Modeling and stability analysis method of brushless doubly-fed wind turbine considering frequency coupling effect

Abstract

The present invention discloses a brushless doubly-fed wind turbine modeling and stability analysis method taking into account the frequency coupling effect. The method takes into account the influence of the asymmetric control link on the input admittance of the system, and establishes an analytical model of the frequency coupling characteristics of the brushless doubly-fed wind turbine. First, based on the harmonic linearization method, the brushless doubly-fed wind turbine body and the control link are linearized and modeled; secondly, through coordinate transformation, the linearized models of the brushless doubly-fed wind turbine body and the control link are combined; thirdly, the complete analytical expression of the brushless doubly-fed wind turbine system is derived; the method also provides the steps of analyzing the stability analysis of the brushless doubly-fed wind turbine under weak power grid conditions by using the generalized Nyquist stability criterion based on the established analytical model. The present invention provides an important reference for the stability analysis of the brushless doubly-fed wind turbine grid-connected system.

Description

Technical Field

[0001] The invention belongs to the field of small signal stability research of a brushless doubly-fed fan, and in particular relates to a modeling and stability analysis method of a brushless doubly-fed fan taking frequency coupling effect into account. Background Art

[0002] Under the current background of "carbon peak" and "carbon neutrality", the large-scale development of new energy has become particularly important. After years of technical practice and commercial application, wind power generation has become one of the most recognized new energy power generation technologies with the most development prospects. However, most of my country's wind farms are located in the "Three Norths" region. The line transmission distance is long and needs to pass through multiple transformers, which leads to the non-negligible grid impedance. The coupling between wind farms and weak power grids continues to deepen, and the stability problems caused by it have attracted widespread attention. It is worth noting that most of the existing wind farm instability accidents at home and abroad have experienced an oscillation phenomenon of sub- / super-synchronous frequency components that are interdependent, which is called the frequency coupling effect, that is, when a disturbance component of a certain frequency appears in the voltage at the grid connection point, it will cause two current components of different frequencies. Existing studies have shown that frequency coupling is mainly caused by the asymmetric control of the phase-locked loop and the current loop in the control system.

[0003] At present, both the state space method and the impedance analysis method are widely used in the small signal stability analysis of doubly fed wind turbines. Among them, the state space method analyzes the stability of the system by writing the state equation of the weak power grid-wind farm system, calculating the characteristic values ​​of each state variable and the participation factors of each link. However, since the state equation of the entire system is written at the same time, any change in any link of the system requires the equation to be re-established for analysis. Moreover, the state space equation requires an accurate model and parameters of the system, which are sometimes difficult to obtain in actual engineering and are difficult to implement.

[0004] The impedance analysis method establishes the input impedance or admittance model of the grid-connected system, and then analyzes its stability according to the generalized Nyquist stability criterion. Compared with the state space method, the impedance analysis method can model the wind farm and the weak power grid separately. Therefore, when a certain link of the system changes, only the link needs to be modeled separately to continue the stability analysis. And the impedance or admittance model required by the impedance analysis method can be directly obtained through experimental measurement or simulation model.

[0005] Domestic and foreign scholars have conducted the following research on the small signal stability of brushless doubly-fed wind turbines:

[0006] According to the impedance analysis method, in the unified vector coordinate system, the input admittance model of the brushless doubly fed wind turbine body was first derived; then, taking into account the transmission path of the grid voltage disturbance in the control system, the transfer function model of the current loop and the phase-locked loop was established; finally, the complete input admittance model of the brushless doubly fed wind turbine system was obtained, and the stability of the system was analyzed according to the generalized Nyquist criterion. However, in the unified vector coordinate system, all variables in the brushless doubly fed wind turbine system are DC quantities, and it is impossible to analyze the influence of the frequency coupling effect caused by the disturbance frequency component on the system stability, resulting in inaccurate stability analysis results.

[0007] It is worth noting that compared with the doubly fed wind turbine, the stability study of the brushless doubly fed wind turbine is somewhat challenging due to its complex motor structure and mathematical model.

[0008] Therefore, it is necessary to establish an input admittance small signal model of the brushless doubly-fed wind turbine that comprehensively considers the motor body and the asymmetric control of the phase-locked loop and current loop in the control system. Summary of the invention

[0009] The purpose of the present invention is to address the deficiencies of the prior art and propose a brushless doubly-fed fan modeling and stability analysis method taking into account the frequency coupling effect. The present invention establishes a brushless doubly-fed fan input admittance small signal model taking into account the frequency coupling effect, and performs stability analysis on the system through stability criteria.

