A power grid power flow regression method and system

Abstract

The present application provides a power grid power flow regression method and system, the method comprising: obtaining power system time series power flow section data, and dividing into a training set and a test set; constructing an ELM power flow regression model based on the training set, and solving the weight connecting the hidden layer and the output layer in the model to minimize the power flow regression error; adding gradient information of the power flow in the model, and then solving the weight connecting the hidden layer and the output layer to minimize the Jacobian matrix error; considering the Jacobian matrix error and the power flow regression error at the same time, embedding the Jacobian matrix into the ELM power flow regression model to obtain an integrated regression model; testing the power flow regression results of the integrated regression model under different neuron numbers of the hidden layer to determine the optimal neuron number of the hidden layer; training the integrated regression model, and taking the average of the output. Based on the method, a power grid power flow regression system is also provided. The present application meets the current requirements of power grid for fast sensing and online regulation of power flow state.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of power system flow calculation, and particularly relates to a power grid flow regression method and system. BACKGROUND

[0002] Flow calculation is the most basic calculation method in power system analysis, which is used to determine the voltage amplitude and phase angle of each bus in the power system, and is widely used in the planning, operation and control of power systems. Through flow calculation, the performance of the system under various operating conditions can be evaluated to ensure the safe and stable operation of the system. With the large-scale integration of renewable energy and various flexible loads into the power system, the node power fluctuation in the grid presents the characteristics of large amplitude, wide range and fast frequency, and the evolution of the system flow state is rapid and complex. Therefore, it is urgent to develop a flow calculation and analysis method with high precision and fast time efficiency to realize the rapid perception and online regulation of the flow state. However, the traditional model-driven flow calculation method is affected by the selection of initial values and the reliability of the iteration process in terms of speed and convergence, and it is difficult to fully meet the needs of modern power system rapid flow calculation and analysis.

[0003] In recent years, with the wide application of synchronous phasor measurement units (PMU) in power systems, high-precision and wide-area flow synchronous electrical quantity (active power, reactive power, voltage and phase) historical and real-time data can be reliably obtained. Data-driven flow calculation and analysis have developed rapidly, providing an effective solution to the problems of difficult initial value selection, time-consuming iterative solution and poor convergence in model-driven flow calculation. Data-driven flow calculation can overcome the above problems by learning an explicit mapping function from the flow data set. However, this model is a "black box" model that only realizes the mapping from the flow input to the output, ignoring the physical rules in flow calculation, resulting in a lack of physical interpretability of the model and poor precision and generalization ability. SUMMARY

[0004] To solve the above technical problems, the present application provides a power grid flow regression method and system, which realizes accurate and rapid flow calculation and provides effective support for modern power system rapid flow calculation and analysis.

[0005] To achieve the above purpose, the present application adopts the following technical solutions:

[0006] A power grid flow regression method, comprising the following steps:

[0007] Obtaining time series flow section data of a power system; and dividing the time series flow section data into a training set and a test set;

[0008] constructing an ELM power flow regression model based on the training set, and solving the weights connecting the hidden layer and the output layer in the ELM power flow regression model by using the least square method to minimize the power flow regression error;

[0009] adding gradient information of power flow in the ELM power flow regression model, and solving the weights connecting the hidden layer and the output layer to minimize the Jacobian matrix error;

[0010] considering the Jacobian matrix error and the power flow regression error in solving the weights connecting the hidden layer and the output layer, embedding the Jacobian matrix into the ELM power flow regression model to obtain an integrated regression model;

[0011] testing the power flow regression results of the integrated regression model under different numbers of neurons in the hidden layer by using a test set, determining an optimal number of neurons in the hidden layer, training the integrated regression model, and averaging the output of the integrated regression model.

[0012] Further, the method further comprises comparing and analyzing the regression accuracy of the ELM power flow regression model and the integrated regression model under random power disturbance by using root mean square error and mean absolute percentage error, respectively.

[0013] Further, the power system time sequence power flow section data comprises active power injected at any node of the power system, reactive power injected at any node of the power system, voltage amplitude, phase, and Jacobian matrix.

[0014] Further, the process of constructing the ELM power flow regression model based on the training set comprises:

[0015] The power equation in polar coordinates is:

[0016]

[0017] wherein, P i is the active power injected at the i-th node of the system; Q i is the reactive power injected at the i-th node of the system; V i is the voltage amplitude at the i-th node of the system; V j is the voltage amplitude at the j-th node of the system; θij is the voltage phase angle difference between the i-th node and the j-th node; G ij is the conductance between the i-th node and the j-th node; B ij is the susceptance between the i-th node and the j-th node; and N is the total number of nodes.

