A method of uncertain modal analysis based on affine

Abstract

The present invention relates to an affine-based uncertainty modal analysis method, comprising the following steps: (1) expressing the compensation capacity of a reactive power compensation device SVC in a complex affine form, and obtaining an expression of the node admittance generated by the SVC on the wind farm grid-connected system; (2) calculating the frequency f The node admittance matrix of the grid-connected system at , performs eigenvalue decomposition on it, and inverts the eigenvalue matrix to obtain the modal impedance matrix; (3) Establish the correlation surface diagram between the affine quantity and the harmonic order of the grid-connected system and the modal impedance of the grid-connected system, and obtain the modal impedance curve under different SVC compensation capacities and the compensation capacity range corresponding to each even-order resonant frequency under any resonant mode. This method is conducive to suppressing the resonance of the wind farm grid-connected system.

Description

Technical Field

[0001] The invention belongs to the technical field of wind power, and in particular relates to an affine-based uncertainty modal analysis method. Background Art

[0002] With the depletion of fossil energy and the continuous deterioration of the environment, new energy represented by wind power has been widely used. There are many grid-connected power quality problems in the process of wind farms being connected to the grid, among which the impact caused by harmonic resonance is particularly obvious. Harmonic resonance can cause the amplitude of a certain harmonic in the wind farm to suddenly rise, forming overvoltage or overcurrent, leading to problems such as protection misoperation and equipment damage in the wind farm. Due to the large uncertainty of wind power generation, the change in the output power of the wind power grid-connected system will make the input and output of the parallel compensation capacitor a dynamic process. In this process, the resonance point of the wind farm will shift with the change of external conditions. The use of a modal analysis method that can obtain dynamic information on wind power grid-connected harmonic resonance is the key to analyzing the impact of uncertainty on harmonic resonance.

[0003] Since the traditional modal analysis method can only perform deterministic analysis on the harmonic resonance of the system, most of the current research on harmonic resonance is deterministic analysis, and the uncertainty impact of uncertain variables on the new energy grid-connected system has not been considered. In order to effectively adjust the resonant frequency of the grid-connected system to control the harmonic resonance phenomenon, it is necessary to further analyze the uncertainty changes of the system resonance caused by the uncertainty of the system parameters. Summary of the invention

[0004] The object of the present invention is to provide an affine-based uncertainty modal analysis method, which is beneficial to suppressing the resonance of a wind farm grid-connected system.

[0005] To achieve the above object, the technical solution adopted by the present invention is: an affine-based uncertainty modal analysis method, comprising the following steps:

[0006] (1) The compensation capacity of the reactive power compensation device SVC is expressed in complex affine form: Obtain the node admittance expression generated by SVC to the wind farm grid-connected system

[0007] (2) Calculate the grid-connected system node admittance matrix Y at frequency f f , perform eigenvalue decomposition on it, and invert the eigenvalue matrix Λ to obtain the modal impedance matrix Λ -1 ;

[0008] (3) Establishing affine quantities The correlation surface diagram with the harmonic order of the grid-connected system and the modal impedance of the grid-connected system is used to obtain the modal impedance curve under different SVC compensation capacities and the corresponding even-numbered resonant frequencies under any resonant mode. interval.

[0009] Furthermore, in the step (1), for the wind farm grid-connected system connected to the reactive power compensation device SVC, when the compensation capacity of the reactive power compensation device SVC changes, the resonant frequency of the wind farm grid-connected system changes accordingly; the complex affine expression of the compensation capacity of the SVC is constructed as follows:

[0010]

[0011] Among them, Q svc,0 is the affine center value of a single reactive power compensation device SVC; Q i Determined by the rated capacity of the SVC, it is the noise element coefficient in the complex affine expression; ε i Indicates the reactive output fluctuation range of SVC, and its value is ε i ∈[-1,1];

[0012] Compensation Capacity of SVC Based on Complex Affine Form The expression for calculating the node admittance generated by SVC to the wind farm grid-connected system is as follows:

[0013]

[0014] Where V B is the rated voltage of SVC, and h is the harmonic order.