[0010] The object of the present invention is achieved through the following technical solution: a grid-connected brushless double-fed wind turbine modeling and stability analysis method taking into account the frequency coupling effect, comprising the following steps:

[0011] (1) Establish a frequency domain analytical model of the grid-connected brushless doubly-fed wind turbine system;

[0012] (2) Based on the brushless doubly-fed wind turbine admittance model taking into account the frequency coupling effect established in step (1) and the frequency domain impedance model of the weak grid impedance, the strength of the frequency coupling effect and the system stability are analyzed.

[0013] Further, step (1) comprises:

[0014] (1.1) Taking into account the frequency coupling characteristics of the brushless doubly fed wind turbine side converter, the frequency coupling analytical model of the brushless doubly fed wind turbine is obtained by using the relationship between the power winding voltage disturbance and the power winding current response, namely:

[0015]

[0016] Among them, the main diagonal elements Y of the admittance matrix Y(s) 11 (s) and Y 22(s) reflects the influence of the power winding voltage disturbance on the current component of the same frequency. s represents the complex frequency, s = j2πf; rather than the diagonal element Y 12 (s) and Y 21 (s) reflects the influence of the power winding voltage disturbance on the coupled frequency current component;

[0017] (1.2) Establish the voltage equation and flux equation of the brushless doubly fed wind turbine in the dq coordinate system, namely:

[0018]

[0019]

[0020] Among them, u w 、u c and u r Represent the power winding voltage, control winding voltage and rotor voltage respectively, i w 、i c and i r Respectively represent the power winding current, control winding current and rotor current, ψ w , c and ψ r Respectively represent the power winding flux, control winding flux and rotor flux; R w , R c and R r Respectively represent the power winding resistance, control winding resistance and rotor winding resistance, L w , L c and L r Respectively represent the power winding inductance, control winding inductance and rotor winding inductance, M wr represents the mutual inductance between the power winding and the rotor, M cr represents the mutual inductance between the control winding and the rotor; ω w ,ω c and ω r Respectively represent the power winding electrical angular frequency, control winding electrical angular frequency and rotor winding electrical angular frequency, where ω r =ω w -P w ω m , P w Indicates the number of power winding pole pairs, ω m Indicates the mechanical angular velocity of the motor; p represents differential operation;

[0021] (1.3) Using the harmonic linearization method, the frequency components of the voltage and current meters and frequency coupling characteristics of the brushless double-fed wind turbine power winding, rotor winding and control winding are defined respectively, namely:

[0022]

[0023]

[0024]

[0025] Among them, V wa 、V ca and V ra They represent the power winding a-phase voltage, control winding a-phase voltage and rotor a-phase voltage respectively, I wa ,I ca and V ra Respectively represent the power winding a-phase current, control winding a-phase current and rotor a-phase current; V w1 、V wp 、V wp2 are the power winding voltage and its disturbance frequency component and coupling frequency component, I w1 ,I wp ,I wp2 are the power winding current and its disturbance frequency component and coupling frequency component respectively; V c1 、V cp 、V cp2 are the control winding voltage and its disturbance frequency component and coupling frequency component, I c1 ,I cp ,I cp2 are the control winding current and its disturbance frequency component and coupling frequency component respectively; V r1 、V rp 、V rp2 are the rotor voltage and its disturbance frequency component and coupling frequency component, I r1 ,I rp ,I rp2 are the rotor current disturbance frequency component and coupling frequency component respectively; f1, f c and f r Respectively represent the fundamental frequency, control winding electrical angular frequency and rotor electrical angular frequency; P c To control the number of winding pole pairs; the above formulas are all functions in the frequency domain, f is the function independent variable, indicating the frequency;

[0026] (1.4) Establish the frequency domain model of the phase-locked loop, that is,

[0027]

[0028] Among them, K p_PLL and K i_PLL Respectively represent the proportional and integral coefficients of the phase-locked loop, V w0 represents the grid voltage amplitude, s represents the complex frequency, s = j2πf;

[0029] (1.5) Establish the frequency domain model of the current loop, that is,

[0030]

[0031] in,

[0032]

[0033] K p_cdi and K p_cqi are the proportional coefficients of the dq axis current loop controller, K i_cdi and K i_cqi are the integral coefficients of the dq axis current loop controller, M cd and M cq are the dq axis harmonic components in the current loop output modulation signal, K cd is the decoupling coefficient, K fw is the feedback coefficient;

[0034] (1.6) The frequency transformation relationship from rotor variable to power winding variable and from control winding variable to power winding variable is defined respectively, namely:

[0035]

[0036] Among them, σ rp (s) and σ rp2 (s) represent the frequency transformation formulas of the rotor disturbance frequency component and the coupling frequency component, σ cp (s) and σ cp2 (s) respectively represent the frequency conversion formulas of the control winding disturbance frequency component and the coupling frequency component; s represents the complex frequency, s = j2πf;

