A method for resonance analysis of a wind power grid-connected system

Abstract

The present invention relates to a method for analyzing resonance in a wind power grid-connected system. By establishing an impedance model of a direct-drive wind turbine, the resonance problem of the wind power grid-connected system is analyzed, considering the influence law of the DC bus capacitor on the impedance model of the direct-drive wind turbine under the condition of power disturbance on the AC side. In addition, in the process of establishing the impedance model of the direct-drive wind turbine, the harmonic state space theory is used to perform a steady-state processing on the linearized single-phase analytical model. The harmonic state space method can represent multiple frequency responses in each variable at the same time, so as to establish an impedance model of the direct-drive wind turbine with a multi-dimensional harmonic transfer function, which can accurately reflect the influence of the DC bus capacitor or asymmetric control on the impedance characteristics of the direct-drive wind turbine; using this impedance model of the direct-drive wind turbine to analyze the resonance problem of the wind power grid-connected system, since it comprehensively reflects the influence mechanism of the DC bus capacitor on the frequency coupling characteristics of the system, the accuracy of resonance analysis of the wind power grid-connected system can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power system transmission and distribution, and particularly relates to a resonance analysis method for a wind power grid-connected system. Background Art

[0002] From 2015 to 2020, the total installed capacity of wind power in China has been continuously increasing. Among them, the newly installed capacity of wind power in the whole country in 2020 was 71.67GW, and the cumulative grid-connected installed capacity reached 282GW. Among them, permanent magnet direct drive wind turbines are widely used in the third-class wind energy resource areas with low wind speeds in China due to their advantages such as small transmission loss, high power generation efficiency, and better adaptability to low wind speed environments.

[0003] With the continuous increase in the installed capacity of wind turbines, the resonance problem of the entire wind power grid-connected system occurs frequently, affecting the safety and stability of the entire power system. The broadband resonance problem of wind power grid connection is one of the key stability problems faced by the power system. At present, it is mainly studied by the time-domain state space method and the frequency impedance analysis method. The state space analysis method is an effective tool traditionally used to analyze the resonance problem of power systems. Generally, the state space method analyzes the resonance problem of the system by solving the eigenvalues of the system. However, obtaining detailed system modeling and all control parameters is required when calculating eigenvalues. In actual operation, it is often difficult to obtain the above information due to the technical confidentiality requirements of manufacturers.

[0004] The impedance stability analysis method based on the Nyquist criterion has been proven to be a feasible method for analyzing systems. This method can effectively determine the stability of interconnected systems by using the impedance ratio between interconnected systems. Moreover, compared with the state space analysis method, the biggest advantage of the impedance stability analysis method is that it can be realized through engineering tests without prior access to detailed information on system parameters. Among them, the MMC impedance model is an important tool for analyzing the stability of the transmission system of direct drive wind farms. At present, the impedance modeling methods for direct drive wind farms can be roughly divided into dq-domain impedance modeling and sequence-domain impedance modeling. The dq-domain impedance modeling method is widely used in the impedance modeling of traditional two-level converters. However, it is difficult to directly measure through experiments due to its lack of clear physical meaning, and the generalized Nyquist stability criterion is required for stability judgment, which has a relatively large difficulty in stability judgment. In addition, due to the frequency coupling characteristics, the traditional sequence-domain impedance modeling that decouples positive and negative sequence impedances has errors in some scenarios and cannot reflect the changes in the system impedance characteristics when the DC bus capacitance is large. In the case where an accurate impedance model cannot be obtained, the resonance analysis results of the wind power grid-connected system will also be difficult to ensure accuracy, which may lead to misjudgment of the stability of the entire power system and cause incalculable economic losses.

