed.

[0010] In the above technical solution, the dynamic threshold of the positive-sequence admittance passivity index The calculation formula is: …… (16) In the formula: η0 = 0.01, corresponding to an ideal power grid with an infinite equivalent short-circuit ratio; is the current evaluation frequency point, in units of rad / s; is the base angular frequency, in units of rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless.

[0011] In the above technical solution, the stability margin index is: the amplitude margin A m ≥6 dB; the phase margin ≥45°.

[0012] In the above technical solution, step (Ⅲ) specifically includes the following steps: (Ⅲ-i) Offline training and online look-up table During offline swept-frequency simulation training within the typical short-circuit ratio range, based on the sensitivity analysis results of the stability margin with respect to the PLL parameters, dense sampling is preferentially performed in the direction of the parameter that has the greatest impact on the system stability, and the simulation step size is encrypted in the sensitive interval of the equivalent short-circuit ratio change; after systematically traversing each operating point, the optimal parameter combination that simultaneously meets the phase margin and amplitude margin requirements and its sensitivity characteristics corresponding to each system equivalent short-circuit ratio ESCR are recorded, and a two-dimensional look-up table containing parameter adjustment rules is generated; (Ⅲ-ii) Calculate the parameter adjustment amount The calculation formula for the parameter adjustment amount is: …… (22) In the formula: Δξ is the adjustment amount of the PLL damping ratio, dimensionless; Δω n is the adjustment amount of the PLL bandwidth, in units of rad / s; ΔESCR is the difference between the real-time measured value and the reference value of the equivalent short-circuit ratio, dimensionless; , is the sensitivity of the damping ratio to the equivalent short-circuit ratio ESCR, dimensionless; , is the sensitivity of the bandwidth to the equivalent short-circuit ratio ESCR, in units of rad / s; (Ⅲ-ⅲ) Dynamically optimize the damping ratio of the phase-locked loop based on the sensitivity coefficient ξ and the bandwidth of the phase-locked loop ω n The damping ratio of the phase-locked loop based on the sensitivity coefficient ξ and the bandwidth of the phase-locked loop ω n The calculation formula is: ……(23) In the formula, ξ old is the original damping ratio of the phase-locked loop, dimensionless; ω n,old is the original bandwidth, with the unit of rad / s; ξ new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; ω n,new * is the bandwidth of the phase-locked loop after dynamic optimization, with the unit of rad / s; Δξ is the adjustment amount of the damping ratio of the phase-locked loop, dimensionless; Δω n is the adjustment amount of the bandwidth of the phase-locked loop, with the unit of rad / s; (Ⅲ-ⅳ)Back-calculate the PI parameters of the phase-locked loop through the damping ratio ξ new * and the bandwidth of the phase-locked loop ω n,new * The calculation formula for the PI parameters of the phase-locked loop is: The calculation formula for the PI parameters of the phase-locked loop is: ……(24) In the formula: k p is the proportionality of the PI controller of the phase-locked loop, dimensionless; k i is the integral coefficient of the PI controller of the phase-locked loop, with the unit of second -1 ; V d is the current d axis voltage measurement value, with the unit of V; ξ new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; ω n,new * is the bandwidth of the phase-locked loop after dynamic optimization, with the unit of rad / s.

[0013] In the above technical solution, the typical short - circuit ratio range is ESCR ∈ [0.8, 3.0]; the equivalent short - circuit ratio change sensitive interval is the interval where the equivalent short - circuit ratio ESCR ∈ [1.0, 2.0]; the specific encrypted simulation step size is set to 0.1.

[0014] The beneficial effects of the present invention are as follows: The present invention provides a method for self - adaptive optimization of phase - locked loop parameters under a weak grid based on passivity, which is applicable to the dynamic optimization of the phase - locked loop parameters of a wind turbine in a low short - circuit ratio weak grid scenario, and is particularly applicable to a distributed energy system containing a high proportion of power electronic devices; the present invention can significantly improve the dynamic stability and robustness of a wind turbine under low short - circuit ratio weak grid conditions.