[0037] (1.7) Introduce the matrix C(s) and the matrix F(s), which are defined as:

[0038]

[0039] Among them, the matrix C(s) represents the effect of the current loop controller of the brushless doubly-fed machine side converter on the control winding current, the matrix F(s) represents the control effect of the voltage feedforward link in the phase-locked loop and the current loop on the power winding voltage, s represents the complex frequency, s=j2πf;

[0040] Solved:

[0041]

[0042]

[0043] Among them, V dc Indicates DC bus voltage; M c1 =M cd1+jM cq1 , is the static operating point of the modulation signal, For its conjugation; I c1 =I cd1 +jI cq1 , is the dq axis command value of the control winding current, I* c1 is its conjugate; s represents the complex frequency, s = j2πf;

[0044] Modulation gain and control delay of the generator-side converter:

[0045]

[0046] L c_p and L c_p2 is the equivalent self-inductance of the control winding caused by frequency conversion, and

[0047]

[0048] and is the asymmetric control effect of the current loop, and

[0049]

[0050] (1.8) Admittance model Y of brushless doubly-fed fan considering frequency coupling effect BDFIG ,Right now

[0051]

[0052] Among them, L w_p and L w_p2 is the equivalent self-inductance of the power winding caused by frequency conversion, and

[0053]

[0054] M p and M p2 is the equivalent mutual inductance caused by frequency conversion, and

[0055]

[0056] (9) Establish the frequency domain impedance model Z of the weak power grid impedance g ,Right now

[0057]

[0058] Among them, R g is the weak grid resistance, L g is the weak grid inductance, ω1 is the grid angular frequency, s represents the complex frequency, s=j2πf.

[0059] Further, step (2) comprises:

[0060] (2.1) Using Y 12 (s) and Y 11 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio, the stronger the frequency coupling degree in this frequency band. Similarly, for the image frequency component of the power winding, Y 21 (s) and Y 22 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio, the stronger the frequency coupling degree in the frequency band.

[0061] (2.2) The generalized Nyquist criterion is used to judge the stability of the grid-connected system. When the brushless double-fed wind turbine admittance model Y BDFIG With weak grid impedance Z g When the impedance ratio matrix satisfies the generalized Nyquist criterion, the grid-connected system is in a small signal stable state, otherwise it is in a small signal unstable state.

[0062] The beneficial effects of the present invention are as follows: the input admittance model of the brushless doubly-fed wind turbine established by the present invention not only considers the influence of the motor body and the phase-locked loop and current loop in the control system on the input admittance of the system, but also incorporates the frequency coupling effect caused by the asymmetric control structure of the phase-locked loop into the modeling process, and establishes a frequency coupling characteristic model of the brushless doubly-fed wind turbine. During the model establishment process, the meaning of each physical quantity is clear, and the input admittance model has good accuracy; the stability analysis method of the present invention considers the influence of the frequency coupling effect on the system, and improves the accuracy of the analysis results; the present invention provides a model and method for the stability analysis and frequency coupling effect research of the brushless doubly-fed wind turbine under weak power grid conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 The system block diagram of the brushless double-fed wind turbine; PCC represents the grid connection point, MSC represents the machine-side converter, GSC represents the grid-side converter, PW represents the power winding, CW represents the control winding, and Rotor represents the rotor; R g and L g Represents the grid impedance; V dc is the DC bus voltage; θ p ,θ c and θ r Respectively represent the power winding phase angle, control winding phase angle and rotor phase angle; ω w ,ω c and ω r Respectively represent the electrical angular frequency of the power winding, the electrical angular frequency of the control winding and the electrical angular frequency of the rotor winding; U wabc Indicates the three-phase voltage of the power winding, I wabc and I wabcRespectively represent the three-phase current of the power winding and the three-phase current of the control winding; U wdq and U cdq They represent the dq axis component of the power winding voltage and the dq axis component of the control winding voltage, respectively. wdq and I cdq They represent the dq axis component of the power winding voltage and the dq axis component of the control winding voltage, respectively. cdq_ref Indicates the control winding current command value, ψ cdq Indicates the dq-axis component of the control winding flux, U wαβ Represents the αβ axis component of the control winding voltage; S abc Indicates the converter switching signal output by the control system;

[0064] Figure 2 is the equivalent circuit diagram of the brushless doubly-fed fan; where U w , U c and U r Represent the power winding voltage, control winding voltage and rotor voltage respectively, I w ,I c and r Respectively represent the power winding current, control winding current and rotor current, ψ w , c and ψ r Respectively represent the power winding flux, control winding flux and rotor flux; R w , R c and R r Respectively represent the power winding resistance, control winding resistance and rotor winding resistance, L w , L c and L r Respectively represent the power winding inductance, control winding inductance and rotor winding inductance, M wr represents the mutual inductance between the power winding and the rotor, M cr represents the mutual inductance between the control winding and the rotor;

