Power transmission system harmonic state estimation method based on sparse Bayesian learning

Abstract

The invention belongs to the technical field of power systems, and particularly discloses a power transmission system harmonic state estimation method based on sparse Bayesian learning, which combines the space sparsity and the structure sparsity of a harmonic source, provides a harmonic state estimation form, and stacks harmonic measurement values of all orders into a high-dimensional vector. A sparse Bayesian algorithm is proposed to describe a state variable, and a hyper-parameter vector and an error variance are estimated through an expectation maximization algorithm, so that a harmonic estimator is calculated and obtained, and the underdetermined harmonic state estimation problem is effectively solved. In addition, according to the characteristic that different harmonic orders have different noise values, the noise values of different harmonic orders can be independently estimated, and the estimation precision is further improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and in particular relates to a method for estimating harmonic states of a power transmission system based on sparse Bayesian learning. Background Art

[0002] In the power industry, the application of renewable energy is becoming more and more widespread. This trend not only promotes the reduction of greenhouse gas emissions, but also leads to the increase of harmonic pollution in the power grid. Harmonics exist in the power system and distort the basic waveforms of voltage and current, which in turn causes equipment overheating, functional interference of control and protection systems, and even potential damage to electrical equipment. Therefore, effective monitoring of power harmonics is particularly important.

[0003] However, due to the high cost of harmonic monitoring devices, only limited measurement equipment is deployed at key nodes in the current power network. This situation leads to the problem of underdetermination of harmonic state estimation in the transmission system, that is, limited measurement data cannot uniquely determine the harmonic state of the system, and there is the possibility of multiple solutions. The traditional least squares method fails in such underdetermined situations, limiting its in-depth application in the field of harmonic monitoring. On the other hand, although the singular value decomposition technology can handle underdetermination problems, it is difficult to predict or evaluate the harmonic conditions of nodes that are not directly monitored. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the defect in the prior art that the power transmission system cannot effectively estimate the harmonic state, thereby providing a power transmission system harmonic state estimation method based on sparse Bayesian learning.

[0005] A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning comprises the following steps: Step S1: describing the power transmission system through an undirected graph, wherein the nodes of the undirected graph are the nodes of the power transmission system, and the edges of the undirected graph are the power transmission lines; modeling the power transmission line as an equivalent π-type circuit, modeling the load as a parallel circuit, modeling the generator as a transient reactance, modeling the transformer as a short-circuit impedance, and modeling the nonlinear load generating harmonics as an injection current source; constructing a system with known network topology and component parameters into a harmonic admittance matrix and a branch admittance matrix under multiple harmonics; Step S2: measuring the amplitude and phase angle of harmonic voltage and harmonic current of some nodes in the power transmission system by a harmonic measurement device, which are recorded as harmonic vector measurement quantities; Step S3: Under the harmonic order, a relationship between a harmonic vector measurement quantity, a measurement matrix, a state variable and a measurement error is established, wherein the measurement matrix is ​​constructed based on the harmonic admittance matrix and the branch admittance matrix; Step S4: The harmonic vector measurements of all harmonic orders are stacked into a high-dimensional harmonic vector measurement, and represented by a high-dimensional state variable, a high-dimensional measurement matrix, and a high-dimensional noise matrix; Step S5: applying a Gaussian distribution with a mean of 0 to the high-dimensional state variable, defining a priori distribution of the high-dimensional state variable based on the hyperparameter vector, and defining a high-dimensional harmonic vector measurement based on the error variance; Step S6: Set the high-dimensional state variable as a hidden variable, estimate the hyperparameter vector and error variance through the expectation maximization algorithm, and obtain the desired harmonic estimator; Step S7: Based on the harmonic estimation, a relationship between all operating states and state variables of the power transmission system is established by utilizing a power flow calculation equation to obtain the operating state of the power transmission system.

[0006] Furthermore, in step S1, The undirected graph is represented as: ; in, Represents a collection of nodes. represents a collection of transmission lines; The harmonic admittance matrix is ​​expressed as: ; Where S is a symmetric complex matrix; The branch admittance matrix is ​​expressed as: ; Where C is a complex matrix; ， ； ， ； in, is the number of nodes, Indicates the number of branches, Indicates the consideration harmonic order, represents the transmitter admittance matrix, represents the receiving end admittance matrix; and Respectively indicate lines Series admittance value and parallel admittance value, Indicates the node number, Indicates the branch number. .

