Method for analyzing broadband oscillation influence factors of low-frequency power transmission system

Abstract

The invention discloses a broadband oscillation influence factor analysis method for a low-frequency power transmission system, and the method comprises the steps: selecting system operation and control parameters as predictive variables, and selecting the broadband oscillation stability of the system as a response variable to construct a low-frequency power transmission system training set; constructing a multiple linear regression function, and solving a regression coefficient of each prediction variable based on a least square method; and carrying out significance test on the constructed multiple linear regression function, introducing a confidence interval, and carrying out interval estimation on a regression coefficient to carry out hypothesis test. And retaining the predictive variables meeting the requirements, reconstructing a multiple linear regression function, solving a regression coefficient, and obtaining the influence of each predictive variable on the broadband oscillation stability of the system based on regression analysis. According to the method, the influence rule of each parameter on the broadband oscillation stability of the system under the full working condition of the system is described, and the method has a good application prospect.

Description

Technical Field

[0001] The present invention relates to the field of broadband oscillation of power systems, and in particular to a method for analyzing influencing factors of broadband oscillation of low-frequency power transmission systems. Background Art

[0002] With the rapid development of renewable energy power generation, flexible direct current transmission, flexible alternating current transmission and flexible low-frequency transmission, the number of power electronic devices in the system continues to increase. Their interaction will induce wide-band oscillations with frequencies ranging from a few hertz to several thousand hertz, which has gradually become the main dynamic problem facing the power system.

[0003] With the large-scale grid connection of new energy and the commissioning of a large number of power electronic equipment, modern power systems show a high proportion of renewable energy and a high proportion of power electronic equipment. Compared with traditional fossil energy, the use of new energy can reduce carbon emissions and achieve green power generation. Compared with traditional power systems, new power systems can better match energy supply and demand, maximize energy use and reduce energy waste through intelligent management and control.

[0004] However, the significant disadvantages of the prior art are mainly reflected in the following aspects: in the analysis of factors affecting broadband oscillation, the traditional analysis method of factors affecting oscillation is difficult to find the affecting rules under all working conditions.

[0005] Therefore, it is urgent to invent a more effective method for analyzing the factors affecting broadband oscillation. Summary of the invention

[0006] In order to solve the defects existing in the prior art, the present invention discloses a method for analyzing the influencing factors of broadband oscillation of a low-frequency power transmission system, and its technical solution is as follows:

[0007] A method for analyzing factors affecting broadband oscillation based on multiple linear regression, characterized by comprising:

[0008] Step 1: Select the operation and control parameters of the low-frequency transmission system as the prediction variables, and the broadband oscillation stability of the low-frequency transmission system as the response variable to construct a training set;

[0009] Step 2: Obtain the regression coefficient of each predictor variable based on the least squares method and construct a multiple linear regression function;

[0010] Step 3: Conduct a significance test on the constructed multiple linear regression function, introduce confidence intervals, and perform interval estimation on the regression coefficients to conduct hypothesis testing. Obtain the confidence interval of the regression coefficients, retain the prediction variables that meet the requirements, reconstruct the multiple linear regression function, obtain the regression coefficients, and obtain the influence of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

[0011] The present invention also discloses a device for analyzing factors affecting broadband oscillation in a low-frequency power transmission system, which is characterized by comprising:

[0012] Training set module: The operation and control parameters of the low-frequency transmission system are selected as the prediction variables, and the broadband oscillation stability of the low-frequency transmission system is selected as the response variable to construct the training set;

[0013] Multiple linear regression function model module: Based on the least squares method, the regression coefficients of each prediction variable are obtained and the multiple linear regression function is constructed;

[0014] Regression coefficient calculation module: Conduct significance test on the constructed multiple linear regression function, introduce confidence interval, and estimate the regression coefficient to conduct hypothesis test. Calculate the confidence interval of regression coefficient, retain the prediction variables that meet the requirements, reconstruct the multiple linear regression function, calculate the regression coefficient, and obtain the influence of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

[0015] The present invention also discloses a non-volatile storage medium, characterized in that the non-volatile storage medium includes a stored program, wherein when the program is running, the device where the non-volatile storage medium is located is controlled to execute the above method.

[0016] The present invention also discloses an electronic device applied to a flexible low-frequency power transmission system, characterized in that it comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to run the computer-readable instructions, wherein the above method is executed when the computer-readable instructions are run.