[0065] Figure 3 is the linearized phase-locked loop control structure diagram; where G SOGI represents SOGI filter, u d 、u q The voltage dq axis components, K p_PLL and K i_PLL They represent the proportional coefficient and integral coefficient of the phase-locked loop respectively, and θ is the output phase angle of the phase-locked loop;

[0066] Figure 4 Schematic diagram of the ideal synchronous rotating coordinate system and the actual synchronous rotating coordinate system; where the subscript "1" represents the phase-locked loop dq axis coordinate system, the subscript "real" represents the actual dq coordinate system of the system, θ1 is the actual phase angle of the system, and Δθ is the phase-locking error;

[0067] Figure 5 is the control structure diagram of the current loop; where H cdi and H cqi They are the current loop dq axis transfer function, K cd is the decoupling coefficient, K fw is the feedforward coefficient, M cd and M cq They are the dq-axis harmonic components in the current loop output modulation signal respectively;

[0068] Figure 6 The generalized Nyquist curve of the brushless doubly-fed wind turbine under different working conditions;

[0069] Figure 7 The simulation waveform diagram of the power winding current of the brushless double-fed fan under different working conditions;

[0070] Figure 8 This is the FFT analysis result of the brushless double-fed wind turbine power winding current waveform under working condition II;

[0071] Fig. 9 This is a comparison chart of the frequency coupling degree of the brushless doubly fed wind turbine under different working conditions. DETAILED DESCRIPTION

[0072] In order to describe the present invention in more detail, the present invention is further illustrated below with reference to the accompanying drawings and specific implementation examples.

[0073] The research object of the embodiment of the present invention is a BDFIG with a capacity of 2MW and a rated voltage of 690V. Taking different phase-locked loop bandwidths as an example, the modeling and stability analysis proposed by the present invention are implemented. The model is built using the motor convention. The parameters of the BDFIG are as follows: power winding resistance R w =0.067pu, control winding resistance R c =0.073pu, rotor resistance R r =0.13pu, power winding self-inductance L w =24.51pu, control winding self-inductance L c =2.66pu, rotor self-inductance L r =27.25pu, power winding rotor mutual inductance L wr =24.28pu, control winding rotor mutual inductance L cr =2.54pu, power winding pole pair number P w =1, control winding pole pair number P c =3.

[0074] like Figure 1As shown, the present invention provides a brushless doubly-fed fan input admittance modeling and stability analysis method taking into account the frequency coupling effect. According to the voltage equation and flux equation of the brushless doubly-fed fan, the relationship between the voltage and current of the brushless doubly-fed fan can be obtained. Then, the current loop and the phase-locked loop are modeled with small signals. The control winding variables are represented by power winding variables. After being combined with the motor equation, the power winding variables can be decoupled from the control winding variables to obtain the relationship between the power winding voltage and current, thereby obtaining the frequency coupling analytical model Y of the brushless doubly-fed fan. BDFIG Based on the established brushless double-fed input admittance Y BDFIG The small signal model, weak grid impedance model and generalized Nyquist criterion can be used to determine the stability of the brushless doubly fed wind turbine under weak grid conditions. The specific steps include:

[0075] (1) Establish a frequency domain analytical model of the grid-connected brushless doubly-fed wind turbine system, specifically:

[0076] (1.1) Taking into account the frequency coupling characteristics of the brushless doubly fed wind turbine side converter, the relationship between the power winding voltage disturbance and the power winding current response is used to obtain the frequency coupling analytical model of the brushless doubly fed wind turbine, namely:

[0077]

[0078] Among them, the main diagonal elements Y of the admittance matrix Y(s) 11 (s) and Y 22 (s), reflects the effect of the power winding voltage disturbance on the current component of the same frequency, rather than the diagonal element Y 12 (s) and Y 21 (s) reflects the influence of the power winding voltage disturbance on the coupling frequency current component, s represents the complex frequency, s = j2πf. wp ,I wp2 are the power winding current disturbance frequency component and coupling frequency component, respectively, p is the disturbance frequency, f1 is the fundamental frequency, V wp 、V wp2 They are the power winding voltage disturbance frequency component and the coupling frequency component respectively.

