CN114912277B - Complex vector impedance modeling method and system for permanent magnet direct-drive wind turbine based on HSS - Google Patents

Abstract

The present invention relates to a complex vector impedance modeling method and system of a permanent magnet direct-drive fan based on HSS, and relates to the technical field of modeling of permanent magnet direct-drive fans. The method comprises: obtaining a linear time-domain periodic system and expressing it as a Fourier series expansion; obtaining the steady-state periodic operation trajectory of each frequency harmonic of the linear time-domain periodic system; linearizing the linear time-domain periodic system to obtain a complex frequency-domain linear time-invariant system; obtaining a state space matrix containing arbitrary frequency harmonic components based on the complex frequency-domain linear time-invariant system; and establishing an equivalent impedance model of the AC side of a permanent magnet direct-drive fan containing each harmonic according to the state space matrix. The present invention can describe the harmonic characteristics of each frequency of a periodic time-varying system, and is suitable for frequency-domain modeling of each harmonic of a converter containing a large number of switching devices.

Description

Complex vector impedance modeling method and system for permanent magnet direct-drive wind turbine based on HSS

Technical Field

The present invention relates to the technical field of permanent magnet direct-drive fan modeling, and in particular to a method and system for modeling complex vector impedance of a permanent magnet direct-drive fan based on HSS.

Background Art

Permanent Magnetic Synchronous Generator (PMSG) has multiple magnetic poles, does not require gearbox transmission, and has low maintenance costs. It is widely used in onshore and offshore wind farms. Wind turbines are a typical multi-harmonic source system. The PWM pulse modulation and switching signals of the power electronic converter will generate some harmonic components when the system is running, and the interaction of harmonics of different frequencies will affect the dynamic characteristics of the AC and DC sides of the PMSG, which may cause system oscillation and instability. In addition, the multi-frequency harmonic coupling characteristics may also cause strong interactions between different wind turbines, thereby causing system instability.

Technical methods and existing problems of existing PMSG models:

The existing PMSG models mainly include: the traditional time-domain state-space model and the single-input single-output (or single-input dual-output) impedance model. One of these two models is based on time domain modeling, and the other is to regard the wind turbine as an input-output system in the form of impedance. The PMSG modeling is not considered from the perspective of frequency harmonics, and the frequency coupling characteristics generated by PMSG pulse modulation and switching signals cannot be accurately characterized, and its impact on the dynamic stability of the wind turbine grid-connected system cannot be analyzed.

Therefore, the present invention proposes a PMSG complex vector impedance modeling method based on harmonic state space (HSS). This method fully considers the frequency coupling of PMSG, can describe the harmonic characteristics of each frequency of the periodic time-varying system, and is suitable for frequency domain modeling of each harmonic of a converter containing a large number of switching devices.

Summary of the invention

The purpose of the present invention is to provide a method and system for complex vector impedance modeling of a permanent magnet direct-drive wind turbine based on HSS, which can describe the harmonic characteristics of each frequency of a periodic time-varying system and is suitable for frequency domain modeling of each harmonic of a converter containing a large number of switching devices.

To achieve the above object, the present invention provides the following solutions:

A complex vector impedance modeling method for a permanent magnet direct-drive wind turbine based on HSS, comprising:

Acquire a linear time-domain periodic system, wherein the linear time-domain periodic system includes a permanent magnet direct-drive fan system;

Representing the linear time-domain periodic system as a Fourier series expansion;

Obtaining the steady-state periodic operation trajectory of each frequency harmonic of the linear time-domain periodic system;

Based on the Fourier series expansion and the steady-state periodic operation trajectory of each frequency harmonic, the linear time-domain periodic system is linearized to obtain a complex frequency-domain linear time-invariant system;

Based on the complex frequency domain linear time-invariant system, a state space matrix containing arbitrary frequency harmonic components is obtained;

An equivalent impedance model of the AC side of a permanent magnet direct-drive wind turbine containing various harmonics is established according to the state space matrix.

Optionally, the state space model of the linear time-domain periodic system is:

Among them, this equation is the system state space expression expressed in the complex frequency domain, and the original equation is in That is the state matrix A(t) of the state space expression, is the state vector x(t) of the state space expression, is the input matrix B(t) of the state-space expression, It is the input vector of the state space expression, also called the control vector u(t).