[0007] Furthermore, in step S2: The harmonic measurement devices are arranged on some branches of the power transmission system, the total number of which is , the amplitude and phase angle of harmonic voltage and harmonic current are expressed as: ; in, Indicates the highest harmonic order measured, ; The harmonic vector measurement is expressed as: ; in, Indicates the number of harmonic voltage measuring devices, Indicates the number of harmonic current measuring devices, , represents a mapping from the index of the harmonic measuring device to its location in the power transmission network, Furthermore, in step S3, The relationship between harmonic vector measurement, measurement matrix, state variable and measurement error is expressed as: ; in, Respectively represent harmonic phasor measurement, measurement matrix, state variable, and measurement error; among them, is less than n; The measurement matrix is ​​expressed as: ; in, , i A harmonic measurement device is at the transmitting end, then , i A harmonic measurement device is at the receiving end, then ; The state variables are represented as: ; And the state variable is the injected harmonic current ,Right now: ; The measurement error is modeled as a Gaussian distribution: ; Indicates The noise variance of the subharmonics, for OK The unit matrix of the column.

[0008] Furthermore, in step S4, The high-dimensional harmonic vector measurement is expressed as: ; Right now ; in, for No. i elements; high-dimensional measurement matrix Depend on According to the rearrangement of high-dimensional state variables, we can get: ; in, represent Middle OK i The elements of the column, .definition ,in, for No. Column to A matrix consisting of columns; High-dimensional state variables Expressed as , Representation Node Injected currents of all harmonic orders; The high-dimensional noise matrix is ​​expressed as: ; in, represents a high-dimensional noise vector, is the covariance matrix of the noise; for OK The unit matrix of the column.

[0009] Furthermore, in step S5, The prior distribution of high-dimensional state variables is expressed as: ; Among them, the hyperparameter vector ; Represents state variables The mean is 0 and the covariance matrix is Gaussian distribution of The likelihood probability of high-dimensional harmonic vector measurements is expressed as: .

[0010] Furthermore, in step S6, definition , the marginalized probability density function is: ; in ; When the hyperparameter values ​​are fixed, the posterior density is a Gaussian distribution: ; in , .

[0011] Furthermore, in step S7, the second type of maximum likelihood estimation is used to solve and ,Right now , which is equivalent to minimizing ,in is a natural logarithmic function, the loss function is: ; The expectation maximization algorithm is used to minimize the loss function, as follows: In the k+1th iteration, the hyperparameter vector and error variance estimated in the kth round are defined as and ,use and The calculated mean and variance are defined as and , the algorithm calculation process is as follows: Step S6.1: Step E: ; Step S6.2: M step: ; in for No. elements, , for The element in the tth row and tth column of , , , , ; Step S6.3: In the k+1th round of the expectation-maximization algorithm, according to the estimated and , calculate the mean and variance of the k+1th round: , ; Step S6.4: Repeat steps S6.1 to S6.3 until the algorithm converges and obtains the estimated values ​​of the hyperparameter vector and error variance. and , thereby calculating the estimated value of the high-dimensional state variable, that is, the harmonic estimator: ; Furthermore, in step S7, in each iteration, ensure that the loss function .

[0012] Furthermore, in step S7, Based on the obtained harmonic estimate , obtain the harmonic current of each harmonic order , the relationship between all the operating states and state variables of the power transmission system is established by using the power flow calculation equation to obtain the operating state of the power transmission system, that is, the voltage of all nodes in the system: .

[0013] Beneficial effects: The present invention discloses a harmonic state estimation method for a power transmission system based on sparse Bayesian learning. Combining the spatial sparsity and structural sparsity of harmonic sources, a harmonic state estimation form is proposed. Harmonic measurement values ​​of all orders are stacked into a high-dimensional vector. A sparse Bayesian algorithm is proposed to describe the state variables. The hyperparameter vector and error variance are estimated by the expectation maximization algorithm, thereby calculating the harmonic estimator and effectively solving the underdetermined harmonic state estimation problem. In addition, this method can estimate the noise values ​​of different harmonic orders separately according to the characteristics that different harmonic orders have different noise values, further improving the estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 The figure is a flowchart of the method steps of the present invention.