[0079] (1.2) Figure 2 As shown, the voltage equation and flux equation of the brushless doubly fed wind turbine are established in the dq coordinate system, namely:

[0080]

[0081]

[0082] Among them, u w 、u c and u rRepresent the power winding voltage, control winding voltage and rotor voltage respectively, i w 、i c and i r Respectively represent the power winding current, control winding current and rotor current, ψ w , c and ψ r Respectively represent the power winding flux, control winding flux and rotor flux; R w , R c and R r Respectively represent the power winding resistance, control winding resistance and rotor winding resistance, L w , L c and L r Respectively represent the power winding inductance, control winding inductance and rotor winding inductance, M wr represents the mutual inductance between the power winding and the rotor, M cr represents the mutual inductance between the control winding and the rotor; ω w ,ω c and ω r Respectively represent the power winding electrical angular frequency, control winding electrical angular frequency and rotor winding electrical angular frequency, where ω r =ω w -P w ω m , P w Indicates the number of power winding pole pairs, ω m Represents the mechanical angular velocity of the motor; p represents the differential operation.

[0083] (1.3) Using the harmonic linearization method, the voltage V, current I and frequency components of the frequency coupling characteristics of the brushless double-fed wind turbine power winding, rotor winding and control winding are defined respectively, namely:

[0084]

[0085]

[0086]

[0087] Among them, V wa 、V ca and V ra They represent the power winding a-phase voltage, control winding a-phase voltage and rotor a-phase voltage respectively, I wa ,I ca and V ra Respectively represent the power winding a-phase current, control winding a-phase current and rotor a-phase current; V w1 、V wp 、V wp2 are the power winding voltage and its disturbance frequency component and coupling frequency component, Iw1 ,I wp ,I wp2 are the power winding current and its disturbance frequency component and coupling frequency component respectively; V c1 、V cp 、V cp2 are the control winding voltage and its disturbance frequency component and coupling frequency component, I c1 ,I cp ,I cp2 are the control winding current and its disturbance frequency component and coupling frequency component respectively; V r1 、V rp 、V rp2 are the rotor voltage and its disturbance frequency component and coupling frequency component, I r1 ,I rp ,I rp2 are the rotor current disturbance frequency component and coupling frequency component respectively; f1, f c and f r Respectively represent the fundamental frequency, control winding electrical angular frequency and rotor electrical angular frequency; P c To control the number of winding pole pairs; the above formulas are all functions in the frequency domain, f is the function independent variable, representing the frequency.

[0088] (1.4) Establish a frequency domain model of the phase-locked loop. Figure 3 This is the linearized phase-locked loop control structure diagram, refer to Figure 3 , find the small signal model transfer function of the phase-locked loop:

[0089]

[0090] Among them, K p_PLL and K i_PLL Respectively represent the proportional and integral coefficients of the phase-locked loop, V w0 Indicates the grid voltage amplitude. In this implementation, under working condition I, K p_PLL1 =0.5, K i_PLL1 =5; K under working condition II p_PLL2 =0.7, K i_PLL2 =7; s represents the complex frequency, s=j2πf.

[0091] In a weak power grid, the grid voltage will produce voltage disturbances due to the grid impedance, and this disturbance will cause an angle error in the phase-locked loop. Figure 4 This is a schematic diagram of the ideal synchronous rotating coordinate system and the actual synchronous rotating coordinate system. Figure 4 , linearize the coordinate transformation, the specific derivation steps are as follows:

[0092]

[0093] Where T represents the coordinate transformation function; θ PLL (t) represents the phase angle of the phase-locked loop output, Δθ(t) = θ PLL (t)-θ c (t), represents the phase-locked loop angle error; Δθ1(t)=jω1·t=j2πf1·t, represents the actual phase angle of the system, ω1 represents the fundamental angular frequency;

[0094] θ c (t) = jω c ·t=j2πf c ·t, represents the phase angle of the control winding.

[0095] Then the angle error of the phase-locked loop output can be written as:

[0096]

[0097] Furthermore, cos(θ PLL (t)-θ c (t)) can be expressed by cos(Δθ(t)+θ1(t)-θ c (t)) to obtain:

[0098]

[0099] (1.5) Establish the frequency domain model of the current loop. For the current loop control of the machine-side converter, the control winding current must first be transformed from the stationary coordinate system to the unified vector coordinate system. Since the phase-locked loop output produces errors under weak power grids, the expression for controlling the winding current should be:

[0100]

[0101] Among them, I cd and I cq Respectively represent the dq axis components of the control winding current, Indicates the phase angle of the control winding current.

[0102] Figure 5 For the control structure of the current loop, refer to Figure 5 , the transfer function of the current loop can be written as:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Among them, K p_cdi and K p_cqi are the proportional coefficients of the dq axis current loop controller, K i_cdi and K i_cqi are the integral coefficients of the dq axis current loop controller, respectively. In this embodiment, K p_cdi =K p_cqi =1.5, K i_cdi =K i_cqi =100. M cd and M cq They are the dq axis harmonic components in the current loop output modulation signal respectively. wd Represents the d-axis component of the power winding voltage. wr is the power winding rotor mutual inductance, L cr To control the winding rotor mutual inductance. s represents the complex frequency, s = j2πf. K cd is the decoupling coefficient, K fw is the feed-forward coefficient.

