Permanent magnet direct drive wind turbine impedance modeling method and system based on complex vector

Abstract

The application discloses a kind of permanent magnet direct drive fan impedance modeling method and system based on complex vector, which comprises: the transfer function frequency domain transformation rule between the transformation matrix of complex plane under complex vector and stationary coordinate system and conjugate base vector input and output is established;Based on the transformation matrix of complex plane under complex vector and stationary coordinate system and the transfer function frequency domain transformation rule, the main circuit complex vector model and control circuit model of permanent magnet direct drive fan are established;According to the main circuit complex vector model and the control circuit model, the PMSG equivalent impedance model considering the multi-frequency coupling characteristics is established.The application considers the influence of frequency coupling characteristics on permanent magnet direct drive fan impedance modeling, based on complex vector to characterize the multi-input multi-output characteristics caused by frequency coupling characteristics, improve the accuracy of permanent magnet direct drive fan impedance modeling, and then improve the accuracy of the stability determination of the power grid accessed by permanent magnet direct drive fan.

Description

Technical Field

[0001] This invention relates to the field of power grid control technology, and in particular to a method and system for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors. Background Technology

[0002] New energy sources are gradually replacing traditional fossil fuels and becoming an important part of future energy. Permanent magnet synchronous generators (PMSGs) are widely used in onshore and offshore wind farms due to their high reliability, high efficiency, and high power density. However, the large-scale integration of new energy equipment is leading to the evolution of power systems towards high-proportion new energy power systems, with the "dual-high" trend becoming increasingly apparent. In high-proportion new energy power systems, the control methods and structure of the power grid undergo significant changes. The complex control effects of new energy power generation devices intertwine with the characteristics of a weak power grid, resulting in a wider range of power system oscillation frequencies and entirely new characteristics, highlighting stability issues.

[0003] Impedance analysis has become an effective method for analyzing and solving oscillations in new energy power electronic devices due to its clear physical meaning and convenient modeling. However, among the commonly used impedance modeling methods, impedance modeling in the dq coordinate system requires the use of nonlinear Park transform and its inverse transform, which increases the analytical complexity, and the resulting impedance matrix lacks physical meaning. Although sequence component impedance modeling considers the interaction of multiple frequencies, it requires convolution operations of different frequencies in the frequency domain, resulting in a huge computational burden. More importantly, research results show that due to the asymmetry of the dq axis control of wind power converters, when a voltage disturbance of a specific frequency is injected into the interconnected system, in addition to generating current response components of the same frequency, current response components of different frequencies will also be generated, giving permanent magnet direct-drive wind turbines frequency coupling characteristics. The frequency coupling characteristics will change the original single-input single-output (SISO) characteristic of the system to a multi-input multi-output (MIMO) characteristic. At this time, the impedance model with positive and negative sequence decoupling and the single-input single-output stability criterion can no longer accurately determine the system stability. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors. By using complex vectors to characterize the multi-input multi-output characteristics caused by frequency coupling, the accuracy of impedance modeling of permanent magnet direct-drive wind turbines is improved, thereby improving the accuracy of determining the stability of the power grid connected to the permanent magnet direct-drive wind turbine.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] This invention provides an impedance modeling method for permanent magnet direct-drive wind turbines based on complex vectors, the method comprising the following steps:

[0007] Establish the frequency domain transformation rule of the transfer function between the transformation matrix of the complex vector and the stationary coordinate system and the input and output of the conjugate basis vectors in the complex plane;

[0008] Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, a complex vector model of the main circuit of the permanent magnet direct-drive fan is established.

[0009] Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane, a control circuit model of the permanent magnet direct drive fan is established.

[0010] Based on the complex vector model of the main circuit and the control circuit model, a PMSG equivalent impedance model considering multi-frequency coupling characteristics is established.

[0011] Optionally, establish the frequency domain transformation rule of the transfer function between the transformation matrix and the input / output conjugate basis vectors of the complex vector in the complex plane and the stationary coordinate system, specifically including:

[0012] The transformation matrix between the complex vector in the complex plane and the stationary coordinate system is established as follows:

[0013]

[0014] in, Let x be the two-dimensional basis vector output by the αβ coordinate system in the complex plane. p and x n These are the positive and negative rotation vectors output from the αβ coordinate system in the complex plane, respectively, x p and x n Mutually conjugate, x a x b and x c is the three-dimensional coordinate in a stationary coordinate system, and j represents the imaginary number;

[0015] The frequency domain relationship between the input and output quantities of a rotating coordinate system in the complex domain is established as follows:

[0016]

[0017] in, Y is a two-dimensional basis vector output in the dq coordinate system under the complex plane. dq (s) and The positive and negative rotation vectors output by the dq coordinate system in the complex plane, respectively, Y dq (s) and Mutually conjugate, G d1 (s), G d2 (s), These are the transfer functions of the input and output of a two-dimensional dynamic system in the dq coordinate system in the complex plane. U is a two-dimensional basis vector input in the dq coordinate system under the complex plane. dq (s), Let be the forward rotation vector and the reverse rotation vector, respectively, input from the dq coordinate system in the complex plane, and s be the differential operator;

[0018] Based on signal analysis and Hilbert transform, the transfer function relationship between the input complex vector and the output complex vector in the frequency domain is established as follows:

[0019]

[0020] in, Y is the two-dimensional basis vector output by the two-phase stationary coordinate system in the complex plane. p (s) and Y n (s) represent the positive and negative rotation vectors output by the two-phase stationary coordinate system in the complex plane, respectively, G d1 (s-jω1), G d2 (s-j2ω1) Let ω1 be the transfer functions of the input and output of the two-dimensional dynamic system in the complex plane in a two-phase stationary coordinate system, respectively: ω1 is the fundamental frequency angular velocity. The initial fundamental frequency voltage phase angle, U is a two-dimensional basis vector input in a two-phase stationary coordinate system in the complex plane. p (s) and U n (s) represent the forward rotation vector and the reverse rotation vector, respectively, input to the two-phase stationary coordinate system in the complex plane.