Optionally, linearizing the linear time-domain periodic system to obtain a complex frequency-domain linear time-invariant system specifically includes:

The linearization adopts the following formula:

Among them, (jnω ₁ +s)x _n is the differential of the nth harmonic component of the system state variable x(t), is the product of the harmonic state coefficient matrix and the state vector, It is the multiplication of the harmonic input coefficient matrix and the input vector.

Optionally, establishing an equivalent impedance model of the permanent magnet direct-drive wind turbine AC side containing harmonics according to the state space matrix specifically includes:

constructing a harmonic transfer function based on the state-space matrix;

Obtain the AC side voltage and AC side current of the permanent magnet direct drive fan;

Constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the AC side voltage and the AC side current;

An equivalent impedance model of the permanent magnet direct-drive fan on the AC side is constructed according to the state space model of the permanent magnet direct-drive fan.

Optionally, the state space model of the permanent magnet direct-drive fan is:

Among them, Δv _αβ = Δv _α + Δjv _β is the complex vector of the small signal disturbance of the voltage at the PCC point in the αβ stationary coordinate system, which is combined into a matrix as the input vector matrix of the state space model; Δi _αβ = Δi _α + Δji _β is the complex vector of the small signal disturbance of the current at the PCC point in the αβ stationary coordinate system, which is combined into a matrix as the state vector of the state space model; "*" represents the conjugate of the complex vector, and the whole is in the form of In the format of, the derivative form of the state variable = state matrix * state vector + input matrix * input vector.

Optionally, the equivalent impedance model expression of the permanent magnet direct-drive fan AC side is:

<Δv _αβ (s)>＝<Z _wf (s)><Δi _αβ (s)>

Among them, Z _wf (s) is the equivalent impedance matrix of the permanent magnet direct-drive wind turbine on the AC side, and Z _wf (s) is a 2*2 matrix; are the state variables and periodic inputs of the state space model of the permanent magnet direct-drive wind turbine, respectively; Δv _αβ ＝Δv _α +Δjvβ, is the complex vector of the small signal disturbance of the voltage at the PCC point in the αβ stationary coordinate system; Δi _αβ ＝Δi _α +Δji _β , is the complex vector of the small signal disturbance of the current at the PCC point in the αβ stationary coordinate system; “*” indicates the conjugate of the complex vector.

Optionally, there are multiple state space matrices.

Optionally, the state space matrix is in the form of:

Among them, the matrix A is a Toeplitz matrix, _Ah is the Fourier coefficient of the h-th harmonic component of the state matrix A(t) of the permanent magnet direct-drive wind turbine state space model, for example: _A0 is the Fourier coefficient of the 0-th harmonic component of the state matrix A(t).

A complex vector impedance modeling system for a permanent magnet direct-drive wind turbine based on HSS, comprising:

A linear time-domain periodic system acquisition module, used to acquire a linear time-domain periodic system, wherein the linear time-domain periodic system includes a permanent magnet direct-drive fan system;

A Fourier series expansion module, used for expressing the linear time-domain periodic system as a Fourier series expansion;

A steady-state periodic operation trajectory acquisition module is used to acquire the steady-state periodic operation trajectory of each frequency harmonic of the linear time-domain periodic system;

A linearization module, used for linearizing the linear time-domain periodic system based on the Fourier series expansion and the steady-state periodic operation trajectory of each frequency harmonic to obtain a complex frequency-domain linear time-invariant system;

A state space matrix determination module, used for obtaining a state space matrix containing arbitrary frequency harmonic components based on the complex frequency domain linear time invariant system;

The permanent magnet direct-drive fan AC side equivalent impedance model establishment module is used to establish the permanent magnet direct-drive fan AC side equivalent impedance model containing each harmonic according to the state space matrix.

Optionally, the permanent magnet direct-drive fan AC side equivalent impedance model establishment module specifically includes:

A harmonic transfer function construction unit, used for constructing a harmonic transfer function according to the state space matrix;

An AC side voltage and AC side current acquisition unit, used to acquire the AC side voltage and AC side current of the permanent magnet direct-drive fan;

A permanent magnet direct-drive fan state space model building unit, used to build a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the AC side voltage and the AC side current;

The permanent magnet direct-drive fan AC side equivalent impedance model construction unit is used to construct the permanent magnet direct-drive fan AC side equivalent impedance model according to the permanent magnet direct-drive fan state space model.

