Wind power plant equivalent virtual inertia identification method based on symbol regression

Abstract

The invention discloses a wind power plant equivalent virtual inertia identification method based on symbol regression, and relates to the technical field of novel power system frequency safety and stability, and the method comprises the steps: S1, building a doubly-fed fan inertia response dynamic mechanism model containing comprehensive inertia control; according to the method, the problems of lack of physical mechanisms, poor evaluation interpretability and the like of an equivalent virtual inertia evaluation method for a current wind power plant are solved, the method is based on system operation data and is associated with an inertia response dynamic mechanism model, and the interpretability of a system physical process is reserved; a sparse dynamic modeling method is adopted, an input-output linear combination feature library of system electromagnetic torque-rotor rotating speed change is constructed, sparse solution of parameters is achieved through a sequence threshold value least square algorithm, and the equivalent virtual inertia of the wind power plant is obtained through evaluation. According to the method, model priori knowledge and operation data are fully applied, and the evaluation result is high in accuracy and high in interpretability.

Description

Technical Field

[0001] The present invention relates to the technical field of new power system frequency security and stability, and specifically to a method for identifying the equivalent virtual inertia of a wind farm based on symbolic regression. Background Technique

[0002] With the gradual increase in the proportion of new energy units such as wind power and photovoltaic power in the power system output, the system inertia level has decreased significantly, weakening the ability of the system to maintain frequency stability under sudden faults or load fluctuation disturbances, and restricting the further improvement of the new energy consumption ratio. Accurately evaluating the system inertia level helps to evaluate the system frequency stability safety risk and further implement stability control, which is the key to the safe and stable operation of the system. In recent years, many scholars have evaluated the inertia level of wind farms from the perspectives of physical analytical model derivation and data-driven methods.

[0003] In terms of the physical analytical model, some scholars have derived the physical connection between the control modules of a doubly-fed wind turbine unit with virtual inertia control, and on this basis, obtained an analytical expression of the frequency dynamic characteristic quantity, and then quantitatively characterized the inertia calculation method of the doubly-fed wind farm. However, such methods often rely on the control parameters of each control module in the system, and these parameters are often difficult to obtain in the actual power system. Therefore, it is difficult to directly calculate the inertia of the wind farm by this method and apply it to actual engineering.

[0004] With the rapid development of wide-area measurement technology and artificial intelligence algorithms, data-driven methods have been widely used in wind farm inertia assessment due to their outstanding advantages in data mining and processing of the nonlinear relationship between state variables. It learns the mapping relationship between the grid transient frequency and system state variables through historical data of a large number of frequency events, and based on the optimization parameter identification algorithm of inertia response, the inertia of the system is identified. However, the current data-driven inertia assessment method abandons the prior physical information, and the identification accuracy depends on a large amount of frequency data; at the same time, the identified model has no specific analytical form, and the result lacks the matching mechanism with physical mechanism parameters, so there is a problem of poor physical interpretability. Summary of the Invention

[0005] The purpose of the present invention is to propose a method for identifying the equivalent virtual inertia of a wind farm based on symbolic regression in order to solve the problems mentioned in the above background technique.

[0006] The purpose of the present invention can be achieved by the following technical solutions: A method for identifying the equivalent virtual inertia of a wind farm based on symbolic regression, including the following steps:

[0007] S1: Establish a dynamic mechanism model of the inertia response of a doubly-fed wind turbine with comprehensive inertia control;

[0008] S2: Based on the definition of the virtual inertia time constant of the wind turbine generator set, derive the mathematical analytical formula for the equivalent virtual inertia time constant of the doubly-fed wind farm;

[0009] S3: Analyze the inertia response mechanism model of the doubly-fed wind turbine, divide each control module involved in the inertia response in the wind farm into independent modules to form a clear modular structure; through the control equations of each control module, establish the corresponding linear function library, and construct a symbolic regression model reflecting the inertia response characteristics of the wind farm by associating with the system operation data;

[0010] S4: Adopt the sequential threshold least squares identification algorithm to identify and solve the unknown control parameters in the model, and then obtain the frequency-domain analytical expression of the equivalent virtual inertia time constant that can quantitatively characterize the inertia support ability of the wind farm. The effectiveness and accuracy of the method are verified in the IEEE 3-machine 9-bus system containing the doubly-fed wind power cluster.