[0018] Further, the process of solving the weights connecting the hidden layer and the output layer in the ELM power flow regression model by using the least square method to minimize the power flow regression error comprises:

[0019] y = (σ(Wx + b)) β = Hβ; (2)

[0020] wherein, y is an output quantity; x is an input quantity; σ is an activation function; H is a feature matrix of a hidden layer; W is a weight connecting an input layer and the hidden layer; b is a bias connecting the input layer and the hidden layer; β is a weight connecting the hidden layer and an output layer;

[0021] The weight β is solved to minimize a power flow regression error: min||Hβ-y||; (3)

[0022] The calculation formula of β is: β=H + y; (4)

[0023] H + is a generalized inverse matrix of the matrix H.

[0024] Further, the process of adding gradient information of power flow in the ELM power flow regression model comprises:

[0025] The correction equation of power flow calculation is:

[0026]

[0027] wherein, represents a small increment of active power of a grid node; represents a small increment of reactive power of the grid node; represents a correction value of a phase of the grid node; represents a correction value of a voltage of the grid node; T, Z, E and L are corresponding sub-matrices of the Jacobian matrix J;

[0028] The inverse matrix of J is multiplied with both sides of formula (5) to obtain:

[0029]

[0030] wherein, T', Z', E' and L' are corresponding sub-matrices of the inverse Jacobian matrix J'.

[0031] Further, the process of solving the weight connecting the hidden layer and the output layer to minimize the Jacobian matrix error comprises:

[0032] The Jacobian matrix is:

[0033]

[0034] The weight β is solved to minimize the Jacobian matrix error function:

[0035]

[0036] The β can be obtained by the following formula:

[0037]

[0038] Further, the Jacobian matrix error and the power flow regression error are considered simultaneously in solving the weight connecting the hidden layer and the output layer, the Jacobian matrix is embedded into the ELM power flow regression model to obtain an integrated regression model, and the expression of beta is:

[0039]

[0040] Wherein, μ is the weight coefficient of the power flow regression error.

[0041] Further, the process of taking the average value of the output of the integrated regression model comprises:

[0042]

[0043] Wherein, The output of the kth ELM power flow regression model is represented by k; The power flow output of the integrated regression model is represented by M.

[0044] The application further provides a power grid power flow regression system, comprising a data acquisition module, a first solving module, a second solving module, a model construction module and a model output module.

[0045] The data acquisition module is used for acquiring power system time series power flow section data; and dividing the time series power flow section data into a training set and a test set.

[0046] The first solving module is used for constructing an ELM power flow regression model based on the training set, and solving the weight connecting the hidden layer and the output layer in the ELM power flow regression model by using the least square method to minimize the power flow regression error.

[0047] The second solving module is used for adding the gradient information of the power flow in the ELM power flow regression model, and then solving the weight connecting the hidden layer and the output layer to minimize the Jacobian matrix error.

[0048] The model construction module is used for considering the Jacobian matrix error and the power flow regression error simultaneously in solving the weight connecting the hidden layer and the output layer, embedding the Jacobian matrix into the ELM power flow regression model to obtain an integrated regression model.

[0049] The model output module is used for testing the power flow regression result of the hidden layer in the integrated regression model under different neuron numbers by using the test set, determining the optimal number of hidden layer neurons, training the integrated regression model, and taking the average value of the output of the integrated regression model.

[0050] The effects provided in the summary are only the effects of the examples, not all the full effects of the application, and one of the technical solutions has the following advantages or beneficial effects:

[0051] The application provides a power grid power flow regression method and system, and the method comprises the following steps: obtaining power system time sequence power flow section data; and dividing the time sequence power flow section data into a training set and a test set; constructing an ELM power flow regression model based on the training set, and solving the weights connecting the hidden layer and the output layer in the ELM power flow regression model by using the least square method to minimize the power flow regression error; increasing the gradient information of the power flow in the ELM power flow regression model, and then solving the weights connecting the hidden layer and the output layer to minimize the Jacobian matrix error; considering the Jacobian matrix error and the power flow regression error in the process of solving the weights connecting the hidden layer and the output layer, embedding the Jacobian matrix into the ELM power flow regression model to obtain an integrated regression model; testing the power flow regression results of the integrated regression model under different numbers of neurons of the hidden layer by using the test set, determining the optimal number of neurons of the hidden layer, training the integrated regression model, and taking the average value of the output of the integrated regression model. Based on the power grid power flow regression method, a power grid power flow regression system is also provided. By embedding the power flow Jacobian information into the ELM power flow regression model, the application reduces the instability caused by the random initialization of the weights and the bias of the ELM, enhances the interpretability of the model, improves the precision and generalization ability of the model, and meets the requirements of the current power grid for fast perception and online regulation of the power flow state.