[0005] Therefore, how to consider the dynamics of the DC bus capacitor and comprehensively reflect the influence mechanism of the DC bus capacitor on the system frequency coupling characteristics has become an urgent problem to be solved in the current resonance analysis of the wind power grid-connected system. Summary of the Invention

[0006] Aiming at the deficiencies of the above-mentioned existing technologies, the present invention provides a resonance analysis method for a wind power grid-connected system, which can consider the dynamics of the DC bus capacitor and comprehensively reflect the influence mechanism of the DC bus capacitor on the system frequency coupling characteristics.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] A resonance analysis method for a wind power grid-connected system includes the following steps:

[0009] Step S1: Based on the dynamic characteristics of the direct-drive wind turbine unit in the wind power system, obtain a simplified dynamic model of the direct-drive wind turbine unit;

[0010] Step S2: Based on the simplified dynamic model of the direct-drive wind turbine unit and Kirchhoff's law, obtain an electrical analytical model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor;

[0011] Step S3: Inject a small AC voltage disturbance on the AC side, linearize the electrical analytical model of the direct-drive wind turbine, and obtain a linearized single-phase analytical model;

[0012] Step S4: Use the harmonic state space theory to perform a steady-state processing on the linearized single-phase analytical model, and construct a harmonic matrix model of the direct-drive wind turbine;

[0013] Step S5: Based on the mathematical relationship between the control variables in the power grid system, establish a small-signal model of the control link and convert it into a matrix form;

[0014] Step S6: Based on the physical definition of impedance and the harmonic matrix model of the direct-drive wind turbine, obtain an impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor;

[0015] Step S7: According to the impedance model of the direct-drive wind turbine obtained in S6, analyze the resonance problem of the wind power grid-connected system.

[0016] Preferably, in S1, the simplified dynamic model of the direct-drive wind turbine is a grid-connected inverter model in which the electromagnetic and electromechanical dynamic behaviors of the generator and the machine-side converter are ignored, and the DC side is a parallel connection of a DC current source and a DC bus capacitor.

[0017] Preferably, in S2, the electrical analytical model of the direct-drive wind turbine is:

[0018]

[0019] Among them, L is the AC filtering inductor, C is the DC bus capacitor, and i gj is the phase current on the AC side of the j-th phase flowing through the filtering inductor, and u gj is the grid voltage on the AC side of the j-th phase, m j is the modulation signal of the j-th phase of the grid-side converter, and u dc is the DC bus voltage, and i dc is the equivalent output DC current at the front end of the direct-drive wind turbine. j represents a variable and j = a, b, c, where a, b, and c represent the a-phase, b-phase, and c-phase respectively.

[0020] Preferably, in S3, assuming that a small AC voltage perturbation is injected into the AC side of the direct-drive wind turbine, applying the small-signal linearization method and combining the symmetry characteristics of the three-phase balanced system, a linearized single-phase analytical model of the direct-drive wind turbine is obtained;

[0021]

[0022] Among them, L is the AC filtering inductor, Δi g is the small perturbation of the AC current, and Δu g is the small perturbation of the AC voltage, and Δm is the small perturbation of the modulation signal, and Δu dc is the small perturbation of the DC bus, C is the DC bus capacitor, and Δi dc is the small-signal component of the DC load current, M is the steady-state value of the modulation signal, and i g is the steady-state value of the AC current, and t is the time.

[0023] Preferably, in S4, using the harmonic state space theory to convert the periodic time-varying signals in the linearized single-phase analytical model into time-invariant signals, any periodic time-varying variable x(t) in the linearized single-phase analytical model of the direct-drive wind turbine is converted after HHS to:

[0024] x = [... x -n ... x0... x n ...] T ;

[0025] Among them, x represents the column vector formed after the harmonic state space transformation of the variable x(t), x0 is the DC component of x(t), and x n is the Fourier coefficient of the n-th harmonic, and n is the harmonic order;

[0026] The small-signal component Δx(t) of any variable in the linearized single-phase analytical model is converted after HHS to:

[0027] Δx = [... x p-n ... x p ... x p+n ...] T

[0028] where Δx represents the column vector formed by the small-signal component Δx(t) after harmonic state-space transformation, x p is the Fourier coefficient corresponding to the perturbation frequency, x p-n is the Fourier coefficient with the harmonic frequency of p - n, p is the frequency corresponding to the injected small-signal perturbation component, n is the harmonic order, x p+n is the Fourier coefficient with the harmonic frequency of p + n.

[0029] Preferably, in S4, the product of the small-signal component Δx(t) and the steady-state component a(t) is transformed through harmonic state space as:

[0030]

[0031] where A is the Toeplitz matrix of a(t), a0 is the DC component of the steady-state parameter, a ±1 represents a pair of conjugate fundamental-frequency Fourier coefficients of the steady-state parameter, a ±2 represents a pair of conjugate second-harmonic Fourier coefficients of the steady-state parameter, x p-1 is the Fourier coefficient with the frequency of p -, x p is the Fourier coefficient with the frequency of p + 1, x p+1 is the Fourier coefficient with the frequency of p + 1.

