Inertia estimation method based on physical information neural network

Abstract

The application discloses a kind of inertia estimation methods based on physical information neural network, the method comprises: constructing the dynamic response data set required for inertia estimation;Inertia estimation fully connected neural network is constructed;Inertia estimation fully connected neural network loss function is constructed, which contains differential form and integral form swing equation physical residual;The physical distinguishability score of the two kinds of physical residuals is calculated;The inertia estimation deviation score of the two kinds of physical residuals is calculated;According to the two scores, the adaptive loss weight of the two kinds of physical residuals is calculated respectively;Inertia estimation fully connected neural network is trained;In actual operation, the trained neural network is used to estimate inertia.The present application adaptively selects the loss weight of differential and integral swing equation physical loss based on physical distinguishability score and inertia estimation deviation score, improves the inertia estimation precision, and does not need real inertia as label.

Description

Technical Field

[0001] This invention relates to the field of power system inertia estimation, and specifically to an inertia estimation method based on a physical information neural network. Background Technology

[0002] As the integration of wind power, photovoltaics, and energy storage into power systems continues to increase, the proportion of traditional synchronous generators is gradually decreasing, leading to a decline in the natural inertia provided by rotating mass in the power system. Inertia is a crucial parameter affecting power system stability, and accurately estimating the inertia of the inertia supply unit is of great significance for system frequency stability analysis, control parameter tuning, and operational safety assessment.

[0003] With the development of artificial intelligence technology, data-driven machine learning or deep learning methods have become an important research direction for inertia estimation. Data-driven deep learning methods can extract dynamic features related to inertia from dynamic response data, but existing methods usually require a large number of perturbation samples with real inertia labels for training. For inertia supply units that use virtual synchronous machine control methods, such as wind power, photovoltaics, and energy storage, their virtual inertia labels are often difficult to obtain accurately, especially when equipment control parameters are not public and operating modes change frequently. Constructing a large-scale, accurately labeled dataset is very difficult, thus limiting the engineering application of data-driven inertia estimation methods.

[0004] Although some inertia estimation methods based on physical information neural networks can construct physical losses using differential form of the swing equation, reducing dependence on inertia labels, their physical residuals contain frequency derivatives. When there are fluctuations or local dynamic differences in the measurement data, derivative calculations can easily amplify various noises and deviations caused by model simplification, operating condition differences, and measurement fluctuations, resulting in large variations in physical residuals and affecting the accuracy of inertia estimation. Summary of the Invention

[0005] In order to overcome the problems of existing methods for estimating inertia using neural networks, this invention proposes an inertia estimation method based on physical information neural networks.

[0006] The primary objective of this invention is to solve the aforementioned technical problems. The technical solution of this invention is as follows: S1: Construct the dynamic response dataset required for inertia estimation, that is, when an active disturbance occurs in the power system, collect the active power, frequency and frequency change rate of the inertia supply unit grid connection point within a certain period after the disturbance, and use the active power, frequency and frequency change rate as the feature data for inertia estimation. S2: Construct a fully connected neural network for inertia estimation. The fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer. The input of the input layer is the feature data described in step S1. The several fully connected hidden layers extract the nonlinear correlation features between the active power disturbance dynamic response data and the inertia. The output value of the regression output layer is the inertia estimate. S3: Construct the loss function of the fully connected neural network for inertia estimation. The loss function includes the physical residuals of the differential form of the rocking equation and the physical residuals of the integral form of the rocking equation. The two physical residuals are combined through adaptive loss weights, which are calculated by physical identifiability score and inertia estimation bias score. S4: Calculate the physical identifiability score mentioned in step S3, that is, express the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation mentioned in step S3 as linear residuals with respect to inertia respectively, use the least squares method to calculate the analytical solution of physical inertia based on the linear residuals, then calculate the inertia sensitivity and inertia domain uncertainty corresponding to the two types of linear residuals, and finally calculate the physical identifiability score based on the inertia sensitivity and inertia domain uncertainty; S5: Calculate the inertia estimation deviation score mentioned in step S3. Construct a pre-trained loss function containing the physical residuals of the differential form and integral form of the rocking equation using equal weights. Perform weight selection pre-training on the fully connected neural network for inertia estimation mentioned in step S2. Use the inertia estimate output by the pre-trained neural network as the reference inertia. Calculate the inertia estimation deviation score based on the logarithmic relative distance between the reference inertia and the analytical solution of the physical inertia obtained in step S4. S6: Calculate the adaptive loss weights of the two physical residuals in step S3 respectively. That is, calculate the loss weight adjustment score based on the physical identifiability score in step S4 and the inertia estimation bias score in step S5, and then calculate the adaptive loss weights of the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation based on the loss weight adjustment score. S7: Train the fully connected neural network for inertia estimation. That is, with the goal of minimizing the loss function of the fully connected neural network for inertia estimation described in step S3, perform backpropagation and parameter updates on the neural network. After training, use the trained fully connected neural network for inertia estimation to calculate the inertia estimation result of the inertia supply unit online.