[0011] As a preferred implementation manner of the present invention, in the step S1, establish a dynamic mechanism model of the inertia response of the doubly-fed wind turbine with comprehensive inertia control, including:

[0012] To evaluate the equivalent inertia size of the doubly-fed wind farm, establish a doubly-fed wind turbine model including a generator transient model, a speed controller model, and a comprehensive inertia control model, and make the following assumptions: Do not consider the influence of the dynamic characteristics of the mechanical drive system on the inertia, that is, the mechanical torque remains unchanged; the wind speed remains unchanged during the dynamic process of the inertia response; ignore the stator resistance loss and the change of the magnetic flux; the inertia response speed is much slower than the converter response speed, and simplify the inner current loop of the rotor-side converter into a first-order inertia link, that is, G s = 1 / (τs + 1);

[0013] Generator transient model:

[0014]

[0015]

[0016] Among them, p is the number of pole pairs of the wind turbine generator set; L m is the mutual inductance between the stator and rotor; U s is the stator voltage vector; I d is the d-axis component of the rotor current; ω s is the grid angular frequency; L s is the stator self-inductance; ω r is the rotor speed; H wind is the inherent inertia time constant of the wind turbine generator set; T m is the mechanical torque of the wind turbine generator set;

[0017] Comprehensive inertia control model:

[0018]

[0019] Among them, is the electromagnetic torque provided for the comprehensive inertia control; ω s is the grid angular frequency; ω s0 is the initial grid angular frequency; k p and k d are the proportional coefficient and differential coefficient of the comprehensive inertia control; T f is the time constant of the low-pass filter;

[0020] The electromagnetic torque increment during the inertia response process of the doubly-fed wind turbine is obtained as:

[0021]

[0022] Among them, Δω s is the change in the grid angular frequency.

[0023] As a preferred embodiment of the present invention, in the step S2, the analytical expression of the equivalent virtual inertia of the wind farm is derived, including:

[0024] The virtual inertia time constant of the wind turbine is defined as the ratio of the kinetic energy stored at the rated speed of the generator to the rated capacity, and it is expressed as:

[0025]

[0026] Among them, E k is the kinetic energy stored in the generator rotor at the rated speed of a single wind turbine; S N is the rated capacity of the wind turbine; ω N is the rated angular frequency of the wind turbine; ω s0 , ω r0 , Δω s , Δω r are respectively the initial grid angular frequency, the initial speed of the generator, the change in the grid angular frequency, and the change in the generator speed; J eq is the virtual equivalent moment of inertia of the wind turbine; H wind is the inherent inertia time constant of the wind turbine;

[0027] The incremental rotor motion equation is Laplace-transformed, and the electromagnetic torque increment is substituted to obtain:

[0028]

[0029] Furthermore, the ratio of the change in the rotor speed of the wind turbine to the change in the grid angular frequency is obtained:

[0030]

[0031] Then substitute it into the definition formula of the inertia time constant of the wind turbine to obtain the frequency expression of the equivalent inertia time constant of the doubly-fed wind turbine as follows:

[0032]

[0033] The above frequency expression is the calculation method of the inertia time constant of a single wind turbine; when there are n doubly-fed wind turbines in a wind farm, the wind farm is equivalent to a single unit, and its equivalent virtual inertia is expressed as:

[0034]

[0035] In the formula: H eq is the equivalent virtual inertia of the wind farm; S Nj is the rated capacity of a single wind turbine; H equj is the virtual inertia of a single wind turbine;

[0036] The frequency expression of the equivalent virtual inertia of the wind farm is:

[0037]

[0038] In the formula: ω r0i is the initial angular velocity of the jth wind turbine.

[0039] As a preferred embodiment of the present invention, in the step S3, a corresponding linear function library is established, and the system operation data is associated to construct a symbolic regression model reflecting the inertia response characteristics of the wind farm, which specifically includes:

[0040] S31: Preprocess the measurement data to ensure that the collected operation time series data is the optimal data set, thereby improving the accuracy of inertia identification and the robustness of the model. Specifically:

[0041] The mean filtering method is used to remove the DC component in the data. By calculating the sliding mean of the signal, the signal is transformed into a zero-mean form, thereby eliminating the influence of false features caused by the DC component on the identification accuracy;

[0042] A low-pass filter is used to remove the frequency perturbation and the high-frequency components in the active power data to achieve the effects of smoothing and denoising;

[0043] The processed data is normalized to eliminate the differences in dimension and magnitude between different physical quantities;

[0044] S32: For a dynamic system, its dynamic equation is characterized by the following formula:

[0045]