[0109] It should be noted that the current loop output also needs to be modulated by the machine-side converter. Considering the modulation gain and delay of the machine-side converter, its transfer function is:

[0110]

[0111] Among them, K m is the modulation gain, T d is the digital control delay, which can be considered to be equal to 1.5 times the sampling period. s represents the complex frequency, s = j2πf.

[0112] After the current loop output passes through the machine-side converter, it becomes the control winding voltage. The expression of the control winding voltage of phase a in the frequency domain can be written as:

[0113]

[0114]

[0115] in, and is the asymmetric control effect of the current loop, V dc is the DC bus voltage.

[0116] M c1 =M cd1 +jM cq1 , is the static operating point of the modulation signal, For its conjugation; I c1 =I cd1 +jI cq1 , is the dq axis command value of the control winding current, I* c1Its conjugate can be obtained by the following equation: cd 、M cq calculate:

[0117]

[0118] in, Indicates the motor leakage inductance coefficient. M cd and M cq are the dq axis harmonic components in the current loop output modulation signal respectively. cd1 、M cq1 Indicates M c1 The dq axis component, I cd1 ,I cq1 I c1 The dq axis components of V w0 It represents the steady-state value of the power winding voltage. P represents active power and Q represents reactive power.

[0119] (1.6) Since there is a frequency difference between the power winding, the control winding and the rotor, the frequency conversion formulas from the rotor variable to the power winding variable and from the control winding variable to the power winding variable are defined respectively:

[0120]

[0121] Among them, σ rp (s) and σ rp2 (s) represent the frequency transformation formulas of the rotor disturbance frequency component and the coupling frequency component, σ cp (s) and σ cp2 (s) respectively represent the frequency conversion formulas of the control winding disturbance frequency component and the coupling frequency component. s represents the complex frequency, s = j2πf.

[0122] After frequency conversion, the expressions for the harmonic components in the power and control windings can be written as:

[0123]

[0124] Wherein, s represents the complex frequency, s=j2πf.

[0125] L c_p and L c_p2 is the equivalent self-inductance of the control winding caused by frequency conversion, and

[0126]

[0127] L w_p and L w_p2 The equivalent self-inductance of the power winding caused by frequency conversion:

[0128]

[0129] M p and M p2 is the equivalent mutual inductance caused by frequency conversion:

[0130]

[0131] It can be seen that the indirect coupling effect of the rotor has been reflected in the equivalent self-inductance and equivalent mutual inductance.

[0132] (1.7) Simplify the calculation process: introduce matrix C(s) and matrix F(s):

[0133]

[0134] Among them, the matrix The matrix represents the effect of the current loop controller of the brushless doubly-fed machine side converter on controlling the winding current. It represents the control effect of the voltage feedforward link in the phase-locked loop and the current loop on the power winding voltage. s represents the complex frequency, s = j2πf.

[0135] Combining equations (1)-(17), we can obtain:

[0136]

[0137]

[0138] (1.8) According to step 1, the analytical model of the frequency coupling characteristics of the brushless doubly fed wind turbine can be obtained:

[0139]

[0140] Wherein, s represents the complex frequency, s=j2πf.

[0141] (9) Establish the frequency domain impedance model Z of the weak power grid impedance g ,Right now

[0142]

[0143] Among them, R g is the weak grid resistance, L g is the weak grid inductance, ω1 is the grid angular frequency.

[0144] Formulas (20) and (21) together constitute the frequency domain analytical model of the grid-connected brushless doubly-fed wind turbine system of the present invention.

[0145] (2) Based on the brushless doubly-fed wind turbine admittance model taking into account the frequency coupling effect established in step (1) and the frequency domain impedance model of the weak grid impedance, the strength of the frequency coupling effect and the system stability are analyzed, specifically:

[0146] (2.1) Using Y 12 (s) and Y 11 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio, the stronger the frequency coupling degree in this frequency band. Similarly, for the image frequency component of the power winding, Y 21 (s) and Y 22 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio is, the stronger the frequency coupling is in the frequency band.

[0147] (2.2) Use the generalized Nyquist criterion to determine the stability of the grid-connected system. DFIG With weak grid impedance Z g When the impedance ratio matrix satisfies the generalized Nyquist criterion, the grid-connected system is in a small signal stable state, otherwise it is in a small signal unstable state.

[0148] The working condition parameters studied in this embodiment are: Working condition I: K p_PLL1 =0.5, K i_PLL1 =5; Working condition II: K p_PLL2 =0.7, K i_PLL2 =7; other parameters remain the same, that is: SCR = 1, K p_cdi =K p_cqi =1.5, K i_cdi =K i_cqi =100.