[0016] Figure 2 It is a performance bar chart of the method of the present invention compared with other methods in the experiment. DETAILED DESCRIPTION

[0017] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0018] Reference Figure 1 As shown, this embodiment provides a method for estimating harmonic state of a power transmission system based on sparse Bayesian learning, comprising the following steps: Step S1: describing the power transmission system through an undirected graph, wherein the nodes of the undirected graph are the nodes of the power transmission system, and the edges of the undirected graph are the power transmission lines; modeling the power transmission line as an equivalent π-type circuit, modeling the load as a parallel circuit, modeling the generator as a transient reactance, modeling the transformer as a short-circuit impedance, and modeling the nonlinear load that generates harmonics as an injection current source, i.e., a harmonic source; constructing a system with known network topology and component parameters into a harmonic admittance matrix and a branch admittance matrix under multiple harmonics; Step S2: measuring the amplitude and phase angle of harmonic voltage and harmonic current of some nodes in the power transmission system by a harmonic measurement device, which are recorded as harmonic vector measurement quantities; Step S3: Under the harmonic order, a relationship between a harmonic vector measurement quantity, a measurement matrix, a state variable and a measurement error is established, wherein the measurement matrix is ​​constructed based on the harmonic admittance matrix and the branch admittance matrix; Step S4: The harmonic vector measurements of all harmonic orders are stacked into a high-dimensional harmonic vector measurement, and represented by a high-dimensional state variable, a high-dimensional measurement matrix, and a high-dimensional noise matrix; Step S5: applying a Gaussian distribution with a mean of 0 to the high-dimensional state variable, defining a priori distribution of the high-dimensional state variable based on the hyperparameter vector, and defining a high-dimensional harmonic vector measurement based on the error variance; Step S6: Set the high-dimensional state variable as a hidden variable, estimate the hyperparameter vector and error variance through the expectation maximization algorithm, and obtain the desired harmonic estimator; Step S7: Based on the harmonic estimation, a power flow calculation equation is used to establish a relationship between all operating states and state variables of the power transmission system to obtain the operating state of the power transmission system.

[0019] Specifically, in step S1, The undirected graph is represented as: ; in, Represents a collection of nodes. represents a collection of transmission lines; The harmonic admittance matrix is ​​expressed as: ; Where S is a symmetric complex matrix; The branch admittance matrix is ​​expressed as: ; Where C is a complex matrix; ， ； ， ； in, is the number of nodes, Indicates the number of branches, Indicates the consideration harmonic order, represents the transmitter admittance matrix, represents the receiving end admittance matrix; and Indicates line Indicates the node number, Indicates the branch number. In step S1 of this embodiment, the The plurality of harmonic orders may be discontinuous.

[0020] In step S2: The harmonic measurement devices are arranged on some branches of the power transmission system, the total number of which is , the amplitude and phase angle of harmonic voltage and harmonic current are expressed as: ; in, Indicates the number of harmonic orders generated by the harmonic source, ; The harmonic vector measurement is expressed as: ; in, Indicates the number of harmonic voltage measuring devices, Indicates the number of harmonic current measuring devices, , represents a mapping from the index of the harmonic measuring device to its location in the power transmission network, represents harmonic voltage, Indicates harmonic current.

[0021] In step S3, The relationship between harmonic vector measurement, measurement matrix, state variable and measurement error is expressed as: ; in, h They represent harmonic phasor measurement, measurement matrix, state variable, and measurement error respectively. Due to the high cost of harmonic monitoring devices, only limited measurement equipment is deployed at key nodes in the power network. Less than n; in this embodiment, Much smaller than n.

[0022] The measurement matrix is ​​expressed as: ; in, , i A harmonic measurement device is at the transmitting end, then , i A harmonic measurement device is at the receiving end, then ; The state variables are represented as: ; And the state variable is the injected harmonic current ,Right now: ; The measurement error is modeled as a Gaussian distribution: ; Indicates The noise variance of the subharmonics, for OK The unit matrix of the column.

[0023] In this embodiment, The number of measurements in is much smaller than the number of state variables, that is, Much smaller than Therefore, the above equation has countless feasible solutions. In order to find the real state variable, this embodiment uses the spatial sparsity of the harmonic source as a constraint: there are only a few harmonic sources in the system at the same time, and the state variable satisfy: ; In addition, the harmonics generated by the harmonic source contain multiple frequencies, and the high-dimensional state variable θ is group sparse, so any node Injected harmonic current vector Both are zero or non-zero at the same time, and the harmonic source has structural sparseness.