[0052] The application constructs a power system power flow mapping model based on the physical Jacobian embedded ELM integration, solves the problems of slow calculation speed and poor convergence reliability of the traditional model-driven power flow model, realizes accurate and fast calculation of the power flow, and provides effective support for fast power flow calculation and analysis of the modern power system.

[0053] The application constructs a power system power flow mapping model based on the physical Jacobian embedded ELM integration, embeds the power flow Jacobian information into the ELM, makes the gradient of the ELM regression model consistent with the gradient of the physical power flow model, reduces the instability caused by the random initialization of the weights and the bias of the ELM, enhances the interpretability of the model, improves the precision and generalization ability of the model, and meets the requirements of the current power grid for fast perception and online regulation of the power flow state.

[0054] The integrated regression model constructed by the application uses the method of integrated learning to reduce the instability caused by the random initialization of the weights and the bias of the ELM, and enhances the accuracy of the mapping model in perceiving the voltage state. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1A power grid power flow regression method for embodiment 1 of the present application is proposed in the overall flow chart;

[0056] Figure 2 A physical Jacobian embedded ELM principle block diagram for embodiment 1 of the present application is proposed;

[0057] Figure 3 A wiring diagram for the IEEE30 standard node system in embodiment 1 of the present application is proposed;

[0058] Figure 4 A voltage phase angle power flow regression result graph under ±20 power disturbance in embodiment 1 of the present application is proposed;

[0059] Figure 5 A voltage amplitude power flow regression result graph under ±20 power disturbance in embodiment 1 of the present application is proposed;

[0060] Figure 6 A voltage phase angle power flow regression result graph under ±30 power disturbance in embodiment 1 of the present application is proposed;

[0061] Figure 7 A voltage amplitude power flow regression result graph under ±30 power disturbance in embodiment 1 of the present application is proposed;

[0062] Figure 8 A voltage phase angle power flow regression result graph under ±40 power disturbance in embodiment 1 of the present application is proposed;

[0063] Figure 9 A voltage amplitude power flow regression result graph under ±40 power disturbance in embodiment 1 of the present application is proposed;

[0064] Figure 10 A power grid power flow regression system schematic diagram for embodiment 2 of the present application is proposed. DETAILED DESCRIPTION

[0065] In order to clearly illustrate the technical features of the present scheme, the present application will be described in detail below with specific embodiments, and in conjunction with the accompanying drawings. The following disclosure provides many different embodiments or examples for implementing the different structures of the present application. In order to simplify the disclosure of the present application, the components and settings of specific examples are described below. In addition, the present application can repeatedly refer to numbers and / or letters in different examples. Such repetition is for the purpose of simplification and clarity, and it does not indicate the relationship between the various embodiments and / or settings discussed. It should be noted that the components illustrated in the drawings are not necessarily drawn to scale. The present application omits the description of well-known components and processing techniques and processes to avoid unnecessary limitation of the present application.

[0066] Embodiment 1

[0067] Embodiment 1 of the present application proposes a power grid power flow regression method, which is used to solve the technical problem that the prior art model only realizes the mapping from the power flow input to the output, ignores the physical rules in the power flow calculation, and causes the model to lack physical interpretability, poor precision and generalization ability.

[0068] Figure 1 The overall flowchart of the power grid power flow regression method proposed in Embodiment 1 of the present application is shown in the figure;

[0069] In step S100, power system time series power flow section data is obtained. The power system time series power flow section data includes active power injected at any node of the power system, reactive power injected at any node of the power system, voltage amplitude, phase and Jacobian matrix.

[0070] The power system time series power flow section data is divided into a training set and a test set according to a preset proportion.

[0071] In step S110, an ELM power flow regression model is constructed based on the training set, and the least squares method is used to solve the weights connecting the hidden layer and the output layer in the ELM power flow regression model to minimize the power flow regression error.

[0072] The ELM power flow regression model is based on the power equation of the nodes written according to Kirchhoff's law.

[0073] The power equation in polar coordinates is:

[0074]

[0075] Where, P i is the active power injected at the i-th node of the system; Q i is the reactive power injected at the i-th node of the system; V i is the voltage amplitude at the i-th node of the system; V j is the voltage amplitude at the j-th node of the system; θij is the voltage phase angle difference between the i-th node and the j-th node; G ij is the conductance between the i-th node and the j-th node; B ij is the susceptance between the i-th node and the j-th node; and N is the total number of nodes.