[0015] The present invention introduces an adaptive adjustment algorithm into the phase - locked loop control loop. By real - time sensing the change of the grid short - circuit ratio (ESCR), the bandwidth coefficient ω n and the damping ratio ξ of the phase - locked loop are dynamically optimized, and the optimal PI control parameters are inversely deduced based on the characteristics of the second - order system, effectively solving the stability problem caused by the fixed - parameter phase - locked loop under weak grid conditions, and enabling the system to maintain a phase margin of at least 45° within the full operating range. Description of the Drawings

[0016] Figure 1 is the inverter circuit topology diagram containing the adaptive adjustment algorithm; Figure 2 is the mathematical model of the grid - connected inverter control system; Figure 3 is the equivalent circuit of the grid - connected inverter system containing the phase - locked loop; Figure 4 is the grid current without using the dynamic tuning method of phase - locked loop parameters; Figure 5 is the grid current using the dynamic tuning method of phase - locked loop parameters.

[0017] For those of ordinary skill in the art, without creative efforts, other relevant drawings can be obtained based on the above drawings. Detailed Embodiments

[0018] In order to enable the personnel in the technical field to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below in conjunction with the drawings in the specification and through specific embodiments.

[0019] Embodiment 1 Based on Figure 1 the method for self - adaptive optimization of phase - locked loop parameters under a weak grid based on the inverter circuit topology diagram containing the adaptive adjustment algorithm shown, includes the following steps: (I) Establish a dynamic coupling model of the phase-locked loop and the converter system under weak grid conditions, and analyze the influence mechanism of the phase-locked loop parameters on the system stability. The specific steps are as follows: (I-i) According to Figure 2 the mathematical model of the grid-connected inverter control system shown, establish the mathematical model of the grid-connected current of the inverter; The expression of the mathematical model of the grid-connected current is: … (1) Where: is the grid-connected current, with the unit of A; I ref is the command current, with the unit of A; is the grid-connected voltage at the PCC point, with the unit of V; G (s) is the current loop transfer function of the double closed-loop control; G pll (s) is the equivalent transfer function of the phase-locked loop; Y inv (s) is the equivalent admittance of the inverter; The current loop transfer function G (s) of the double closed-loop control has the following expression: …… (2) Where: G i (s) is the current regulator, which is PI controller; L 1 is the inductor on the inverter side, with the unit of henry (H); L 2 is the inductor on the grid side, with the unit of henry (H); C is the filter capacitor, with the unit of farad (F); s is the Laplace operator, representing the complex frequency domain variable, with the unit of second -1 .

[0020] The equivalent transfer function G pll (s) of the phase-locked loop has the following expression: …… (3) Where: k p is the proportionality of the PI controller of the phase-locked loop, dimensionless; k i is the integral coefficient of the PI controller of the phase-locked loop, with the unit of second -1 ; V d is d the steady-state value of the axis voltage, with the unit of volt (V);s is the Laplace operator, with the unit of seconds -1 ; j is the imaginary unit, dimensionless; is the center frequency, with the unit of rad / s.

[0021] The equivalent admittance of the inverter Y inv (s) are expressed as follows: …… (4) In the formula: s is the Laplace operator, with the unit of seconds -1 ; L 1 is the inductor on the inverter side, with the unit of henry (H); L 2 is the inductor on the grid side, with the unit of henry (H); C is the filter capacitor, with the unit of farad (F); G i (s) is the current regulator.

[0022] The current regulator G i (s) is expressed as: …… (5) In the formula: K p represents the proportional gain, dimensionless; K i represents the integral gain, with the unit of seconds -1 ; s is the Laplace operator, with the unit of seconds -1 .