[0032] Preferably, in S4, the harmonic matrix model of the direct-drive wind turbine is:

[0033]

[0034] where Δs is the differential operator matrix, Δi g is the column vector formed by the alternating current after harmonic state-space transformation, Δu g is the column vector formed by the alternating voltage after harmonic state-space transformation, Δm is the column vector formed by the modulation signal after harmonic state-space transformation, U dc is the steady-state value of the DC voltage, M is the time-invariant coefficient matrix of the modulation signal; Δu dc is the column vector formed by the DC bus voltage after harmonic state-space transformation, Δi dc is the column vector formed by the DC bus current after harmonic state-space transformation, I g is the time-invariant coefficient matrix of the alternating current;

[0035]

[0036] where ΔI p+n and ΔI p-n are respectively the amplitudes of the small perturbations of the alternating current with frequencies of f p +nf1, f p -nf1; α p+n and αp-n are the phase angles of small disturbances of alternating current with frequencies of f p +nf1 and f p -nf1 respectively; ΔU p+n and ΔU p-n are the amplitudes of small disturbances of alternating voltage with frequencies of f p +nf1 and f p -nf1 respectively; θ p+n and θ p-n are the phase angles of small disturbances of alternating voltage with frequencies of f p +nf1 and f p -nf1 respectively; ΔM p+n and ΔM p-n are the amplitudes of small disturbances of modulation signals with frequencies of f p +nf1 and f p -nf1 respectively; β p+n and β p-n are the phase angles of small disturbances of modulation signals with frequencies of f p +nf1 and f p -nf1 respectively; ΔU dc is the amplitude of small disturbance of direct current voltage; ΔI dc is the amplitude of small disturbance of direct current current.

[0037] Preferably, in S5, the matrix form of the small-signal model of the control link is:

[0038]

[0039] G u =-T d- G i G udc ;

[0040] G i =T d- (G i T d+ +K d T q+ )+T q- (G i T q+ -K d T d+ );

[0041] where Δm is the column vector formed after the harmonic state space transformation of the modulation signal; G u represents the transfer function matrix of the current control loop, G i represents the transfer function matrix of the current control loop, T d- represents the d-axis dq inverse transformation transfer matrix, G udcDenotes the transfer function matrix between the DC voltage loop and the modulation signal; T d+ Denotes the d-axis dq positive transformation transfer matrix, K d Denotes the decoupling coefficient matrix, T q+ Denotes the q-axis dq positive transformation transfer matrix, T q- Denotes the q-axis dq inverse transformation transfer matrix.

[0042] Preferably, in S6, the impedance model of the direct-drive wind turbine based on considering the dynamics of the DC bus capacitor is:

[0043]

[0044] Wherein, Z ac Denotes the AC-side impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor, G iac Is the transfer function matrix between the current control loop and the modulation signal.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. The impedance model of the direct-drive wind turbine established by the present invention considers the influence law of the DC bus capacitor on the impedance model of the direct-drive wind turbine in the case of power disturbance on the AC side. Using this impedance model of the direct-drive wind turbine to analyze the resonance problem of the wind power grid-connected system, due to considering the dynamics of the DC bus capacitor, it can comprehensively reflect the influence mechanism of the DC bus capacitor on the frequency coupling characteristics of the system, and can improve the accuracy of the resonance analysis of the wind power grid-connected system.

[0047] 2. In the process of establishing the impedance model of the direct-drive wind turbine, the present invention uses the harmonic state space theory to perform a steady-state processing on the linearized single-phase analytical model, and the harmonic state space method can represent multiple frequency responses in each variable at the same time, so as to establish an impedance model of the direct-drive wind turbine with a multi-dimensional harmonic transfer function, which can accurately reflect the influence of the DC bus capacitor or asymmetric control on the impedance characteristics of the direct-drive wind turbine.