[0076] ELM is a single-hidden-layer feedforward neural network, which consists of an input layer, a hidden layer and an output layer. In the training process of the model, the weights W and the bias b connecting the input layer and the hidden layer are randomly selected without iteration, and the weights β connecting the hidden layer and the output layer are solved by the least squares method, thereby establishing a explicit mapping relationship from the power flow input x to the power flow output y:

[0077] y=(σ(Wx+b))β=Hβ; (2)

[0078] where y is the output; x is the input; σ is the activation function; H is the feature matrix of the hidden layer; W is the weight connecting the input layer and the hidden layer; b is the bias connecting the input layer and the hidden layer; and β is the weight connecting the hidden layer and the output layer.

[0079] The weight β is solved to minimize the power flow regression error: min||Hβ-y||; (3)

[0080] The calculation formula of β is: β=H + y; (4) H + is the generalized inverse matrix of the matrix H.

[0081] The above formula is the solution method of β in the traditional ELM power flow regression model, which is solved based on the power flow input and output, and the gradient information of the power flow is not considered.

[0082] In step S120, the gradient information of the power flow is added in the ELM power flow regression model, and the weight connecting the hidden layer and the output layer is solved to minimize the Jacobian matrix error.

[0083] The Jacobian matrix is the gradient information of the model-driven power flow calculation, which represents the physical characteristics of the power flow model, including the topology structure, the sensitivity and the admittance; and the correction equation of the power flow calculation is:

[0084]

[0085] where represents the small increment of the active power of the grid node; represents the small increment of the reactive power of the grid node; represents the correction value of the phase of the grid node; represents the correction value of the voltage of the grid node; T, Z, E and L are corresponding sub-matrices of the Jacobian matrix J;

[0086] The inverse matrix of J is multiplied on both sides of formula (5) to obtain:

[0087]

[0088] where T', Z', E' and L' are corresponding sub-matrices of the inverse Jacobian matrix J'.

[0089] The Jacobian matrix of the data-driven ELM power flow regression model can be obtained by chain derivation:

[0090]

[0091] The weight β is solved to minimize the Jacobian matrix error function:

[0092]

[0093] β can be obtained by the following formula:

[0094]

[0095] In step S130, the Jacobian matrix error and the power flow regression error are considered simultaneously in solving the weight connecting the hidden layer and the output layer, the Jacobian matrix is embedded into the ELM power flow regression model to obtain an integrated regression model;

[0096] By allowing the weight β to consider the Jacobian matrix error and the power flow regression error simultaneously in the solving process, the physical Jacobian matrix is embedded into the ELM power flow regression model, and at this time β can be represented by the following formula

[0097]

[0098] Wherein, μ is the weight coefficient of the power flow regression error.

[0099] The test set is used to test the power flow regression results of the hidden layer in the integrated regression model under different numbers of neurons, to determine the optimal number of hidden layer neurons; the integrated regression model is trained, and the output of the integrated regression model is averaged.

[0100] The process of averaging the output of the integrated regression model includes:

[0101]

[0102] Wherein, represents the output of the kth ELM power flow regression model; represents the power flow output of the integrated regression model; M is the number of integration.

[0103] Given the integration scale for integrated learning, the number of physical Jacobian embedded ELM power flow regression models for integration is determined according to the scale of the model-data driven power flow regression problem.

[0104] In order to fully illustrate the process realized by the present application, the IEEE30 node system is used as a test system to illustrate the realized process in detail. Simulation verification is carried out in the IEEE57 node system. The simulation test environment is Intel(R) Core(TM) i7-7700HQ CPU@2.80GHz processor, 8GB memory, Windows10 computer operating system, and the simulation tool uses the "TensorFlow 2.5.0" open source software library under Python.

[0105] Step (1) data generation, the IEEE30 node system is used as a test system, Figure 3The IEEE30 standard node system wiring diagram in embodiment 1 of the application is wired; for the node power at the original level, ±20% random uniform power disturbance is applied, 150 groups of power flow time series section data are generated, wherein 100 groups of data are used as a training set, 50 groups of data are used as a test set, and power flow regression is carried out.

[0106] Step (2) constructs an ELM power flow regression model, ELM is a single hidden layer feedforward neural network, and a display mapping of power flow input x to power flow output y is established. The weights and biases of the ELM power flow regression model are randomly generated, the number of hidden layer neurons is 100, the activation function is a sigmoid function, and the output weight matrix β is solved by the least square method to minimize the power flow regression error.

