A passive-based phase-locked loop parameter adaptive optimization method under a weak power grid

Abstract

The application discloses a passive-based phase-locked loop parameter adaptive optimization method under a weak power grid, which comprises the following steps: (I) a dynamic coupling model of a phase-locked loop and a converter system under a weak power grid is established, and the influence mechanism of the phase-locked loop parameters on the stability of the system is analyzed; (II) a real-time calculation method of an equivalent short-circuit ratio of the system is derived based on the passive theory, and a short-circuit ratio-parameter sensitivity relationship matrix is constructed; (III) the short-circuit ratio of the power grid is dynamically perceived, the bandwidth coefficient and the damping ratio parameters of the phase-locked loop are adaptively adjusted, and the harmonic oscillation or instability risk caused by the fixed parameters is eliminated. The application ensures the stable operation of the system under all working conditions, and can significantly improve the dynamic stability and robustness of the wind turbine under the working condition of the low short-circuit ratio weak power grid.

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 x =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:

[0005] A passivity-based phase-locked loop parameter adaptive optimization method under weak power grid conditions includes the following steps:

[0006] (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;

[0007] (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;

[0008] (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.

[0009] In the above technical solution, step (I) specifically includes the following steps:

[0010] (I-i) Establishing a mathematical model of the grid-connected current of the inverter based on the mathematical model of the grid-connected inverter control system;

[0011] The mathematical model expression of the grid-connected current is:

[0012] …(1)

[0013] Where: is the grid-connected current, in A; I ref is the command current, the unit is A; is the grid-connected voltage at the PCC point, in 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 inverter equivalent admittance;

[0014] (I-ii) Derivation of the inverter output impedance 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) expression;

[0015] …… (6)

[0016] Where: Z inv ( s ) is the output impedance of the inverter, in Ω; Y inv ( s ) is the inverter equivalent admittance, unit is S; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, in F; s is the Laplace operator, in seconds -1 ; G i (s) is a current regulator;

[0017] The equivalent impedance of the phase-locked loop Z pll The expression of (s) is:

[0018] …… (7)

[0019] Where: Z pll ( s ) is the equivalent impedance of the phase-locked loop, in Ω; I ref is the command current, the unit is 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 inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, in F; s is the Laplace operator, in seconds -1 ; G i ( s ) is a current regulator;

[0020] (I-III) Establish a dynamic coupling model of the phase-locked loop and converter system that comprehensively considers the mutual influence of the phase-locked loop and inverter control;

[0021] The expression of the dynamic coupling model of the phase-locked loop and converter system is:

[0022] ……(8)

[0023] Where: Z O (s) is the equivalent impedance after comprehensive consideration of the mutual influence between the phase-locked loop and the inverter, in Ω; is the grid-connected voltage at the PCC point, in V; i g (s) is the grid-connected current, in A; Z inv ( s ) is the inverter output impedance, in Ω; Z pll ( s ) is the equivalent impedance of the phase-locked loop, in Ω; s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; I ref is the command current, the unit is A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; Gi ( s ) is a current regulator.

[0024] In the above technical solution, the current loop transfer function of the dual closed-loop control is G The expression of (s) is:

[0025] …… (2)

[0026] Where: G i (s) is a current regulator; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; s is the Laplace operator, representing the complex frequency domain variable, in seconds -1 ;

[0027] The phase-locked loop equivalent transfer function G pll The expression of (s) is:

[0028] …… (3)

[0029] Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; V d for d Steady-state value of shaft voltage, in V; s is the Laplace operator, in seconds -1 ; j It is an imaginary unit and dimensionless; is the center frequency, in rad / s;

[0030] The inverter equivalent admittance Y inv The expressions of (s) are:

[0031] …… (4)

[0032] Where: s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in H; L2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; G i (s) is the current regulator.

[0033] The current regulator G i (s) The expression is:

[0034] ……(5)

[0035] Where: K p represents the proportional gain, dimensionless; K i Represents the integral gain, in seconds -1 ; s is the Laplace operator, the unit is second -1 .