[0048] 3. The present invention solves the problems of complex impedance modeling process and low accuracy of the direct-drive wind farm considering the characteristics of the DC bus capacitor, and has high practical value for analyzing the resonance problem of the wind power grid-connected system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to make the objectives, technical solutions and advantages of the invention clearer, the present invention will be further described in detail below with reference to the drawings, wherein:

[0050] Figure 1 Is the flowchart of the embodiment of the present invention;

[0051] Figure 2 Is the electrical structure schematic diagram of the complete direct-drive wind turbine in the embodiment;

[0052] Figure 3 It is the circuit diagram of the simplified direct-drive wind turbine in the embodiment. Specific implementation manners

[0053] The following is a further detailed description through specific implementation manners:

[0054] Embodiment

[0055] Such as Figure 1 shown, in this embodiment, a resonance analysis method for a wind power grid-connected system is disclosed. For the convenience of description, in the power grid system of this embodiment, the complete electrical structure of the direct-drive wind turbine is as Figure 2 shown. The direct-drive wind turbine includes a wind turbine, a permanent magnet synchronous generator, and a back-to-back voltage source converter (including a machine-side converter and a grid-side converter). The generator is directly coupled to the wind turbine, and the energy generated by the wind turbine is transmitted to the power grid through the back-to-back voltage source converter.

[0056] This method includes the following steps:

[0057] Step S1, based on the dynamic characteristics of the direct-drive wind turbine device in the power grid system, obtain a simplified dynamic model of the direct-drive wind turbine. Specifically, ignoring the electromagnetic and electromechanical dynamic behaviors of the generator and the machine-side converter, the wind turbine, the permanent magnet synchronous generator, and the machine-side converter are equivalent to current sources, and are connected in parallel with the DC bus capacitor, and finally together with the grid-side converter form a simplified direct-drive wind turbine model as Figure 3 shown, and obtain the corresponding simplified dynamic model of the direct-drive wind turbine.

[0058] Step S2, based on the simplified dynamic model of the direct-drive wind turbine and Kirchhoff's law, obtain an electrical analysis model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor.

[0059]

[0060] Among them, L is the AC filter inductor, C is the DC bus capacitor, i gj is the phase current of the j-phase AC side flowing through the filter inductor, u gj is the grid voltage of the j-phase AC side, m j is the modulation signal of the j-phase of the grid-side converter, u dc is the DC bus voltage, i dc is the equivalent output DC current at the front end of the direct-drive wind turbine, and j represents the phase variable and j = a, b, c, where a, b, and c respectively represent the a-phase, b-phase, and c-phase.

[0061] Step S3, inject a small AC voltage perturbation on the AC side, linearize the electrical analysis model of the direct-drive wind turbine, and obtain a linearized single-phase analysis model. Specifically, when implementing, assume that a small AC voltage perturbation is injected on the AC side of the direct-drive wind turbine, apply the small-signal linearization method and combine the symmetry characteristics of the three-phase balanced system to obtain the linearized single-phase analysis model of the direct-drive wind turbine;

[0062]

[0063] where L is the AC filter inductor, Δi g is the small perturbation of the AC current, Δu g is the small perturbation of the AC voltage, Δm is the small perturbation of the modulation signal, Δu dc is the small perturbation of the DC bus, C is the DC bus capacitor, Δi dc is the small-signal component of the DC load current, M is the steady-state value of the modulation signal, i g is the steady-state value of the AC current, and t is the time.

[0064] Step S4, use the harmonic state space theory to perform a steady-state processing on the linearized single-phase analysis model, and construct a harmonic matrix model of the direct-drive wind turbine. Specifically, when implementing, use the harmonic state space theory to convert the periodic time-varying signals in the linearized single-phase analysis model into time-invariant signals. Any periodic time-varying variable x(t) in the linearized single-phase analysis model of the direct-drive wind turbine is converted after HHS to:

[0065] x = [… x -n … x0 … x n …] T (3)

[0066] where x represents the column vector formed after the variable x(t) undergoes a harmonic state space transformation, x0 is the DC component of x(t), x n is the Fourier coefficient of the nth harmonic, and n is the harmonic order;

[0067] The small-signal component Δx(t) of any variable in the linearized single-phase analysis model is converted after HHS to:

[0068] Δx = [… x p-n … x p … x p+n …] T (4)

[0069] where Δx represents the column vector formed after the small-signal component Δx(t) undergoes a harmonic state space transformation, x p is the Fourier coefficient corresponding to the perturbation frequency, x p-n is the Fourier coefficient with the harmonic frequency of p - n, p is the frequency corresponding to the injected small-signal perturbation component, n is the harmonic order, xp+n is the Fourier coefficient with the harmonic frequency of p + n.