[0023] (Ⅰ-ⅱ) Derive the output impedance of the inverter Z inv (s) and the equivalent impedance of the phase-locked loop Z pll (s) according to the expression (formula 1) of the mathematical model of the grid-connected current in step (Ⅰ-ⅰ); The output impedance of the inverter Z inv (s) is expressed as: …… (6) In the formula: Z inv ( s ) is the output impedance of the inverter, with the unit of ohm (Ω); Y inv ( s) is the equivalent admittance of the inverter, with the unit of Siemens (S); L 1 is the inductor on the inverter side, with the unit of Henry (H); L 2 is the inductor on the grid side, with the unit of Henry (H); C is the filter capacitor, with the unit of Farad (F); s is the Laplace operator, with the unit of second -1 ; G i (s) is the current regulator, which is a PI controller; The equivalent impedance of the phase-locked loop Z pll (s) has the following expression: …… (7) In the formula: Z pll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ohm (Ω); I ref is the command current, with the unit of Ampere (A); G pll ( s ) is the equivalent transfer function of the phase-locked loop; G ( s ) is the current loop transfer function of the double closed-loop control; L 1 is the inductor on the inverter side, with the unit of Henry (H); L 2 is the inductor on the grid side, with the unit of Henry (H); C is the filter capacitor, with the unit of Farad (F); s is the Laplace operator, with the unit of second -1 ; G i ( s ) is the current regulator, which is a PI controller; (Ⅰ-ⅲ) Establish a dynamic coupling model of the phase-locked loop and the converter system after comprehensively considering the mutual influence of the control of the phase-locked loop and the inverter; The expression of the dynamic coupling model (equivalent impedance model) of the phase-locked loop and the converter system is: …… (8) In the formula: Z O (s) is the equivalent impedance after comprehensively considering the mutual influence of the phase-locked loop and the inverter, with the unit of Ω; is the grid-connected voltage at the PCC point, with the unit of V; i g (s) is the grid-connected current, with the unit of A; Z inv ( s ) is the output impedance of the inverter, with the unit of Ω; Zpll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ω; s is the Laplace operator, with the unit of second -1 ; L L1 is the inductor on the inverter side, with the unit of H; L L2 is the inductor on the grid side, with the unit of H; C C is the filter capacitor, with the unit of F; I ref i* is the command current, with the unit of A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G i ( s ) is the current regulator; Grid impedance Z g (s) is expressed as: …… (9) In the formula: Z g Z(s) is the grid impedance, with the unit of Ω; R g R is the resistance of the grid line, with the unit of Ω; L g L is the inductance of the grid line, with the unit of H; C g C is the capacitance of the grid line, with the unit of F; Thus, the equivalent circuit diagram corresponding to the equivalent impedance model can be obtained as shown in Figure 3 . It can be seen that any admittance model that ignores the dynamics of the phase-locked loop will cause serious errors under a weak grid.

[0024] The dynamic coupling model of the phase-locked loop and the converter system is the equivalent parallel impedance model. From the dynamic coupling model of the phase-locked loop and the converter system, it can be seen that considering the interaction between the phase-locked loop and the control comprehensively, the broadband equivalent impedance model of the grid-connected inverter can be equivalent to a parallel impedance model. From the dynamic coupling model of the phase-locked loop and the converter system, the influence mechanism of the phase-locked loop parameters on the system stability can be analyzed. Specifically: Since Z O (s) is strongly coupled in parallel with Z inv (s) and Z pll (s), and it can be seen from equation (8) that Z pll (s) is a negative impedance, and the equivalent transfer function G pll (s) of the phase-locked loop in Z pll (s) exhibits a low-pass filtering characteristic at frequencies higher than the fundamental frequency. The larger its bandwidth, the lower the amplitude of 1 / G pll (s) at high frequencies, and thus Z pllThe amplitude of (s) will also be lower, and the phase angle will be smaller, thereby reducing the output impedance Z O The amplitude and phase angle of (s) lead to a reduction in the system stability margin and may even cause system instability. Therefore, if fixed PLL bandwidth parameters are adopted, the stability requirements under all operating conditions cannot be covered.

[0025] (II) Establish a system passivity criterion, derive a calculation method for the system equivalent short-circuit ratio, and construct a short-circuit ratio-parameter sensitivity relationship matrix, which specifically includes the following steps: (II-i) Establish a system passivity criterion Convert the dynamic coupling model of the PLL and the converter system into an equivalent admittance matrix of the inverter and grid interaction system. The expression of the equivalent admittance matrix is: …… (10) In the formula: Y sys ([[]] jω ) is the equivalent admittance matrix of the inverter and grid interaction system; Y O ([[]] jω ) is the equivalent admittance considering the mutual influence of the PLL and the inverter; Y g ([[]] jω ) is the grid admittance; For Y sys ([[]] jω ), the strict passivity criterion of the system needs to simultaneously satisfy the following three conditions: (a) …… (11) In the formula: ω min = 2π×10rad / s, ω max = 2π×1000rad / s; is the real part of the time-domain expression of Y sys ([[]] jω ) in the equivalent admittance matrix of the inverter and grid interaction system; (b) …… (12) In the formula: Ω = [10rad / s, 1000rad / s] is the sub / super-synchronous frequency band; Y sys ([[]] jω ) is the system equivalent admittance matrix (including the PLL and grid impedance coupling effects), with the unit of Siemens (S); is Y sys ([[]] jω)'s conjugate transpose matrix, with the unit of Siemens (S); det is the determinant calculation of the matrix, dimensionless; (c) Positive-sequence admittance passivity index The real-time value of is less than 3 times continuously (the positive-sequence admittance passivity index The real-time value of is continuously lower than the dynamic threshold of the positive-sequence admittance passivity index The positive-sequence admittance passivity index The calculation formula of ...... (13) In the formula: is to separate the positive-sequence component from the admittance matrix; is the real part of the time-domain expression of the positive-sequence admittance component; , are the off-diagonal elements of the admittance matrix, representing the dq-axis coupling; is the discrete frequency point with a logarithmically uniform distribution;