[0046] In the formula, x(t) = [x 1 (t), x2 (t),…x n (t)] T is a state quantity that changes over time, and the non-linear function f(x(t)) represents the dynamic constraint of the system motion equation; at the same time, an augmented matrix library Θ(Ξ) is constructed, which consists of candidate non-linear functions of the state quantity X and is composed of functions such as constant terms, polynomials, and trigonometric terms. Each column of Θ(X) represents a candidate function on the right side of the equation; however, in an actual dynamic system, only a few functions in each row of f satisfy the requirements of the dynamic equation. Therefore, a sparse vector Ξ = [ξ 1 ξ 2 ... ξ n is constructed to determine which functions are valid, and thus the dynamic equation is written as:

[0047]

[0048] Each column ξ of Ξ k represents a sparse vector, which determines which terms on the right side of the equation are valid. Once confirmed, the following dynamic equation model is constructed:

[0049]

[0050] where Θ(X T ) is the sign function vector of the elements of X, and Θ(X) is a data matrix, thus obtaining the corresponding model:

[0051]

[0052] S33: According to the equations of each control module in the doubly-fed wind turbine, its state equation is:

[0053]

[0054] The input is defined as the electromagnetic torque disturbance quantity of each control module in the wind farm The output is the deviation of the rotor speed of the wind turbine and the grid angular frequency X = [Δω r , ω s of the wind farm, and the parameters to be identified U = [k i1 , k p1 , k d , k p , T f ; The time series matrix of the wind farm operation data that needs to be collected is as follows:

[0055] X = [x 1 x 2 L x k L x n ​T

[0056] U = [u 1 u 2 L u k L u n T ;

[0057] Specifically, for the speed controller, consider constructing a sparse model to describe the relationship between the system state variables and the input disturbance electromagnetic torque as follows:

[0058]

[0059] Since the dynamic equation structure of the speed controller is known, the feature library Θ(X) is expressed as:

[0060]

[0061] Furthermore, the following identification model is obtained:

[0062]

[0063] The parameter solution of the final identification model can be converted into the following regression problem:

[0064]

[0065] In the formula, R represents the sparse regularization operator, which is selected as the 1-norm to ensure that the problem is a convex optimization problem; λ is the optimization hyperparameter used to control the sparsity degree of the sparse model.

[0066] As a preferred embodiment of the present invention, in the step S4, the least squares method and the stepwise thresholding strategy are combined to gradually screen the feature terms and iteratively optimize the model sparsity to obtain a sparse solution, which specifically includes:

[0067] Apply the least squares method to update the regression coefficients and truncate the coefficients through a set threshold, so as to set the unimportant feature coefficients to zero; specifically: First, use the least squares method to fit the current residuals to obtain a set of updated regression coefficients; Second, according to the preset threshold rule, perform thresholding on these coefficients to remove the coefficients whose absolute values are less than the threshold. This process gradually realizes the sparsification of the model through alternating regression optimization and threshold operations.

[0068] Compared with the prior art, the beneficial effects of the present invention are:

[0069] ​1. In view of the problems existing in the current research on the inertia evaluation method of wind farms, such as the lack of physical mechanism and poor interpretability of evaluation results, the present invention proposes a method for identifying the equivalent virtual inertia of wind farms based on symbolic regression. The proposed method can fully utilize the prior knowledge of the model and operation data to accurately evaluate the inertia level of doubly-fed wind farms;

[0070] 2. The present invention establishes a dynamic mechanism model of the inertia response of doubly-fed wind turbines and theoretically derives an explicit analytical expression for the equivalent virtual inertia of doubly-fed wind farms.

[0071] 3. Based on a data-physics hybrid-driven method, the present invention constructs a symbolic regression model of the inertia response characteristics of the system by correlating the system operation data, and uses the sequential threshold least squares method to solve the control parameters in the identification model, thereby accurately obtaining the inertia magnitude of the wind farm. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art.

[0073] Figure 1 It is the control block diagram of the simplified model of the doubly-fed wind turbine established in this embodiment;

[0074] Figure 2 It is the flow chart of applying the proposed scheme in this embodiment;

[0075] Figure 3 It is the simulation system diagram in this embodiment;

[0076] Figure 4 It is the partial operation data diagram of the system after being disturbed in this embodiment.