[0007] In this scheme, the specific steps for constructing the dynamic response dataset required for inertia estimation in step S1 are as follows: S1-1: Determine the active power disturbance, that is, if the change in the active power of the inertia supply unit grid connection point exceeds 1% of the steady-state active power at a certain moment, determine that the inertia supply unit is subjected to active power disturbance at this moment, and determine that moment as the active power disturbance occurrence time. S1-2: When the m-th active power disturbance occurs in the power system, the time series of active power, frequency, and rate of frequency change of an inertial supply unit at the grid connection point are collected over a period of time after the active power disturbance occurs. Its specific expression form is as follows: In the formula, This represents the active power time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the frequency-time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the time series of the frequency change rate of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the active power at the grid connection point collected at the k-th sampling time during the m-th active power disturbance. This represents the grid connection point frequency obtained at the k-th sampling time during the m-th active power disturbance. It represents the rate of change of the grid connection point frequency collected at the k-th sampling time during the m-th active power disturbance, and K represents the total number of sampling points during one disturbance process; Simultaneously, the sampling time of each sampling point relative to the time of active power disturbance occurrence is recorded, forming the sampling time sequence of the m-th active power disturbance sample: In the formula, This represents the sampling time sequence of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the relative sampling time corresponding to the k-th sampling point when the time of the m-th active power disturbance is taken as the time zero point; S1-3: Combine the active power time series, frequency time series, and frequency change rate time series to obtain the characteristic data of the m-th active power disturbance sample. : In the formula, the superscript T indicates the transpose symbol. Represents a 3K-dimensional real vector space; S1-4: Integrate the feature data of the M active disturbance samples to obtain the dataset X required for inertia estimation: In the formula, M represents the total number of active disturbance samples.

[0008] In this scheme, step S2, which involves constructing a fully connected neural network for inertia estimation, comprises the following specific steps: S2-1: Construct a fully connected neural network for inertia estimation, wherein the fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer; S2-2: Use the feature data of the m-th active disturbance sample described in step S1-3 as the input vector of the fully connected neural network for inertia estimation, and receive it using the input layer. S2-3: The input vector received by the input layer is input into several fully connected hidden layers. The nonlinear correlation features between the active disturbance dynamic response data and inertia are extracted through the fully connected hidden layers. The output of the l-th fully connected layer is expressed as: In the formula, This represents the output feature of the l-th fully connected hidden layer. and Let these represent the weight matrix and bias vector of the l-th fully connected hidden layer, respectively. represents a non-linear activation function, and L represents the total number of fully connected hidden layers; S2-4: Input the non-linear correlation features output from the last fully connected hidden layer into the regression output layer to obtain the neural network output value: In the formula, This represents the neural network output value corresponding to the m-th active disturbance sample. and These represent the weights and biases of the regression output layer, respectively. S2-5: Mapping the neural network output to inertia estimates: In the formula, Let represent the estimated inertia value corresponding to the m-th active disturbance sample. and These represent the preset lower bound and the preset upper bound of inertia, respectively. Represents a mapping function; S2-6: Construct the set of parameters for the network to be trained by using the weights and biases of each fully connected hidden layer and the regression output layer in the fully connected neural network for inertia estimation. In the formula, This represents the set of network parameters to be trained in a fully connected neural network for inertia estimation.

[0009] In this scheme, the loss function for constructing the fully connected neural network for inertia estimation described in step S3 is as follows: S3-1: Select the steady-state active power before the active power disturbance occurs as the reference active power, and construct the active power deviation. and frequency deviation Its specific form of expression is: In the formula, f0 represents the reference active power corresponding to the m-th active power disturbance, and f0 represents the rated frequency of the power system. S3-2: Let the starting and ending sampling points of the physical constraint time window be respectively... and Within a preset physical constraint time window, construct the physical residuals of the differential form of the swing equation: In the formula, Let represent the physical residual of the swing equation in differential form at the k-th sampling time during the m-th active disturbance. Indicates the rated capacity of the inertia supply unit; S3-3: Calculate the value from the first... using the trapezoidal integral method. Integral of active power deviation from the kth sampling time to the kth sampling time: In the formula, Indicates from the first The active power deviation integral from the first sampling time to the kth sampling time; S3-4: Constructing the physical residuals of the integral form of the rocking equation: In the formula, This represents the physical residual of the swing equation in integral form at the k-th sampling time during the m-th active disturbance. Indicates the duration of the integral. This indicates the preset minimum integration time; The physical residuals of the integral form of the rocking equation are normalized by the duration of integration, so that they have the same dimensions as the physical residuals of the differential form of the rocking equation.

[0010] S3-5: Construct the differential physical residual loss, its specific expression is as follows: In the formula, This represents the differential physical residual loss. The adaptive loss weight represents the differential physical residual corresponding to the m-th active disturbance sample. S3-6: Construct the integral physical residual loss, its specific expression is as follows: In the formula, This represents the loss of the physical residual during integration. The adaptive loss weight represents the integral physical residual corresponding to the m-th active disturbance sample. S3-7: Construct the loss function for the fully connected neural network for inertia estimation based on the differential physical residual loss and the integral physical residual loss: In the formula, This represents the loss function of a fully connected neural network for inertia estimation. The loss function of the fully connected neural network for inertia estimation is used as the training objective function of the fully connected neural network for inertia estimation.

[0011] In this scheme, the calculation of the physical identifiability score in step S4 is carried out in the following specific steps: S4-1: Express the physical residuals of the differential and integral forms of the rocking equations in linear form with respect to the inertia variable H: In the formula, Let H represent the linear expression of the physical residual of the j-th swing equation at the k-th sampling time during the m-th active disturbance process with respect to the inertia variable H. This represents the inertia sensitivity term in the j-th type of physical residual. Let represent the non-inertia term in the j-th type of physical residual, and d and i represent the physical residuals of the differential form and integral form of the rocking equation, respectively; Among them, the inertia sensitivity term and non-inertia term corresponding to the physical residuals of the differential form of the rocking equation are respectively: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the differential form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the differential form of the rocking equation; The inertia sensitivity term and non-inertia term corresponding to the physical residuals of the integral form of the rocking equation are as follows: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the integral form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the integral form of the rocking equation; S4-2: Calculate the inertia sensitivity energy of the j-th type of physical residual within the physical constraint time window: In the formula, This represents the inertia sensitivity energy of the physical residual within the physical constraint time window. The time allocation point weights of the physical residuals are represented when... The value is 1 if the condition is met, and 0 otherwise. S4-3: Calculate the analytical solution for the physical inertia corresponding to the j-th type of physical residual using the least squares method: In the formula, This represents the analytical solution for the physical inertia corresponding to the j-th type of physical residual. This is used to prevent extremely small positive numbers with a denominator of 0; S4-4: Substitute the analytical solution of the physical inertia into the corresponding linear residual to calculate the uncertainty in the inertia domain: In the formula, This represents the uncertainty in the inertia domain corresponding to the j-th physical residual; S4-5: Calculate the physical identifiability of the j-th type of physical residual based on the inertia domain uncertainty: In the formula, Indicates the physical identifiability of the j-th physical residual. and These represent the absolute lower bound coefficient and the relative lower bound coefficient of the uncertainty in the inertia domain, respectively, and are usually both taken as 0.001; S4-6: Construct a physical identifiability score based on the physical identifiability of the physical residuals in differential and integral forms: In the formula, Indicates the physical identifiability score. The physical identifiability of the physical residuals in the differential form is represented. This represents the physical identifiability of the physical residual in integral form.