[0026] Admittance matrix Y(jω k ) is 20 frequency points with a logarithmically uniform distribution, obtained by calculating the admittance for each frequency point; ...... (14) Y pos (jω) The calculation formula of ...... (15) In the formula: Y dd (jω k ) is the admittance of the d-axis voltage to the d-axis current (self-admittance), with the unit of Siemens (S); Y qq (jω k ) is the admittance of the q-axis voltage to the q-axis current (self-admittance), with the unit of Siemens (S); Y dq (jω k ) is the admittance of the q-axis voltage to the d-axis current (mutual admittance), with the unit of Siemens (S); Y qd (jωk ) is the admittance of the d-axis voltage with respect to the q-axis current (mutual admittance), in Siemens (S).

[0027] The positive-sequence admittance passivity index dynamic threshold has the following calculation formula: …… (16) where: η0 = 0.01, corresponding to an ideal power grid with infinite equivalent short-circuit ratio; is the current evaluation frequency point, in rad / s; is the base angular frequency (taking the power frequency), in rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless; Subsequent operations are based on passivity. If passivity is satisfied, the PLL coefficient does not need to be adjusted. If any one of the passivity criteria is not met and the PLL parameter adjustment is triggered, then it is necessary to calculate the PLL parameters to be adjusted according to the constructed short-circuit ratio - parameter sensitivity relationship matrix and stability margin sensitivity matrix; (Ⅱ-ⅱ) Online estimation of the grid impedance Inject a small current perturbation Δ i at the PCC point (point of common coupling in the power system), and measure the voltage response Δ v to calculate the grid impedance value; The calculation formula for the grid impedance value is: , …… (17) where: Z grid (jω k ） is the grid impedance value, in Ω; Δ v is the voltage response, in V; Δ i is the current perturbation, in A; j is the imaginary unit, dimensionless; ω k is the frequency at the PCC point, in rad / s; ω k covers 10 Hz to 1 kHz; The small current perturbation Δ i is a white noise signal of 0.5% of the rated current; (Ⅱ-ⅲ) Take the impedance value at the fundamental frequency , and calculate the equivalent short-circuit ratio; The calculation formula for the equivalent short-circuit ratio is: …… (18) where: ESCR is the equivalent short-circuit ratio, dimensionless; is the impedance value at the fundamental frequency, in Ω, calculated according to formula (17); S base is the system base capacity, in VA; If , trigger re - sampling of data; If ESCR > 10, it is determined that the measurement is abnormal (possibly close to an ideal voltage source).