[0107] Step (3) constructs an ELM power flow regression model based on physical Jacobian embedding, that is, an integrated regression model, Figure 2 The principle diagram of the physical Jacobian embedding ELM is proposed for embodiment 1 of the application;

[0108] The output weight matrix β is solved by the least square method to minimize the error of the Jacobian matrix and the ELM regression model based on the ELM regression model, so that the gradient of the ELM regression model is consistent with the gradient of the integrated regression model. The output weight matrix β is solved while considering the power flow regression error and the Jacobian matrix error, and the physical Jacobian matrix is embedded into the ELM power flow regression model to obtain the integrated regression model.

[0109] Step (4) adjusts the parameters of the physical Jacobian embedding ELM, and determines that the power flow regression error weight coefficient is 50 and the number of hidden layer neurons is 100.

[0110] Step (5) constructs an integrated power flow regression model based on the physical Jacobian embedding ELM, that is, an integrated regression model. The integrated learning integrates the regression model multiple times, and averages the results, which significantly improves the reliability of the model and reduces the instability caused by the random initialization of the weights and biases of the ELM.

[0111] Step (6) determines the number M of ELMs used for integration according to the size of the integrated regression model, and M is 50, so that the power flow regression results synthesized by the physical Jacobian embedding ELM are more accurate and reliable.

[0112] Step (7) compares and analyzes the regression accuracy of the ELM power flow regression model and the integrated regression model under random power disturbance, and takes the root mean square error (RMSE) and the mean absolute percentage error (MAPE) as the evaluation indexes of the test accuracy, which are defined as:

[0113]

[0114]

[0115] wherein, E RMSE and E MAPE denote the root mean square error and the mean absolute percentage error of the tide regression, respectively, y denotes the real tide output data, denotes the trained tide output data, m and n denote the row number and the column number of y, respectively, o and p denote the oth row and the pth column of y, respectively. Table 1 gives the tide calculation regression error (E RMSE ) of the different models.

[0116] Table 1: Tide calculation regression error (E RMSE ) of the different models

[0117]

[0118] It can be seen from Table 1 that the tide calculation result of the integrated regression model is more accurate than that of the ELM regression model. Figure 4 is a voltage phase angle tide regression result graph under ±20 power disturbance in embodiment 1 of the present application; Figure 5 is a voltage amplitude tide regression result graph under ±20 power disturbance in embodiment 1 of the present application;

[0119] Figure 6 is a voltage phase angle tide regression result graph under ±30 power disturbance in embodiment 1 of the present application; Figure 7 is a voltage amplitude tide regression result graph under ±30 power disturbance in embodiment 1 of the present application;

[0120] Figure 8 is a voltage phase angle tide regression result graph under ±40 power disturbance in embodiment 1 of the present application; Figure 9 is a voltage amplitude tide regression result graph under ±40 power disturbance in embodiment 1 of the present application;

[0121] Figures 4 to 9 reflects the cumulative distribution results of the average absolute error of the node phase and voltage based on the integrated regression model and the ELM regression model under different load fluctuations (±20%, ±30%, ±40%). From Figure 4 and Figure 9 it can be seen that the average absolute error of the node phase and voltage of the integrated regression model is smaller, and the regression result is more accurate, which fully embodies the accuracy and effectiveness of the method.

[0122] Step (8) compares and analyzes the Jacobian matrix based on the ELM tide regression model and the integrated regression model with the real Jacobian matrix, and Table 2 is the Jacobian regression error result of the different models.

[0123] Table 2: Jacobian regression error result of the different models

[0124] Model Regression Error (ERMSE) ELM Regression Model 0.5767 Ensemble Regression Model 0.1507

[0125] As can be seen from Table 2, the error of the Jacobian matrix obtained through the integrated regression model training is small, the gradient of the model is consistent with the true Jacobian matrix, and the model's interpretability is improved.

[0126] Step (9) compares and analyzes the calculation time of 10000 power flows of the Newton-Raphson power flow calculation method and the integrated regression model calculation method 10000, and Table 3 is a time comparison of different methods.

[0127] Table 3: Time comparison of different methods

[0128] Calculation Method Calculation Time (s) Newton-Raphson Power Flow Calculation 1371.25 Ensemble Regression Model Calculation 0.11

[0129] As can be seen from Table 3, the time calculated based on the integrated regression model is much smaller than the traditional Newton-Raphson power flow calculation method, and is suitable for the current needs of fast power flow calculation of the power grid.

[0130] In summary, the integrated regression model reduces the instability caused by the random initialization of the weight and bias of the ELM, enhances the interpretability of the model, improves the accuracy and generalization ability of the model, and meets the current requirements of the power grid for fast perception and online regulation of the power flow state. And the method does not require a power grid model and parameters, has the ability of fast power flow calculation, is suitable for the current complex background of the evolution of the power flow state of the system, and has great application potential.