[0021] Optionally, the main circuit complex vector model includes: the main circuit complex vector model of the permanent magnet direct-drive wind turbine, the complex vector model of the machine-side converter, and the complex vector model of the grid-side converter;

[0022] Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, a complex vector model of the main circuit of the permanent magnet direct-drive fan is established, specifically including:

[0023] Establish the dynamic equations of a permanent magnet direct-drive synchronous generator in a rotating coordinate system;

[0024] The dynamic equations are linearized using small-signal methods to obtain a linearized small-signal model of the permanent magnet direct-drive synchronous generator.

[0025] Based on the frequency domain transformation rule of the transfer function, and according to the linearized small-signal model of the permanent magnet direct-drive synchronous generator, the linearized small-signal model of the permanent magnet direct-drive synchronous generator represented by a complex vector is determined as the complex vector model of the permanent magnet direct-drive synchronous generator.

[0026] Establish the main circuit equations of the generator-side converter and the grid-side converter of the permanent magnet direct-drive synchronous generator;

[0027] Based on the transformation matrix between complex vectors in the complex plane and the stationary coordinate system, the main circuit equations of the machine-side converter and the grid-side converter, expressed in complex vectors, are determined according to the main circuit equations of the machine-side converter and the grid-side converter, respectively.

[0028] Small-signal linearization is performed on the main circuit equations of the machine-side converter and the grid-side converter, respectively, to obtain the linearized small-signal model of the machine-side converter, which is used as the complex vector model of the machine-side converter, and the linearized small-signal model of the grid-side converter, which is used as the complex vector model of the grid-side converter.

[0029] Optionally, the control circuit model includes a complex vector model of the machine-side control circuit and a complex vector model of the grid-side control circuit;

[0030] The control circuit model of the permanent magnet direct-drive fan is established based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, specifically including:

[0031] Establish a linearized small-signal model of the machine-side control circuit in the dq coordinate system;

[0032] Based on the frequency domain transformation rule of the transfer function, and according to the linearized small-signal model of the machine-side control circuit in the dq coordinate system, the linearized small-signal model of the machine-side control circuit represented by a complex vector is determined, which serves as the complex vector model of the machine-side control circuit.

[0033] Establish a linearized small-signal model of the grid-side control circuit in the dq coordinate system;

[0034] Establish a linearized small-signal model of the phase-locked loop;

[0035] By substituting the linearized small-signal model of the phase-locked loop into the linearized small-signal model of the grid-side control circuit in the dq coordinate system, a linearized small-signal model of the grid-side control circuit considering the dynamic characteristics of the phase-locked loop is obtained.

[0036] Based on the frequency domain transformation rules of the transfer function, and according to the linearized small-signal model of the grid-side control circuit considering the dynamic characteristics of the phase-locked loop, the linearized small-signal model of the grid-side control circuit represented by a complex vector is determined as the complex vector model of the grid-side control circuit.

[0037] Optionally, the PMSG equivalent impedance model includes the DC-side impedance model of the machine-side converter and the AC-side impedance model of the grid-side converter;

[0038] Based on the complex vector model of the main circuit and the control circuit model, a PMSG equivalent impedance model considering multi-frequency coupling characteristics is established, specifically including:

[0039] Based on the main circuit complex vector model and the control circuit model, the DC-side impedance model of the machine-side converter is established as follows:

[0040]

[0041] in:

[0042]

[0043]

[0044]

[0045] Z dc (s) represents the DC-side impedance model of the machine-side converter, v dc0 For DC side voltage, d sis d svs Z sw h1(s) and h2(s) are variables used to simplify the formulas during the model building process, I is the identity matrix, and v sp0 v sno i sp0 i sn0 D sp0 D sn0 These are the initial values ​​of the voltage, current, and machine-side converter switch duty cycle at the output of the permanent magnet direct-drive synchronous motor, respectively, expressed as complex vectors representing the forward and reverse rotating vectors, i. dc0 Where m is the DC side current, L is the machine side line inductance, and m is the DC side current. sf H is the modulation amplitude ratio of the machine-side converter. i1 K represents the outer loop PI control parameters of the machine-side converter. g ω1 is the decoupling coefficient of the dq axis of the inner ring of the machine-side converter, ω1 is the fundamental frequency angular velocity, and ω s For synchronous speed, L sd For the PMSG stator-side d-axis inductance, L sq For PMSG stator-side q-axis inductance;

[0046] Based on the main circuit complex vector model and the control circuit model, the AC side impedance model of the grid-side converter is established as follows:

[0047]

[0048]

[0049]

[0050] K1=(Id dc1 g1) -1 ;

[0051] d vs =d vs1 +d vs2 +d vs3 ;

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Among them, Z wac (s) represents the AC side impedance model of the grid-side converter, Z wpp Z wpn Z wnp Z wnn These represent the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance, respectively. I is the identity matrix, and v dc0 For DC voltage measurement, K pvs K pis K1, d vs d vs1 d vs2 d vs3 g1, d is d dc1 g2 are variables used to simplify formulas during model building, and D p0 D n0 L represents the initial values ​​of the forward and reverse rotating vectors, expressed in complex vector form, for the duty cycle of the grid-side converter. f For grid-side line inductance;

[0060] v pccd0 Let be the initial value of the AC voltage at point PCC. The initial fundamental frequency voltage phase angle, m f For the modulation amplitude ratio of the grid-side converter, T pll Let i be the transfer function of the phase-locked loop with respect to the quadrature-axis voltage disturbance. sd0 The initial value of the direct-axis output current of the permanent magnet direct-drive synchronous generator, H dH i2 K m These are the outer loop PI control parameters, inner loop PI control parameters, and inner loop dq-axis decoupling coefficients of the grid-side converter, respectively. cdc The equivalent impedance of the machine-side system and DC capacitor, i p0 i n0 These are the initial values ​​of the forward and reverse rotating vectors, respectively, representing the current at the PCC point of the wind turbine in complex vector form.

[0061] A complex vector-based impedance modeling system for permanent magnet direct-drive wind turbines, wherein the system is applied to the aforementioned method, and the system comprises:

[0062] The transformation relationship determination module is used to establish the frequency domain transformation rules of the transfer function between the transformation matrix and the input and output of the conjugate basis vectors of the complex vector in the complex plane and the stationary coordinate system.