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

The present invention is based on the harmonic state space, expresses each state variable of the system as a Fourier series, linearizes the system based on the steady-state periodic operation trajectory of each frequency harmonic, transforms the linear time domain periodic system into a complex frequency domain linear time-invariant system, and on this basis, derives the state space matrix containing arbitrary frequency harmonic components, thereby obtaining the PMSG AC side equivalent impedance model with multi-frequency harmonic coupling characteristics. This method fully considers the frequency coupling of PMSG, can describe the harmonic characteristics of each frequency of the periodic time-varying system, and is suitable for frequency domain modeling of each harmonic of converters containing a large number of switching devices.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

FIG1 is a flow chart of a method for modeling complex vector impedance of a permanent magnet direct-drive wind turbine based on HSS according to the present invention;

FIG2 is a flow chart of constructing the harmonic transfer function of the LTP system using the HSS method of the present invention;

FIG3 is a classic structure diagram of a PMSG according to the present invention;

FIG4 is a schematic diagram of a transfer function of a multi-input multi-output system according to the present invention;

FIG5(a) is a comparison diagram of the equivalent impedance analytical model (h=3) of the PMSG AC side of the present invention and the PSCAD simulation results, respectively comparing the amplitude and phase angle of Z _wf11 (s) and Z _wf22 (s);

FIG5( b ) is a comparison diagram of the equivalent impedance analytical model (h=3) of the PMSG AC side of the present invention and the PSCAD simulation results, respectively comparing the amplitude and phase angle of Z _wf12 (s) and Z _wf21 (s);

FIG6(a) is a schematic diagram showing the influence of the harmonic order of the HSS model of the present invention on the accuracy of the equivalent impedance analytical model of the PMSG AC side, and compares the amplitude and phase angle of Z _wf11 (s) and Z _wf22 (s);

FIG6( b ) is a schematic diagram showing the influence of the harmonic order of the HSS model of the present invention on the accuracy of the equivalent impedance analytical model of the PMSG AC side, and compares the amplitude and phase angle of Z _wf12 (s) and Z _wf21 (s);

FIG. 7 is a schematic diagram showing a comparison between the PMSG AC side equivalent impedance analytical model (h=3) of the present invention and the RTDS hardware-in-the-loop experimental results.

DETAILED DESCRIPTION

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

The purpose of the present invention is to provide a method and system for complex vector impedance modeling of a permanent magnet direct-drive wind turbine based on HSS, which can describe the harmonic characteristics of each frequency of a periodic time-varying system and is suitable for frequency domain modeling of each harmonic of a converter containing a large number of switching devices.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

First, the technical concept of the present invention is summarized as follows:

The present invention proposes a PMSG complex vector impedance modeling method containing various harmonics based on HSS, which can be used for multi-frequency coupling mechanism analysis of the system.

The method mainly includes the following contents: Considering that each state variable and state space matrix in the PMSG system are periodic time-varying signals, the proposed method expresses each state variable in the form of Fourier series expansion, and then linearizes the system based on the steady-state periodic operation trajectory of each frequency harmonic, thereby transforming the linear time-varying periodic system (LTP) into a complex frequency domain linear time invariant system (LTI). On this basis, the state space matrix containing arbitrary frequency harmonic components is derived, and the equivalent impedance model of the PMSG AC side containing each harmonic is established. Finally, an example is used to analyze the influence of multi-frequency coupling characteristics on the equivalent impedance of the PMSG AC side and the system stability criterion.

Specifically, FIG. 1 is a flow chart of a method for modeling complex vector impedance of a permanent magnet direct-drive wind turbine based on HSS of the present invention. As shown in FIG. 1 , a method for modeling complex vector impedance of a permanent magnet direct-drive wind turbine based on HSS includes:

Step 101: Acquire a linear time-domain periodic system, wherein the linear time-domain periodic system includes a permanent magnet direct-drive fan system.