[0012] In this scheme, the specific steps for calculating the inertia estimation bias score in step S5 are as follows: S5-1: Set the weights of differential physical residual loss and integral physical residual loss to be equal, and perform pre-training of the fully connected neural network for inertia estimation for a preset number of weight selection rounds. S5-2: Freeze the weights to select the pre-trained fully connected neural network for inertia estimation, use the frozen network as the reference inertia network, and obtain the reference inertia corresponding to the m-th active disturbance sample through the reference inertia network: In the formula, Indicates network parameters as Frozen reference inertia network, This represents the reference inertia corresponding to the m-th active disturbance sample; S5-3: Calculate the logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia, respectively: In the formula, This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the j-th physical residual and the reference inertia; S5-4: Construct an inertia estimation bias score based on the difference in logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia: In the formula, This indicates the score for the inertia estimation bias. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the differential physical residual and the reference inertia. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the physical residual in integral form and the reference inertia.

[0013] In this scheme, step S6 involves calculating the adaptive loss weights for the two types of physical residuals, and the specific steps are as follows: S6-1: Combining the physical identifiability score described in step S4-6 and the inertia estimation bias score described in step S5-4, the adaptive loss weight adjustment score corresponding to the m-th active disturbance sample is obtained: In the formula, This represents the adaptive loss weight adjustment score corresponding to the m-th active disturbance sample; S6-2: Based on the adaptive loss weight adjustment score and the preset maximum weight ratio R, calculate the original adaptive loss weights of the physical residuals in differential and integral forms: In the formula, and These represent the original adaptive loss weights for the differential physical residual and the integral physical residual, respectively. and These represent the preset initial loss weights for the differential physical residual and the integral physical residual, respectively. Indicates exponentiation; S6-3: Normalizing the original adaptive loss weights yields the adaptive loss weights: In the formula, and Let represent the differential physical residual loss weight and the integral physical residual loss weight corresponding to the m-th active disturbance sample, respectively.

[0014] In this scheme, the training of the fully connected neural network for inertia estimation in step S7 is carried out in the following specific steps: S7-1: Reinitialize all initial parameters of the fully connected neural network for inertia estimation. The parameters obtained from the pre-trained neural network in step S5 are only used to calculate the inertia estimation bias score and do not participate in the formal training. S7-2: Calculate the gradient of the loss function described in step S3 with respect to the inertia estimation fully connected neural network using the backpropagation algorithm: In the formula, Let q represent the gradient of the loss function with respect to the inertia estimation fully connected neural network, and let q represent the number of times the network parameters are updated. This represents the network parameters after the (q-1)th parameter update. This represents the gradient of the network parameters corresponding to the q-th parameter update; S7-3: Using the AdamW optimization algorithm, first-order and second-order moment estimates are calculated for the gradients of network parameters.

[0015] In the formula, The first moment estimate of the gradient is used to characterize the moving average of the gradient; The second moment estimate of the gradient is used to characterize the moving average of the squared gradient. and Let represent the attenuation coefficients of the first-order moment estimate and the second-order moment estimate, respectively. This represents element-wise multiplication; S7-4: Bias correction is applied to the first-order and second-order moment estimates, and its specific expression is as follows:

[0016] In the formula, and These represent the first and second moment estimates of the gradient, respectively, for the q-th network parameter update after bias correction. and Let q represent the decay coefficients raised to the power of the first-order moment estimate and the gradient second-order moment estimate, respectively. S7-5: Update the parameters of the fully connected neural network for inertia estimation based on the bias-corrected first-order moment and second-order moment estimates: In the formula, This represents the network parameters after the q-th parameter update. This represents the learning rate corresponding to the q-th parameter update. This represents the weight decay coefficient. This indicates a positive number that prevents the denominator from being zero; S7-6: Repeat steps S7-2 to S7-5 to complete the forward calculation, loss function calculation, gradient backpropagation and network parameter update for each training batch until the loss function described in step S3 converges or the preset maximum number of training rounds is reached. S7-7: After training is complete, input the feature data of the active disturbance sample to be estimated into the trained fully connected neural network for inertia estimation to obtain the inertia estimate corresponding to the sample.