[0036] In the above technical solution, the step (II) specifically includes the following steps:

[0037] (II-i) Establish strict passivity criteria for the system

[0038] The strict passivity criteria of the system include:

[0039] (a) …… (11)

[0040] Where: oh min =2π×10rad / s, oh max =2π×1000rad / s; is the equivalent admittance matrix of the inverter and grid interaction system Y sys ( yes )’s real part in the time domain expression;

[0041] (b) …… (12)

[0042] Where: Ω = [10rad / s, 1000rad / s] is the sub- / super-synchronous frequency band; Y sys ( yes ) is the system equivalent admittance matrix, unit is S; for Y sys ( yes ) is the conjugate transposed matrix of , in units of S; det is the determinant of the matrix, dimensionless;

[0043] (c) Positive sequence admittance passivity index The real-time value of is lower than the dynamic threshold of the positive sequence admittance passivity index The number of consecutive times is less than 3 times (positive sequence admittance passivity index The real-time value of is lower than the dynamic threshold of the positive sequence admittance passivity index for three consecutive times , triggering the phase-locked loop parameter adjustment);

[0044] (II-II) Online estimation of grid impedance

[0045] A small current perturbation Δ is injected into the PCC point i , measuring the voltage response Δ v , calculate the grid impedance value;

[0046] The calculation formula of the grid impedance value is:

[0047] ,……(17)

[0048] Where: Z grid (yes) k ） is the grid impedance value, in Ω; Δ v is the voltage response, in V; Δ i is the current disturbance, in A; j It is an imaginary unit and dimensionless; oh k is the frequency at the PCC point, in rad / s; oh k Covering 10Hz~1kHz; the small current disturbance Δ i It is a white noise signal of 0.5% rated current;

[0049] (II-III) Take the impedance value at the fundamental frequency , calculate the equivalent short-circuit ratio;

[0050] The calculation formula of the equivalent short-circuit ratio is:

[0051] …… (18)

[0052] 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 baseline capacity, in VA;

[0053] (II-IV) Construct the short-circuit ratio-sensitivity relationship matrix and the stability margin-sensitivity matrix;

[0054] The expression of the stability margin-sensitivity matrix is:

[0055] …… (19)

[0056] The expression of the short circuit ratio-sensitivity relationship matrix is:

[0057] …… (20)

[0058] Where: A m is the amplitude margin, in dB; is the phase margin, in degrees; x is the damping ratio, dimensionless; oh n is the bandwidth, in rad / s, S ξ (ESCR) is the damping ratio x Sensitivity coefficient to equivalent short circuit ratio ESCR, dimensionless; x* 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.

[0059] In the above technical solution, the positive sequence admittance passivity index The calculation formula is:

[0060] …… (13)

[0061] Where: 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; 、 is the off-diagonal element of the admittance matrix, representing the dq axis coupling; is a discrete frequency point with uniform logarithmic distribution.

[0062] In the above technical solution, the positive sequence admittance passivity index dynamic threshold The calculation formula is:

[0063] …… (16)

[0064] Where: η0=0.01, corresponding to the ideal power grid with infinite equivalent short-circuit ratio; is the current evaluation frequency, in rad / s; is the reference angular frequency, unit is rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless.

[0065] In the above technical solution, the stability margin index is: amplitude margin A m ≥6dB; phase margin ≥45°.

[0066] In the above technical solution, the step (III) specifically includes the following steps:

[0067] (III-i) Offline training and online table lookup

[0068] When conducting offline frequency sweep simulation training within a typical short-circuit ratio range, based on the sensitivity analysis results of the phase-locked loop parameters to the stability margin, intensive sampling is prioritized for the parameters that have the greatest impact on system stability, and the simulation step size is increased in the sensitive range of equivalent short-circuit ratio changes. After systematically traversing each operating point, the optimal parameter combination and its sensitivity characteristics corresponding to each system's equivalent short-circuit ratio (ESCR) that simultaneously meets the phase margin and amplitude margin requirements are recorded, and a two-dimensional lookup table containing parameter adjustment rules is generated.

[0069] (III-II) Calculation parameter adjustment

[0070] The calculation formula of the parameter adjustment amount is:

[0071] ……(twenty two)

[0072] Where: Right is the phase-locked loop damping ratio adjustment value, dimensionless; Give n is the phase-locked loop bandwidth adjustment value, in rad / s; ESCR is the difference between the real-time measurement 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 bandwidth to equivalent short circuit ratio ESCR, in rad / s;

[0073] (III-III) Dynamic optimization of the phase-locked loop damping ratio based on the sensitivity coefficient x and PLL bandwidth oh n

[0074] The sensitivity coefficient-based phase-locked loop damping ratio x and PLL bandwidth oh n The calculation formula is:

[0075] ……(twenty three)