[0131] The power grid power flow regression method provided in Embodiment 1 of the present application reduces the instability caused by the random initialization of the weight and bias of the ELM by embedding the power flow Jacobian information into the ELM power flow regression model, enhances the interpretability of the model, improves the accuracy and generalization ability of the model, and meets the current requirements of the power grid for fast perception and online regulation of the power flow state.

[0132] The power grid power flow regression method provided in Embodiment 1 of the present application constructs a power system power flow mapping model based on physical Jacobian embedded ELM integration by using a large amount of power flow time series section data, solves the problems of slow calculation speed and poor convergence reliability of the traditional model-driven power flow model, realizes accurate and fast calculation of the power flow, and provides effective support for fast power flow calculation and analysis of modern power systems.

[0133] The power grid power flow regression method provided in Embodiment 1 of the present application constructs a power system power flow mapping model based on physical Jacobian embedded ELM integration, embeds the power flow Jacobian information into the ELM, makes the gradient of the ELM regression model consistent with the gradient of the physical power flow model, reduces the instability caused by the random initialization of the weight and bias of the ELM, enhances the interpretability of the model, improves the accuracy and generalization ability of the model, and meets the current requirements of the power grid for fast perception and online regulation of the power flow state.

[0134] The power flow regression method provided in Embodiment 1 of the present application is a method of constructing an integrated regression model by using the method of integrated learning, reducing the instability caused by the random initialization of weights and biases of ELM, and enhancing the accuracy of the mapping model in perceiving the voltage state.

[0135] Embodiment 2

[0136] Based on the power flow regression method provided in Embodiment 1 of the present application, Embodiment 2 of the present application further provides a power flow regression system, Figure 10 A schematic diagram of the power flow regression system provided in Embodiment 2 of the present application is shown in the figure, which comprises a data acquisition module, a first solving module, a second solving module, a model construction module and a model output module.

[0137] The data acquisition module is used to acquire time-series power flow section data of a power system, and divide the time-series power flow section data into a training set and a test set.

[0138] The first solving module is used to construct an ELM-based power flow regression model based on the training set, and solve the weights connecting the hidden layer and the output layer in the ELM-based power flow regression model by using the least square method to minimize the power flow regression error.

[0139] The second solving module is used to add gradient information of the power flow in the ELM-based power flow regression model, and then solve the weights connecting the hidden layer and the output layer to minimize the error of the Jacobian matrix.

[0140] The model construction module is used to consider the error of the Jacobian matrix and the power flow regression error in solving the weights connecting the hidden layer and the output layer, so as to embed the Jacobian matrix into the ELM-based power flow regression model to obtain an integrated regression model.

[0141] The model output module is used to test the power flow regression results of the hidden layer in the integrated regression model under different numbers of neurons by using the test set, determine the optimal number of neurons of the hidden layer, train the integrated regression model, and take the average value of the output of the integrated regression model.

[0142] In the data acquisition module, the time-series power flow section data of the power system comprises active power injected by any node of the power system, reactive power injected by any node of the power system, voltage amplitude, phase and the Jacobian matrix.

[0143] In the first solving module, the process of constructing the ELM-based power flow regression model based on the training set comprises:

[0144] The power equation in polar coordinates is:

[0145]

[0146] where, P i is the active power injected into the system i node; Q i is the reactive power injected into the system i node; V i is the voltage amplitude of the system i node; V j is the voltage amplitude of the system j node; θij is the voltage phase angle difference between the node i and the node j; G ij is the conductance between the node i and the node j; B ij is the susceptance between the node i and the node j; and N is the total number of nodes.

[0147] The process of solving the weight connecting the hidden layer and the output layer in the ELM power flow regression model by using the least square method to minimize the power flow regression error comprises:

[0148] y = (σ(Wx + b)) β = Hβ; (2)

[0149] where, y is an output quantity; x is an input quantity; σ is an activation function; H is a feature matrix of the hidden layer; W is a weight connecting the input layer and the hidden layer; b is a bias connecting the input layer and the hidden layer; and β is a weight connecting the hidden layer and the output layer;

[0150] The weight β is solved to minimize the power flow regression error: min||Hβ - y||; (3)

[0151] The calculation formula of the weight β is: β = H + y; (4)

[0152] H + is a generalized inverse matrix of the matrix H.