[0063] The main circuit complex vector model establishment module is used to establish the main circuit complex vector model of the permanent magnet direct drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane.

[0064] The control circuit model building module is used to build a control circuit model of a permanent magnet direct-drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane.

[0065] The PMSG equivalent impedance model establishment module is used to establish a PMSG equivalent impedance model considering multi-frequency coupling characteristics based on the main circuit complex vector model and the control circuit model.

[0066] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0067] A computer-readable storage medium having a computer program stored thereon, which, when executed, implements the above-described method.

[0068] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0069] This invention discloses a method and system for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors. The method includes: establishing a frequency domain transformation rule for the transfer function between the transformation matrix of the complex vector and the stationary coordinate system in the complex plane and the input / output of the conjugate basis vectors; establishing a complex vector model of the main circuit of the permanent magnet direct-drive wind turbine based on the transformation matrix of the complex vector and the stationary coordinate system in the complex plane and the frequency domain transformation rule of the transfer function; establishing a control circuit model of the permanent magnet direct-drive wind turbine based on the transformation matrix of the complex vector and the stationary coordinate system in the complex plane and the frequency domain transformation rule of the transfer function; and establishing a PMSG equivalent impedance model considering multi-frequency coupling characteristics based on the main circuit complex vector model and the control circuit model. This invention considers the influence of frequency coupling characteristics on the impedance modeling of permanent magnet direct-drive wind turbines, and improves the accuracy of impedance modeling of permanent magnet direct-drive wind turbines by using complex vectors to characterize the multi-input multi-output characteristics caused by frequency coupling characteristics, thereby improving the accuracy of stability determination of the power grid connected to the permanent magnet direct-drive wind turbine.

[0070] The embodiments of the present invention also solve the problems of large computational load, lack of physical meaning of impedance matrix, and failure to consider frequency coupling characteristics in the existing impedance method for permanent magnet direct drive wind turbines. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0072] Figure 1 A flowchart illustrating an impedance modeling method for permanent magnet direct-drive wind turbines based on complex vectors, provided as an embodiment of the present invention;

[0073] Figure 2 A diagram showing the relationship between a stationary coordinate system and a rotating coordinate system provided in an embodiment of the present invention;

[0074] Figure 3 This is a structural diagram of a permanent magnet direct-drive fan system provided in an embodiment of the present invention;

[0075] Figure 4 This is a control block diagram of the PMSG machine-side converter provided in an embodiment of the present invention;

[0076] Figure 5 This is a control block diagram of a PMSG grid-side converter provided in an embodiment of the present invention;

[0077] Figure 6 This is a structural diagram of a permanent magnet direct-drive fan that represents the machine-side system as a DC-side system, provided in an embodiment of the present invention.

[0078] Figure 7The figure shows a comparison between the analytical model and simulation results of the PMSG AC side equivalent impedance provided in the embodiments of the present invention. Figure 7 (a), (b), (c), and (d) are comparison diagrams of the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance of the PMSG AC side equivalent impedance analytical model and simulation, respectively.

[0079] Figure 8 A comparison diagram of the detailed and simplified models of the PMSG AC side equivalent impedance provided in this embodiment of the invention is shown. Figure 8 (a), (b), (c), and (d) are comparison diagrams of the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance of the detailed model and simulation of the equivalent impedance of the AC side of the PMSG, respectively.

[0080] Figure 9 This is a schematic diagram illustrating the influence of the phase-locked loop bandwidth on the amplitude / phase frequency characteristics of the PMSG, provided in an embodiment of the present invention. Figure 9 (a), (b), (c), and (d) are schematic diagrams of the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance of the phase-locked loop bandwidth on the amplitude / phase frequency characteristics of the PMSG, respectively. Detailed Implementation

[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] The purpose of this invention is to provide a method and system for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors. By using complex vectors to characterize the multi-input multi-output characteristics caused by frequency coupling, the accuracy of impedance modeling of permanent magnet direct-drive wind turbines is improved, thereby improving the accuracy of determining the stability of the power grid connected to the permanent magnet direct-drive wind turbine.

[0083] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0084] Most current studies still establish SISO impedance models for wind turbines, without considering their frequency coupling characteristics, and therefore cannot accurately determine system stability.

[0085] To address the above issues, this invention proposes a complex vector-based impedance modeling method for permanent magnet direct-drive wind turbines. This method aims to solve the problems of high computational complexity, lack of physical meaning in the impedance matrix, and failure to consider frequency coupling characteristics in existing impedance models. Furthermore, based on the established MIMO impedance model and combined with the generalized Nyquist stability criterion, the stability of wind farm grid-connected systems can be effectively determined, thereby improving the reliability of wind farm grid-connected system operation.

[0086] This invention proposes a complex vector-based impedance modeling method based on the frequency shift characteristics of Fourier transform and the flexible application of exponential rotation factors. The innovation of this invention lies in its consideration of the wind turbine-side system, taking into account the frequency coupling characteristics of the PMSG. Combined with the proposed complex vector method, an accurate and complete wind turbine impedance model can be established. More importantly, the analytical modeling has low complexity and clear physical meaning, which can improve the stability determination results of subsequent system stability analysis.

[0087] Example 1

[0088] Embodiment 1 of this invention provides a method for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors, such as... Figure 1 As shown, the method includes the following steps:

[0089] Step 101: Establish the frequency domain transformation rule of the transfer function between the transformation matrix of the complex vector and the stationary coordinate system in the complex plane and the input and output of the conjugate basis vectors, specifically including:

[0090] (1) Coordinate transformation in the complex field

[0091] The transformation rules between a three-phase stationary coordinate system and a rotating coordinate system are as follows:

[0092]

[0093] In the formula: x d x q Let x be an electrical quantity in a rotating coordinate system. a x b x c Let n be the electrical quantity in a three-phase stationary coordinate system, n be the harmonic order, and θ be the electric angular velocity. The initial phase angle of the electrical quantity.