[0076] Where, x old is the damping ratio of the original phase-locked loop, dimensionless; oh n,old is the original bandwidth, in rad / s; x new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; oh n,new * is the bandwidth of the phase-locked loop after dynamic optimization, in rad / s; Right is the phase-locked loop damping ratio adjustment value, dimensionless; Give n is the phase-locked loop bandwidth adjustment value, in rad / s;

[0077] (III-IV) Phase-locked loop damping ratio after dynamic optimization x new * and PLL bandwidth oh n,new * Inversely derive the PI parameters of the phase-locked loop

[0078] The PI parameter calculation formula of the phase-locked loop is:

[0079] ……(twenty four)

[0080] Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; V d For the current d Shaft voltage measurement value, in V; x new * is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; oh n,new * is the bandwidth of the phase-locked loop after dynamic optimization, in rad / s.

[0081] 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 equivalent short circuit ratio ESCR∈[1.0,2.0] interval; and the encryption simulation step size is specifically set to 0.1.

[0082] The beneficial effects of the present invention are:

[0083] The present invention provides a passivity-based adaptive optimization method for phase-locked loop parameters under weak power grid conditions, which is suitable for dynamic optimization of phase-locked loop parameters of wind turbines in low short-circuit ratio weak power grid scenarios, and is particularly suitable for distributed energy systems containing a high proportion of power electronic equipment. The present invention can significantly improve the dynamic stability and robustness of wind turbines under low short-circuit ratio weak power grid conditions.

[0084] The present invention introduces an adaptive adjustment algorithm into the phase-locked loop control loop, which dynamically optimizes the bandwidth coefficient ω of the phase-locked loop by sensing the changes in the grid short circuit ratio (ESCR) in real time. n The optimal PI control parameters are generated by inverse calculation based on the second-order system characteristics, which effectively solves the stability problem caused by the fixed-parameter phase-locked loop under weak grid conditions and enables the system to maintain a phase margin of at least 45° over the entire operating range. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is the topology diagram of the inverter circuit with adaptive adjustment algorithm;

[0086] Figure 2 It is the mathematical model of the grid-connected inverter control system;

[0087] Figure 3 It is the equivalent circuit of the grid-connected inverter system including a phase-locked loop;

[0088] Figure 4 is the grid current without adopting the dynamic tuning method of the phase-locked loop parameters;

[0089] Figure 5 It is the grid current using the dynamic tuning method of the phase-locked loop parameters.

[0090] For ordinary technicians in this field, other relevant drawings can be obtained based on the above drawings without any creative work. DETAILED DESCRIPTION

[0091] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention will be further described below with reference to the accompanying drawings and through specific implementation methods.

[0092] Example 1

[0093] based on Figure 1 The passivity-based phase-locked loop parameter adaptive optimization method under weak power grid conditions of the inverter circuit topology diagram including the adaptive adjustment algorithm shown in the figure includes the following steps:

[0094] (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. The specific steps include:

[0095] (I-i) According to Figure 2 The mathematical model of the grid-connected inverter control system shown is used to establish the mathematical model of the grid-connected current of the inverter;

[0096] The mathematical model of the grid-connected current is expressed as follows:

[0097] …(1)

[0098] Where: is the grid-connected current, in A; I ref is the command current, the unit is A; is the grid-connected voltage at the PCC point, in 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 inverter equivalent admittance;

[0099] The current loop transfer function of the dual closed-loop control is G The expression of (s) is:

[0100] …… (2)

[0101] Where: G i (s) is the current regulator, PI Controller; L 1 is the inductance on the inverter side, in Henry (H); L 2 is the inductance on the grid side, in Henry (H); C is the filter capacitor, the unit is Farad (F); s is the Laplace operator, representing the complex frequency domain variable, in seconds -1 .

[0102] The phase-locked loop equivalent transfer function G pll The expression of (s) is:

[0103] …… (3)

[0104] Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; Vd for d The steady-state value of the shaft voltage, in volts (V); s is the Laplace operator, in seconds -1 ; j It is an imaginary unit and dimensionless; is the center frequency in rad / s.

[0105] The inverter equivalent admittance Y inv The expressions of (s) are:

[0106] …… (4)

[0107] Where: s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in Henry (H); L 2 is the inductance on the grid side, in Henry (H); C is the filter capacitor, the unit is Farad (F); G i (s) is the current regulator.

[0108] The current regulator G i (s) The expression is:

[0109] ……(5)

[0110] Where: K p represents the proportional gain, dimensionless; K i Represents the integral gain, in seconds -1 ; s is the Laplace operator, the unit is second -1 .