[0024] In step S4, The high-dimensional harmonic vector measurement is expressed as: ; Right now ; in, for No. i elements; high-dimensional measurement matrix Depend on According to the rearrangement of high-dimensional state variables, we can get: ; in, represent Middle OK i The elements of the column, .definition ,in, for No. Column to A matrix consisting of columns; High-dimensional state variables Expressed as , Representation Node The injected current of all harmonic orders, due to the sparse structure mentioned above, The elements in are either all 0 or all non-0; The high-dimensional noise matrix is ​​expressed as: ; in, represents a high-dimensional noise vector, is the covariance matrix of the noise; for OK The unit matrix of the column.

[0025] In step S5, because With group sparsity, All elements of Description, so the prior distribution of high-dimensional state variables is expressed as: ; Among them, the hyperparameter vector ; Represents state variables The mean is 0 and the covariance matrix is Gaussian distribution of The likelihood probability of high-dimensional harmonic vector measurements is expressed as: .

[0026] In this embodiment, when When the subvector The probability of being zero is 1, resulting in group sparsity.

[0027] In step S6, definition , the marginalized probability density function is: ; in ； When the hyperparameter values ​​are fixed, the posterior density is a Gaussian distribution: ; in , .

[0028] In step S6, the second type of maximum likelihood estimation is used to solve and ,Right now , which is equivalent to minimizing ,in is a natural logarithmic function, the loss function is: ; The expectation maximization algorithm is used to minimize the loss function, as follows: In the round iteration, let The hyperparameter vector and error variance of the round estimation are defined as and ,use and The calculated mean and variance are defined as and , the algorithm calculation process is as follows: Step S6.1: Step E: ; Step S6.2: M step: ; in for No. elements, , for No. OK The elements of the column, , , , , ; Step S6.3: In the expectation maximization algorithm round, according to the estimated and , calculate the The mean and variance of the round: , ; Step S6.4: Repeat steps S6.1 to S6.3 until the algorithm converges and obtains the estimated values ​​of the hyperparameter vector and error variance. and , thereby calculating the estimated value of the high-dimensional state variable, that is, the harmonic estimator: ; In this embodiment, the proposed group sparse Bayesian algorithm uses the expectation maximization algorithm to solve the parameters. According to the properties of the expectation maximization algorithm, as a preferred embodiment of this invention, in each round of iteration, ensure that the loss function ,at the same time There is a lower bound, namely Non-increasing and convergent, thus ensuring that the proposed group sparse Bayesian algorithm can converge to a set of local optimal solutions.

[0029] In step S7, Based on the obtained harmonic estimate , obtain the harmonic current of each harmonic order , the relationship between all the operating states and state variables of the power transmission system is established by using the power flow calculation equation to obtain the operating state of the power transmission system, that is, the voltage of all nodes in the system: .

[0030] This embodiment discloses a method for estimating the harmonic state of a power transmission system based on sparse Bayesian learning. Combining the spatial sparsity and structural sparsity of harmonic sources, a form of harmonic state estimation is proposed. Harmonic measurements of all orders are stacked into a high-dimensional vector. A sparse Bayesian algorithm is proposed to describe the state variables. The hyperparameter vector and error variance are estimated by the expectation maximization algorithm, thereby calculating the harmonic estimator and effectively solving the underdetermined harmonic state estimation problem. In addition, this method can estimate the noise values ​​of different harmonic orders separately according to the characteristics that different harmonic orders have different noise values, further improving the estimation accuracy.

[0031] The harmonic state estimation method (denoted as M1) provided in this embodiment is tested on the IEEE 14-node benchmark test system, and the root mean square error (RMSE) is used as the measurement indicator: ; It is compared with the classic lasso method (denoted as M3) and the classic sparse Bayesian learning method SBL (denoted as M2).

[0032] The experimental results are as follows Figure 2 As shown, it can be seen that the estimation method provided by this embodiment achieves the best performance.

[0033] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0034] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be construed as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent application shall be subject to the attached claims.