Step 102: Express the linear time-domain periodic system as a Fourier series expansion.

Step 103: Obtain the steady-state periodic operation trajectory of each frequency harmonic of the linear time-domain periodic system.

Step 104: Linearize the linear time-domain periodic system based on the Fourier series expansion and the steady-state periodic operation trajectory of each frequency harmonic to obtain a complex frequency-domain linear time-invariant system.

Step 105: Obtain a state space matrix containing arbitrary frequency harmonic components based on the complex frequency domain linear time-invariant system.

Step 106: Establishing an equivalent impedance model of the permanent magnet direct-drive wind turbine on the AC side including each harmonic according to the state space matrix.

Based on the above steps 101 to 106, the specific implementation process of the present invention is as follows:

Step 1: Derive the exponential periodic signal and its properties.

The purpose of step 1 is to derive a theorem applicable to any LTP system, namely, "for any LTP system, the state variables and the state space matrix can be expressed in exponential form in the complex domain" and derive the derivation of the HSS model in subsequent step 2 based on the result of step 1. The purpose of step 1 is to prove that for any LTP system, the state variables and the state space matrix can be expressed in exponential form in the complex domain.

Specifically, assume that the state space expression of an LTP system is:

in, is the derivative form of the state vector, A(t) is the state matrix, x(t) is the state variable, B(t) is the input matrix, u(t) is the input vector also called the control vector, y is the output vector, C(t) is the output matrix, and D(t) is the feedforward matrix.

To convert the LTP system into an LTI system in the frequency domain, we must first transform the periodic signal into an exponential form in the complex domain. The periodic signal in the complex domain exponential form (Exponentially Modulated Periodic Signal, EMPS) is usually expressed as the product of a periodic signal and a complex domain exponential signal. Let u(t) be the periodic input signal of the system, and its complex domain exponential form is expressed as follows:

Where, _un —coefficient of the Fourier series of periodic signal;

ω — Arbitrary reference frequency of a periodic system.

The above formula is a periodic signal in the exponential form of the complex domain. The above formula shows that all signals in the complex domain can be expressed in EMPS form, that is, EMPS can equivalently represent all signals with physical meaning, which is a necessary condition for the conversion of the LTP system to the LTI system in the frequency domain. In addition, according to Floquet theory, the transient response of the LTP system can be equivalently represented by the state transfer matrix:

Where Ф(t)=e ^A(t) represents the state transfer matrix of the system, the term P ^-1 ( _t0 )x( _t0 ) on the right side of the equation is a constant, the term e ^Q(t-t0) represents the exponential matrix, P(t) is a periodic transformation matrix, and Q represents the diagonal matrix composed of the eigenvalues of the state space matrix of the LTP system. According to the properties of the state transfer matrix, equation (3) is substituted into equation (1) and expressed in EMPS form, that is:

There exists a variable v(t) such that the state x(t) satisfies the following similarity transformation:

x(t)＝P(t)v(t)

Assuming t ₀ = 0, the variable v(t) can be represented by the state transfer matrix:

Among them, Ф(t,τ)＝Ф(t,0)·Ф(0,τ), and Ф(t,0)＝e ^Q(t) , Ф(0,τ)＝e ^-Q(τ) . Therefore, equation (6) can be rewritten as:

Substituting equation (2) into equation (7) yields the EMPS form of the variable v(t):

Assuming s _l =jω ₁ +s, equation (8) can be rewritten as:

set up

Substituting formula (9) into formula (4) yields:

In formula (10), _xs (t) is the state variable x(t) in EMPS form.

The above analysis process shows that the state variables and state space matrix of the LTP system can be expressed in exponential form in the complex domain. This condition is the basis for establishing the HSS model.

Step 2: Derive the HSS method to rewrite the LTP system, where step 2 derives the corresponding "state space matrix containing arbitrary frequency harmonic components", which is formula (16), and the derived state space equation is formula (15).