[0070] The product of the small-signal component Δx(t) and the steady-state component a(t) is transformed through the harmonic state space as follows:

[0071]

[0072] where A is the Toeplitz matrix of a(t), a0 is the steady-state parameter DC component, a ±1 represents a pair of conjugate fundamental-frequency Fourier coefficients of the steady-state parameters, a ±2 represents a pair of conjugate second-harmonic Fourier coefficients of the steady-state parameters, x p-1 is the Fourier coefficient with the frequency of p -, x p is the Fourier coefficient with the frequency of p + 1, x p+1 is the Fourier coefficient with the frequency of p + 1.

[0073] Combining equations (2), (3), (4), and (5), the harmonic matrix model of the direct-drive wind turbine is obtained as follows:

[0074]

[0075] where Δs is the differential operator matrix, Δi g is the column vector formed after the harmonic state space transformation of the alternating current, Δu g is the column vector formed after the harmonic state space transformation of the alternating voltage, Δm is the column vector formed after the harmonic state space transformation of the modulation signal, U dc is the steady-state value of the DC voltage, M is the time-invariant coefficient matrix of the modulation signal; Δu dc is the column vector formed after the harmonic state space transformation of the DC bus voltage, Δi dc is the column vector formed after the harmonic state space transformation of the DC bus current, I g is the time-invariant coefficient matrix of the alternating current. The specific expressions of the above vectors are as follows:

[0076]

[0077] where ΔI p+n and ΔI p-n are the amplitudes of the small disturbances of the alternating current with frequencies of f p + nf1 and f p - nf1 respectively; α p+n and α p-n are the phase angles of the small disturbances of the alternating current with frequencies of f p + nf1 and f p - nf1 respectively; ΔU p+n and ΔU p-nare the amplitudes of small disturbances of the AC voltage and current with frequencies of f p +nf1 and f p -nf1 respectively; θ p+n and θ p-n are the phase angles of small disturbances of the AC voltage with frequencies of f p +nf1 and f p -nf1 respectively; ΔM p+n and ΔM p-n are the amplitudes of small disturbances of the modulation signal with frequencies of f p +nf1 and f p -nf1 respectively; β p+n and β p-n are the phase angles of small disturbances of the modulation signal with frequencies of f p +nf1 and f p -nf1 respectively; ΔU dc is the amplitude of the small disturbance of the DC voltage; ΔI dc is the amplitude of the small disturbance of the DC current.

[0078] Step S5: Based on the mathematical relationships between the control variables in the power grid system, establish a small-signal model of the control link and convert it into matrix form; the matrix form of the small-signal model of the control link is:

[0079]

[0080] G u =-T d- G i G udc (8)

[0081] G i =T d- (G i T d+ +K d T q+ )+T q- (G i T q+ -K d T d+ ) (9)

[0082] where, Δm is the column vector formed after the modulation signal undergoes harmonic state space transformation; G u represents the current control loop transfer function matrix, G i represents the current control loop transfer function matrix, T d- represents the d-axis dq inverse transformation transfer matrix, G udc represents the transfer function matrix between the DC voltage loop and the modulation signal; T d+ represents the d-axis dq forward transformation transfer matrix, K drepresents the decoupling coefficient matrix, T q+ is represented as the q-axis dq positive transformation transfer matrix, T q- is represented as the q-axis dq inverse transformation transfer matrix.

[0083] Step S6: Based on the physical definition of impedance and the harmonic matrix model of the direct-drive wind turbine, obtain the impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor:

[0084]

[0085] where, Z ac represents the AC-side impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor, G iac is the transfer function matrix between the current control loop and the modulation signal.

[0086] Step S7: Analyze the resonance problem of the wind power grid-connected system according to the impedance model of the direct-drive wind turbine obtained in S6.