[0111] (I-ii) Based on the expression of the mathematical model of the grid current in step (I-i) (Formula 1), the output impedance of the inverter is derived. Z inv (s) and the equivalent impedance of the phase-locked loop Z pll (s) expression;

[0112] The output impedance of the inverter Z inv The expression of (s) is:

[0113] …… (6)

[0114] Where: Z inv ( s ) is the output impedance of the inverter, in ohms (Ω); Y inv ( s ) is the inverter equivalent admittance, in Siemens (S); L 1 is the inductance on the inverter side, in Henry (H); L 2 is the inductance on the grid side, in Henry (H); C is the filter capacitor, the unit is Farad (F); s is the Laplace operator, the unit is second -1 ; G i (s) is the current regulator, which is a PI controller;

[0115] The equivalent impedance of the phase-locked loop Z pll The expression of (s) is:

[0116] …… (7)

[0117] Where: Z pll ( s ) is the equivalent impedance of the phase-locked loop, in ohms (Ω); I ref is the command current, in amperes (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 inductance on the inverter side, in Henry (H); L 2 is the inductance on the grid side, in Henry (H); C is the filter capacitor, the unit is Farad (F); s is the Laplace operator, the unit is second -1 ; G i ( s ) is a current regulator, is a PI controller;

[0118] (I-III) Establish a dynamic coupling model of the phase-locked loop and converter system that comprehensively considers the mutual influence of the phase-locked loop and inverter control;

[0119] The dynamic coupling model (equivalent impedance model) of the phase-locked loop and converter system is expressed as follows:

[0120] ……(8)

[0121] Where: Z O (s) is the equivalent impedance after comprehensive consideration of the mutual influence between the phase-locked loop and the inverter, in Ω; is the grid-connected voltage at the PCC point, in V; i g (s) is the grid-connected current, in A; Z inv ( s ) is the output impedance of the inverter, in Ω; Z pll ( s ) is the equivalent impedance of the phase-locked loop, in Ω; s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; I ref is the command current, the unit is A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G i ( s ) is a current regulator;

[0122] Grid impedance Z g The expression of (s) is:

[0123] …… (9)

[0124] Where: Z g (s) is the grid impedance, in Ω; R g is the resistance of the grid line, in Ω; L g is the inductance of the grid line, in H; C g is the capacitance of the grid line, in F;

[0125] From this, we can get the equivalent circuit diagram corresponding to the equivalent impedance model as follows Figure 3 As shown, it can be seen that any admittance model that ignores the dynamics of the phase-locked loop will lead to serious errors under weak power grid conditions.

[0126] 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 the wide-frequency domain equivalent impedance model of the grid-connected inverter can be equivalent to the parallel impedance model after comprehensively considering the interaction between the phase-locked loop and the control. 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: due to Z O (s) is Z inv (s) and Z pll (s) are strongly coupled in parallel, and from Equation (8) we can see that Z pll (s) is negative impedance, Z pll The equivalent transfer function G of the phase-locked loop in (s) pll (s) presents low-pass filtering characteristics when the frequency is higher than the fundamental frequency. The larger the bandwidth, the higher the 1 / G pll The amplitude of (s) is lower at high frequencies, so Z pll The amplitude of (s) will be lower and the phase angle will be smaller, which will reduce the output impedance Z O The amplitude and phase angle of (s) will reduce the system stability margin and may even cause system instability. Therefore, if a fixed phase-locked loop bandwidth parameter is used, it will not be able to meet the stability requirements of all working conditions.

[0127] (II) Establish the system passivity criterion, derive the calculation method of the system equivalent short-circuit ratio, and construct the short-circuit ratio-parameter sensitivity relationship matrix, which specifically includes the following steps:

[0128] (II-i) Establishing the system passivity criterion

[0129] The dynamic coupling model of the phase-locked loop and converter system is converted into the equivalent admittance matrix of the inverter and grid interaction system. The expression of the equivalent admittance matrix is:

[0130] …… (10)

[0131] Where: Y sys ( yes ) is the equivalent admittance matrix of the inverter and grid interaction system; Y O ( yes ) is the equivalent admittance after considering the mutual influence between the phase-locked loop and the inverter; Y g ( yes ) is the grid admittance;

[0132] for Y sys ( yes ), the strict passivity criterion of the system must simultaneously meet the following three conditions:

[0133] (a) …… (11)

[0134] Where: ω min =2π×10rad / s,ω max =2π×1000rad / s; is the equivalent admittance matrix of the inverter and grid interaction system Y sys ( yes )’s real part in the time domain expression;

[0135] (b) …… (12)

[0136] Where: Ω = [10rad / s, 1000rad / s] is the sub- / super-synchronous frequency band; Y sys ( yes ) is the system equivalent admittance matrix (including the phase-locked loop and grid impedance coupling effects), in Siemens (S); for Y sys ( yes ) is the conjugate transposed matrix of , in Siemens (S); det is the determinant of the matrix, dimensionless;

[0137] (c) Positive sequence admittance passivity index The real-time value of is lower than the dynamic threshold of the positive sequence admittance passivity index The number of consecutive times is less than 3 times (positive sequence admittance passivity index The real-time value of is lower than the dynamic threshold of the positive sequence admittance passivity index for three consecutive times , triggering the phase-locked loop parameter adjustment);

[0138] The positive sequence admittance passivity index The calculation formula is:

[0139] …… (13)

[0140] Where: 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; 、 is the off-diagonal element of the admittance matrix, representing the dq axis coupling; To take the discrete frequency points with uniform logarithmic distribution;

[0141] Admittance matrix Y(jω k ) To obtain the result, we take 20 frequency points that are evenly distributed on the logarithm and calculate the admittance for each frequency point;

[0142] … (14)

[0143] Y pos (y) The calculation formula is:

[0144] … (15)

[0145] In the formula: Y dd (y) k ) is the admittance (self-admittance) of the d-axis voltage to the d-axis current, with the unit of Siemens (S);

[0146] Y qq (y) k ) is the admittance (self-admittance) of the q-axis voltage to the q-axis current, with the unit of Siemens (S);

[0147] Y dq (y) k ) is the admittance (mutual admittance) of the q-axis voltage to the d-axis current, with the unit of Siemens (S);

[0148] Y qd (y) k ) is the admittance (mutual admittance) of the d-axis voltage to the q-axis current, with the unit of Siemens (S).

[0149] The positive sequence admittance passivity index dynamic threshold The calculation formula is:

[0150] … (16)

[0151] In the formula: η0=0.01, corresponding to an ideal power grid with an equivalent short-circuit ratio of infinity; is the current evaluation frequency, with the unit of rad / s; is the reference angular frequency (taking the power frequency), with the unit of rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless;

[0152] The subsequent is carried out on the basis of passivity. If the passivity is satisfied, the phase-locked loop coefficient does not need to be adjusted. If any one of the passivity criteria is not satisfied, the phase-locked loop parameter adjustment is triggered. Then, the phase-locked loop parameter that needs to be adjusted is calculated according to the constructed short-circuit ratio-parameter sensitivity relationship matrix and the stability margin sensitivity matrix.

[0153] (II-ii) online estimate grid impedance

[0154] inject a small current disturbance Δ at the PCC (point of common coupling in power system) i measure the voltage response Δ v calculate the grid impedance value;

[0155] The formula for calculating the grid impedance value is:

[0156] , … (17)

[0157] In the formula: Z grid (yes) k ） is the grid impedance value, with units of Ω; Δ v is the voltage response, with units of V; Δ i is the current disturbance, with units of A; j is the imaginary unit, dimensionless; oh k is the frequency at the PCC, with units of rad / s; oh k covers 10 Hz ~ 1 kHz;

[0158] The small current disturbance Δ i is a white noise signal of 0.5% rated current;

[0159] (II-iii) take the impedance value at the fundamental frequency calculate the equivalent short circuit ratio;

[0160] The formula for calculating the equivalent short circuit ratio is:

[0161] … (18)

[0162] In the formula: ESCR is the equivalent short circuit ratio, dimensionless;

[0163] is the impedance value at the fundamental frequency, with units of Ω, calculated according to formula (17);

[0164] S base is the system reference capacity, with units of VA;

[0165] If trigger data re-sampling;

[0166] If ESCR > 10, determine that the measurement is abnormal (may be close to an ideal voltage source).