[0153] In the second solving module, the process of adding the gradient information of the power flow in the ELM power flow regression model comprises: the correction equation of the power flow calculation is:

[0154]

[0155] where, represents a small increment of the active power of the grid node; represents a small increment of the reactive power of the grid node; represents a correction value of the phase of the grid node; represents a correction value of the voltage of the grid node; T, Z, E and L are corresponding sub-matrices of the Jacobian matrix J;

[0156] The inverse matrix of J is multiplied by both sides of formula (5) to obtain:

[0157]

[0158] where, T', Z', E' and L' are corresponding sub-matrices of the inverse Jacobian matrix J'.

[0159] The process of minimizing the Jacobian matrix error by solving the weights connecting the hidden layer and the output layer comprises:

[0160] The Jacobian matrix is:

[0161]

[0162] The Jacobian matrix error function is minimized by solving the weight β:

[0163]

[0164] The β can be obtained by:

[0165]

[0166] In the model construction module, the Jacobian matrix error and the power flow regression error are considered simultaneously in solving the weights connecting the hidden layer and the output layer, the Jacobian matrix is embedded into the ELM power flow regression model to obtain an integrated regression model, and the expression of β at this time is:

[0167]

[0168] Wherein, μ is the weight coefficient of the power flow regression error.

[0169] In the model output module, the process of taking the average value of the output of the integrated regression model comprises:

[0170]

[0171] Wherein, The output of the kth ELM power flow regression model is represented by: The power flow output of the integrated regression model is represented by M, and M is the number of integration.

[0172] The regression accuracy of the ELM power flow regression model and the integrated regression model under random power disturbance is compared and analyzed by using the root mean square error and the average absolute percentage error.

[0173] The power grid power flow regression system provided in the embodiment 2 of the present application embeds the power flow Jacobian information into the ELM power flow regression model, reduces the instability caused by the random initialization of the weights and the bias of the ELM, enhances the interpretability of the model, improves the accuracy and the generalization ability of the model, and meets the requirements of the current power grid for the rapid perception and online regulation of the power flow state.

[0174] The power grid power flow regression system provided in Embodiment 2 of the present application solves the problems of slow calculation speed and poor convergence reliability of the traditional model-driven power flow model by constructing a power system power flow mapping model based on physical Jacobian embedding ELM integration, and realizes accurate and rapid calculation of power flow, thereby providing effective support for rapid power flow calculation and analysis of a modern power system.

[0175] The power grid power flow regression system provided in Embodiment 2 of the present application constructs a power system power flow mapping model based on physical Jacobian embedding ELM integration, embeds power flow Jacobian information into ELM, makes the gradient of the ELM regression model consistent with the gradient of the physical power flow model, reduces the instability caused by random initialization of weights and bias of ELM, enhances the interpretability of the model, improves the accuracy and generalization ability of the model, and meets the requirements of current power grid for rapid perception and online regulation of power flow state.

[0176] The power grid power flow regression system provided in Embodiment 2 of the present application constructs an integrated regression model using an integrated learning method, reduces the instability caused by random initialization of weights and bias of ELM, and enhances the accuracy of the mapping model in perceiving voltage state.

[0177] The description of the related parts of the power grid power flow regression system provided in Embodiment 2 of the present application can refer to the detailed description of the corresponding parts of the power grid power flow regression method provided in Embodiment 1 of the present application, and will not be repeated here.

[0178] It should be noted that, in this paper, relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between the entities or operations. Moreover, the term "includes", "contains" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or device inherent in the process, method, article or device including a series of elements. Without more limitations, the element defined by the sentence "includes a" does not exclude the presence of other identical elements in the process, method, article or device including the element. In addition, the above technical solutions provided in the embodiments of the present application have not been described in detail, which are consistent with the implementation principles of the corresponding technical solutions in the prior art, so as not to be too verbose.

[0179] The above describes the specific embodiments of the present application in combination with the drawings, but is not a limitation on the protection scope of the present application. Based on the above description, other different forms of modifications or changes can be made by those skilled in the art. Here, all the embodiments need not and cannot be exhausted. Various modifications or changes made by those skilled in the art on the basis of the technical solutions of the present application without creative labor are still within the protection scope of the present application.

Claims

1. A power grid flow regression method, characterized in that, Includes the following steps: Acquire time-series power flow profile data of the power system; The time-series power flow section data is then divided into a training set and a test set. Based on the training set, an ELM-based power flow regression model is constructed. The weights connecting the hidden layer and the output layer in the ELM power flow regression model are solved using the least squares method to minimize the power flow regression error. In the ELM power flow regression model, gradient information of power flow is added, and the Jacobian matrix error is minimized by solving the weights connecting the hidden layer and the output layer. In solving the weights connecting the hidden layer and the output layer, both the Jacobian matrix error and the power flow regression error are considered simultaneously, so that the Jacobian matrix is ​​embedded into the ELM power flow regression model to obtain the integrated regression model. The test set was used to test the power flow regression results of the hidden layer in the ensemble regression model under different numbers of neurons, and the optimal number of neurons in the hidden layer was determined. Train the ensemble regression model and average its output.