[0087] The impedance model of the direct-drive wind turbine established by the present invention considers the influence law of the DC bus capacitor on the impedance model of the direct-drive wind turbine in the case of power disturbance on the AC side. In addition, in the process of establishing the impedance model of the direct-drive wind turbine, the harmonic state space theory is used to perform a steady-state processing on the linearized single-phase analytical model, and the harmonic state space method can represent multiple frequency responses in each variable at the same time. In this way, the impedance model of the direct-drive wind turbine with a multi-dimensional harmonic transfer function is established, which can accurately reflect the influence of the DC bus capacitor or asymmetric control on the impedance characteristics of the direct-drive wind turbine. Using this impedance model of the direct-drive wind turbine to analyze the resonance problem of the wind power grid-connected system, due to considering the dynamics of the DC bus capacitor and comprehensively reflecting the influence mechanism of the DC bus capacitor on the frequency coupling characteristics of the system, the accuracy of the resonance analysis of the wind power grid-connected system can be improved.

[0088] In summary, the present invention solves the problems of complex impedance modeling process and low accuracy of the direct-drive wind farm considering the characteristics of the DC bus capacitor, and has high practical value for analyzing the resonance problem of the wind power grid-connected system.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the technical solutions. Those of ordinary skill in the art should understand that any modifications or equivalent replacements to the technical solutions of the present invention without departing from the purpose and scope of the present technical solution shall be covered by the scope of the claims of the present invention.

Claims

1. A method for resonance analysis of a wind power grid-connected system, characterized in that It includes the following steps: Step S1: Based on the dynamic characteristics of the direct-drive wind turbine unit in the wind power system, obtain a simplified dynamic model of the direct-drive wind turbine unit; Step S2: Based on the simplified dynamic model of the direct-drive wind turbine unit and Kirchhoff's law, obtain an electrical analytical model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor; Step S3: Inject a small AC voltage perturbation on the AC side, linearize the electrical analytical model of the direct-drive wind turbine, and obtain a linearized single-phase analytical model; Step S4: Use the harmonic state space theory to perform a steady-state processing on the linearized single-phase analytical model, and construct a harmonic matrix model of the direct-drive wind turbine; Step S5: Based on the mathematical relationship between the control variables in the power grid system, establish a small-signal model of the control link and convert it into a matrix form; Step S6: Based on the physical definition of impedance and the harmonic matrix model of the direct-drive wind turbine, obtain an impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor; Step S7: According to the impedance model of the direct-drive wind turbine obtained in S6, analyze the resonance problem of the wind power grid-connected system.

2. The resonance analysis method for a wind power grid-connected system according to claim 1, characterized in that: In S1, the simplified dynamic model of the direct-drive wind turbine is a grid-connected inverter model in which the electromagnetic and electromechanical dynamic behaviors of the generator and the machine-side converter are ignored, and the DC side is a parallel connection of a DC current source and a DC bus capacitor.

3. The resonance analysis method for a wind power grid-connected system according to claim 2, characterized in that: In S2, the electrical analytical model of the direct-drive wind turbine is: Among them, L is the AC filtering inductor, C is the DC bus capacitor, and i gj is the phase current of the j-phase AC side flowing through the filtering inductor, and u gj is the grid voltage of the j-phase AC side, m j is the modulation signal of the j-phase of the grid-side converter, and u dc is the DC bus voltage, and i dc is the equivalent output DC current at the front end of the direct-drive wind turbine. j represents a variable and j = a, b, c, where a, b, and c represent phase a, phase b, and phase c respectively.

4. The resonance analysis method for a wind power grid-connected system according to claim 3, wherein: In S3, assume that a small AC voltage perturbation is injected on the AC side of the direct-drive wind turbine, apply the small-signal linearization method and combine the symmetry characteristics of the three-phase balanced system to obtain a linearized single-phase analytical model of the direct-drive wind turbine; Among them, L is the AC filter inductor, Δi g is a small disturbance of the AC current, Δu g is a small disturbance of the AC voltage, Δm is a small disturbance of the modulation signal, Δu dc is a small disturbance of the DC bus, C is the DC bus capacitor, Δi dc is the small-signal component of the DC load current, M is the steady-state value of the modulation signal, i g is the steady-state value of the AC current, t is time.