[0167] (II-IV) Constructing the short-circuit ratio-sensitivity relationship matrix and the stability margin-sensitivity relationship matrix

[0168] Defining the Phase-Locked Loop Transfer Function G pll (s) stability margin index, based on the phase-locked loop transfer function G pll (s) The stability margin index establishes the short circuit ratio-sensitivity relationship matrix;

[0169] The phase-locked loop transfer function G pll The stability margin index of (s) is:

[0170] Amplitude margin A m ≥6dB; phase margin ≥45°;

[0171] The expression of the stability margin-sensitivity matrix is:

[0172] …… (19)

[0173] The expression of the short circuit ratio-sensitivity relationship matrix is:

[0174] …… (20)

[0175] Where: A m is the amplitude margin, in dB; is the phase margin, in degrees; x is the damping ratio, dimensionless; oh n is the bandwidth in rad / s, is the damping ratio x Sensitivity coefficient to equivalent short circuit ratio ESCR, dimensionless; x* 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, in rad / s;

[0176] (III) When the system 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 short-circuit ratio of the power grid. Specifically, the following steps are included:

[0177] (III-i) Offline training and online table lookup

[0178] When conducting offline frequency sweep simulation training within a typical short-circuit ratio range, based on the sensitivity analysis results of the phase-locked loop parameters to the stability margin, intensive sampling is prioritized for the parameter directions that have the greatest impact on system stability, and the simulation step size is increased in the sensitive range of equivalent short-circuit ratio changes. After systematically traversing each operating point, the optimal parameter combination and its sensitivity characteristics corresponding to each system's equivalent short-circuit ratio (ESCR) that simultaneously meets the phase margin and amplitude margin requirements are recorded, and a two-dimensional lookup table containing parameter adjustment rules is generated. During actual online operation, the system only needs to directly obtain parameter adjustment instructions based on the real-time measured ESCR value through bilinear interpolation of the pre-stored lookup table, completely avoiding real-time complex calculations and ensuring the rapid response of the control system.

[0179] The typical short circuit ratio range is ESCR∈[0.8,3.0];

[0180] The sensitive interval of the equivalent short circuit ratio change is the interval of the equivalent short circuit ratio ESCR∈[1.0,2.0]; the encryption simulation step size is specifically set to 0.1;

[0181] At the same time, the step size is relaxed to 0.3 in the low sensitivity area (equivalent short circuit ratio ESCR>2.5) during the frequency sweep simulation;

[0182] The two-dimensional lookup table satisfies the following expression conditions:

[0183] ……(twenty one)

[0184] Where: is the rate of change calculated by the difference of damping ratios of adjacent ESCR points through the lookup table; Damping ratio obtained for offline training x -Equivalent short circuit ratio ESCR sensitivity function theoretical value; the two-dimensional lookup table meets the conditions to ensure that the online lookup value is consistent with the theoretical sensitivity; the two-dimensional lookup table is x 、 oh n Sensitivity lookup table;

[0185] (III-II) Calculation parameter adjustment

[0186] The calculation formula of the parameter adjustment amount is:

[0187] ……(twenty two)

[0188] Where: Right is the phase-locked loop damping ratio adjustment value, dimensionless; Give n is the phase-locked loop bandwidth adjustment value, in rad / s; ESCRis the difference between the real-time measurement value and the reference value of the equivalent short-circuit ratio, dimensionless;

[0189] , is the sensitivity of the damping ratio to the equivalent short-circuit ratio ESCR (obtained by looking up the table), dimensionless; , is the sensitivity of bandwidth to equivalent short circuit ratio ESCR, in rad / s;

[0190] (III-III) Dynamic optimization of the phase-locked loop damping ratio based on the sensitivity coefficient x and PLL bandwidth oh n ;

[0191] Phase-locked loop damping ratio based on sensitivity coefficient x and PLL bandwidth oh n The calculation formula is:

[0192] ……(twenty three)

[0193] Where, is the damping ratio of the original phase-locked loop, dimensionless; is the original bandwidth, in rad / s; is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; is the bandwidth of the phase-locked loop after dynamic optimization, in rad / s; is the phase-locked loop damping ratio adjustment value, dimensionless; is the phase-locked loop bandwidth adjustment value, in rad / s;

[0194] (III-IV) Phase-locked loop damping ratio after dynamic optimization x new * and PLL bandwidth oh n,new * Inversely deduce the PI parameters of the phase-locked loop:

[0195] The PI parameter calculation formula of the phase-locked loop is:

[0196] ……(twenty four)

[0197] Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; V d For the current d Shaft voltage measurement value, in V; is the damping ratio of the phase-locked loop after dynamic optimization, dimensionless; is the bandwidth of the phase-locked loop after dynamic optimization, in rad / s.