[0028] (II - iv) Construct the short - circuit ratio - sensitivity relationship matrix and the stability margin - sensitivity relationship matrix Define the phase - locked loop transfer function G pll The stability margin index of (s), based on the phase - locked loop transfer function G pll Establish the short - circuit ratio - sensitivity relationship matrix based on the stability margin index of (s); The phase - locked loop transfer function G pll The stability margin index of (s) is: Gain margin A m ≥6 dB; Phase margin ≥45°; The expression of the stability margin - sensitivity matrix is: …… (19) The expression of the short - circuit ratio - sensitivity relationship matrix is: …… (20) In the formula: A m is the gain margin, in dB; is the phase margin, in °; ξ is the damping ratio, dimensionless; ω n is the bandwidth, in rad / s, is the damping ratio ξ The sensitivity coefficient to the equivalent short - circuit ratio ESCR, dimensionless; ξ* is the optimal damping ratio that makes the system satisfy<s ≥45° at a specific ESCR, dimensionless; is the bandwidth ω n The sensitivity coefficient to the equivalent short - circuit ratio ESCR, dimensionless; is the optimal bandwidth that makes the system satisfy Am≥6 dB at a specific ESCR, in rad / s; (III) When the system does not meet the passivity criterion, by dynamically sensing the change of the grid short-circuit ratio, the phase-locked loop bandwidth coefficient and damping ratio parameters are adaptively adjusted, which specifically includes the following steps: (III-i) Offline training and online look-up table When performing offline swept-frequency simulation training within the typical short-circuit ratio range, based on the sensitivity analysis results of the phase-locked loop parameters to the stability margin, intensive sampling is preferentially carried out in the parameter direction that has the greatest impact on the system stability, and the simulation step size is encrypted in the sensitive interval of the equivalent short-circuit ratio change; after systematically traversing each operating condition point, record the optimal parameter combination and its sensitivity characteristics that simultaneously meet the requirements of phase margin and amplitude margin corresponding to each system equivalent short-circuit ratio ESCR, and generate a two-dimensional look-up table containing parameter adjustment rules; during actual online operation, the system only needs to directly obtain the parameter adjustment instruction through the bilinear interpolation of the pre-stored look-up table according to the real-time measured ESCR value, completely avoiding real-time complex operations and ensuring the rapid response of the control system; The typical short-circuit ratio range is ESCR ∈ [0.8, 3.0]; The sensitive interval of the equivalent short-circuit ratio change is the interval where the equivalent short-circuit ratio ESCR ∈ [1.0, 2.0]; the encrypted simulation step size is specifically set to a step size of 0.1; At the same time, when performing swept-frequency simulation, the step size is relaxed to 0.3 in the low-sensitivity region (equivalent short-circuit ratio ESCR > 2.5); The two-dimensional look-up table satisfies the following expression conditions: ...... (21) In the formula: is the change rate calculated by the damping ratio difference of adjacent ESCR points in the look-up table; is the damping ratio obtained from offline training ξ - The theoretical value of the equivalent short-circuit ratio ESCR sensitivity function; the two-dimensional look-up table satisfies the condition to ensure that the online look-up table value is consistent with the theoretical sensitivity; the two-dimensional look-up table is [[ID= 、 ​ n Sensitivity look-up table; (III-ii) Calculate the parameter adjustment amount The calculation formula for the parameter adjustment amount is: ...... (22) In the formula: ​ is the adjustment amount of the phase-locked loop damping ratio, dimensionless; ​ n is the adjustment amount of the phase-locked loop bandwidth, with the unit of rad / s; ​ is the difference between the real-time measured value and the reference value of the equivalent short-circuit ratio, dimensionless; , which is the sensitivity of the damping ratio to the equivalent short - circuit ratio ESCR (obtained by looking up the table), dimensionless; , which is the sensitivity of the bandwidth to the equivalent short - circuit ratio ESCR, with the unit of rad / s; (Ⅲ - ⅲ) Dynamic optimization of the PLL damping ratio based on the sensitivity coefficient ​ and the PLL bandwidth ​ n ; The PLL damping ratio based on the sensitivity coefficient ​ and the PLL bandwidth ​ n The calculation formulas are as follows: ...... (23) In the formula, is the original PLL damping ratio, dimensionless; is the original bandwidth, with the unit of rad / s; is the dynamically optimized PLL damping ratio, dimensionless; is the dynamically optimized PLL bandwidth, with the unit of rad / s; is the adjustment amount of the PLL damping ratio, dimensionless; is the adjustment amount of the PLL bandwidth, with the unit of rad / s; (Ⅲ - ⅳ) Through the dynamically optimized PLL damping ratio ​ new * and the PLL bandwidth ​ n,new * The PI parameters of the PLL are deduced inversely: The calculation formulas for the PI parameters of the PLL are as follows: ...... (24) In the formula: k p is the proportion of the PLL loop PI controller, dimensionless; k i is the integral coefficient of the PLL loop PI controller, with the unit of second -1 ; V d is the current d axis voltage measurement value, with the unit of V; is the dynamically optimized PLL damping ratio, dimensionless; is the dynamically optimized PLL bandwidth, with the unit of rad / s.