[0077] Figure 5 It is the comparison diagram of the inertia evaluation value and the simulation actual value under different operating conditions in this embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0078] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0079] Embodiment 1

[0080] Please refer to Figures 1-5 shown, a method for identifying the equivalent virtual inertia of a wind farm based on symbolic regression, the steps include:

[0081] S1. Establish a dynamic mechanism model of the inertia response of a doubly-fed wind turbine with comprehensive inertia control;

[0082] S2. Based on the definition of the virtual inertia time constant of a wind turbine, derive the mathematical analytical formula for the equivalent virtual inertia time constant of a doubly-fed wind farm;

[0083] S3. Analyze the inertia response mechanism model of a doubly-fed wind turbine, divide each control module involved in the inertia response in the wind farm into independent modules to form a clear modular structure. On this basis, establish a corresponding linear function library through the control equations of each module, and construct a symbolic regression model reflecting the inertia response characteristics of the wind farm by associating with the system operation data;

[0084] S4. Use the sequential threshold least squares identification algorithm to identify and solve the unknown control parameters in the model, and then obtain the frequency-domain analytical expression of the equivalent virtual inertia time constant that can quantitatively characterize the inertia support ability of the wind farm. The effectiveness and accuracy of the method are verified in the IEEE 3-machine 9-bus system containing a doubly-fed wind power cluster.

[0085] In the step S1, construct a dynamic mechanism model of the inertia response of a doubly-fed wind turbine with comprehensive inertia control, including:

[0086] S11. To evaluate the equivalent inertia size of a doubly-fed wind farm, a doubly-fed wind turbine model including a generator transient model, a speed controller model, and a comprehensive inertia control model is established, and the following assumptions are made:

[0087] 1) Do not consider the influence of the dynamic characteristics of the mechanical drive system on inertia, that is, the mechanical torque remains unchanged;

[0088] 2) The wind speed remains unchanged during the dynamic process of inertia response;

[0089] 3) Ignore the stator resistance loss and the change of magnetic flux;

[0090] 4) The inertia response speed is much slower than the converter response speed. In this paper, the inner current loop of the rotor-side converter is simplified to a first-order inertia link, that is, G s = 1 / (τs + 1).

[0091] Generator transient model:

[0092]

[0093]

[0094] Among them, p is the number of pole pairs of the wind turbine; L m is the mutual inductance between the stator and rotor; U s is the stator voltage vector; I d is the d-axis component of the rotor current; ω sis the grid angular frequency; L s is the stator self-inductance; ω r is the rotor speed; H wind is the inherent inertia time constant of the wind turbine; T m is the mechanical torque of the wind turbine.

[0095] Speed controller model:

[0096]

[0097] Among them, ΔT 1 * is the electromagnetic torque output by the speed controller; Δω r is the change in the rotor speed of the wind turbine; k i1 and k p1 are the integral gain and proportional gain of the speed controller respectively.

[0098] Integrated inertia control model:

[0099]

[0100] Among them, is the electromagnetic torque provided by the integrated inertia control; ω s is the grid angular frequency; ω s0 is the initial grid angular frequency; k p and k d are the proportional coefficient and differential coefficient of the integrated inertia control; T f is the time constant of the low-pass filter.

[0101] Based on the above analysis, the electromagnetic torque increment in the inertia response process of the doubly-fed wind turbine is obtained as:

[0102]

[0103] Among them, Δω s is the change in the grid angular frequency.

[0104] As described in step S2, the mathematical analytical formula for the equivalent virtual inertia time constant of the doubly-fed wind farm is derived. Combining the doubly-fed inertia response model established in step S1 and the definition of the virtual inertia time constant of the wind turbine, the analytical expression for the equivalent virtual inertia of the wind farm is further derived. Specifically, it includes:

[0105] S21. The virtual inertia time constant of the wind turbine is defined as the ratio of the kinetic energy stored at the rated speed of the generator to the rated capacity, and it can be expressed as:

[0106]

[0107] Among them, E kStores the kinetic energy of the generator rotor at the rated speed of a single wind turbine; S N Is the rated capacity of the wind turbine; ω N Is the rated angular frequency of the wind turbine; ω s0 、ω r0 、Δω s 、Δω r Are respectively the initial angular frequency of the power grid, the initial rotational speed of the generator, the change in the angular frequency of the power grid, and the change in the rotational speed of the generator; J eq Is the virtual equivalent moment of inertia of the wind turbine; H wind Is the inherent inertia time constant of the wind turbine.