Step 1 has proved that for any LTP system, its state variables and state space matrix can be expressed in exponential form in the complex domain. Therefore, the state variables and state space matrix of formula (1) are expressed in exponential form in the complex domain, and formula (11) is obtained. That is, since the state variables, input and output quantities and state transfer matrix in the state space model of the LTP system are periodic functions, they can be expressed by EMPS. Then the system state space model can be rewritten as:

Among them, this equation is the system state space expression expressed in the complex frequency domain, and the original equation is in That is the state matrix A(t) of the state space expression, is the state vector x(t) of the state space expression, is the input matrix B(t) of the state-space expression, It is the input vector of the state space expression, also called the control vector u(t).

The solution of the state variable in the above equation is in the form of Fourier series, x _-∞ ,…,x _-1 ,x ₀ ,x ₁ ,…,x _∞ . According to the harmonic balance theory, the steady-state values of the harmonics of the LTP system are linearly independent, so the derivatives of the harmonics in their periodic steady-state operation trajectory are also linearly independent. Then equation (11) can be simplified as:

Divide both sides of equation (12) We can get:

Among them, (jnω ₁ +s)x _n is the differential of the nth harmonic component of the system state variable x(t), is the product of the harmonic state coefficient matrix and the state vector, It is the multiplication of the harmonic input coefficient matrix and the input vector.

In the above formula, the differential equivalent of the nth harmonic component of the LTP system state variable x(t) is expressed as the sum of the harmonic state coefficient matrix and the input coefficient matrix. When linearized in the neighborhood of the system steady-state periodic operation trajectory, all coefficients in formula (13) are time-invariant. The above process converts the LTP system into an LTI system in the frequency domain. Similarly, the output of the state space model can also be expressed in Fourier series:

Considering each harmonic and writing it in matrix form, equations (13) and (14) can be expressed as:

Among them, matrices A, B, C, and D are all Toeplitz matrices. Taking matrix A as an example, its form is shown in formula (16), where _Ah is the Fourier coefficient of the h-th harmonic component of A(t), and N is the diagonal matrix composed of each harmonic component, as shown in formula (17). The above model is the harmonic state space matrix, which can be used to construct the harmonic transfer function (HTF). The process is shown in Figure 2.

Among them, the matrix A is a Toeplitz matrix, _Ah is the Fourier coefficient of the h-th harmonic component of the state matrix A(t) of the permanent magnet direct-drive wind turbine state space model, for example: _A0 is the Fourier coefficient of the 0-th harmonic component of the state matrix A(t).

Step 3: Establish the PMSG harmonic state space model, where steps 1 and 2 express an arbitrary LTP system in the form of formula (1) in the form of formulas (15), (16) and (17), and derive the state space matrix containing arbitrary frequency harmonic components. Then step 3 uses the method of steps 1 and 2 to derive and establish the "PMSG AC side equivalent impedance model containing each harmonic", which is equivalent to the universal results derived in steps 1 and 2. Step 3 applies it to the PMSG model. PMSG is also an LTP system, so the AC side equivalent impedance model of the PMSG system is derived.

Specifically, in order to establish the harmonic state space model of PMSG, it is necessary to first derive the PMSG state space model based on complex vectors, as shown in equation (18):

in:

In formula (19), Δv _αβ = Δv _α + Δjv _β is the complex vector of the small signal disturbance of the voltage at the PCC point in the αβ stationary coordinate system, Δi _αβ = Δi _α + Δji _β is the complex vector of the small signal disturbance of the current at the PCC point in the αβ stationary coordinate system; “*” represents the conjugate of the complex vector. According to the circuit structure of PMSG in Figure 3, the complex vector expressions of the voltage and current on the AC side of PMSG can be obtained:

Where, Δd _αβ , Δd _α ^* _β —complex vectors of GSC switch duty cycle disturbance response in the stationary coordinate system;

Δv _αβ , Δv _α ^* _β —complex vectors of grid-side voltage disturbance components in the stationary coordinate system;

Δi _αβ , Δi _α ^* _β —complex vector of the grid-side current disturbance component in the stationary coordinate system;

In formula (20), D _αβ0 (t) = D _α0 (t) + jD _β0 (t), which represents the complex vector of the GSC switch duty cycle in the stationary coordinate system; and V _dc0 · D _αβ0 (t) = V _c0 (t) = ωL _f i _αβ0 (t) + v _αβ0 (t), V _c (t) represents the voltage of the PMSG grid-side filter capacitor to the ground in the stationary coordinate system. When considering the multi-frequency harmonics of the converter, the expressions of V _c (t) and its conjugate V _C ^* (t) are:

Where V _c0 , V c1, …, V _ch represent the coefficients of the Fourier series of V _c0 (t); the PMSG state space model is:

in:

It can be seen that:

In the above formula, i _αβ0 (t) represents the steady-state value of the PMSG output current complex vector in the stationary coordinate system, v _αβ0 (t) represents the steady-state value of the PMSG grid-connected point voltage complex vector in the stationary coordinate system, and:

Combining equations (15), (22) and (25), the harmonic state space model of PMSG can be obtained, namely:

Among them, Δv _αβ = Δv _α + Δjv _β is the complex vector of the small signal disturbance of the voltage at the PCC point in the αβ stationary coordinate system, which is combined into a matrix as the input vector matrix of the state space model; Δi _αβ = Δi _α + Δji _β is the complex vector of the small signal disturbance of the current at the PCC point in the αβ stationary coordinate system, which is combined into a matrix as the state vector of the state space model; "*" represents the conjugate of the complex vector, and the whole is in the form of In the format of, the derivative form of the state variable = state matrix * state vector + input matrix * input vector.

A ₀ (s) is the Laplace transform of the state space matrix A(t) when D _αβ0 (t) = V _c 0, i _αβ0 (t) = I ₀ , v _αβ0 (t) = V _0. Similarly, A _±1 (s), A _±2 (s), ..., A _±h (s) can be obtained; similarly, B _±1 (s), B _±2 (s), ..., B _±h (s) can be obtained. The equivalent impedance of the PMSG AC side considering the multi-frequency coupling characteristics can be deduced from equation (26), which is expressed as:

Among them, Z _wf (s) is the equivalent impedance matrix of the PMSG AC side, which is a 2*2 matrix. are the state variables and periodic inputs of the PMSG state space model. Referring to formulas (18) and (19), Δv _αβ ＝Δv _α +Δjvβ, which is the complex vector of the small signal disturbance of the voltage at the PCC point in the αβ stationary coordinate system, Δi _αβ ＝Δi _α +Δjiβ, which is the complex vector of the small signal disturbance of the current at the PCC point in the αβ stationary coordinate system; “*” represents the conjugate of the complex vector.

For ease of understanding, the transfer function of the multi-input and multi-output PMSG grid-connected system is shown in Figure 4. From the graph, it can be seen that the HSS model constructs the transfer function of the multi-frequency harmonic disturbance response component of the PMSG AC side current with respect to the small disturbance harmonic voltage input, thereby equivalently obtaining the PMSG impedance model considering multi-frequency coupling.

The present invention verifies the effectiveness and accuracy of the proposed method through simulation and RTDS hardware-in-the-loop experiments.

The complete structure of the PMSG used in the simulation is shown in Figure 3, and its parameters are shown in Table 1. The d-axis and q-axis parameters of the inner loop current controller are set as follows: k _pid = 0.92, k _iid = 105; k _piq = 0.71, k _iiq = 158. The comparison of the equivalent impedance of the PMSG AC side considering multi-frequency coupling derived by the proposed analytical method and the amplitude-frequency characteristics obtained by the PSCAD/EMTDC simulation frequency sweep is shown in Figures 5(a) and 5(b). The solid line represents the analytical result, and the dotted line represents the simulation result.

Table 1 Parameters of permanent magnet direct drive synchronous generator

The harmonic order of the analytical model is h = 3. It can be seen that the two curves are highly similar, which shows the effectiveness of this method. In addition, Z _wf11 (s) and Z _wf22 (s) in Figure 5 represent the diagonal elements in the PMSG AC side equivalent impedance matrix Z _wf (s) derived based on the HSS method. By observing Figures 5(a) and 5(b), the following conclusions can be drawn:

1) The phase of Z _wf11 (s) jumps at a frequency of about 50 Hz, which is mainly caused by the phase-locked loop;

2) The high-frequency characteristics of the system mainly depend on the parameters of the PMSG port filter capacitor and inductor, and the high-frequency characteristics of the positive and negative sequence impedances are the same.