[0017] Beneficial Effects

[0018] The present invention can quantify the influence of various parameters in the flexible low-frequency power transmission system on the broadband oscillation of the system. Compared with the conventional mechanism analysis which can only focus on the influence in specific scenarios, this method can analyze the influence of various parameters on the broadband oscillation stability of the system under all working conditions, and can be used for broadband oscillation risk analysis of low-frequency power transmission systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of a method for analyzing factors affecting broadband oscillation in a low-frequency power transmission system provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The technical scheme of the present invention will be clearly and completely described below in conjunction with specific embodiments, but those skilled in the art should understand that the embodiments described below are only used to illustrate the present invention and should not be regarded as limiting the scope of the present invention. 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.

[0021] Embodiment 1:

[0022] See also Figure 1 As described above, this figure is a flow chart of a method for analyzing factors affecting broadband oscillation based on multivariate linear regression according to an embodiment of the present invention.

[0023] A method for analyzing factors affecting broadband oscillation of a low-frequency power transmission system includes:

[0024] Step S101, selecting the operation and control parameters of the low-frequency power transmission system as the prediction variables, taking the broadband oscillation stability of the low-frequency power transmission system as the response variable, and constructing a training set;

[0025] Specifically, this step includes impedance modeling of the wind turbine grid-side converter, line power electronic equipment, and line. Since the small signal stability in the new energy grid-connected system is equivalent to the output voltage V of the new energy subsystem at the common coupling point, out and the current component I out In practical situations, since the power grid itself can be considered stable and the new energy subsystem is also stable, the stability of the system can be observed by the characteristic root of the rate matrix. The prediction variables are selected through the characteristic root expression. According to the Nyquist criterion, the rate matrix is ​​constructed, its characteristic root expression is obtained, and the corresponding prediction variables are selected according to its expression.

[0026] The system broadband oscillation stability corresponding to the prediction variable is taken as its corresponding response variable to construct a training set.

[0027] Based on the above description, for the low-frequency power transmission system, the impedance modeling of the wind turbine grid-side converter and the modular multi-level matrix converter is carried out based on the small signal analysis method. Since in actual situations, it can be considered that the power grid itself and the new energy subsystem are stable. Therefore, the stability of the system can be determined by G(s)=1+Z g (s) / Z i (s). Its return matrix is: L(s) = Z g (s)*Y i (s) Z g (s) is the grid impedance, Z i (s) is the grid-side inverter impedance, Y i (s) is the grid-side inverter admittance. The system stability can be determined by whether the eigenvalue curve of the rate matrix is ​​around (-1,0j).

[0028] In summary, the selection of prediction variables is based on the system operation and control parameters contained in the characteristic root expression of the return rate matrix. When the prediction variables change, the stability of the corresponding system is obtained according to the above Nyquist criterion as the response variable. The training set is constructed based on the selected prediction variables and their corresponding response variables.

[0029] Step S102, obtaining the regression coefficient of each prediction variable based on the least squares method, and constructing a multivariate linear regression function.

[0030] Construct a multiple linear regression function: y = β0x0 + β1x1 + β2x2…β i x i +ε

[0031] Where: β0 is the intercept; β i For x i The regression coefficient of , where i = 1, 2, 3, …, m; m is the number of predictor variables; ε is the residual term, which is usually assumed to satisfy the normal distribution;

[0032] Specifically, the specific theoretical process of obtaining the regression coefficients of each predictor variable in the multivariate linear regression model based on the least squares method is as follows:

[0033] In multiple linear regression, mean square error is used as a metric; the regression coefficient solution of the corresponding multiple linear regression function is as follows:

[0034] Assume that the estimator of β is Then the residual vector The residual sum of squares is Q = e T e; To ensure the minimum residual sum of squares, it is necessary to Find the partial derivative, then we have:

[0035]

[0036] So we get: Due to X T X is reversible so we can get

[0037] in Y=[y1 y2 … y n ] T ;y i is the response variable of the i-th group of data; x ij is the jth predictor variable of the i-th group of data; X and Y are the matrices consisting of the predictor variables and response variables respectively.

[0038] Step S103, conduct a significance test on the constructed multiple linear regression function, introduce a confidence interval, and perform interval estimation on the regression coefficient to conduct hypothesis testing. Obtain the confidence interval of the regression coefficient, retain the prediction variables that meet the requirements, reconstruct the multiple linear regression function, obtain the regression coefficient, and obtain the influence of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

[0039] (1) The significance test process mainly includes:

[0040] In order to ensure that the predictor variable x i It has a good correlation with the response variable y, and the regression coefficient β i The following significance hypothesis test is performed:

[0041] H0:β i =0; H1:β i ≠0

[0042] In the formula: H0 is the null hypothesis; H1 is the alternative hypothesis.