2. The power flow regression method according to claim 1, characterized in that, The method also includes comparing and analyzing the regression accuracy of the ELM-based power flow regression model and the ensemble regression model under random power disturbances using root mean square error and mean absolute percentage error, respectively.

3. The power flow regression method according to claim 1, characterized in that, The power system time-series power flow profile data includes the active power injected at any node of the power system, the reactive power injected at any node of the power system, the voltage amplitude, the phase, and the Jacobian matrix.

4. The power flow regression method according to claim 3, characterized in that, The process of constructing an ELM-based power flow regression model based on the training set includes: The power equation in polar coordinates is: Among them, P i Inject active power into the system's i-node; Q i Inject reactive power into the system's i-node; V i V represents the voltage amplitude at node i of the system. j G represents the voltage amplitude at node j of the system; θij represents the voltage phase angle difference between node i and node j; ij B is the electrical conductance between node i and node j; ij Let N be the susceptance between node i and node j; N is the total number of nodes.

5. The power grid flow regression method according to claim 4, characterized in that, The process of solving for the weights connecting the hidden layer and the output layer in the ELM power flow regression model using the least squares method to minimize the power flow regression error includes: y=(σ(Wx+b))β=Hβ; (2) Where y is the output; x is the input; σ is the activation function; H is the feature matrix of the hidden layer; W is the weight connecting the input layer and the hidden layer; b is the bias connecting the input layer and the hidden layer; β is the weight connecting the hidden layer and the output layer. The power flow regression error is minimized by solving for the weight β: min||Hβ-y||; (3) The formula for calculating β is: β = H + y; (4) H + Let H be the generalized inverse matrix of H.

6. The power flow regression method according to claim 5, characterized in that, The process of adding gradient information of the power flow to the ELM power flow regression model includes: The corrected equation for power flow calculation is: in, This represents a small increment in the active power of a power grid node; This represents a small increment in reactive power at a power grid node; This indicates the correction value for the phase of a power grid node; Represents the correction value of the grid node voltage; T, Z, E and L are all corresponding submatrices of the Jacobian matrix J; Multiplying both sides of formula (5) by the inverse of J, we get: Where T', Z', E' and L' are all corresponding submatrices of the Jacobian inverse matrix J'.

7. The power grid flow regression method according to claim 6, characterized in that, The process of minimizing the Jacobian matrix error by solving for the weights connecting the hidden layer and the output layer includes: The Jacobian matrix is: The Jacobian matrix error function is minimized by solving for the weight β. β can be obtained from the following formula: (9).

8. The power flow regression method according to claim 7, characterized in that, The step of simultaneously considering the Jacobian matrix error and power flow regression error in solving the weights connecting the hidden layer and the output layer, and embedding the Jacobian matrix into the ELM power flow regression model to obtain the integrated regression model, is as follows: The expression for β at this point is: Where μ is the weighting coefficient of the power flow regression error.

9. The power grid flow regression method according to claim 1, characterized in that, The process of averaging the output of an integrated regression model includes: in, This represents the output of the k-th ELM power flow regression model; This represents the power flow output of the ensemble regression model; M is the number of ensembles.

10. A power grid flow return system, characterized in that, It includes a data acquisition module, a first solution module, a second solution module, a model building module, and a model output module; The data acquisition module is used to acquire time-series power flow profile data of the power system; and divide the time-series power flow profile data into a training set and a test set; The first solution module is used to construct an ELM-based power flow regression model based on the training set, and to solve the weights connecting the hidden layer and the output layer in the ELM power flow regression model using the least squares method to minimize the power flow regression error. The second solution module is used to add gradient information of power flow to the ELM power flow regression model, and then minimize the error of the Jacobian matrix by solving the weights connecting the hidden layer and the output layer. The model building module is used to simultaneously consider the Jacobian matrix error and the power flow regression error when solving the weights connecting the hidden layer and the output layer, so that the Jacobian matrix is ​​embedded into the ELM power flow regression model to obtain an integrated regression model. The model output module is used to test the power flow regression results of the hidden layer in the ensemble regression model with different numbers of neurons using the test set, and to determine the optimal number of neurons in the hidden layer. Train the ensemble regression model and average its output.

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