3) Z _wf11 (s) and Z _wf22 (s) show a negative resistance effect near the fundamental frequency. In this frequency band, wind turbines are prone to interact with the AC power grid, which may lead to system oscillation.

4) The off-diagonal elements Z _wf12 (s) and Z _wf21 (s) in Z _wf (s) reflect the frequency coupling characteristics of the system. Moreover, when the dq-axis controller parameters are asymmetric, the amplitudes of Z _wf12 (s) and _{Z wf21} (s) in the low frequency band are close to Z _wf11 (s). At this time, the frequency coupling characteristics generated by PMSG grid connection cannot be ignored.

Figure 6(a) and Figure 6(b) reflect the influence of the harmonic order considered in the HSS model of PMSG on the accuracy of PMSG impedance modeling. It can be seen from the figure that the higher the harmonic order considered in the HSS model, the more accurate the analytical impedance model. However, the higher the harmonic order in the HSS model, the greater the amount of calculation. Generally, the analytical model has a higher accuracy when h=3.

In addition, the present invention verifies the effectiveness of the proposed method by comparing and analyzing the analytical model and the RTDS hardware-in-the-loop experimental results. Figure 7 compares the equivalent impedance of the PMSG AC side obtained by the analytical model and the frequency sweep experiment. It can be seen from the figure that the experimental results are basically consistent with the analytical model. It is worth noting that the difference between the experimental sweep results in the low frequency range (frequency <200Hz) and the analytical model is greater than the difference in the high frequency range, which is related to the presence of more interference signals in the fundamental frequency range.

In addition, based on the above method, the present invention also provides a permanent magnet direct-drive wind turbine complex vector impedance modeling system based on HSS, comprising:

The linear time-domain periodic system acquisition module is used to acquire a linear time-domain periodic system, wherein the linear time-domain periodic system includes a permanent magnet direct-drive fan system.

The Fourier series expansion module is used to express the linear time-domain periodic system as a Fourier series expansion.

The steady-state periodic operation trajectory acquisition module is used to acquire the steady-state periodic operation trajectory of each frequency harmonic of the linear time-domain periodic system.

The linearization module is used to linearize the linear time-domain periodic system based on the Fourier series expansion and the steady-state periodic operation trajectory of each frequency harmonic to obtain a complex frequency-domain linear time-invariant system.

The state space matrix determination module is used to obtain a state space matrix containing arbitrary frequency harmonic components based on the complex frequency domain linear time-invariant system.

The permanent magnet direct-drive fan AC side equivalent impedance model establishment module is used to establish the permanent magnet direct-drive fan AC side equivalent impedance model containing each harmonic according to the state space matrix.

In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims (5)

1. The complex vector impedance modeling method of the permanent magnet direct-driven fan based on the HSS is characterized by comprising the following steps of:

acquiring a linear time domain period system, wherein the linear time domain period system comprises a permanent magnet direct-drive fan system;

representing the linear time domain periodic system as a fourier series expansion;

Acquiring a steady-state periodic running track of each frequency harmonic of the linear time domain periodic system;

linearizing the linear time domain periodic system based on the Fourier series expansion and steady-state periodic running tracks of each frequency harmonic to obtain a complex frequency domain linear time invariant system, which comprises the following steps:

linearization uses the following formula:

Where (jn omega ₁+s)x_n) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,Multiplying each subharmonic input coefficient matrix with an input vector;

obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time-invariant system;

Establishing an equivalent impedance model of the alternating current side of the permanent magnet direct-driven fan containing each subharmonic according to the state space matrix, wherein the equivalent impedance model comprises the following specific steps:

Constructing a harmonic transfer function according to the state space matrix;

Acquiring alternating-current side voltage and alternating-current side current of a permanent magnet direct-drive fan;

constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current, wherein the permanent magnet direct-drive fan state space model is as follows:

The Deltav _αβ＝Δv_α+Δjv_β is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi _αβ＝Δi_α+Δji_β is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; ". Times" represent the conjugate of complex vectors;

Constructing a permanent magnet direct-drive fan alternating-current side equivalent impedance model according to the permanent magnet direct-drive fan state space model, wherein the permanent magnet direct-drive fan alternating-current side equivalent impedance model expression is as follows:

Δv_αβ(s)＝Z_wf(s)Δi_αβ(s)