[0043] The confidence interval is introduced to conduct hypothesis testing by performing interval estimation on the regression coefficient. The confidence interval is an interval centered on the expected value of the regression coefficient, and the probability that the regression coefficient has a confidence level falls within this interval. For multiple linear regression analysis, the confidence interval of the regression coefficient can be calculated by the following formula. The specific method of hypothesis testing is to determine whether 0 falls within the confidence interval. When the following formula is satisfied, H0 is accepted; otherwise, H0 is rejected.

[0044]

[0045]

[0046] P(T n-2 >t n-2,α / 2 )=α / 2

[0047] Where: s is the unbiased estimator, given by the above formula; c ii The matrix C = (X'X) -1 The element in the i-th row and i-th column of n-2,α / 2 is the critical value of t distribution. It satisfies the above relationship and can be obtained by looking up the table; P(*) is the probability function; α is the significance level, which means the probability of rejecting the null hypothesis when it is correct, usually 0.05; T n-2 is a random variable that follows a t-distribution with n-2 degrees of freedom.

[0048] (2) The process of reconstructing the multivariate linear regression function is:

[0049] After the constructed multiple linear regression function is tested for significance, the predictor variables that do not meet the requirements are removed, and then the regression coefficients of the retained predictor variables are obtained based on the least squares method, and then reconstructed as y = β0x0 + β1x1 + β2x2…β k x k +ε, where k is the number of remaining predictor variables, and then the above significance test is performed on them.

[0050] (3) Prediction impact conclusion

[0051] Among them, the influence of various influencing factors on the broadband oscillation of the system is mainly manifested in positive correlation and negative correlation. Positive correlation means that the corresponding prediction variable regression coefficient is greater than 0, indicating that when the influencing factor increases, the system becomes more unstable; negative correlation means that the corresponding prediction variable regression coefficient is less than 0, indicating that when the influencing factor increases, the system becomes more stable.

[0052] Specifically, in order to ensure a good linear relationship between the predictor variable and the response variable, the regression coefficient is tested for significance and the confidence interval of the regression coefficient is obtained.

[0053] If the confidence interval contains 0, the corresponding element is removed, the multivariate linear regression model is rebuilt and the regression coefficient is obtained. If the confidence interval does not contain 0, the influence of each prediction variable on the broadband oscillation stability of the system is obtained based on regression analysis.

[0054] Embodiment 2;

[0055] The following takes the offshore wind power transmission system via flexible low-frequency transmission as an example to further explain a method for analyzing the factors affecting broadband oscillations in low-frequency transmission systems.

[0056] Step S101, selecting the operation and control parameters of the low-frequency power transmission system as the prediction variables, taking the broadband oscillation stability of the low-frequency power transmission system as the response variable, and constructing a training set;

[0057] The wind farm consists of 200 direct-drive wind turbines with an output power of 5MW. The voltage is boosted to 66KV and then collected. It is then boosted to 525KV and passed through low-frequency transmission lines. After passing through modular multi-level matrix converters, it is stepped down to 165KV and then collected into the infinite power grid.

[0058] Construct wind turbine grid-side converter, modular multi-level matrix converter and line impedance models.

[0059] The grid-side converter of the wind turbine is controlled by constant reactive power and constant DC voltage. Its impedance model is:

[0060]

[0061] Where H dc (s) is the proportional coefficient and integral coefficient of the DC voltage control PI link; Hid (s), H iq (s) are the PI parameters of the d-axis and q-axis current control links; H pll (s) is the PI parameter of the phase-locked loop control link; G pll (s) is the transfer function of the q-axis voltage disturbance at the grid connection point; C dc is the DC capacitance; L c is the AC filter; u cd0 、u cq0 is the steady-state component of the converter output voltage; u dc0 is the steady-state component of the DC voltage; u d0 、i d0 is the steady-state component of the grid-connected voltage and current d-axis voltage; ω0 is the angular frequency.

[0062] The low-frequency side of the modular multi-level matrix converter adopts VF control, and the impedance model of the low-frequency side is:

[0063]

[0064] Where H l-i is the PI parameter of the inner loop current control link on the low-frequency side; H i-el is the PI parameter of the outer loop control on the low-frequency side; C f is the low-frequency side filter capacitor; R and L are the low-frequency side resistance and inductance.