[0029] As ​ shown, when the dynamic tuning method of PLL parameters is not adopted, after the short - circuit ratio suddenly changes at 0.3 s for the grid - connected inverter, the grid current shows significant oscillations (THD rises to 18.7%). In contrast,​ The figure shows the current waveforms under the same operating conditions after the proposed dynamic tuning method of the present invention is applied at 0.36 s. The experimental results show that after the adaptive parameter adjustment, the total harmonic distortion (THD) of the current is reduced to less than 2.3%, and the transient regulation time is shortened to 15 ms, meeting the transient response requirements for fault ride-through in GB / T 19963-2021 (<50 ms); at the same time, the system robustness is improved by 87.7% (evaluated according to the IEEE 1547-2018 standard).

[0030] The applicant declares that the above description is only a specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily conceived by any person skilled in the art within the technical scope disclosed by the present invention fall within the protection scope and the disclosure scope of the present invention.

Claims

1. A parameter adaptive optimization method for a phase-locked loop under a weak power grid based on passivity, characterized in that: It includes the following steps: (Ⅰ) Establish a dynamic coupling model of the phase-locked loop and the converter system under weak grid conditions, and analyze the influence mechanism of the phase-locked loop parameters on the system stability; (Ⅱ) Establish a system passivity criterion, and based on the passivity theory, derive a real-time calculation method for the equivalent short-circuit ratio of the system, and construct a short-circuit ratio - parameter sensitivity relationship matrix and a stability margin sensitivity matrix; (Ⅲ) When any one of the systems does not meet the passivity criterion, adaptively adjust the phase-locked loop bandwidth coefficient and damping ratio parameters by dynamically sensing the change of the grid short-circuit ratio.

2. The method for adaptively optimizing the parameters of the phase-locked loop under a weak power grid based on passivity according to claim 1, wherein: The specific steps of the step (Ⅰ) include the following steps: (Ⅰ-i) According to the mathematical model of the grid-connected inverter control system, establish the mathematical model of the grid-connected current of the inverter; The expression of the mathematical model of the grid-connected current is: ； Where: is the grid-connected current, with the unit of A; I ref is the reference current, with the unit of A; is the grid-connected voltage at the PCC point, with the unit of V; G (s) is the transfer function of the current loop in the double closed-loop control; G pll (s) is the equivalent transfer function of the phase-locked loop; Y inv (s) is the equivalent admittance of the inverter; (Ⅰ-ⅱ)Derive the output impedance of the inverter based on the mathematical model expression of the grid-connected current in step (Ⅰ-ⅰ) Z inv (s) and the equivalent impedance of the phase-locked loop Z pll (s); The output impedance of the inverter Z inv (s) is expressed as: ； Wherein: Z inv ( s ) is the output impedance of the inverter, with the unit of Ω; Y inv ( s ) is the equivalent admittance of the inverter, with the unit of S; L L1 is the inductor on the inverter side, with the unit of H; L L2 is the inductor on the grid side, with the unit of H; C C is the filter capacitor, with the unit of F; s is the Laplace operator, with the unit of second -1 ; G i G(s) is the current regulator; The equivalent impedance of the phase-locked loop Z pll (s) is expressed as: ； Wherein: Z pll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ω; I ref is the command current, with the unit of A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G ( s ) is the current-loop transfer function of the double closed-loop control; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; s is the Laplace operator, with the unit of second -1 ; G i ( s ) is the current regulator; (Ⅰ-iii) Establish a dynamic coupling model of the phase-locked loop and the converter system after comprehensively considering the mutual influence of the control of the phase-locked loop and the inverter; The expression of the dynamic coupling model of the phase-locked loop and the converter system is: ； Wherein: Z O (s) is the equivalent impedance after comprehensively considering the mutual influence between the phase-locked loop and the inverter, with the unit of Ω; is the grid-connected voltage at the PCC point, with the unit of V; i g (s) is the grid-connected current, with the unit of A; Z inv ( s ) is the output impedance of the inverter, with the unit of Ω; Z pll ( s ) is the equivalent impedance of the phase-locked loop, with the unit of Ω; s is the Laplace operator, with the unit of second -1 ; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; I ref is the command current, with the unit of A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G i ( s ) is the current regulator.