[0108] Taking the Laplace transform of the incremental rotor motion equation and substituting formula (5) gives:

[0109]

[0110] Furthermore, the ratio of the change in the rotor speed of the wind turbine to the change in the angular frequency of the power grid can be obtained:

[0111]

[0112] Substituting this formula into the definition formula of the inertia time constant of the wind turbine, the frequency expression of the equivalent inertia time constant of the doubly-fed wind turbine can be obtained as:

[0113]

[0114] The above formula (9) is the calculation method of the inertia time constant of a single wind turbine. When the wind farm contains n doubly-fed wind turbines, considering the wind farm as equivalent to one unit, its equivalent virtual inertia can be expressed as:

[0115]

[0116] In the formula: H eq Is the equivalent virtual inertia of the wind farm; S Nj Is the rated capacity of a single wind turbine; H equj Is the virtual inertia of a single wind turbine.

[0117] Substituting this formula into formula (9), the frequency expression of the equivalent virtual inertia of the wind farm can be obtained as:

[0118]

[0119] In the formula: ω r0i Is the initial angular velocity of the j-th wind turbine.

[0120] From the analytical expression of the equivalent virtual inertia calculation of the doubly-fed wind farm derived above, it can be seen that the equivalent virtual inertia of the wind turbine is a quantity that changes with time. Its value is mainly related to the control parameters of the wind turbine, the inherent inertia time constant, and the corresponding operating parameters. In the actual power system, due to factors such as commercial confidentiality, new energy equipment manufacturers usually only provide black / gray box models, which only describe the input-output characteristics of the system, and the key parameters inside the system are generally regarded as confidential by manufacturers and are difficult to obtain directly. Therefore, to accurately evaluate the equivalent virtual inertia of the doubly-fed wind farm, it is necessary to identify the control parameters of each control structure in the wind turbine first.

[0121] In step S3, through the control equations of each module, a corresponding linear function library is established, and the system operation data is associated to construct a symbolic regression model reflecting the inertia response characteristics of the wind farm. A linear function library reflecting the system frequency response characteristics is established, and a data-physics fusion-driven convex optimization regression model is constructed in combination with each control module involved in the inertia response in the wind farm. Specifically, it includes:

[0122] S31. Generally speaking, the data collected directly affects the accuracy and effectiveness of the subsequent model, and the measured data of the wind farm usually contains noise, irregular fluctuations, and outliers. Therefore, it is necessary to preprocess the measured data to ensure that the collected operation time series data is the optimal data set, thereby improving the accuracy of inertia identification and the robustness of the model. The main steps are as follows:

[0123] (a) The mean filtering method is used to remove the DC component in the data. By calculating the sliding mean of the signal, the signal is transformed into a zero-mean form, thereby eliminating the influence of the "false features" caused by the DC component on the identification accuracy.

[0124] (b) A low-pass filter is used to remove the frequency disturbance and the high-frequency components in the active power data to achieve the effect of smoothing and denoising.

[0125] (c) The processed data is normalized to eliminate the differences in dimension and magnitude between different physical quantities.

[0126] S32. For a dynamic system, its dynamic equation can be characterized by the following formula:

[0127]

[0128] where x(t) = [x 1 (t), x 2 (t), … x n (t)] Tis a state quantity that changes over time, and the non-linear function f(x(t)) represents the dynamic constraint of the system motion equation. At the same time, an augmented matrix library Θ(Ξ) is constructed, which consists of candidate non-linear functions of the state quantity X and can usually be composed of functions such as constant terms, polynomials, and trigonometric terms. Each column of Θ(X) represents a candidate function on the right side of equation (12). However, in an actual dynamic system, only a few functions in each row of f satisfy the requirements of the dynamic equation. Therefore, a sparse vector Ξ = [ξ 1 ξ 2 ... ξ n can be constructed to determine which functions are valid. Thus, the general dynamic equation can be written as:

[0129]

[0130] Each column ξ of Ξ k represents a sparse vector, which determines which terms on the right side of equation are valid. Once confirmed, the following dynamic equation model can be constructed:

[0131]

[0132] In the formula, Θ(X T ) is the sign function vector of the elements of X, and Θ(X) is a data matrix, thus obtaining the corresponding model:

[0133]

[0134] S33. Based on the above analysis, according to the equations of each control module in the doubly-fed fan, its state equation can be obtained as:

[0135]

[0136] The input of the system is defined as the electromagnetic torque disturbance quantity of each control module in the wind farm The output is the deviation of the rotor speed of the wind turbine and the grid angular frequency X = [Δω r , ω s of the wind farm. The parameters to be identified are U = [k i1 , k p1 , k d , k p , T f . The time series matrix of the wind farm operation data to be collected is as follows:

[0137] X = [x 1 x 2 L x k L x n T ​

[0138] U = [u 1 u 2 L u k L u n T (17)

[0139] Taking the speed controller as an example, consider constructing a sparse model to describe the relationship between the system state variables and the input disturbance electromagnetic torque as follows:

[0140]

[0141] Since the dynamic equation structure of the speed controller is known, the feature library Θ(X) is expressed as:

[0142]

[0143] Furthermore, the following identification model can be obtained:

[0144]

[0145] The parameter solution of the final identification model can be transformed into the following regression problem:

[0146]

[0147] In the formula, R represents the sparse regularization operator, which is selected as the l1 norm to ensure that the problem is a convex optimization problem; λ is the optimization hyperparameter, which is used to control the sparsity degree of the sparse model.

[0148] Using the sequential threshold least squares identification algorithm described in step S4, identify and solve the unknown control parameters in the model, and then obtain the equivalent virtual inertia time constant frequency domain analytical expression that can quantitatively characterize the inertia support ability of the wind farm. Combine the least squares method and the step-by-step thresholding strategy to gradually screen the feature terms and iteratively optimize the model sparsity, so as to obtain the sparse solution. Specifically, it includes:

[0149] S41. The core idea of this algorithm is that in each iteration, first, the least squares method is used to update the regression coefficients, and the coefficients are truncated by the set threshold, so as to set the unimportant feature coefficients to zero. Specifically, first, the least squares method is used to fit the current residuals to obtain a set of updated regression coefficients; secondly, according to the preset threshold rule, these coefficients are thresholded to remove the coefficients whose absolute values are less than the threshold. This process gradually realizes the sparsity of the model by alternately performing regression optimization and threshold operations.

[0150] ​In the step S1, a transient model of the generator, a speed controller model, and a comprehensive inertia control model are respectively constructed. In the step S2, combining the double-fed inertia response model established in the step S1 and the definition of the virtual inertia time constant of the wind turbine generator set, an analytical expression of the equivalent virtual inertia of the wind farm is derived. In the step S3, a linear function library reflecting the system frequency response characteristics is established, and combined with each control module involved in the inertia response in the wind farm, a data-physics fusion-driven convex optimization regression model is constructed. In the step S4, the sequential threshold least squares identification algorithm is used to identify and solve the unknown control parameters in the model, and combined with the analytical expression of the equivalent virtual inertia of the wind farm derived in the step S2, the size of the equivalent virtual inertia of the wind farm is accurately evaluated.

[0151] To verify the accuracy and effectiveness of the present invention, the example method of the present invention is now applied to the IEEE 3-machine 9-bus scenario, and a double-fed wind farm is used to replace one of the synchronous generators. The average wind speed in the wind farm is considered for simulation calculation, and the operating conditions of the wind farm under different average wind speeds and different control parameters are simulated. Four different working conditions are set:

[0152] The average wind speeds of the double-fed wind farm are 9 m / s and 10 m / s respectively, and the control parameters are: k p1 = 6, k i1 = 2, k p = 15, k d = 10, T f = 0.5;

[0153] The average wind speed of the double-fed wind farm is 9 m / s, and the control parameters are: k p1 = 6, k i1 = 2, k p = 20, k d = 10, T f = 0.5;

[0154] The average wind speeds of the double-fed wind farm are 9 m / s, and the control parameters are: k p1 = 6, k i1 = 2, k p = 15, k d = 15, T f = 0.5;

[0155] The average wind speed of the double-fed wind farm is 9 m / s, and the control parameters are: k p1 = 6, k i1 = 2, k p = 15, k d = 10, T f = 1.

[0156] At t = 10 s, the L1 load is suddenly increased to simulate the frequency disturbance condition of the wind farm, and the simulation time is set to 35 s.

[0157] The simulation data obtained under different wind speed conditions and different control parameters are respectively input into the identification models of each control module for iterative optimization. The identification results of the control parameters of each module of the wind farm are shown in Table 1 below:

[0158] Table 1: Identification results of controller parameters at a wind speed of 9 m / s

[0159]

[0160] It can be seen from the identification results in Table 1 that the error between the identification results and the actual values is within an acceptable range, and the proposed method can accurately identify the control parameters of the doubly-fed wind farm.

[0161] Now, the method for evaluating the inertia of the wind farm proposed in the present invention is compared and verified with the simulation values. Among them, the simulation value of the equivalent inertia time constant of the wind farm is obtained by extracting the ratio of / and substituting it into the theoretical derivation analytical expression.