[0065] Based on the Nyquist criterion, construct the recovery matrix. Find the characteristic root expression of the recovery matrix.

[0066] The characteristic roots of the matrix are obtained as:

[0067]

[0068] Where l1 and l2 are the characteristic roots of the return matrix. pp , L pn , L np , L nn is the element in the return rate matrix.

[0069] According to the characteristic root expression, the prediction variables are selected as:

[0070] Active output P, ​​grid voltage U, low-frequency line impedance Z, impedance ratio Filter capacitor C f , DC capacitor voltage U dc , AC filter L c , phase-locked loop PI control parameters, DC voltage outer loop PI control parameters, wind turbine grid-side converter dq current control PI parameters; modular multi-level matrix converter low-frequency side inner loop PI control parameters, modular multi-level matrix converter low-frequency side outer loop PI control parameters.

[0071] According to the change of the prediction variables, the broadband oscillation stability of the system is characterized as 0 and 1, 0 means the system is stable, and 1 means the system generates broadband oscillation. At the same time, the prediction variables are normalized based on the parameters of each prediction variable when the system is stable, so as to construct the training set.

[0072] Step S102, obtaining the regression coefficient of each prediction variable based on the least squares method, and constructing a multivariate linear regression function.

[0073] The regression coefficient parameters are obtained based on the least squares method.

[0074] Table 1 shows the regression coefficients corresponding to each predictor variable.

[0075]

[0076]

[0077] Where: K pudc , K iudc K is the DC voltage outer loop PI control proportional coefficient and integral coefficient; pd , K id K is the proportional coefficient and integral coefficient of the PI link of the d-axis current of the wind turbine grid-side converter; pq , K iq K is the proportional coefficient and integral coefficient of the PI link of the q-axis current of the wind turbine grid-side converter; ppll , K ipll K is the proportional coefficient and integral coefficient of the fan phase-locked loop PI link; pl_i , K il_i K is the proportional coefficient and integral coefficient of the inner loop PI link on the low-frequency side of M3C; pl_el , K il_el are the proportional coefficient and integral coefficient of the outer loop PI link on the low-frequency side of M3C;

[0078] Step 2: Conduct a significance test on the constructed multivariate linear regression function, introduce a confidence interval, and perform interval estimation on the regression coefficient to conduct hypothesis testing. Retain the prediction variables that meet the requirements, and obtain the impact of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

[0079] In order to determine whether there is a correlation between the predictor variable and the response variable, a significance test is performed on the regression coefficient.

[0080] Confidence intervals are introduced to conduct hypothesis testing by performing interval estimation on regression coefficients.

[0081] Find confidence intervals for each predictor variable

[0082] Table 2 shows the 95% confidence intervals of the regression coefficients for each predictor variable.

[0083]

[0084]

[0085] It can be seen that in the test of regression coefficients, the confidence intervals of some regression coefficients all contain 0.

[0086] Table 3 shows the regression coefficients and confidence intervals obtained by discarding the non-significant predictor variables and reconstructing the multiple linear regression function.

[0087]

[0088]

[0089] Through the above analysis, it can be concluded that the AC filter inductor L c , low frequency side outer loop control K pl_el , confidence interval elements are all greater than 0, and the confidence intervals of other parameters are all less than 0.

[0090] The analysis results are shown in Table 4. Among them, the influence of each parameter on the system broadband oscillation is mainly positive correlation and negative correlation. Positive correlation indicates that when the influencing factor increases, the system becomes more unstable; negative correlation indicates that when the influencing factor increases, the system becomes more stable.

[0091] Table 4 Influence of main factors on broadband oscillation stability of low-frequency transmission system

[0092]

[0093] The present invention proposes a method for analyzing factors affecting broadband oscillation of a low-frequency power transmission system, including: selecting system operation and control parameters as predictive variables, and broadband oscillation stability of the low-frequency power transmission system as a response variable, to construct a training set; constructing a multivariate linear regression function, and obtaining the regression coefficient of each predictive variable based on the least squares method; performing a significance test on the constructed multivariate linear regression function, and conducting hypothesis testing by introducing a confidence interval and performing interval estimation on the regression coefficient. Obtain the confidence interval of the regression coefficient, retain the predictive variables that meet the requirements, and obtain the influence of each predictive variable on the broadband oscillation stability of the system based on regression analysis. This patent describes the influence of various parameters on the broadband oscillation stability of the system under all operating conditions, and has good application prospects.

[0094] Although the present invention has been described in detail above by general description and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to the present invention. Therefore, these modifications or improvements made without departing from the spirit of the present invention all belong to the scope of protection claimed by the present invention.