[0094] The transformation rules between the three-phase stationary coordinate system and the two-phase stationary coordinate system are as follows:

[0095]

[0096] In the formula: x α x β Let x be an electrical quantity in a two-phase stationary coordinate system. a x bx c Let n be the electrical quantity in a three-phase stationary coordinate system, n be the harmonic order, and θ be the electric angular velocity. Let be the initial phase angle of the electrical quantity. When the system is running stably, the rotational speed of the rotating coordinate system is the same as the synchronous rotational speed. At this time, the d-axis coincides with the vector x, and the relationship between the coordinate systems is as follows: Figure 2 As shown:

[0097] Since both equations (1) and (2) involve trigonometric functions, and Euler's formula is:

[0098]

[0099] Combining Euler's formula, let Substituting equations (1) and (2) into equation (3) and calculating, we can obtain:

[0100]

[0101] These are the two-dimensional basis vectors output by the αβ coordinate system in the complex plane. Let be the two-dimensional basis vectors output in the dq coordinate system under the complex plane. According to the frequency shift characteristics of the Fourier transform, the relationship of equation (4) in the frequency domain is:

[0102]

[0103] Here x p x n Defined as a complex vector. As can be seen from the above equation, when a complex vector is transformed with a rotating coordinate system, it not only causes a frequency shift but also a phase deviation.

[0104] Furthermore, according to x p x n By substituting equation (2) into the definition, we can derive the relationship between the three-phase stationary coordinate system and x. p x n The relationship in the time domain is as follows:

[0105]

[0106] in, Let x be the two-dimensional basis vector output by the αβ coordinate system in the complex plane. p and x n These are the positive and negative rotation vectors output from the αβ coordinate system in the complex plane, respectively, x p and x n Mutually conjugate, x a x b and x c is the three-dimensional coordinate in a stationary coordinate system, and j represents the imaginary number.

[0107] It is easy to see that the matrix in the above formula is precisely the matrix of the symmetric component method. Therefore, x p x n It has a clear physical meaning.

[0108] (2) Analysis of transfer function characteristics based on complex vectors

[0109] Assume the input of a two-dimensional dynamic system in a rotating coordinate system is u = [u d ,u q ] T The output quantity is y = [y d ,y q ] T The frequency domain transfer functions of the input and output are:

[0110]

[0111] make The frequency domain relationship between the input and output quantities of the rotating coordinate system in the complex domain is as follows:

[0112]

[0113] in, Y is a two-dimensional basis vector output in the dq coordinate system under the complex plane. dq (s) and The positive and negative rotation vectors output by the dq coordinate system in the complex plane, respectively, Y dq (s) and Mutually conjugate, G d1 (s), G d2 (s), These are the transfer functions of the input and output of a two-dimensional dynamic system in the dq coordinate system in the complex plane. U is a two-dimensional basis vector input in the dq coordinate system under the complex plane. dq (s), denoted as the forward rotation vector and the reverse rotation vector, respectively, in the dq coordinate system under the complex plane, and s is the differential operator.

[0114] Based on signal analysis and Hilbert transform, and combining the frequency domain relationship between the complex vector and the rotating coordinate system in equation (5), substituting equation (5) into equation (7) yields the following transfer function relationship between the input and output complex vectors in the frequency domain:

[0115]

[0116] in, Y is the two-dimensional basis vector output by the two-phase stationary coordinate system in the complex plane. p (s) and Y n(s) represent the positive and negative rotation vectors output by the two-phase stationary coordinate system in the complex plane, respectively, G d1 (s-jω1), G d2 (s-j2ω1) Let be the transfer functions of the two-dimensional dynamic system in a two-phase stationary coordinate system in the complex plane, and be the input and output, respectively. Let ω1 be the fundamental frequency angular velocity. The initial fundamental frequency voltage phase angle, U is a two-dimensional basis vector input in a two-phase stationary coordinate system in the complex plane. p (s) and U n (s) represent the forward rotation vector and the reverse rotation vector, respectively, input to the two-phase stationary coordinate system in the complex plane.

[0117] This step derives the transformation matrix between the complex vector and the stationary coordinate system in the complex plane and studies the frequency domain characteristics of the transfer function in the complex plane. Among them, the transformation matrix of equation (6) lays the mathematical foundation for the subsequent complex vector modeling of the PMSG main circuit, and the frequency domain transformation rules of the transfer function in equations (7) and (8) lay the theoretical foundation for the subsequent PMSG control circuit modeling.

[0118] Step 102: Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, establish the complex vector model of the main circuit of the permanent magnet direct-drive fan, specifically including:

[0119] like Figure 3 As shown, the permanent magnet direct-drive wind turbine system includes a permanent magnet direct-drive synchronous generator, a machine-side converter, and a grid-side converter.

[0120] (1) Impedance modeling of permanent magnet direct-drive synchronous generator

[0121] The dynamic equations of a permanent magnet direct-drive synchronous generator in a rotating coordinate system are:

[0122]

[0123] In the formula: v sd v sq For the PMSG stator side d-axis and q-axis voltages; i sd i sq For PMSG stator side d-axis and q-axis currents; L sd L sq For PMSG stator side d, q axis inductance; R s The stator-side resistance; ω s Synchronous rotational speed; ψ f This represents the rotor flux linkage amplitude.

[0124] Because of R s The value is relatively small and can generally be ignored. Therefore, performing small-signal linearization on the above equation yields:

[0125]

[0126] Substituting the transformation rules of equations (7) and (8) into equation (10), we can obtain the linearized small-signal model of the voltage and current of the permanent magnet synchronous generator expressed in complex vector form as follows:

[0127]

[0128] In the formula: ω1=2πf1, f1 is the fundamental frequency. ω s This refers to the stator-side electrical angular velocity of the PMSG. Here, the synchronous generator uses an embedded motor.

[0129] The above equation is the complex vector model of a permanent magnet synchronous generator.