[0017] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: 1. This invention constructs a physical residual of the swing equation that combines differential and integral forms. The differential physical residual can reflect the local instantaneous dynamic characteristics of the active disturbance process, while the integral physical residual can utilize the cumulative dynamic response information within the physical constraint time window. By combining the two forms of physical residual, their complementary effects under different dynamic response conditions can be leveraged, which not only eliminates the dependence on inertia labels but also improves the accuracy of inertia estimation. 2. This invention proposes a physical identifiability score and an inertia estimation bias score, and establishes sample-level adaptive loss weights corresponding to the two physical residuals. This allows different active disturbance samples to adjust the weights of the differential and integral physical residuals in the loss function according to their own dynamic response characteristics, giving full play to their complementary effects and further improving the accuracy of inertia estimation. Attached Figure Description

[0018] Figure 1 This is a flowchart of an inertia estimation method based on a physical information neural network proposed in this invention. Detailed Implementation

[0019] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0020] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0021] In a specific embodiment, such as Figure 1 As shown, an inertia estimation method based on a physical information neural network includes the following steps: S1: Construct the dynamic response dataset required for inertia estimation, that is, when an active disturbance occurs in the power system, collect the active power, frequency and frequency change rate of the inertia supply unit grid connection point within a certain period after the disturbance, and use the active power, frequency and frequency change rate as the feature data for inertia estimation. S2: Construct a fully connected neural network for inertia estimation. The fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer. The input of the input layer is the feature data described in step S1. The several fully connected hidden layers extract the nonlinear correlation features between the active power disturbance dynamic response data and the inertia. The output value of the regression output layer is the inertia estimate. S3: Construct the loss function of the fully connected neural network for inertia estimation. The loss function includes the physical residuals of the differential form of the rocking equation and the physical residuals of the integral form of the rocking equation. The two physical residuals are combined through adaptive loss weights, which are calculated by physical identifiability score and inertia estimation bias score. S4: Calculate the physical identifiability score mentioned in step S3, that is, express the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation mentioned in step S3 as linear residuals with respect to inertia respectively, use the least squares method to calculate the analytical solution of physical inertia based on the linear residuals, then calculate the inertia sensitivity and inertia domain uncertainty corresponding to the two types of linear residuals, and finally calculate the physical identifiability score based on the inertia sensitivity and inertia domain uncertainty; S5: Calculate the inertia estimation deviation score mentioned in step S3. Construct a pre-trained loss function containing the physical residuals of the differential form and integral form of the rocking equation using equal weights. Perform weight selection pre-training on the fully connected neural network for inertia estimation mentioned in step S2. Use the inertia estimate output by the pre-trained neural network as the reference inertia. Calculate the inertia estimation deviation score based on the logarithmic relative distance between the reference inertia and the analytical solution of the physical inertia obtained in step S4. S6: Calculate the adaptive loss weights of the two physical residuals in step S3 respectively. That is, calculate the loss weight adjustment score based on the physical identifiability score in step S4 and the inertia estimation bias score in step S5, and then calculate the adaptive loss weights of the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation based on the loss weight adjustment score. S7: Train the fully connected neural network for inertia estimation. That is, with the goal of minimizing the loss function of the fully connected neural network for inertia estimation described in step S3, perform backpropagation and parameter updates on the neural network. After training, use the trained fully connected neural network for inertia estimation to calculate the inertia estimation result of the inertia supply unit online.

[0022] In this scheme, the specific steps for constructing the dynamic response dataset required for inertia estimation in step S1 are as follows: S1-1: Determine the active power disturbance, that is, if the change in the active power of the inertia supply unit grid connection point exceeds 1% of the steady-state active power at a certain moment, determine that the inertia supply unit is subjected to active power disturbance at this moment, and determine that moment as the active power disturbance occurrence time. S1-2: When the m-th active power disturbance occurs in the power system, the time series of active power, frequency, and rate of frequency change of an inertial supply unit at the grid connection point are collected over a period of time after the active power disturbance occurs. Its specific expression form is as follows: In the formula, This represents the active power time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the frequency-time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the time series of the frequency change rate of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the active power at the grid connection point collected at the k-th sampling time during the m-th active power disturbance. This represents the grid connection point frequency obtained at the k-th sampling time during the m-th active power disturbance. It represents the rate of change of the grid connection point frequency collected at the k-th sampling time during the m-th active power disturbance, and K represents the total number of sampling points during one disturbance process; Simultaneously, the sampling time of each sampling point relative to the time of active power disturbance occurrence is recorded, forming the sampling time sequence of the m-th active power disturbance sample: In the formula, This represents the sampling time sequence of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the relative sampling time corresponding to the k-th sampling point when the time of the m-th active power disturbance is taken as the time zero point; S1-3: Combine the active power time series, frequency time series, and frequency change rate time series to obtain the characteristic data of the m-th active power disturbance sample. : In the formula, the superscript T indicates the transpose symbol. Represents a 3K-dimensional real vector space; S1-4: Integrate the feature data of the M active disturbance samples to obtain the dataset X required for inertia estimation: In the formula, M represents the total number of active disturbance samples.

[0023] In this scheme, step S2, which involves constructing a fully connected neural network for inertia estimation, comprises the following specific steps: S2-1: Construct a fully connected neural network for inertia estimation, wherein the fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer; S2-2: Use the feature data of the m-th active disturbance sample described in step S1-3 as the input vector of the fully connected neural network for inertia estimation, and receive it using the input layer. S2-3: The input vector received by the input layer is input into several fully connected hidden layers. The nonlinear correlation features between the active disturbance dynamic response data and inertia are extracted through the fully connected hidden layers. The output of the l-th fully connected layer is expressed as: In the formula, This represents the output feature of the l-th fully connected hidden layer. and Let these represent the weight matrix and bias vector of the l-th fully connected hidden layer, respectively. represents a non-linear activation function, and L represents the total number of fully connected hidden layers; S2-4: Input the non-linear correlation features output from the last fully connected hidden layer into the regression output layer to obtain the neural network output value: In the formula, This represents the neural network output value corresponding to the m-th active disturbance sample. and These represent the weights and biases of the regression output layer, respectively. S2-5: Mapping the neural network output to inertia estimates: In the formula, Let represent the estimated inertia value corresponding to the m-th active disturbance sample. and These represent the preset lower bound and the preset upper bound of inertia, respectively. Represents a mapping function; S2-6: Construct the set of parameters for the network to be trained by using the weights and biases of each fully connected hidden layer and the regression output layer in the fully connected neural network for inertia estimation. In the formula, This represents the set of network parameters to be trained in a fully connected neural network for inertia estimation.