[0015] Furthermore, in step (2), the modal impedance is calculated as follows:

[0016] The node admittance matrix Y of the wind farm grid-connected system connected to SVC at frequency f f :

[0017]

[0018] If the system produces parallel resonance with a frequency of f, the node voltage and current equations are:

[0019]

[0020] Among them, Y f is the grid-connected system node admittance matrix at frequency f, V f and I f are the node voltage and node injection current vector respectively; the node admittance matrix Y f This breaks down as follows:

[0021] Y f =LΛT (5)

[0022] Where Λ is the diagonal eigenvalue matrix, Λ=diag(λ1,λ2,…λk ,…); L=[l1,l2,…l k ,…], T=[t1,t2,…t k ,…] are the left and right eigenvector matrices respectively, and L=T -1 ;

[0023] Substituting formula (5) into formula (4) yields:

[0024] V f =LΛ -1 TI f (6)

[0025] Definition U f =TV f is the modal voltage vector, J f =TI f is the modal current vector, then U f =Λ -1 J f ;Right now:

[0026]

[0027] In the formula, Λ -1 is the modal impedance matrix.

[0028] Furthermore, the specific steps of using the modal analysis method to analyze grid-connected resonance uncertainty are as follows:

[0029] 1) Based on the modal analysis model, the complex affine expression of the SVC compensation capacity is calculated according to formula (1): Then, the complex affine expression of the node admittance is calculated according to formula (2):

[0030] 2) Calculate the system node admittance matrix Y(s);

[0031] 3) Perform eigenvalue decomposition on the node admittance matrix Y(s), that is, Y(s) = L(s)Λ(s)T(s), thereby obtaining the left and right eigenvector matrices L(s), T(s) and the diagonal eigenvalue matrix Λ(s);

[0032] 4) Calculate the modal impedance of each mode when the system frequency is f;

[0033] 5) Repeat steps 2)-4) until all harmonic frequencies that may cause system resonance are traversed, so as to obtain the system modal impedance curve at each harmonic frequency, and then analyze the grid-connected resonance phenomenon of the wind farm; combine the affine model of SVC and the complex affine expression of node admittance to obtain the system modal impedance curve at each harmonic frequency, and then obtain the correlation curve between SVC compensation capacity and system resonant frequency.

[0034] Furthermore, in step (3), modal analysis is performed on the wind power grid-connected system to establish an affine quantity The surface diagram associated with the harmonic order of the grid-connected system and the modal impedance of the grid-connected system; by analyzing the location of the maximum modal impedance, different The grid-connected system resonant frequency under the condition of SVC compensation capacity Correlation curve with the grid-connected system resonant frequency; there is a positive correlation between the grid-connected system resonant frequency and the SVC compensation capacity. Based on this law, we analyze how to adjust The size of the wind farm grid-connected system is adjusted to achieve the adjustment of the resonant frequency. Since there are almost no even-order harmonics in the actual power system, the resonant frequency of the grid-connected system is adjusted to an even number to achieve the purpose of suppressing the resonance of the wind farm grid-connected system.

[0035] Compared with the prior art, the present invention has the following beneficial effects: Based on affine operation, the present invention fully considers the uncertainty of wind farm parameters, studies and analyzes the correlation between the compensation capacity of SVC, the resonant frequency of the grid-connected system and the modal impedance of the grid-connected system, obtains the correlation curve between the SVC reactive compensation capacity and the resonant frequency of the wind farm grid-connected system, and the corresponding even-numbered resonant frequencies under a certain resonant mode. Based on this, we can analyze how to adjust the reactive power compensation capacity The size of the resonant frequency band is effectively moved to the target frequency band (even harmonics), thereby achieving the purpose of suppressing the resonance of the wind farm grid-connected system. The present invention can not only be used to analyze the impact of parameter uncertainty on the system resonant frequency, but also provide a basis for harmonic resonance control. The control method does not require the introduction of new filtering devices and will not generate additional resonant frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of a method implementation of an embodiment of the present invention;

[0037] Figure 2 is a modal impedance curve diagram under different SVC compensation capacities in an embodiment of the present invention;

[0038] Figure 3 It is a correlation curve diagram of the SVC compensation capacity and the resonant frequency of the grid-connected system in the embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0040] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0041] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0042] like Figure 1 As shown, this embodiment provides an affine-based uncertainty modal analysis method, comprising the following steps:

[0043] (1) The compensation capacity of the reactive power compensation device SVC is expressed in complex affine form: Obtain the node admittance expression generated by SVC to the wind farm grid-connected system

[0044] (2) Calculate the grid-connected system node admittance matrix Y at frequency f f , perform eigenvalue decomposition on it, and invert the eigenvalue matrix Λ to obtain the modal impedance matrix Λ -1 .