[0130] (2) Impedance modeling of the main circuit of the PMSG grid-side converter

[0131] Both the machine-side and network-side of PMSG use VSG, so their modulation methods are the same. Taking the machine-side as an example, the relationship between its switching duty cycle and the modulating signal can be expressed as:

[0132]

[0133] In the formula: d sj Let j be the duty cycle of the camera-side switch. Let m be a j-phase PWM modulation signal, j∈(a,b,c). sf This is the modulation amplitude ratio.

[0134] Depend on Figure 3 It can be seen that the main circuit equation of the machine-side converter is:

[0135]

[0136] In the formula: v sj i sj These are the terminal voltage and terminal current of the permanent magnet direct-drive synchronous generator.

[0137] The main circuit equations of the grid-side converter are as follows:

[0138]

[0139] According to the transformation rule of equation (6), the main circuit equation of the machine-side converter expressed in complex vector form is:

[0140]

[0141] Small-signal linearization yields:

[0142]

[0143] The above equation is the complex vector model of the main circuit on the machine side.

[0144] According to the transformation rule in (6), the main circuit equation of the grid-side converter expressed in complex vector form is:

[0145]

[0146] Small-signal linearization yields:

[0147]

[0148] The above equation represents the complex vector model of the main circuit on the grid side. Where d p d n Denotes the grid-side switching function, d sp d sn Represents the machine-side switching function, v pccp v pccn This represents the AC voltage at point PCC, v. sp v sn This represents the terminal voltage of the synchronous generator.

[0149] Thus, the main circuit equations of PMSG and MMC expressed in complex vectors have been established. It can be seen that by using the transformation rules of equations (6), (7) and (8), the process of modeling the main circuit is simple and has clear physical meaning.

[0150] Step 103: Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane, establish the control circuit model of the permanent magnet direct-drive fan, specifically including:

[0151] (1) Dynamic characteristics of phase-locked loop

[0152] According to harmonic balance theory, when the system voltage experiences a small disturbance, the phase angle tracked by the phase-locked loop includes a deviation Δθ in addition to the fundamental frequency. Mapped to a stationary coordinate system in the complex domain, this can be expressed as:

[0153]

[0154] For e -jΔθ e jΔθ Taylor expansion yields:

[0155]

[0156] Without considering second-order and higher-order components, the linearized small-signal model of electrical quantities in the rotating coordinate system can be expressed as:

[0157]

[0158] From the dynamic characteristics and transfer function equation of the phase-locked loop, the expression for Δθ is:

[0159]

[0160] In the formula: K ppll K is the proportionality constant of the phase-locked loop. ipll is the integral constant of the phase-locked loop.

[0161] Since the grid-side control section of the wind turbine uses a phase-locked loop (PLL), the disturbance of the PLL needs to be considered when mathematically modeling it. The embodiments of this invention analyze the characteristics of the PLL, laying a theoretical foundation for the modeling of the grid-side control section.

[0162] (2) Modeling of PMSG machine-network side control part

[0163] like Figure 3 As shown, since the voltage and current on the turbine side are collected from the output of the permanent magnet synchronous generator, when the wind turbine outlet is subjected to a small disturbance, it is assumed that the AC voltage and current on the turbine side are unaffected. Therefore, when establishing a small-signal model for the turbine side control section, the influence of the outer loop and the phase-locked loop can be ignored. According to Figure 4 From the control block diagram shown, the linearized small-signal model of the PMSG machine-side control part in the dq coordinate system can be obtained as follows:

[0164]

[0165] According to the transformation rules of equations (7) and (8), the linearized small-signal model of the PMSG machine-side control part represented by complex vectors can be obtained as follows:

[0166]

[0167] The above equation represents the complex vector model of the PMSG generator-side control circuit. The impedance model of the PMSG generator-side DC side can be obtained by combining the complex vector model of the PMSG generator-side main circuit and the complex vector model of the permanent magnet synchronous generator. Where:

[0168] In practical engineering, to ensure the PMSG power factor is close to 1, the reactive power reference value is set to 0. Therefore, under small disturbances, the reactive power disturbance ΔQ is approximately considered to be 0. According to... Figure 5 From the control block diagram shown, the linearized small-signal model of the PMSG network-side control part in the dq coordinate system can be obtained as follows:

[0169]

[0170] Substituting equations (21), (22), and (23) from step 3(1) into the above equation, we can obtain the linearized small-signal model of the PMSG network-side control section considering the dynamic characteristics of the phase-locked loop as follows:

[0171]

[0172] According to the transformation rules of equations (7) and (8), the linearized small-signal model of the PMSG network-side control part represented by complex vectors is as follows:

[0173]

[0174] The above equation represents the complex vector model of the PMSG grid-side control circuit. The impedance model of the PMSG AC side can be obtained by combining this complex vector model with the PMSG grid-side main circuit model.

[0175] In the formula:

[0176]

[0177]

[0178]

[0179] Thus, the PMSG control circuit has been established using a complex vector impedance model. Compared with traditional frequency domain impedance modeling, it can be seen that the PMSG control circuit model can be written more easily according to the transformation rules of equations (7) and (8), avoiding frequency domain convolution operations and repeated coordinate transformations, and greatly reducing the complexity of analytical modeling.

[0180] Step 104: Establish a PMSG equivalent impedance model considering multi-frequency coupling characteristics based on the main circuit complex vector model and the control circuit model.

[0181] (1) Complex vector representation of the DC-side impedance model of the PMSG machine side

[0182] Neglecting converter power losses, the DC-side power equals the AC-side power. That is...

[0183]

[0184] The relationship between DC current and AC current is as follows:

[0185] i dc =d sp i sn +d sn i sp (30)

[0186] Based on the above two equations, the initial duty cycle value of the VSC switch on the machine side can be obtained as follows:

[0187]

[0188] Substituting the permanent magnet synchronous power generation model derived in step one and the main circuit model of the generator side derived in step two into the generator side control circuit model derived in step three, we get:

[0189]

[0190] Equation (29) can be linearized using small signals and expressed as a complex vector as follows:

[0191]

[0192] Substituting equation (32) into equation (33), we obtain the DC-side impedance of the machine-side converter as follows:

[0193]

[0194] This invention derives the impedance model of the DC side of the rectifier converter, which can be used to replace the permanent magnet synchronous generator and the machine-side converter. Therefore, the structural diagram of the permanent magnet direct-drive wind turbine is shown below. Figure 6 As shown.