3. The method for adaptively optimizing the parameters of the phase-locked loop under a weak power grid based on passivity according to claim 2, wherein: The transfer function of the current loop in the double closed-loop control G (s) is expressed as: ； Wherein: G i (s) is the current regulator; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; s is the Laplace operator, representing the complex frequency domain variable, with the unit of second -1 ; The equivalent transfer function of the phase-locked loop G pll (s) is expressed as: ； In the formula: k p is the proportionality of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, with the unit of seconds -1 ; V d is d the steady-state value of the shaft voltage, with the unit of V; s the Laplace operator, with the unit of seconds -1 ; j the imaginary unit, dimensionless; the center frequency, with the unit of rad / s; The equivalent admittance of the inverter Y inv (s) are respectively expressed as: ； In the formula: s is the Laplace operator, with the unit of second -1 ; L 1 is the inductor on the inverter side, with the unit of H; L 2 is the inductor on the grid side, with the unit of H; C is the filter capacitor, with the unit of F; G i (s) is the current regulator; The current regulator G i (s) has the following expression: ； In the formula: K p represents the proportional gain, dimensionless; K i Represents the integral gain, in seconds -1 ; s is the Laplace operator, with the unit of seconds -1 .

4. The method for adaptively optimizing the parameters of a phase-locked loop under a weak power grid based on passivity according to claim 1, characterized in that: The specific steps of the step (Ⅱ) include the following steps: (Ⅱ-i) Establish a strict passivity criterion for the system The strict passivity criterion of the system includes: （a） ； Wherein: ω min = 2π × 10 rad / s, ω max = 2π × 1000 rad / s; is the real part of the time-domain expression of Y sys ( jω ) in the equivalent admittance matrix of the inverter and grid interaction system; （b） ； where: Ω = [10 rad / s, 1000 rad / s] is the sub / super-synchronous frequency band; Y sys ( jω ) is the system equivalent admittance matrix, with the unit of S; is Y sys ( jω )'s conjugate transpose matrix, with the unit of S; det is the determinant calculation of the matrix, dimensionless; (c) Positive-sequence admittance passivity index The real-time value of which is continuously lower than the dynamic threshold of the positive-sequence admittance passivity index for three consecutive times, triggering the adjustment of the PLL parameters; (Ⅱ-ii) Online estimate the grid impedance Inject a small current perturbation Δ at the PCC point i , measure the voltage response Δ v , and calculate the grid impedance value; The calculation formula of the grid impedance value is: ； Where: Z grid (jω k ） is the power grid impedance value, with the unit of Ω; Δ v is the voltage response, with the unit of V; Δ i is the current perturbation, with the unit of A; j is the imaginary unit, dimensionless; ω k is the frequency at the PCC point, with the unit of rad / s; ω k covers 10 Hz to 1 kHz; the tiny current perturbation Δ i is a white noise signal of 0.5% rated current; (II-iii) Take the impedance value at the fundamental frequency , and calculate the equivalent short-circuit ratio; The calculation formula of the equivalent short-circuit ratio is: ； Where: ESCR is the equivalent short - circuit ratio, dimensionless; is the impedance value at the fundamental frequency, with the unit of Ω; S base is the system base capacity, with the unit of VA; (Ⅱ-iv) Construct a short-circuit ratio - sensitivity relationship matrix and a stability margin - sensitivity matrix; The expression of the stability margin - sensitivity matrix is: ； The expression of the short-circuit ratio - sensitivity relationship matrix is: ； In the formula: A m is the amplitude margin, in dB; is the phase margin, in °; ξ is the damping ratio, dimensionless; ω n is the bandwidth, in rad / s, S ξ (ESCR) is the damping ratio ξ The sensitivity coefficient of the equivalent short-circuit ratio ESCR, dimensionless; ξ* is to make the system satisfy at a specific ESCR ≥45° of the optimal damping ratio, dimensionless; is the bandwidth ω n The sensitivity coefficient of the equivalent short-circuit ratio ESCR, dimensionless; is the optimal bandwidth to make the system satisfy Am≥6dB at a specific ESCR, in rad / s.