Wherein Z _wf(s) is an equivalent impedance matrix of the alternating current side of the permanent magnet direct drive fan, Z _wf(s) is a matrix of 2x 2, The method is characterized in that the method comprises the steps of respectively inputting state variables and periods of a state space model of a permanent magnet direct-driven fan, wherein Deltav _αβ＝Δv_α+Δjv_β is a complex vector of small-signal disturbance of PCC point voltage under an alpha beta static coordinate system, deltai _αβ＝Δi_α+Δji_β is a complex vector of small-signal disturbance of PCC point current under the alpha beta static coordinate system, and 'x' represents conjugation of the complex vector.

2. The HSS-based complex vector impedance modeling method of a permanent magnet direct drive fan of claim 1, wherein the state space model of the linear time domain periodic system is:

wherein the equation is a system state space expression expressed in the complex frequency domain, wherein I.e. a state matrix a (t) which is a state space expression,A state vector x (t) which is a state space expression,An input matrix B (t) being a state space expression,I.e. the input vector u (t) of the state space expression.

3. The HSS-based permanent magnet direct drive fan complex vector impedance modeling method of claim 1, wherein the state space matrix is a plurality of.

4. The HSS-based complex vector impedance modeling method of permanent magnet direct drive fan of claim 3, wherein one of said state space matrices has a matrix form of:

The matrix A is Toeplitz matrix, A _h is the Fourier coefficient of the h harmonic component of the state matrix A (t) of the state space model of the permanent magnet direct drive fan, and A ₀ is the Fourier coefficient of the 0 th harmonic component of the state matrix A (t).

5. The utility model provides a permanent magnetism direct drive fan complex vector impedance modeling system based on HSS which characterized in that includes:

The linear time domain periodic system acquisition module is used for acquiring a linear time domain periodic system, wherein the linear time domain periodic system comprises a permanent magnet direct-drive fan system;

The Fourier series expansion module is used for representing the linear time domain periodic system as Fourier series expansion;

The steady-state periodic operation track acquisition module is used for acquiring steady-state periodic operation tracks of all frequency harmonics of the linear time domain periodic system;

The linearization module is used for linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system, and specifically comprises the following steps:

linearization uses the following formula:

Where (jn omega ₁+s)x_n) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,Multiplying each subharmonic input coefficient matrix with an input vector;

the state space matrix determining module is used for obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time invariant system;

the permanent magnet direct-driven fan alternating current side equivalent impedance model building module is used for building a permanent magnet direct-driven fan alternating current side equivalent impedance model containing various subharmonics according to the state space matrix, and specifically comprises the following steps:

a harmonic transfer function construction unit for constructing a harmonic transfer function according to the state space matrix;

the alternating-current side voltage and alternating-current side current acquisition unit is used for acquiring alternating-current side voltage and alternating-current side current of the permanent magnet direct-drive fan;

the permanent magnet direct-drive fan state space model construction unit is used for constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current, and the permanent magnet direct-drive fan state space model is as follows:

The Deltav _αβ＝Δv_α+Δjv_β is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi _αβ＝Δi_α+Δji_β is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; ". Times" represent the conjugate of complex vectors;

The permanent magnet direct-driven fan alternating-current side equivalent impedance model construction unit is used for constructing a permanent magnet direct-driven fan alternating-current side equivalent impedance model according to the permanent magnet direct-driven fan state space model, and the permanent magnet direct-driven fan alternating-current side equivalent impedance model expression is as follows:

Δv_αβ(s)＝Z_wf(s)Δi_αβ(s)

Wherein Z _wf(s) is an equivalent impedance matrix of the alternating current side of the permanent magnet direct drive fan, Z _wf(s) is a matrix of 2x 2, The method is characterized in that the method comprises the steps of respectively inputting state variables and periods of a state space model of a permanent magnet direct-driven fan, wherein Deltav _αβ＝Δv_α+Δjv_β is a complex vector of small-signal disturbance of PCC point voltage under an alpha beta static coordinate system, deltai _αβ＝Δi_α+Δji_β is a complex vector of small-signal disturbance of PCC point current under the alpha beta static coordinate system, and 'x' represents conjugation of the complex vector.