[0195] (2) Complex vector representation of the AC side impedance model of the outlet of a permanent magnet direct-drive fan

[0196] according to Figure 2 The relationship between the DC voltage and current on the grid side is as follows:

[0197]

[0198] Note: The DC current specified here is in the opposite direction to the AC current, hence the negative sign.

[0199] Small-signal linearization yields:

[0200]

[0201] In the formula,

[0202] Substituting the grid-side control circuit model and equations (31) and (34) into the grid-side control circuit model, the AC side impedance of the PMSG can be obtained as follows:

[0203]

[0204] In the formula: I is the identity matrix.

[0205] K1=(Id dc1 g1) -1

[0206]

[0207]

[0208] Among them, Z wac (s) represents the equivalent impedance of the AC side of the PMSG, Z wpp Z wpn Z wnp Z wnn These represent the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance, respectively. I is the identity matrix, and v dc0 For DC voltage measurement, K pvs K pis K1, d vs g1, d is d dc1 g2 and g2 are the variables used to simplify the formulas during the model building process, respectively. p0 D n0 L represents the initial value of the grid-side converter switching duty cycle in terms of the conjugate basis vectors expressed in complex vector form. f This refers to the inductance of the grid-side line.

[0209] Thus, the PMSG impedance model based on complex vectors and considering multi-frequency coupling characteristics is now complete. The resulting PMSG mathematical model is a 2×2 matrix, reflecting the multi-input multi-output characteristics of the PMSG. Compared to the traditional single-input single-output model, the established model is more accurate. More importantly, for subsequent stability analysis of wind farms, the multi-input multi-output model can provide more accurate stability assessment results.

[0210] This invention first addresses the challenges of unclear physical meaning and high analytical difficulty in traditional wind turbine impedance modeling. It proposes a complex vector impedance modeling method by utilizing the transformation relationship between stationary and rotating coordinate systems in the complex domain. This method flexibly applies an exponential rotation factor to derive the rules governing the input and output changes of a two-dimensional dynamic system in the complex domain. Compared to traditional frequency domain modeling methods, this significantly reduces the analytical difficulty of the model. The derived frequency domain components have strict correspondences and clear physical meanings. Secondly, considering the inability of traditional simplified wind turbine models to accurately represent the dynamic characteristics of wind turbines, this invention takes into account the influence of the wind turbine's dynamic characteristics on its impedance characteristics. The resulting impedance model is more accurate than the simplified model, and the obtained dynamic characteristics of the wind turbine more closely match the actual wind turbine model. Next, this invention addresses the issue that offshore wind farms are prone to frequency-coupled oscillations via flexible DC transmission systems, and that positive and negative sequence decoupling impedance models and single-input single-output stability criteria are no longer sufficient to accurately determine system stability. It considers the frequency coupling effect within the wind turbine and establishes a single-input multi-output impedance model for the wind turbine. This model takes into account the frequency coupling characteristics of the wind turbine's grid-side phase-locked loop and DC voltage loop, allowing for more accurate stability analysis results.

[0211] In summary, the proposed complex vector modeling method is suitable for frequency domain modeling of converters with a large number of switching devices. The established PMSG model not only reveals the frequency coupling mechanism of the wind turbine, but also studies the influence of changes in control parameters on the amplitude / phase frequency characteristics of the PMSG, providing a reference for the selection of control parameters. More importantly, this model, combined with the MMC impedance model and the generalized Nyquist stability criterion, can analyze the influence of various control parameters of the PMSG on the stability of the offshore wind farm through the flexible DC transmission system.

[0212] To verify the accuracy and precision of the established model, a time-domain simulation model of a direct-drive wind turbine was built in the PSCAD / EMTDC platform. The impedance model was verified using an offline simulation frequency sweep method. The parameters of the permanent magnet direct-drive wind turbine used for offline simulation are shown in Table 1.

[0213] Table 1 Parameter Table of Permanent Magnet Direct Drive Wind Turbine Unit

[0214]

[0215]

[0216] (1) Validation of PMSG model

[0217] The analytical model and simulation results of the equivalent impedance of the AC side of the PMSG are, for example... Figure 7 As shown, Figure 7 In the diagram, the solid lines represent theoretically calculated values ​​derived using the complex vector method, and the asterisks represent the frequency sweep results from PSCAD / EMTDC simulations. Figure 7 Figures (a), (b), (c), and (d) in the diagram compare the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance of the PMSG AC side equivalent impedance analytical model and simulation, respectively. Figure 7 As can be seen, the analytical solution and the frequency sweep measurement are in high agreement, proving the effectiveness and accuracy of the PMSG AC side equivalent impedance analytical modeling method.

[0218] Currently, most literature, when modeling PMSG, considers the grid-side and machine-side converters of direct-drive wind turbines to be decoupled through DC-side capacitors. Therefore, the wind turbine, permanent magnet direct-drive generator, and machine-side converter are aggregated and equated as a single current source, such as... Figure 6 As shown.

[0219] The method proposed in this invention considers the influence of the generator-side converter and the permanent magnet direct-drive generator. Based on the previously proposed frequency sweeping method, simulation frequency sweeping analyses were performed on the complete PMSG model (considering the generator and generator-side components) and the simplified model (ignoring the generator-side components and treating the generator and generator-side components as equivalent to DC current sources). The frequency characteristic comparison results are as follows: Figure 8 As shown. Figure 8The solid line represents the detailed frequency response curve of the PMSG AC side considering the machine-side system, while the dashed line represents the simplified frequency response curve of the PMSG AC side when the machine-side system is equivalent to a current source. Figure 8 Figures (a), (b), (c), and (d) show a comparison of the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance between the detailed model and simulation of the PMSG AC side equivalent impedance. Figure 8 As can be seen, there is a significant error (<100Hz) between the simplified model and the detailed model. This is because when considering the turbine-side system, it is ultimately equivalent to a DC voltage source with internal impedance, while when the turbine-side system is not considered, it is equivalent to an ideal current source. Due to the different properties of the two power sources, the resulting PMSG AC-side frequency response curves are different. Therefore, ignoring the dynamic characteristics of the turbine-side system will lead to deviations in the stability assessment results of the offshore wind farm via the flexible DC transmission system. Furthermore, the uncoupling term (Z... pp Z nn The error of ) is greater than that of the coupling term (Z). pn Z np The reason is that the main reason affecting the frequency coupling characteristics of PMSG is the asymmetry of d-axis and q-axis control caused by the phase-locked loop and control parameters. However, the machine-side system does not have an asymmetry problem when the model is built. Therefore, the influence of the machine-side system on the coupled terms is less than that on the uncoupled terms.