[0149] Figure 6 is the generalized Nyquist curve of the brushless doubly-fed wind turbine under different working conditions. Figure 6 It can be obtained that according to the stability analysis results, under working condition I, the generalized Nyquist curve does not surround the point (-1, j0), and the system can operate stably; under working condition II, the generalized Nyquist curve surrounds the point (-1, j0), the system is unstable, and the frequency at which the generalized Nyquist curve crosses the unit circle is 121Hz.

[0150] Figure 7 The simulation waveform of the power winding current of the brushless double-fed fan under different working conditions is shown in Figure 2. Figure 7 It can be obtained that the harmonic content of the power winding current under working condition I is 1.16%, and the system can operate stably; the harmonic content of the power winding current under working condition II is 11.96%, and the system is unstable. Figure 6 The stability analysis results are the same.

[0151] Figure 8 This is the FFT analysis result of the brushless double-fed fan power winding current waveform under working condition II. Figure 8 It can be obtained that the oscillation frequency of the power winding current under working condition II is 20 / 120Hz, which is consistent with Figure 6The frequency at which the generalized Nyquist curve crosses the unit circle is basically the same.

[0152] Fig. 9 The frequency coupling degree of brushless doubly fed wind turbine is compared under different working conditions. Fig. 9 It can be seen that for the disturbance frequency component, the frequency coupling effect is more significant between 50 and 200 Hz; for the image frequency component, the frequency coupling effect is more significant below 50 Hz. In terms of different working conditions, when the bandwidth of the phase-locked loop increases, the frequency coupling effect of the disturbance frequency component and the image frequency component is significantly enhanced, which is similar to Figure 6 The stability results are consistent with .

[0153] In summary, the input admittance model of the brushless doubly-fed wind turbine established by the present invention not only considers the influence of the motor body and the phase-locked loop and current loop in the control system on the input admittance of the system, but also incorporates the frequency coupling effect caused by the asymmetric control structure of the phase-locked loop into the modeling process, and establishes a frequency coupling characteristic model of the brushless doubly-fed wind turbine. During the model establishment process, the meaning of each physical quantity is clear, and the input admittance model has good accuracy; the stability analysis method of the present invention considers the influence of the frequency coupling effect on the system, and improves the accuracy of the analysis results; the present invention provides a model and method for the stability analysis and frequency coupling effect research of the brushless doubly-fed wind turbine under weak power grid conditions.

Claims

1. A modeling and stability analysis method for a grid-connected brushless double-fed wind turbine taking into account frequency coupling effects, characterized in that: The steps include: (1) Establish a frequency domain analytical model of the grid-connected brushless doubly-fed wind turbine system; (2) Based on the brushless doubly-fed wind turbine admittance model taking into account the frequency coupling effect and the frequency domain impedance model of the weak grid impedance established in step (1), the strength of the frequency coupling effect and the system stability are analyzed; Admittance model of brushless doubly-fed wind turbine considering frequency coupling effect BDFIG ,Right now Among them, R w represents the power winding resistance; f is the function independent variable, representing the frequency; L w_p and L w_p2 is the equivalent self-inductance of the power winding caused by frequency conversion, and M p and M p2 is the equivalent mutual inductance caused by frequency conversion, and Establish the frequency domain impedance model Z of weak power grid impedance g ,Right now Among them, R g is the weak grid resistance, L g is the weak grid inductance, ω1 is the grid angular frequency, s represents the complex frequency, s=j2πf.