[0045] (3) Establishing affine quantities The correlation surface diagram with the harmonic order of the grid-connected system and the modal impedance of the grid-connected system is used to obtain the modal impedance curve under different SVC compensation capacities and the corresponding even-numbered resonant frequencies under any resonant mode. interval.

[0046] 1. Calculation of affine node admittance

[0047] For a wind farm grid-connected system connected to a reactive power compensation device SVC, when the compensation capacity of the reactive power compensation device SVC changes, the resonant frequency of the wind farm grid-connected system changes accordingly; the complex affine expression of the compensation capacity of the SVC is constructed as follows:

[0048]

[0049] Among them, Q svc,0 is the affine center value of a single reactive power compensation device SVC; Q i Determined by the rated capacity of the SVC, it is the noise element coefficient in the complex affine expression; ε i Indicates the reactive output fluctuation range of SVC, and its value is ε i ∈[-1,1];

[0050] Compensation Capacity of SVC Based on Complex Affine Form The expression for calculating the node admittance generated by SVC to the wind farm grid-connected system is as follows:

[0051]

[0052] Where V B is the rated voltage of SVC, and h is the harmonic order.

[0053] 2. Calculation of modal impedance

[0054] The node admittance matrix Y of the wind farm grid-connected system connected to SVC at frequency f f :

[0055]

[0056] If the system produces parallel resonance with a frequency of f, the node voltage and current equations are:

[0057]

[0058] Among them, Y f is the grid-connected system node admittance matrix at frequency f, V f and I f are the node voltage and node injection current vector respectively; the node admittance matrix Y f This breaks down as follows:

[0059] Y f =LΛT (5)

[0060] Where Λ is the diagonal eigenvalue matrix, Λ=diag(λ1,λ2,…λ k ,…); L=[l1,l2,…l k ,…], T=[t1,t2,…t k ,…] are the left and right eigenvector matrices respectively, and L=T -1 ;

[0061] Substituting formula (5) into formula (4) yields:

[0062] V f =LΛ -1 TI f (6)

[0063] Definition U f =TV f is the modal voltage vector, J f =TI f is the modal current vector, then U f =Λ -1 J f ;Right now:

[0064]

[0065] In the formula, Λ-1 is the modal impedance matrix.

[0066] In this embodiment, the specific steps of using the modal analysis method to analyze grid-connected resonance uncertainty are as follows:

[0067] 1) Based on the modal analysis model, the complex affine expression of the SVC compensation capacity is calculated according to formula (1): Then, the complex affine expression of the node admittance is calculated according to formula (2):

[0068] 2) Calculate the system node admittance matrix Y(s);

[0069] 3) Perform eigenvalue decomposition on the node admittance matrix Y(s), that is, Y(s) = L(s)Λ(s)T(s), thereby obtaining the left and right eigenvector matrices L(s), T(s) and the diagonal eigenvalue matrix Λ(s);

[0070] 4) Calculate the modal impedance of each mode when the system frequency is f;

[0071] 5) Repeat steps 2)-4) until all harmonic frequencies that may cause system resonance are traversed, so as to obtain the system modal impedance curve at each harmonic frequency, and then analyze the grid-connected resonance phenomenon of the wind farm; combine the affine model of SVC and the complex affine expression of node admittance to obtain the system modal impedance curve at each harmonic frequency, and then obtain the correlation curve between SVC compensation capacity and system resonant frequency.

[0072] 3. Correlation analysis between uncertainty and resonant frequency

[0073] Perform modal analysis on wind power grid-connected system and establish affine quantity The surface diagram associated with the harmonic order and modal impedance of the grid-connected system is shown in Figure 2. Figure 2 As shown. Figure 2 , by analyzing the location of the maximum modal impedance, confirm the different The grid-connected system resonant frequency under the condition of SVC compensation capacity The correlation curve with the grid-connected system resonant frequency, such as Figure 3 shown.

[0074] Depend on Figure 3 As shown in the figure, there is a positive correlation between the grid-connected system resonant frequency and the SVC compensation capacity. Based on this rule, by analyzing how to adjust size to adjust the resonant frequency.

[0075] The even-numbered resonant frequencies corresponding to a certain mode The interval is shown in Table 1. Since even harmonics hardly exist in actual power systems, Table 1 is used as the adjustment Based on the above, the grid-connected system resonance frequency is adjusted to an even number to achieve the purpose of suppressing the resonance of the wind farm grid-connected system.