[0220] (3) The effect of phase-locked loop on the amplitude / phase frequency response curve of PMSG

[0221] Phase-locked loops (PLLs) are one of the reasons why PMSGs exhibit frequency coupling; changes in their parameters can affect the frequency coupling characteristics of the PMSG. Therefore, it is necessary to study the parameters of PLLs.

[0222] Depend on Figure 9 It can be seen that, Figure 9 (a), (b), (c), and (d) are schematic diagrams of the positive-sequence impedance, positive-sequence coupling term, negative-sequence coupling term, and negative-sequence impedance of the PMSG amplitude / phase frequency characteristic, respectively, with the increase of the phase-locked loop bandwidth Bp. In the low-frequency band (<20Hz), as the phase-locked loop bandwidth Bp increases, the peak amplitude of the PMSG amplitude frequency characteristic curve becomes larger. Similarly, the phase frequency characteristic curve of the negative sequence and its coupling term will experience a phase jump when the peak is reached. At this time, oscillation instability may occur in the offshore wind farm through the flexible direct transmission system.

[0223] Example 2

[0224] Embodiment 2 of the present invention provides an impedance modeling system for permanent magnet direct-drive wind turbines based on complex vectors. The system is applied to the above-described method and includes:

[0225] The transformation relationship determination module is used to establish the frequency domain transformation rules of the transfer function between the transformation matrix and the input and output of the conjugate basis vectors of the complex vector in the complex plane and the stationary coordinate system.

[0226] The main circuit complex vector model establishment module is used to establish the main circuit complex vector model of the permanent magnet direct drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane.

[0227] The control circuit model building module is used to build a control circuit model of a permanent magnet direct-drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane.

[0228] The PMSG equivalent impedance model establishment module is used to establish a PMSG equivalent impedance model considering multi-frequency coupling characteristics based on the main circuit complex vector model and the control circuit model.

[0229] Example 3

[0230] Embodiment 3 of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0231] Example 4

[0232] Embodiment 4 of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed, implements the above-described method.

[0233] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0234] (1) Compared with dq coordinate system impedance, phase sequence impedance and polar coordinate impedance modeling, the complex vector method has clear physical meaning. The derived time-domain components have practical physical meaning in the frequency domain and have strict correspondence.

[0235] (2) The frequency domain transformation rule of the transfer function obtained by using complex vectors can replace the repeated coordinate transformations in the conventional frequency domain transformation, which greatly reduces the modeling complexity.

[0236] (3) The proposed complex vector method starts from the signal perspective and can decompose any harmonic component, which can be easily extended to the linearization of multiple harmonics.

[0237] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0238] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for impedance modeling of permanent magnet direct-drive wind turbines based on complex vectors, characterized in that, The method includes the following steps: Establish the frequency domain transformation rule of the transfer function between the transformation matrix of the complex vector and the stationary coordinate system and the input and output of the conjugate basis vectors in the complex plane; Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, a complex vector model of the main circuit of the permanent magnet direct-drive fan is established. Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane, a control circuit model of the permanent magnet direct drive fan is established. Based on the complex vector model of the main circuit and the control circuit model, a PMSG equivalent impedance model considering multi-frequency coupling characteristics is established. The PMSG equivalent impedance model includes the DC-side impedance model of the machine-side converter and the AC-side impedance model of the grid-side converter. Based on the complex vector model of the main circuit and the control circuit model, a PMSG equivalent impedance model considering multi-frequency coupling characteristics is established, specifically including: Based on the main circuit complex vector model and the control circuit model, the DC-side impedance model of the machine-side converter is established as follows: ； in: ， ， ， ， ； This is the DC-side impedance model of the machine-side converter. Where I is the DC-side voltage, and I is the identity matrix. , , , , , These are the initial values ​​of the voltage, current, and machine-side converter switch duty cycle at the output of the permanent magnet direct-drive synchronous motor, respectively, expressed as complex vectors representing the forward and reverse rotating vectors. DC side current, For machine-side line inductance, The modulation amplitude ratio of the machine-side converter. These are the outer loop PI control parameters for the machine-side converter. denoted as the dq-axis decoupling coefficient of the inner ring of the machine-side converter. The fundamental frequency angular velocity, To achieve synchronous speed, For PMSG stator-side d-axis inductance, s is the q-axis inductance on the stator side of the PMSG; s is the differential operator; Based on the main circuit complex vector model and the control circuit model, the AC side impedance model of the grid-side converter is established as follows: ； ； ； ； ； ； ； ； ； ； ； ； in, The AC side impedance model of the grid-side converter. , , , These are, respectively, the positive-sequence impedance, the positive-sequence coupling term, the negative-sequence coupling term, and the negative-sequence impedance. , The initial values ​​of the forward and reverse rotating vectors, expressed in complex vector form, represent the duty cycle of the grid-side converter switch. For grid-side line inductance; Let be the initial value of the AC voltage at point PCC. The initial fundamental frequency voltage phase angle, For the modulation amplitude ratio of the grid-side converter, The transfer function of the phase-locked loop with respect to the quadrature-axis voltage disturbance. The initial value of the direct-axis output current of the permanent magnet direct-drive synchronous generator. , , These are the outer loop PI control parameters, inner loop PI control parameters, and inner loop dq-axis decoupling coefficients of the grid-side converter. The equivalent impedance of the machine-side system and DC capacitor, , These are the initial values ​​of the forward and reverse rotating vectors, respectively, representing the current at the PCC point of the wind turbine in complex vector form.