2. The method for modeling and stability analysis of a brushless double-fed wind turbine connected to a grid and taking frequency coupling effect into account according to claim 1 is characterized in that: Step (1) comprises: (1.1) Taking into account the frequency coupling characteristics of the brushless doubly fed wind turbine side converter, the frequency coupling analytical model of the brushless doubly fed wind turbine is obtained by using the relationship between the power winding voltage disturbance and the power winding current response, namely: Among them, the main diagonal elements Y of the admittance matrix Y(s) 11 (s) and Y 22 (s) reflects the influence of the power winding voltage disturbance on the current component of the same frequency. s represents the complex frequency, s = j2πf; rather than the diagonal element Y 12 (s) and Y 21 (s) reflects the influence of the power winding voltage disturbance on the coupled frequency current component; (1.2) Establish the voltage equation and flux equation of the brushless doubly fed wind turbine in the dq coordinate system, namely: Among them, u w 、u c and u r Represent the power winding voltage, control winding voltage and rotor voltage respectively, i w 、i c and i r Respectively represent the power winding current, control winding current and rotor current, ψ w , c and ψ r Respectively represent the power winding flux, control winding flux and rotor flux; R w , R c and R r Respectively represent the power winding resistance, control winding resistance and rotor winding resistance, L w , L c and L r Respectively represent the power winding inductance, control winding inductance and rotor winding inductance, M wr represents the mutual inductance between the power winding and the rotor, M cr represents the mutual inductance between the control winding and the rotor; ω w ,ω c and ω r Respectively represent the power winding electrical angular frequency, control winding electrical angular frequency and rotor winding electrical angular frequency, where ω r =ω w -P w ω m , P w Indicates the number of power winding pole pairs, ω m Indicates the mechanical angular velocity of the motor; p represents differential operation; (1.3) Using the harmonic linearization method, the frequency components of the voltage and current meters and frequency coupling characteristics of the brushless double-fed wind turbine power winding, rotor winding and control winding are defined respectively, namely: Among them, V wa 、V ca and V ra They represent the power winding a-phase voltage, control winding a-phase voltage and rotor a-phase voltage respectively, I wa ,I ca and V ra Respectively represent the power winding a-phase current, control winding a-phase current and rotor a-phase current; V w1 、V wp 、V wp2 are the power winding voltage and its disturbance frequency component and coupling frequency component, I w1 ,I wp ,I wp2 are the power winding current and its disturbance frequency component and coupling frequency component respectively; V c1 、V cp 、V cp2 are the control winding voltage and its disturbance frequency component and coupling frequency component, I c1 ,I cp ,I cp2 are the control winding current and its disturbance frequency component and coupling frequency component respectively; V r1 、V rp 、V rp2 are the rotor voltage and its disturbance frequency component and coupling frequency component, I r1 ,I rp ,I rp2 are the rotor current disturbance frequency component and coupling frequency component respectively; f1, f c and f r Respectively represent the fundamental frequency, control winding electrical angular frequency and rotor electrical angular frequency; P c To control the number of winding pole pairs; the above formulas are all functions in the frequency domain, f is the function independent variable, indicating the frequency; (1.4) Establish the frequency domain model of the phase-locked loop, that is, Among them, K p_PLL and K i_PLL Respectively represent the proportional and integral coefficients of the phase-locked loop, V w0 represents the grid voltage amplitude, s represents the complex frequency, s = j2πf; (1.5) Establish the frequency domain model of the current loop, that is, in, K p_cdi and K p_cqi are the proportional coefficients of the dq axis current loop controller, K i_cdi and K i_cqi are the integral coefficients of the dq axis current loop controller, M cd and M cq are the dq axis harmonic components in the current loop output modulation signal, K cd is the decoupling coefficient, K fw is the feedback coefficient; (1.6) The frequency transformation relationship from rotor variable to power winding variable and from control winding variable to power winding variable is defined respectively, namely: Among them, σ rp (s) and σ rp2 (s) represent the frequency transformation formulas of the rotor disturbance frequency component and the coupling frequency component, σ cp (s) and σ cp2 (s) respectively represent the frequency conversion formulas of the control winding disturbance frequency component and the coupling frequency component; s represents the complex frequency, s = j2πf; (1.7) Introduce the matrix C(s) and the matrix F(s), which are defined as: Among them, the matrix C(s) represents the effect of the current loop controller of the brushless doubly-fed machine side converter on the control winding current, the matrix F(s) represents the control effect of the voltage feedforward link in the phase-locked loop and the current loop on the power winding voltage, s represents the complex frequency, s=j2πf; Solved: Among them, V dc Indicates DC bus voltage; M c1 =M cd1 +jM cq1 , is the static operating point of the modulation signal, For its conjugation; I c1 =I cd1 +jI cq1 , is the dq axis command value of the control winding current, I* c1 is its conjugate; s represents the complex frequency, s = j2πf; Modulation gain and control delay of the generator-side converter: L c_p and L c_p2 is the equivalent self-inductance of the control winding caused by frequency conversion, and and is the asymmetric control effect of the current loop, and 3. The method for modeling and stability analysis of a brushless double-fed wind turbine connected to a grid and taking frequency coupling effect into account according to claim 2 is characterized in that: Step (2) comprises: (2.1) Using Y 12 (s) and Y 11 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio, the stronger the frequency coupling degree in this frequency band. Similarly, for the image frequency component of the power winding, Y 21 (s) and Y 22 The ratio of the amplitudes of (s) describes the frequency coupling effect of each frequency band. The larger the ratio, the stronger the frequency coupling degree in the frequency band. (2.2) The generalized Nyquist criterion is used to judge the stability of the grid-connected system. When the brushless double-fed wind turbine admittance model Y BDFIG With weak grid impedance Z g When the impedance ratio matrix satisfies the generalized Nyquist criterion, the grid-connected system is in a small signal stable state, otherwise it is in a small signal unstable state.

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