Claims

1. A method for analyzing factors affecting broadband oscillation in low-frequency power transmission systems, characterized in that: include: Step 1: Select the operation and control parameters of the low-frequency transmission system as the prediction variables, and the broadband oscillation stability of the low-frequency transmission system as the response variable to construct a training set; Step 2: Obtain the regression coefficient of each predictor variable based on the least squares method and construct a multiple linear regression function; Step 3: Conduct a significance test on the constructed multiple linear regression function, introduce confidence intervals, perform interval estimation on the regression coefficients to conduct hypothesis testing, obtain the confidence interval of the regression coefficients, retain the prediction variables that meet the requirements, reconstruct the multiple linear regression function, obtain the regression coefficients, and obtain the influence of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

2. The method for analyzing factors affecting broadband oscillation in a low-frequency power transmission system according to claim 1, characterized in that: The operation and control parameters of the low-frequency transmission system are selected, normalized and used as prediction variables. When the parameters of the low-frequency transmission system change, the broadband oscillation stability of the low-frequency transmission system is used as the response variable and quantified into 0 and 1 variables, which is 0 when the system is stable and 1 when the system is unstable.

3. The method for analyzing factors affecting broadband oscillation in a low-frequency power transmission system according to claim 2, characterized in that: The significance test of the constructed multiple linear regression function includes: introducing the confidence interval, conducting hypothesis testing by performing interval estimation on the regression coefficient, and ensuring that its confidence interval does not contain 0; retaining the predictor variables that meet the above conditions.

4. The method for analyzing the influencing factors of broadband oscillation in a low-frequency power transmission system according to claim 1, wherein the specific expression for constructing the training set is: D={(x ji ,y j )},i=1,2…m,j=1,2…n; where x i is the predictor variable, y is the response variable, m is the number of predictor variables, and n is the sample size.

5. The method for analyzing the influencing factors of broadband oscillation of a low-frequency power transmission system according to claim 1 is characterized in that the specific process of constructing the multivariate linear regression function is as follows: Multiple linear regression with multiple predictor variables x i To predict the response variable y, where y and x i Satisfies the following functional relationship: y=β0+β1x1+β2x2…β i x i +ε; Where: β0 is the intercept; β i For x i The regression coefficient of , where i = 1, 2, 3, …, m; ε is the residual term, which is usually assumed to satisfy the normal distribution.

6. A method for analyzing the influencing factors of broadband oscillation of a low-frequency power transmission system according to claim 1, characterized in that: the specific theoretical process of obtaining the regression coefficient of each prediction variable based on the least squares method in step 2 is as follows: In multiple linear regression, mean square error is used as a metric; the regression coefficient solution of the corresponding multiple linear regression function is as follows: Assume that the estimator of β is Then the residual vector The residual sum of squares is Q = e T e; To ensure the minimum residual sum of squares, it is necessary to Find the partial derivative, then we have: It turns out that: Due to X T X is reversible so we can get in Y=[y1 y2 … y n ] T ;y i is the response variable of the i-th group of data; x ij is the jth predictor variable of the i-th group of data; X and Y are the matrices consisting of the predictor variables and response variables respectively.

7. A device for analyzing factors affecting broadband oscillation in low-frequency power transmission systems, characterized in that: include: Training set module: The operation and control parameters of the low-frequency transmission system are selected as the prediction variables, and the broadband oscillation stability of the low-frequency transmission system is selected as the response variable to construct the training set; Multiple linear regression function model module: Based on the least squares method, the regression coefficients of each prediction variable are obtained and the multiple linear regression function is constructed; Regression coefficient obtaining module: Conduct significance test on the constructed multiple linear regression function, introduce confidence interval, conduct hypothesis test by interval estimation of regression coefficient, retain the prediction variables that meet the requirements, reconstruct the multiple linear regression function, obtain the regression coefficient, and obtain the influence of each prediction variable on the wide-band oscillation stability of the system based on regression analysis.

8. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is executed, the device where the non-volatile storage medium is located is controlled to execute a method for analyzing factors affecting broadband oscillation of a low-frequency power transmission system as claimed in any one of claims 1 to 6.

9. An electronic device applied to a flexible low-frequency power transmission system, characterized in that: It comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to run the computer-readable instructions, wherein the computer-readable instructions, when running, execute a method for analyzing factors affecting broadband oscillation of a low-frequency power transmission system as described in any one of claims 1 to 6.

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