[0024] In this scheme, the loss function for constructing the fully connected neural network for inertia estimation described in step S3 is as follows: S3-1: Select the steady-state active power before the active power disturbance occurs as the reference active power, and construct the active power deviation. and frequency deviation Its specific form of expression is:

[0025] In the formula, f0 represents the reference active power corresponding to the m-th active power disturbance, and f0 represents the rated frequency of the power system. S3-2: Let the starting and ending sampling points of the physical constraint time window be respectively... and Within a preset physical constraint time window, construct the physical residuals of the differential form of the swing equation: In the formula, Let represent the physical residual of the swing equation in differential form at the k-th sampling time during the m-th active disturbance. Indicates the rated capacity of the inertia supply unit; S3-3: Calculate the value from the first... using the trapezoidal integral method. Integral of active power deviation from the kth sampling time to the kth sampling time: In the formula, Indicates from the first The active power deviation integral from the first sampling time to the kth sampling time; S3-4: Constructing the physical residuals of the integral form of the rocking equation: In the formula, This represents the physical residual of the swing equation in integral form at the k-th sampling time during the m-th active disturbance. Indicates the duration of the integral. This indicates the preset minimum integration time; The physical residuals of the integral form of the rocking equation are normalized by the duration of integration, so that they have the same dimensions as the physical residuals of the differential form of the rocking equation. S3-5: Construct the differential physical residual loss, its specific expression is as follows: In the formula, This represents the differential physical residual loss. The adaptive loss weight represents the differential physical residual corresponding to the m-th active disturbance sample. S3-6: Construct the integral physical residual loss, its specific expression is as follows: In the formula, This represents the loss of the physical residual during integration. The adaptive loss weight represents the integral physical residual corresponding to the m-th active disturbance sample. S3-7: Construct the loss function for the fully connected neural network for inertia estimation based on the differential physical residual loss and the integral physical residual loss: In the formula, This represents the loss function of a fully connected neural network for inertia estimation. The loss function of the fully connected neural network for inertia estimation is used as the training objective function of the fully connected neural network for inertia estimation.

[0026] In this scheme, the calculation of the physical identifiability score in step S4 is carried out in the following specific steps: S4-1: Express the physical residuals of the differential and integral forms of the rocking equations in linear form with respect to the inertia variable H: In the formula, Let H represent the linear expression of the physical residual of the j-th swing equation at the k-th sampling time during the m-th active disturbance process with respect to the inertia variable H. This represents the inertia sensitivity term in the j-th type of physical residual. Let represent the non-inertia term in the j-th type of physical residual, and d and i represent the physical residuals of the differential form and integral form of the rocking equation, respectively; Among them, the inertia sensitivity term and non-inertia term corresponding to the physical residuals of the differential form of the rocking equation are respectively: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the differential form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the differential form of the rocking equation;

[0027] The inertia sensitivity term and non-inertia term corresponding to the physical residuals of the integral form of the rocking equation are as follows: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the integral form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the integral form of the rocking equation; S4-2: Calculate the inertia sensitivity energy of the j-th type of physical residual within the physical constraint time window: In the formula, This represents the inertia sensitivity energy of the physical residual within the physical constraint time window. The time allocation point weights of the physical residuals are represented when... The value is 1 if the condition is met, and 0 otherwise. S4-3: Calculate the analytical solution for the physical inertia corresponding to the j-th type of physical residual using the least squares method: In the formula, This represents the analytical solution for the physical inertia corresponding to the j-th type of physical residual. This is used to prevent extremely small positive numbers with a denominator of 0; S4-4: Substitute the analytical solution of the physical inertia into the corresponding linear residual to calculate the uncertainty in the inertia domain: In the formula, This represents the uncertainty in the inertia domain corresponding to the j-th physical residual; S4-5: Calculate the physical identifiability of the j-th type of physical residual based on the inertia domain uncertainty: In the formula, Indicates the physical identifiability of the j-th physical residual. and These represent the absolute lower bound coefficient and the relative lower bound coefficient of the uncertainty in the inertia domain, respectively, and are usually both taken as 0.001; S4-6: Construct a physical identifiability score based on the physical identifiability of the physical residuals in differential and integral forms: In the formula, Indicates the physical identifiability score. The physical identifiability of the physical residuals in the differential form is represented. This represents the physical identifiability of the physical residual in integral form.

[0028] In this scheme, the specific steps for calculating the inertia estimation bias score in step S5 are as follows: S5-1: Set the weights of differential physical residual loss and integral physical residual loss to be equal, and perform pre-training of the fully connected neural network for inertia estimation for a preset number of weight selection rounds. S5-2: Freeze the weights to select the pre-trained fully connected neural network for inertia estimation, use the frozen network as the reference inertia network, and obtain the reference inertia corresponding to the m-th active disturbance sample through the reference inertia network: In the formula, Indicates network parameters as Frozen reference inertia network, This represents the reference inertia corresponding to the m-th active disturbance sample; S5-3: Calculate the logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia, respectively: In the formula, This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the j-th physical residual and the reference inertia; S5-4: Construct an inertia estimation bias score based on the difference in logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia: In the formula, This indicates the score for the inertia estimation bias. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the differential physical residual and the reference inertia. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the physical residual in integral form and the reference inertia.