[0198] like Figure 4 As shown in the figure, when the dynamic tuning method of the phase-locked loop parameters is not adopted, the grid current oscillates significantly (THD rises to 18.7%) after the grid-connected inverter encounters a sudden change in the short-circuit ratio at 0.3s. Figure 5 The current waveform is shown after the proposed dynamic tuning method is applied at 0.36 seconds under the same operating conditions. Experimental results show that after adaptive parameter adjustment, the total harmonic distortion (THD) of the current is reduced to below 2.3%, and the transient regulation time is shortened to 15ms, meeting the transient response requirement for fault ride-through (<50ms) specified in GB / T 19963-2021. Furthermore, system robustness is improved by 87.7% (as assessed according to the IEEE 1547-2018 standard).

[0199] The applicant declares that the above is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention fall within the scope of protection and disclosure of the present invention.

Claims

1. A passivity-based adaptive optimization method for phase-locked loop parameters in weak power grids, characterized by: The following steps are involved: (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. The specific steps include: (I-i) Establishing a mathematical model of the grid-connected current of the inverter based on the mathematical model of the grid-connected inverter control system; (I-ii) Derivation of the inverter output impedance 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) expression; (I-III) Establish a dynamic coupling model of the phase-locked loop and converter system that comprehensively considers the mutual influence of the phase-locked loop and inverter control; (II) Establishing the system passivity criterion, and deriving the real-time calculation method of the system equivalent short-circuit ratio based on the passivity theory, constructing the short-circuit ratio-parameter sensitivity relationship matrix and the stability margin sensitivity matrix, which specifically includes the following steps: (II-i) Establish strict passivity criteria for the system The strict passivity criteria of the system include: （a） Where: ω min =2π×10rad / s, ω max =2π×1000rad / s; is the equivalent admittance matrix of the inverter and grid interaction system Y sys ( jω )’s real part in the time domain expression; （b） Where: Ω = [10rad / s, 1000rad / s] is the sub- / super-synchronous frequency band; Y sys ( jω ) is the system equivalent admittance matrix, the unit is S; for Y sys ( jω ) is the conjugate transposed matrix of , in units of S; det is the determinant of the matrix, dimensionless; (c) Positive sequence admittance passivity index The real-time value of is lower than the dynamic threshold of the positive sequence admittance passivity index for three consecutive times , trigger the phase-locked loop parameter adjustment; (II-II) Online estimation of grid impedance A small current perturbation Δ is injected into the PCC point i , measuring the voltage response Δ v , calculate the grid impedance value; The calculation formula of the grid impedance value is: ， 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 disturbance, in A; j It 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: Where: ESCR is the equivalent short-circuit ratio, dimensionless; is the impedance value at the fundamental frequency, in Ω; S base is the system baseline 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: The expression of the short circuit ratio-sensitivity relationship matrix is: 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 ≥ 6 dB under a specific ESCR, in rad / s; (III) When any 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 short-circuit ratio of the power grid. Specifically, the following steps are included: (III-i) Offline training and online table lookup When conducting offline frequency sweep simulation training within a typical short-circuit ratio range, based on the sensitivity analysis results of the phase-locked loop parameters to the stability margin, intensive sampling is prioritized for the parameters that have the greatest impact on system stability, and the simulation step size is increased in the sensitive range of equivalent short-circuit ratio changes. After systematically traversing each operating point, the optimal parameter combination and its sensitivity characteristics corresponding to each system's equivalent short-circuit ratio (ESCR) that simultaneously meets the phase margin and amplitude margin requirements are recorded, and a two-dimensional lookup table containing parameter adjustment rules is generated. (III-II) Calculation parameter adjustment The calculation formula of the parameter adjustment amount is: Where: Δξ is the phase-locked loop damping ratio adjustment, dimensionless; Δω n is the phase-locked loop bandwidth adjustment value, in rad / s; Δ ESCR is the difference between the real-time measurement 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 bandwidth to equivalent short circuit ratio ESCR, in rad / s; (III-III) Dynamic optimization of the phase-locked loop damping ratio based on the sensitivity coefficient ξ and PLL bandwidth ω n The sensitivity coefficient-based phase-locked loop damping ratio ξ and PLL bandwidth ω n The calculation formula is: Where, ξ old is the damping ratio of the original phase-locked loop, dimensionless; ω n,old is the original bandwidth, in 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, in rad / s; Δξ is the phase-locked loop damping ratio adjustment, dimensionless; Δω n is the phase-locked loop bandwidth adjustment value, in rad / s; (III-IV) Phase-locked loop damping ratio after dynamic optimization ξ new * and PLL bandwidth ω n,new * Inversely deduce the PI parameters of the phase-locked loop; The PI parameter calculation formula of the phase-locked loop is: Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; V d For the current d Shaft voltage measurement value, in 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, in rad / s.