5. The resonance analysis method for a wind power grid-connected system according to claim 4, characterized in that: In S4, use the harmonic state space theory to convert the periodic time-varying signal in the linearized single-phase analytical model into a time-invariant signal. Any periodic time-varying variable x(t) in the linearized single-phase analytical model of the direct-drive wind turbine is converted after HHS to: x = […x -n …x0…x n …] T ; where \(x\) represents the column vector formed after the harmonic state space transformation of the variable \(x(t)\), \(x_0\) is the DC component of \(x(t)\), and \(x\) n is the Fourier coefficient of the \(n\)th harmonic, and \(n\) is the harmonic order; The small-signal component Δx(t) of any variable in the linearized single-phase analytical model is converted after HHS to: Δx = […x p-n …x p …x p+n …] T where Δx represents the column vector formed by the small-signal component Δx(t) after harmonic state-space transformation, x p is the Fourier coefficient corresponding to the perturbation frequency, x p-n is the Fourier coefficient with a harmonic frequency of p - n, where p is the frequency corresponding to the injected small-signal perturbation component and n is the harmonic order, x p+n is the Fourier coefficient with a harmonic frequency of p + n.

6. The resonance analysis method for a wind power grid-connected system according to claim 5, characterized in that: In S4, the product of the small-signal component Δx(t) and the steady-state component a(t) is changed through the harmonic state space to: Among them, A is the Toeplitz matrix of a(t), a0 is the DC component of the steady-state parameter, and a +1 represents a pair of conjugate fundamental frequency Fourier coefficients of the steady-state parameter, and a +2 represents a pair of conjugate second harmonic Fourier coefficients of the steady-state parameter, x p-1 is the Fourier coefficient with frequency p-, and x p is the Fourier coefficient with frequency p + 1, and x p+1 is the Fourier coefficient with frequency p + 1.

7. The resonance analysis method for a wind power grid-connected system according to claim 6, characterized in that: In S4, the harmonic matrix model of the direct-drive wind turbine is: where Δs is a differential operator matrix, Δi g is a column vector formed after the harmonic state space transformation of the alternating current, Δu g is a column vector formed after the harmonic state space transformation of the alternating voltage, Δm is a column vector formed after the harmonic state space transformation of the modulation signal, U dc is the steady-state value of the DC voltage, M is a time-invariant coefficient matrix of the modulation signal; Δu dc is a column vector formed after the harmonic state space transformation of the DC bus voltage, Δi dc is a column vector formed after the harmonic state space transformation of the DC bus current, I g is a time-invariant coefficient matrix of the alternating current; where, ΔI p+n and ΔI p-n are the amplitudes of small AC current perturbations at frequencies f p +nf1 and f p -nf1 respectively; α p+n and α p-n are the phase angles of small AC current perturbations at frequencies f p +nf1 and f p -nf1 respectively; ΔU p+n and ΔU p-n are the amplitudes of small AC voltage perturbations at frequencies f p +nf1 and f p -nf1 respectively; θ p+n and θ p-n are the phase angles of small AC voltage perturbations at frequencies f p +nf1 and f p -nf1 respectively; ΔM p+n and ΔM p-n are the amplitudes of small modulation signal perturbations at frequencies f p +nf1 and f p -nf1 respectively; β p+n and β p-n are the phase angles of small modulation signal perturbations at frequencies f p +nf1 and f p -nf1 respectively; ΔU dc is the amplitude of the small DC voltage perturbation; ΔI dc is the amplitude of the small DC current perturbation.

8. The resonance analysis method for a wind power grid-connected system according to claim 7, wherein: In S5, the matrix form of the small-signal model of the control link is: G u = -T d- G i G udc ; G i = T d- (G i T d+ + K d T q+ ) + T q- (G i T q+ - K d T d+ ); Among them, Δm is a column vector formed after the modulation signal undergoes harmonic state space transformation; G u represents the current control loop transfer function matrix, G i represents the current control loop transfer function matrix, T d- represents the d-axis dq inverse transformation transfer matrix, G udc represents the transfer function matrix between the DC voltage loop and the modulation signal; T d+ represents the d-axis dq forward transformation transfer matrix, K d represents the decoupling coefficient matrix, T q+ represents the q-axis dq forward transformation transfer matrix, T q- represents the q-axis dq inverse transformation transfer matrix.

9. The method for analyzing resonance of a wind power grid-connected system according to claim 8, characterized in that: In S6, the impedance model of the direct-drive wind turbine considering the dynamics of the DC bus capacitor is: Among them, Z ac represents the impedance model of the AC side of a direct-drive wind turbine considering the dynamics of the DC bus capacitor, and G iac is the transfer function matrix between the current control loop and the modulation signal.

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