[0162] Figure 5 (a) shows the comparison between the simulation values and the evaluation values of the inertia results of the wind farm at different wind speeds. The results show that the evaluated value of the equivalent virtual inertia obtained by the method for evaluating the wind farm proposed in the present invention is basically consistent with the simulation calculation value, verifying the accuracy and effectiveness of the method proposed in the present invention. At the same time, after the power grid is subjected to frequency disturbance, the inertia exhibited by the wind farm with comprehensive inertia control is time-varying, and at different wind speeds, the equivalent virtual inertia of the wind farm is different, and the larger the wind speed, the larger its value. Figure 5 (b), (c), and (d) respectively show the comparison between the simulation values and the evaluation values of the inertia results of the wind farm under different control parameters. The results show that the evaluated value of the inertia obtained by the proposed method still shows a high degree of coincidence with the simulation calculation value, indicating that the method also has a certain degree of applicability, and with different control parameters, the inertia support ability of the wind farm for the power grid is different.

[0163] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the present invention to only the specific implementation manners. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the relevant technical fields can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A wind farm equivalent virtual inertia identification method based on symbolic regression, characterized in that: The following steps are involved: S1: Establish a dynamic mechanism model of inertia response of a doubly-fed wind turbine with integrated inertia control; S2: Based on the definition of virtual inertia time constant of wind turbine, the mathematical analytical formula of equivalent virtual inertia time constant of doubly fed wind farm is derived; S3: Analyze the inertia response mechanism model of the doubly-fed wind turbine, divide the control modules involved in the inertia response in the wind farm into independent modules, and form a clear modular structure; establish the corresponding linear function library through the control equations of each control module, and associate the system operation data to build a symbolic regression model that reflects the inertia response characteristics of the wind farm; S4: The sequential threshold least squares identification algorithm is used to identify and solve the unknown control parameters in the model, and then the frequency domain analytical expression of the equivalent virtual inertia time constant that can quantitatively characterize the inertia support capacity of the wind farm is obtained.

2. The wind farm equivalent virtual inertia identification method based on symbolic regression according to claim 1 is characterized in that: In the step S1, a dynamic mechanism model of inertia response of a doubly-fed wind turbine with integrated inertia control is established, including: In order to evaluate the equivalent inertia of the doubly fed wind farm, a doubly fed wind turbine model including the generator transient model, speed controller model and comprehensive inertia control model is established, and the following assumptions are made: the influence of the dynamic characteristics of the mechanical transmission system on the inertia is not considered, that is, the mechanical torque remains unchanged; the wind speed remains unchanged during the dynamic process of inertia response; the stator resistance loss and flux change are ignored; the inertia response speed is much slower than the converter response speed, and the inner current loop of the rotor-side converter is simplified to a first-order inertia link, that is, G s =1 / (τs+1); Generator transient model: Where p is the number of pole pairs of the wind turbine; Lm is the stator-rotor mutual inductance; U s is the stator voltage vector; Id is the d-axis component of the rotor current; ωs is the grid angular frequency; Ls is the stator self-inductance; ωr is the rotor speed; Hwind is the inherent inertia time constant of the wind turbine; Tm is the mechanical torque of the wind turbine; Comprehensive Inertial Control Model: in, The electromagnetic torque provided for the integrated inertia control; ωs is the grid angular frequency; ωs0 is the initial grid angular frequency; kp and kd are the proportional coefficient and differential coefficient of the integrated inertia control; Tf is the time constant of the low-pass filter; The electromagnetic torque increment during the inertia response process of the doubly fed wind turbine is obtained as: Among them, Δω s is the change of grid angular frequency.