[0076] Table 1 The corresponding grid-connected system resonant frequency

[0077]

[0078] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. An affine-based uncertainty modal analysis method, characterized in that: The following steps are involved: (1) The compensation capacity of the reactive power compensation device SVC is expressed in complex affine form: Obtain the node admittance expression generated by SVC to the wind farm grid-connected system (2) Calculate the grid-connected system node admittance matrix Y at frequency f f , perform eigenvalue decomposition on it, and invert the eigenvalue matrix Λ to obtain the modal impedance matrix Λ -1 ; (3) Establishing affine quantities The correlation surface diagram with the harmonic order of the grid-connected system and the modal impedance of the grid-connected system is used to obtain the modal impedance curve under different SVC compensation capacities and the corresponding even-numbered resonant frequencies under any resonant mode. interval; In the step (1), for the wind farm grid-connected system connected to the reactive power compensation device SVC, when the compensation capacity of the reactive power compensation device SVC changes, the resonant frequency of the wind farm grid-connected system changes accordingly; the complex affine expression of the compensation capacity of the SVC is constructed as follows: Among them, Q svc,0 is the affine center value of a single reactive power compensation device SVC; Q i Determined by the rated capacity of the SVC, it is the noise element coefficient in the complex affine expression; ε i Indicates the reactive output fluctuation range of SVC, and its value is ε i ∈[-1,1]; Compensation Capacity of SVC Based on Complex Affine Form The expression for calculating the node admittance generated by SVC to the wind farm grid-connected system is as follows: Where V B is the rated voltage of SVC, h is the harmonic order; In step (2), the modal impedance is calculated as follows: The node admittance matrix Y of the wind farm grid-connected system connected to SVC at frequency f f : If the system produces parallel resonance with a frequency of f, the node voltage and current equations are: Among them, Y f is the grid-connected system node admittance matrix at frequency f, V f and I f are the node voltage and node injection current vector respectively; the node admittance matrix Y f This breaks down as follows: Y f =LΛT (5) Where Λ is the diagonal eigenvalue matrix, Λ=diag(λ1,λ2,…λ k ,…); L=[l1,l2,…l k ,…], T=[t1,t2,…t k ,…] are the left and right eigenvector matrices respectively, and L=T -1 ; Substituting formula (5) into formula (4) yields: V f =LΛ -1 TI f (6) Definition U f =TV f is the modal voltage vector, J f =TI f is the modal current vector, then U f =Λ -1 J f ;Right now: In the formula, Λ -1 is the modal impedance matrix.

2. The affine-based uncertainty modal analysis method according to claim 1, characterized in that: The specific steps of analyzing the uncertainty of grid-connected resonance using the modal analysis method are as follows: 1) Based on the modal analysis model, the complex affine expression of the SVC compensation capacity is calculated according to formula (1): Then, the complex affine expression of the node admittance is calculated according to formula (2): 2) Calculate the system node admittance matrix Y(s); 3) Perform eigenvalue decomposition on the node admittance matrix Y(s), that is, Y(s) = L(s)Λ(s)T(s), thereby obtaining the left and right eigenvector matrices L(s), T(s) and the diagonal eigenvalue matrix Λ(s); 4) Calculate the modal impedance of each mode when the system frequency is f; 5) Repeat steps 2)-4) until all harmonic frequencies that may cause system resonance are traversed, thereby obtaining a system modal impedance curve at each harmonic frequency, and then analyzing the wind farm grid-connected resonance phenomenon; Combining the affine model of SVC with the complex affine expression of node admittance, the system modal impedance curve at each harmonic frequency is obtained, and then the correlation curve between SVC compensation capacity and system resonant frequency is obtained.

3. The affine-based uncertainty modal analysis method according to claim 1, characterized in that: In the step (3), modal analysis is performed on the wind power grid-connected system to establish an affine quantity The surface diagram associated with the harmonic order of the grid-connected system and the modal impedance of the grid-connected system; by analyzing the location of the maximum modal impedance, different The grid-connected system resonant frequency under the condition of SVC compensation capacity Correlation curve with the grid-connected system resonant frequency; there is a positive correlation between the grid-connected system resonant frequency and the SVC compensation capacity. Based on this law, we analyze how to adjust The size of the wind farm grid-connected system is adjusted to achieve the adjustment of the resonant frequency. Since there are almost no even-order harmonics in the actual power system, the resonant frequency of the grid-connected system is adjusted to an even number to achieve the purpose of suppressing the resonance of the wind farm grid-connected system.

Images