2. The passivity-based adaptive optimization method for phase-locked loop parameters in a weak power grid according to claim 1, characterized in that: The mathematical model expression of the grid-connected current is: Where: is the grid-connected current, in A; I ref is the command current, the unit is A; v PCC (s) is the grid-connected voltage at the PCC point, in 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 inverter equivalent admittance; The output impedance of the inverter Z inv The expression of (s) is: Where: Z inv ( s ) is the output impedance of the inverter, in Ω; Y inv ( s ) is the inverter equivalent admittance, unit is S; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; s is the Laplace operator, in seconds -1 ; G i (s) is a current regulator; The equivalent impedance of the phase-locked loop Z pll The expression of (s) is: Where: Z pll ( s ) is the equivalent impedance of the phase-locked loop, in Ω; I ref is the command current, the unit is 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 inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; s is the Laplace operator, in seconds -1 ; G i ( s ) is a current regulator; The expression of the dynamic coupling model of the phase-locked loop and converter system is: Where: Z O (s) is the equivalent impedance after comprehensive consideration of the mutual influence between the phase-locked loop and the inverter, in Ω; is the grid-connected voltage at the PCC point, in V; i g (s) is the grid-connected current, in A; Z inv ( s ) is the inverter output impedance, in Ω; Z pll ( s ) is the equivalent impedance of the phase-locked loop, in Ω; s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; I ref is the command current, the unit is A; G pll ( s ) is the equivalent transfer function of the phase-locked loop; G i ( s ) is a current regulator.

3. The passivity-based adaptive optimization method for phase-locked loop parameters in a weak power grid according to claim 2, characterized in that: The current loop transfer function of the dual closed-loop control is G The expression of (s) is: Where: G i (s) is a current regulator; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; s is the Laplace operator, representing the complex frequency domain variable, in seconds -1 ; The phase-locked loop equivalent transfer function G pll The expression of (s) is: Where: k p is the ratio of the phase-locked loop PI controller, dimensionless; k i is the integral coefficient of the phase-locked loop PI controller, in seconds -1 ; V d for d Steady-state value of shaft voltage, in V; s is the Laplace operator, in seconds -1 ; j It is an imaginary unit and dimensionless; is the center frequency, in rad / s; The inverter equivalent admittance Y inv The expressions of (s) are: Where: s is the Laplace operator, in seconds -1 ; L 1 is the inductance on the inverter side, in H; L 2 is the inductance on the grid side, in H; C is the filter capacitor, unit is F; G i (s) is a current regulator; The current regulator G i (s) The expression is: Where: K p represents the proportional gain, dimensionless; K i Represents the integral gain, in seconds -1 ; s is the Laplace operator, in seconds -1 .

4. The passivity-based adaptive optimization method for phase-locked loop parameters in a weak power grid according to claim 1, characterized in that: The positive sequence admittance passivity index The calculation formula is: Where: 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; 、 is the off-diagonal element of the admittance matrix, representing the dq axis coupling; is a discrete frequency point with uniform logarithmic distribution.

5. The passivity-based adaptive optimization method for phase-locked loop parameters in a weak power grid according to claim 1, characterized in that: The positive sequence admittance passivity index dynamic threshold The calculation formula is: Where: η 0=0.01, corresponding to an ideal power grid with infinite equivalent short-circuit ratio; is the current evaluation frequency, in rad / s; is the reference angular frequency, unit is rad / s; ESCR is the system equivalent short-circuit ratio, dimensionless.

6. The passivity-based phase-locked loop parameter adaptive optimization method under weak power grid according to claim 1, characterized in that: The stability margin index is: amplitude margin A m ≥6dB; phase margin ≥45°.

7. The passivity-based adaptive optimization method for phase-locked loop parameters in a weak power grid according to claim 1, characterized in that: The typical short circuit ratio range is ESCR∈[0.8,3.0]; the equivalent short circuit ratio change sensitive interval is the equivalent short circuit ratio ESCR∈[1.0,2.0] interval; the encryption simulation step size is specifically set to 0.1.

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