[0029] In this scheme, step S6 involves calculating the adaptive loss weights for the two types of physical residuals, and the specific steps are as follows: S6-1: Combining the physical identifiability score described in step S4-6 and the inertia estimation bias score described in step S5-4, the adaptive loss weight adjustment score corresponding to the m-th active disturbance sample is obtained: In the formula, This represents the adaptive loss weight adjustment score corresponding to the m-th active disturbance sample; S6-2: Based on the adaptive loss weight adjustment score and the preset maximum weight ratio R, calculate the original adaptive loss weights of the physical residuals in differential and integral forms: In the formula, and These represent the original adaptive loss weights for the differential physical residual and the integral physical residual, respectively. and These represent the preset initial loss weights for the differential physical residual and the integral physical residual, respectively. Indicates exponentiation; S6-3: Normalizing the original adaptive loss weights yields the adaptive loss weights: In the formula, and Let represent the differential physical residual loss weight and the integral physical residual loss weight corresponding to the m-th active disturbance sample, respectively.

[0030] In this scheme, the training of the fully connected neural network for inertia estimation in step S7 is carried out in the following specific steps: S7-1: Reinitialize all initial parameters of the fully connected neural network for inertia estimation. The parameters obtained from the pre-trained neural network in step S5 are only used to calculate the inertia estimation bias score and do not participate in the formal training. S7-2: Calculate the gradient of the loss function described in step S3 with respect to the inertia estimation fully connected neural network using the backpropagation algorithm: In the formula, Let q represent the gradient of the loss function with respect to the inertia estimation fully connected neural network, and let q represent the number of times the network parameters are updated. This represents the network parameters after the (q-1)th parameter update. This represents the gradient of the network parameters corresponding to the q-th parameter update; S7-3: Using the AdamW optimization algorithm, first-order and second-order moment estimates are calculated for the gradients of network parameters. In the formula, The first moment estimate of the gradient is used to characterize the moving average of the gradient; The second moment estimate of the gradient is used to characterize the moving average of the squared gradient. and Let represent the attenuation coefficients of the first-order moment estimate and the second-order moment estimate, respectively. This represents element-wise multiplication; S7-4: Bias correction is applied to the first-order and second-order moment estimates, and its specific expression is as follows: In the formula, and These represent the first and second moment estimates of the gradient, respectively, for the q-th network parameter update after bias correction. and Let q represent the decay coefficients raised to the power of the first-order moment estimate and the gradient second-order moment estimate, respectively. S7-5: Update the parameters of the fully connected neural network for inertia estimation based on the bias-corrected first-order moment and second-order moment estimates: In the formula, This represents the network parameters after the q-th parameter update. This represents the learning rate corresponding to the q-th parameter update. This represents the weight decay coefficient. This indicates a positive number that prevents the denominator from being zero; S7-6: Repeat steps S7-2 to S7-5 to complete the forward calculation, loss function calculation, gradient backpropagation and network parameter update for each training batch until the loss function described in step S3 converges or the preset maximum number of training rounds is reached. S7-7: After training is complete, input the feature data of the active disturbance sample to be estimated into the trained fully connected neural network for inertia estimation to obtain the inertia estimate corresponding to the sample.

Claims

1. An inertia estimation method based on a physical information neural network, characterized in that, The specific steps are as follows: S1: Construct the dynamic response dataset required for inertia estimation, that is, when an active disturbance occurs in the power system, collect the active power, frequency and frequency change rate of the inertia supply unit grid connection point within a certain period after the disturbance, and use the active power, frequency and frequency change rate as the feature data for inertia estimation. S2: Construct a fully connected neural network for inertia estimation. The fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer. The input of the input layer is the feature data described in step S1. The several fully connected hidden layers extract the nonlinear correlation features between the active power disturbance dynamic response data and the inertia. The output value of the regression output layer is the inertia estimate. S3: Construct the loss function of the fully connected neural network for inertia estimation. The loss function includes the physical residuals of the differential form of the rocking equation and the physical residuals of the integral form of the rocking equation. The two physical residuals are combined through adaptive loss weights, which are calculated by physical identifiability score and inertia estimation bias score. S4: Calculate the physical identifiability score mentioned in step S3, that is, express the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation mentioned in step S3 as linear residuals with respect to inertia respectively, use the least squares method to calculate the analytical solution of physical inertia based on the linear residuals, then calculate the inertia sensitivity and inertia domain uncertainty corresponding to the two types of linear residuals, and finally calculate the physical identifiability score based on the inertia sensitivity and inertia domain uncertainty; S5: Calculate the inertia estimation deviation score mentioned in step S3. Construct a pre-trained loss function containing the physical residuals of the differential form and integral form of the rocking equation using equal weights. Perform weight selection pre-training on the fully connected neural network for inertia estimation mentioned in step S2. Use the inertia estimate output by the pre-trained neural network as the reference inertia. Calculate the inertia estimation deviation score based on the logarithmic relative distance between the reference inertia and the analytical solution of the physical inertia obtained in step S4. S6: Calculate the adaptive loss weights of the two physical residuals in step S3 respectively. That is, calculate the loss weight adjustment score based on the physical identifiability score in step S4 and the inertia estimation bias score in step S5, and then calculate the adaptive loss weights of the physical residuals of the differential form swing equation and the physical residuals of the integral form swing equation based on the loss weight adjustment score. S7: Train the fully connected neural network for inertia estimation. That is, with the goal of minimizing the loss function of the fully connected neural network for inertia estimation described in step S3, perform backpropagation and parameter updates on the neural network. After training, use the trained fully connected neural network for inertia estimation to calculate the inertia estimation result of the inertia supply unit online.

2. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S1 involves constructing the dynamic response dataset required for inertia estimation. The specific steps are as follows: S1-1: Determine active power disturbance, that is, if the change in active power at the grid connection point of the inertia supply unit exceeds 1% of the steady-state active power at a certain moment, determine that the inertia supply unit is subjected to active power disturbance at this moment, and determine that moment as the moment when the active power disturbance occurs. S1-2: When the m-th active power disturbance occurs in the power system, the time series of active power, frequency, and rate of frequency change of an inertial supply unit at the grid connection point are collected over a period of time after the active power disturbance occurs. Its specific expression form is as follows: In the formula, This represents the active power time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the frequency-time series of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the time series of the frequency change rate of the inertial supply unit obtained from the m-th active disturbance acquisition. This represents the active power at the grid connection point collected at the k-th sampling time during the m-th active power disturbance. This represents the grid connection point frequency obtained at the k-th sampling time during the m-th active power disturbance. It represents the rate of change of the grid connection point frequency collected at the k-th sampling time during the m-th active power disturbance, and K represents the total number of sampling points during one disturbance process; Simultaneously, the sampling time of each sampling point relative to the time of active power disturbance occurrence is recorded, forming the sampling time sequence of the m-th active power disturbance sample: In the formula, This represents the sampling time sequence of the inertial supply unit obtained from the m-th active power disturbance acquisition. This represents the relative sampling time corresponding to the k-th sampling point when the time of the m-th active power disturbance is taken as the time zero point; S1-3: Combine the active power time series, frequency time series, and frequency change rate time series to obtain the characteristic data of the m-th active power disturbance sample. : In the formula, the superscript T indicates the transpose symbol. Represents a 3K-dimensional real vector space; S1-4: Integrate the feature data of the M active disturbance samples to obtain the dataset X required for inertia estimation: In the formula, M represents the total number of active disturbance samples.

3. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S2 involves constructing a fully connected neural network for inertia estimation, and the specific steps are as follows: S2-1: Construct a fully connected neural network for inertia estimation, wherein the fully connected neural network for inertia estimation includes an input layer, several fully connected hidden layers, and a regression output layer; S2-2: Use the feature data of the m-th active disturbance sample described in step S1-3 as the input vector of the fully connected neural network for inertia estimation, and receive it using the input layer. S2-3: The input vector received by the input layer is input into several fully connected hidden layers. The nonlinear correlation features between the active disturbance dynamic response data and inertia are extracted through the fully connected hidden layers. The output of the l-th fully connected layer is expressed as: In the formula, This represents the output feature of the l-th fully connected hidden layer. and Let these represent the weight matrix and bias vector of the l-th fully connected hidden layer, respectively. represents a non-linear activation function, and L represents the total number of fully connected hidden layers; S2-4: Input the non-linear correlation features output from the last fully connected hidden layer into the regression output layer to obtain the neural network output value: In the formula, This represents the neural network output value corresponding to the m-th active disturbance sample. and These represent the weights and biases of the regression output layer, respectively. S2-5: Mapping the neural network output to inertia estimates: In the formula, Let represent the estimated inertia value corresponding to the m-th active disturbance sample. and These represent the preset lower bound and the preset upper bound of inertia, respectively. Represents a mapping function; S2-6: Construct the set of parameters for the network to be trained by using the weights and biases of each fully connected hidden layer and the regression output layer in the fully connected neural network for inertia estimation. In the formula, This represents the set of network parameters to be trained in a fully connected neural network for inertia estimation.

4. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, The loss function for constructing the fully connected neural network for inertia estimation described in step S3 is as follows: S3-1: Select the steady-state active power before the active power disturbance occurs as the reference active power, and construct the active power deviation. and frequency deviation Its specific form of expression is: In the formula, f0 represents the reference active power corresponding to the m-th active power disturbance, and f0 represents the rated frequency of the power system. S3-2: Let the starting and ending sampling points of the physical constraint time window be respectively... and Within a preset physical constraint time window, construct the physical residuals of the differential form of the swing equation: In the formula, Let represent the physical residual of the swing equation in differential form at the k-th sampling time during the m-th active disturbance. Indicates the rated capacity of the inertia supply unit; S3-3: Calculate the value from the first... using the trapezoidal integral method. Integral of active power deviation from the kth sampling time to the kth sampling time: In the formula, Indicates from the first The active power deviation integral from the first sampling time to the kth sampling time; S3-4: Constructing the physical residuals of the integral form of the rocking equation: In the formula, This represents the physical residual of the swing equation in integral form at the k-th sampling time during the m-th active disturbance. Indicates the duration of the integral. This indicates the preset minimum integration time; The physical residuals of the integral form of the rocking equation are normalized by the duration of integration, so that they have the same dimensions as the physical residuals of the differential form of the rocking equation. S3-5: Construct the differential physical residual loss, its specific expression is as follows: In the formula, This represents the differential physical residual loss. The adaptive loss weight represents the differential physical residual corresponding to the m-th active disturbance sample. S3-6: Construct the integral physical residual loss, its specific expression is as follows: In the formula, This represents the loss of the physical residual during integration. The adaptive loss weight represents the integral physical residual corresponding to the m-th active disturbance sample. S3-7: Construct the loss function for the fully connected neural network for inertia estimation based on the differential physical residual loss and the integral physical residual loss: In the formula, This represents the loss function of a fully connected neural network for inertia estimation. The loss function of the fully connected neural network for inertia estimation is used as the training objective function of the fully connected neural network for inertia estimation.

5. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S4, which involves calculating the physical identifiability score, comprises the following steps: S4-1: Express the physical residuals of the differential and integral forms of the rocking equations in linear form with respect to the inertia variable H: In the formula, Let H represent the linear expression of the physical residual of the j-th swing equation at the k-th sampling time during the m-th active disturbance process with respect to the inertia variable H. This represents the inertia sensitivity term in the j-th type of physical residual. Let represent the non-inertia term in the j-th type of physical residual, and d and i represent the physical residuals of the differential form and integral form of the rocking equation, respectively; Among them, the inertia sensitivity term and non-inertia term corresponding to the physical residuals of the differential form of the rocking equation are respectively: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the differential form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the differential form of the rocking equation; The inertia sensitivity term and non-inertia term corresponding to the physical residuals of the integral form of the rocking equation are as follows: In the formula, This represents the inertia sensitivity term corresponding to the physical residuals of the integral form of the rocking equation. This represents the non-inertia term corresponding to the physical residual of the integral form of the rocking equation; S4-2: Calculate the inertia sensitivity energy of the j-th type of physical residual within the physical constraint time window: In the formula, This represents the inertia sensitivity energy of the physical residual within the physical constraint time window. The time allocation point weights of the physical residuals are represented when... The value is 1 if the condition is met, and 0 otherwise. S4-3: Calculate the analytical solution for the physical inertia corresponding to the j-th type of physical residual using the least squares method: In the formula, This represents the analytical solution for the physical inertia corresponding to the j-th type of physical residual. This is used to prevent extremely small positive numbers with a denominator of 0; S4-4: Substitute the analytical solution of the physical inertia into the corresponding linear residual to calculate the uncertainty in the inertia domain: In the formula, This represents the uncertainty in the inertia domain corresponding to the j-th physical residual; S4-5: Calculate the physical identifiability of the j-th type of physical residual based on the inertia domain uncertainty: In the formula, Indicates the physical identifiability of the j-th physical residual. and These represent the absolute lower bound coefficient and the relative lower bound coefficient of the uncertainty in the inertia domain, respectively. S4-6: Construct a physical identifiability score based on the physical identifiability of the physical residuals in differential and integral forms: In the formula, Indicates the physical identifiability score. The physical identifiability of the physical residuals in the differential form is represented. This represents the physical identifiability of the physical residual in integral form.

6. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S5, which involves calculating the inertia estimation bias score, comprises the following steps: S5-1: Set the weights of differential physical residual loss and integral physical residual loss to be equal, and perform pre-training of the fully connected neural network for inertia estimation for a preset number of weight selection rounds. S5-2: Freeze the weights to select the pre-trained fully connected neural network for inertia estimation, use the frozen network as the reference inertia network, and obtain the reference inertia corresponding to the m-th active disturbance sample through the reference inertia network: In the formula, Indicates network parameters as Frozen reference inertia network, This represents the reference inertia corresponding to the m-th active disturbance sample; S5-3: Calculate the logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia, respectively: In the formula, This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the j-th physical residual and the reference inertia; S5-4: Construct an inertia estimation bias score based on the difference in logarithmic relative distance between the analytical solutions of the physical inertia in differential and integral forms and the reference inertia: In the formula, This indicates the score for the inertia estimation bias. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the differential physical residual and the reference inertia. This represents the logarithmic relative distance between the analytical solution of the physical inertia corresponding to the physical residual in integral form and the reference inertia.

7. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S6 involves calculating the adaptive loss weights for the two types of physical residuals, and the specific steps are as follows: S6-1: Combining the physical identifiability score described in step S4-6 and the inertia estimation bias score described in step S5-4, the adaptive loss weight adjustment score corresponding to the m-th active disturbance sample is obtained: In the formula, This represents the adaptive loss weight adjustment score corresponding to the m-th active power disturbance sample; S6-2: Based on the adaptive loss weight adjustment score and the preset maximum weight ratio R, calculate the original adaptive loss weights of the physical residuals in differential and integral forms: In the formula, and These represent the original adaptive loss weights for the differential physical residual and the integral physical residual, respectively. and These represent the preset initial loss weights for the differential physical residual and the integral physical residual, respectively. Indicates exponentiation; S6-3: Normalizing the original adaptive loss weights yields the adaptive loss weights: In the formula, and Let represent the differential physical residual loss weight and the integral physical residual loss weight corresponding to the m-th active disturbance sample, respectively.

8. The inertia estimation method based on a physical information neural network according to claim 1, characterized in that, Step S7 involves training a fully connected neural network for inertia estimation, and the specific steps are as follows: S7-1: Reinitialize all initial parameters of the fully connected neural network for inertia estimation. The parameters obtained from the pre-trained neural network in step S5 are only used to calculate the inertia estimation bias score and do not participate in the formal training. S7-2: Calculate the gradient of the loss function described in step S3 with respect to the inertia estimation fully connected neural network using the backpropagation algorithm: In the formula, Let q represent the gradient of the loss function with respect to the inertia estimation fully connected neural network, and let q represent the number of times the network parameters are updated. This represents the network parameters after the (q-1)th parameter update. This represents the gradient of the network parameters corresponding to the q-th parameter update; S7-3: Using the AdamW optimization algorithm, first-order and second-order moment estimates are calculated for the gradients of network parameters. In the formula, The first moment estimate of the gradient is used to characterize the moving average of the gradient; The second moment estimate of the gradient is used to characterize the moving average of the squared gradient. and Let represent the attenuation coefficients of the first-order moment estimate and the second-order moment estimate, respectively. This represents element-wise multiplication; S7-4: Bias correction is applied to the first-order and second-order moment estimates, and its specific expression is as follows: In the formula, and These represent the first and second moment estimates of the gradient, respectively, for the q-th network parameter update after bias correction. and Let q represent the decay coefficients raised to the power of the first-order moment estimate and the gradient second-order moment estimate, respectively. S7-5: Update the parameters of the fully connected neural network for inertia estimation based on the bias-corrected first-order moment and second-order moment estimates: In the formula, This represents the network parameters after the q-th parameter update. This represents the learning rate corresponding to the q-th parameter update. This represents the weight decay coefficient. This indicates a positive number that prevents the denominator from being zero; S7-6: Repeat steps S7-2 to S7-5 to complete the forward calculation, loss function calculation, gradient backpropagation and network parameter update for each training batch until the loss function described in step S3 converges or the preset maximum number of training rounds is reached. S7-7: After training is complete, input the feature data of the active disturbance sample to be estimated into the trained fully connected neural network for inertia estimation to obtain the inertia estimate corresponding to the sample.

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