5. The method for adaptively optimizing the parameters of a phase-locked loop under a weak power grid based on passivity according to claim 4, wherein: The forward admittance passivity index is calculated by the formula: ； In the formula: is to separate the positive sequence component from the admittance matrix; is the real part of the time-domain expression of the positive sequence admittance component; Y dq (jω k ), Y qd (jω k ) are the off-diagonal elements of the admittance matrix, representing the dq-axis coupling; ω k is the discrete frequency point taking the logarithmic uniform distribution.

6. The method for adaptively optimizing the parameters of the phase-locked loop under a weak power grid based on passivity according to claim 4, wherein: The positive-sequence admittance passivity index dynamic threshold The calculation formula is as follows: ； Wherein: η 0 = 0.01, corresponding to an ideal power grid with an infinite equivalent short-circuit ratio; is the current evaluation frequency point, with the unit of rad / s; is the base angular frequency, with the unit of rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless.

7. The method for adaptively optimizing the parameters of a phase-locked loop under a weak power grid based on passivity according to claim 4, wherein: The stability margin index is: amplitude margin A m ≥ 6 dB; phase margin ≥ 45°.

8. The method for adaptively optimizing the parameters of a phase-locked loop under a weak power grid based on passivity according to claim 1, wherein: The specific steps of the step (Ⅲ) include the following steps: (Ⅲ-i) Offline training and online look-up table When performing offline sweep frequency simulation training in the typical short-circuit ratio range, based on the sensitivity analysis results of the phase-locked loop parameters to the stability margin, preferentially perform dense sampling in the parameter direction with the greatest impact on the system stability, and encrypt the simulation step size in the sensitive interval of the equivalent short-circuit ratio change; after systematically traversing each operating point, record the optimal parameter combination that meets the requirements of both phase margin and amplitude margin and its sensitivity characteristics corresponding to each system equivalent short-circuit ratio ESCR, and generate a two-dimensional look-up table containing parameter adjustment rules; (Ⅲ-ii) Calculate the parameter adjustment amount The calculation formula of the parameter adjustment amount is: ； where: Δξ is the adjustment amount of the PLL damping ratio, dimensionless; Δω n is the adjustment amount of the PLL bandwidth, with the unit of rad / s; Δ ESCR is the difference between the real-time measured value and the reference value of the equivalent short-circuit ratio, dimensionless; , is the sensitivity of the damping ratio to the equivalent short-circuit ratio ESCR, dimensionless; , is the sensitivity of the bandwidth to the equivalent short-circuit ratio ESCR, with the unit of rad / s; (III-iii) Dynamically optimize the damping ratio of the phase-locked loop based on the sensitivity coefficient ξ and the phase-locked loop bandwidth ω n The damping ratio of the phase-locked loop based on the sensitivity coefficient ξ and the phase-locked loop bandwidth ω n are calculated by the following formula: ； where ξ old is the damping ratio of the original phase-locked loop, dimensionless; ω n,old is the original bandwidth, with the unit of rad / s; ξ new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; ω n,new * is the bandwidth of the phase-locked loop after dynamic optimization, with the unit of rad / s; Δξ is the adjustment amount of the phase-locked loop damping ratio, dimensionless; Δω n is the adjustment amount of the phase-locked loop bandwidth, with the unit of rad / s; (III - IV) The damping ratio ξ of the phase - locked loop after dynamic optimization new * and the phase - locked loop bandwidth ω n,new * Back - calculate the PI parameters of the phase - locked loop The calculation formula of the PI parameters of the phase-locked loop is: ； In the formula: K p is the proportionality of the PI controller of the phase-locked loop, dimensionless; K i is the integral coefficient of the PI controller of the phase-locked loop, with the unit of second -1 ; V d is the measured value of the current d-axis voltage, with the unit of V; ξ new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; ω n,new * is the bandwidth of the phase-locked loop after dynamic optimization, with the unit of rad / s.

9. The method for adaptively optimizing the parameters of a phase-locked loop under a weak power grid based on passivity according to claim 8, wherein: The typical short-circuit ratio range is ESCR ∈ [0.8, 3.0]; the sensitive interval of the equivalent short-circuit ratio change is the interval where the equivalent short-circuit ratio ESCR ∈ [1.0, 2.0]; the encrypted simulation step size is specifically set to a step size of 0.1.

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