3. The wind farm equivalent virtual inertia identification method based on symbolic regression according to claim 2 is characterized in that: In step S2, an analytical expression of the equivalent virtual inertia of the wind farm is derived, including: The virtual inertia time constant of a wind turbine is defined as the ratio of the kinetic energy stored at the rated speed of the generator to the rated capacity, which is expressed as: Among them, Ek is the kinetic energy stored in the generator rotor at the rated speed of a single wind turbine; SN is the rated capacity of the wind turbine; ωN is the rated angular frequency of the wind turbine; ωs0, ωr0, Δωs, Δωr are the initial angular frequency of the power grid, the initial speed of the generator, the change in the angular frequency of the power grid, and the change in the speed of the generator, respectively; Jeq is the virtual equivalent moment of inertia of the wind turbine; Hwind is the inherent inertia time constant of the wind turbine; Perform Laplace transform on the incremental rotor motion equation and substitute the electromagnetic torque increment into it to obtain: Then the ratio of the wind turbine rotor speed change to the grid angular frequency change is obtained: Then substitute it into the definition of the inertia time constant of the wind turbine to obtain the frequency expression of the equivalent inertia time constant of the doubly fed wind turbine: The above frequency expression is the calculation method of the inertia time constant of a single wind turbine. When the wind farm contains n double-fed wind turbines, the wind farm is equivalent to one unit, and its equivalent virtual inertia is expressed as: Where: Heq is the equivalent virtual inertia of the wind farm; S Nj is the rated capacity of a single wind turbine; H equj is the virtual inertia of a single wind turbine; The frequency expression of the equivalent virtual inertia of the wind farm is: Where: ωr0i is the initial angular velocity of the j-th wind turbine.

4. The wind farm equivalent virtual inertia identification method based on symbolic regression according to claim 1 is characterized in that: In step S3, a corresponding linear function library is established, and a symbolic regression model reflecting the inertia response characteristics of the wind farm is constructed by associating the system operation data, specifically including: S31: Preprocess the measured data to ensure that the collected running time data is the optimal data set, thereby improving the accuracy of inertia identification and the robustness of the model, specifically: The mean filtering method is used to remove the DC component in the data. By calculating the sliding mean of the signal, the signal is converted into a zero-mean form, thereby eliminating the influence of false features caused by the DC component on the recognition accuracy. Use low-pass filters to remove frequency disturbances and high-frequency components in active power data to achieve smoothing and denoising effects; The processed data is normalized to eliminate the differences between different physical quantities and the differences in dimensions and magnitudes; S32: For a dynamic system, its dynamic equation is represented by the following formula: Where x(t) = [x1(t), x2(t), ... xn(t)]T is the state quantity that changes with time, and the nonlinear function f(x(t)) represents the dynamic constraint of the system motion equation. At the same time, an augmented matrix library Θ(Ξ) is constructed, which consists of candidate nonlinear functions of the state quantity X, consisting of functions such as constant terms, polynomials and trigonometric terms. Θ(X) represents a candidate function on the right side of the equation for each column. However, in actual dynamic systems, only a few functions in each row of f meet the requirements of the dynamic equation. Therefore, a sparse vector Ξ = [ξ1ξ2...ξn] is constructed to determine which functions are valid, so that the dynamic equation is written as: Ξ Each column ξk represents a sparse vector, which determines the equation Once the terms on the right side of are valid, the following dynamic equation model is constructed: In the formula, Θ(X T ) is the symbolic function vector of the X elements, and Θ(X) is a data matrix, resulting in the corresponding model: S33: According to the equations of each control module in the doubly fed wind turbine, its state equation is: The input is defined as the electromagnetic torque disturbance of each control module in the wind farm The output is the deviation of the rotor speed of the wind turbine and the grid angular frequency of the wind farm X = [Δωr, ωs], and the parameter to be identified U = [k i1 ,k p1 ,k d ,k p ,T f ]; the time series matrix of wind farm operation data that needs to be collected is as follows: X= [ x1 x2 Lxk Lxn ] T U} [ u1 u2 Look Long ] T; Specifically for the speed controller, consider building a sparse model to describe the relationship between the system state variables and the input disturbance electromagnetic torque as follows: Since the dynamic equation structure of the speed controller is known, the feature library Θ(X) is expressed as: Then the following identification model is obtained: The parameter solution of the final identification model can be converted into the following regression problem: Where R represents the sparse regularization operator, which is selected as 1 norm to ensure that the problem is a convex optimization problem; λ is the optimization hyperparameter used to control the sparsity of the sparse model.

5. The wind farm equivalent virtual inertia identification method based on symbolic regression according to claim 1 is characterized in that: In step S4, the least square method and the stepwise thresholding strategy are combined to gradually screen the feature items, and the model is iteratively optimized to obtain a sparse solution, which specifically includes: The least squares method is used to update the regression coefficients, and the coefficients are truncated by the set threshold, so that the unimportant characteristic coefficients are set to zero; specifically: first, the least squares method is used to fit the current residual to obtain a set of updated regression coefficients; secondly, according to the preset threshold rule, these coefficients are thresholded and the coefficients with absolute values ​​less than the threshold are eliminated. This process gradually achieves the sparseness of the model by alternating regression optimization and threshold operations.

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