2. The impedance modeling method for permanent magnet direct-drive wind turbines based on complex vectors according to claim 1, characterized in that, Establish the frequency domain transformation rule of the transfer function between the transformation matrix and the input / output conjugate basis vectors of a complex vector in the complex plane and the stationary coordinate system, specifically including: The transformation matrix between the complex vector in the complex plane and the stationary coordinate system is established as follows: ； in, Let be a set of two-dimensional basis vectors in a two-phase stationary coordinate system in the complex plane. and These are the forward and reverse rotation vectors in the two-phase stationary coordinate system under the complex plane, respectively. and Mutually conjugate , and Three-dimensional coordinates in a three-phase stationary coordinate system. represents an imaginary number; The frequency domain relationship between the input and output quantities of a rotating coordinate system in the complex domain is established as follows: ； in, This is a set of two-dimensional basis vectors output in a rotated coordinate system in the complex plane. and The positive and negative rotation vectors output in the rotating coordinate system under the complex plane are respectively... and Mutually conjugate , , , These are the transfer functions of the input and output of a two-dimensional dynamic system in the dq coordinate system in the complex plane. Let be the two-dimensional basis vectors input in the rotating coordinate system under the complex plane. , These are the forward and reverse rotation vectors input to the rotating coordinate system in the complex plane, respectively, and s is the differential operator; Based on signal analysis and Hilbert transform, the transfer function relationship between the input complex vector and the output complex vector in the frequency domain is established as follows: ； in, This represents a set of two-dimensional basis vectors output by a two-phase stationary coordinate system in the complex plane. and These are the positive and negative rotation vectors output by the two-phase stationary coordinate system in the complex plane, respectively. , , , Let be the transfer functions of the input and output of the two-dimensional dynamic system in the complex plane, respectively. The fundamental frequency angular velocity, The initial fundamental frequency voltage phase angle, Let be the two-dimensional basis vectors input to the two-phase stationary coordinate system in the complex plane. and These are the forward rotation vector and the reverse rotation vector, respectively, input from the two-phase stationary coordinate system in the complex plane.

3. The impedance modeling method for permanent magnet direct-drive wind turbines based on complex vectors according to claim 1, characterized in that, The main circuit complex vector model includes: the main circuit complex vector model of the permanent magnet direct-drive wind turbine, the complex vector model of the machine-side converter, and the complex vector model of the grid-side converter; Based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, a complex vector model of the main circuit of a permanent magnet direct-drive fan is established, specifically including: Establish the dynamic equations of a permanent magnet direct-drive synchronous generator in a rotating coordinate system; The dynamic equations are linearized using small-signal methods to obtain a linearized small-signal model of the permanent magnet direct-drive synchronous generator. Based on the frequency domain transformation rule of the transfer function, and according to the linearized small-signal model of the permanent magnet direct-drive synchronous generator, the linearized small-signal model of the permanent magnet direct-drive synchronous generator represented by a complex vector is determined as the complex vector model of the permanent magnet direct-drive synchronous generator. Establish the main circuit equations of the generator-side converter and the grid-side converter of the permanent magnet direct-drive synchronous generator; Based on the transformation matrix between complex vectors in the complex plane and the stationary coordinate system, the main circuit equations of the machine-side converter and the grid-side converter, expressed in complex vectors, are determined according to the main circuit equations of the machine-side converter and the grid-side converter, respectively. Small-signal linearization is performed on the main circuit equations of the machine-side converter and the grid-side converter, respectively, to obtain the linearized small-signal model of the machine-side converter, which is used as the complex vector model of the machine-side converter, and the linearized small-signal model of the grid-side converter, which is used as the complex vector model of the grid-side converter.

4. The impedance modeling method for permanent magnet direct-drive wind turbines based on complex vectors according to claim 1, characterized in that, The control circuit model includes a complex vector model of the machine-side control circuit and a complex vector model of the grid-side control circuit. The control circuit model of the permanent magnet direct-drive fan is established based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector in the complex plane and the stationary coordinate system, specifically including: Establish a linearized small-signal model of the machine-side control circuit in the dq coordinate system; Based on the frequency domain transformation rule of the transfer function, and according to the linearized small-signal model of the machine-side control circuit in the dq coordinate system, the linearized small-signal model of the machine-side control circuit represented by a complex vector is determined, which serves as the complex vector model of the machine-side control circuit. Establish a linearized small-signal model of the grid-side control circuit in the dq coordinate system; Establish a linearized small-signal model of the phase-locked loop; By substituting the linearized small-signal model of the phase-locked loop into the linearized small-signal model of the grid-side control circuit in the dq coordinate system, a linearized small-signal model of the grid-side control circuit considering the dynamic characteristics of the phase-locked loop is obtained. Based on the frequency domain transformation rules of the transfer function, and according to the linearized small-signal model of the grid-side control circuit considering the dynamic characteristics of the phase-locked loop, the linearized small-signal model of the grid-side control circuit represented by a complex vector is determined as the complex vector model of the grid-side control circuit.

5. A complex vector-based impedance modeling system for permanent magnet direct-drive wind turbines, characterized in that, The system is applied to the method according to any one of claims 1-4, the system comprising: The transformation relationship determination module is used to establish the frequency domain transformation rules of the transfer function between the transformation matrix and the input and output of the conjugate basis vectors of the complex vector in the complex plane and the stationary coordinate system. The main circuit complex vector model establishment module is used to establish the main circuit complex vector model of the permanent magnet direct drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane. The control circuit model building module is used to build a control circuit model of a permanent magnet direct-drive fan based on the transformation matrix and frequency domain transformation rules of the transfer function between the complex vector and the stationary coordinate system in the complex plane. The PMSG equivalent impedance model establishment module is used to establish a PMSG equivalent impedance model considering multi-frequency coupling characteristics based on the main circuit complex vector model and the control circuit model.

6. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed, implements the method as described in any one of claims 1 to 4.

Images