Claims

1. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning, characterized in that: The following steps are involved: Step S1: describing the power transmission system through an undirected graph, wherein the nodes of the undirected graph are the nodes of the power transmission system, and the edges of the undirected graph are the power transmission lines; modeling the power transmission line as an equivalent π-type circuit, modeling the load as a parallel circuit, modeling the generator as a transient reactance, modeling the transformer as a short-circuit impedance, and modeling the nonlinear load generating harmonics as an injection current source; constructing a system with known network topology and component parameters into a harmonic admittance matrix and a branch admittance matrix under multiple harmonics; Step S2: measuring the amplitude and phase angle of harmonic voltage and harmonic current of some nodes in the power transmission system by a harmonic measurement device, which are recorded as harmonic vector measurement quantities; Step S3: Under the harmonic order, a relationship between a harmonic vector measurement quantity, a measurement matrix, a state variable and a measurement error is established, wherein the measurement matrix is ​​constructed based on the harmonic admittance matrix and the branch admittance matrix; Step S4: The harmonic vector measurements of all harmonic orders are stacked into a high-dimensional harmonic vector measurement, and represented by a high-dimensional state variable, a high-dimensional measurement matrix, and a high-dimensional noise matrix; Step S5: applying a Gaussian distribution with a mean of 0 to the high-dimensional state variable, defining a priori distribution of the high-dimensional state variable based on the hyperparameter vector, and defining a high-dimensional harmonic vector measurement based on the error variance; Step S6: Set the high-dimensional state variable as a hidden variable, estimate the hyperparameter vector and error variance through the expectation maximization algorithm, and obtain the desired harmonic estimator; Step S7: Based on the harmonic estimation, a power flow calculation equation is used to establish a relationship between all operating states and state variables of the power transmission system to obtain the operating state of the power transmission system.

2. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 1, characterized in that: In step S1, The undirected graph is represented as: ； in, Represents a collection of nodes. represents a collection of transmission lines; The harmonic admittance matrix is ​​expressed as: ; Where S is a symmetric complex matrix; The branch admittance matrix is ​​expressed as: ; Where C is a complex matrix; ， ； ， ； in, is the number of nodes, Indicates the number of branches, h Indicates the consideration harmonic order, represents the transmitter admittance matrix, represents the receiving end admittance matrix; and Respectively indicate lines The series and parallel admittance values ​​of , Indicates the node number, Indicates the branch number. .

3. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 2, characterized in that: In step S2: The harmonic measurement devices are arranged on some branches of the power transmission system, the total number of which is , the amplitude and phase angle of harmonic voltage and harmonic current are expressed as: ； in, Indicates the number of harmonic orders generated by the harmonic source, ; The harmonic vector measurement is expressed as: ； in, Indicates the number of harmonic voltage measuring devices, Indicates the number of harmonic current measuring devices, , represents a mapping from the index of the harmonic measuring device to its location in the power transmission network, represents harmonic voltage, Indicates harmonic current.

4. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 3, characterized in that: In step S3, The relationship between harmonic vector measurement, measurement matrix, state variable and measurement error is expressed as: ； in, h They represent harmonic phasor measurement, measurement matrix, state variable, and measurement error respectively; Less than ; The measurement matrix is ​​expressed as: ； in, , i A harmonic measurement device is at the transmitting end, then , i A harmonic measurement device is at the receiving end, then ; The state variables are represented as: ； And the state variable is the injected harmonic current ,Right now: ； The measurement error is modeled as a Gaussian distribution: ； Indicates The noise variance of the subharmonics, for OK The unit matrix of the column.

5. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 4, characterized in that: In step S4, The high-dimensional harmonic vector measurement is expressed as: ； Right now ; in, for No. i elements; high-dimensional measurement matrix Depend on According to the rearrangement of high-dimensional state variables, we can get: ； in, represent Middle OK i The elements of the column, ;definition ,in, for No. Column to A matrix consisting of columns; High-dimensional state variables Expressed as , Representation Node Injected currents of all harmonic orders; The high-dimensional noise matrix is ​​expressed as: ； in, represents a high-dimensional noise vector, is the covariance matrix of the noise; for OK The unit matrix of the column.

6. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 5, characterized in that: In step S5, The prior distribution of high-dimensional state variables is expressed as: ； Among them, the hyperparameter vector ; Represents state variables The mean is 0 and the covariance matrix is Gaussian distribution of The likelihood probability of high-dimensional harmonic vector measurements is expressed as: 。 7. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 6, characterized in that: In step S6, definition , the marginalized probability density function is: ； in ; When the hyperparameter values ​​are fixed, the posterior density is a Gaussian distribution: ； in , .

8. The method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 7, characterized in that: In step S7, the second type of maximum likelihood estimation is used to solve and ,Right now , which is equivalent to minimizing ,in is a natural logarithmic function, the loss function is: ； The expectation maximization algorithm is used to minimize the loss function, as follows: In the k+1th iteration, the hyperparameter vector and error variance estimated in the kth round are defined as and ,use and The calculated mean and variance are defined as and , the algorithm calculation process is as follows: Step S6.1: Step E: ； Step S6.2: M step: ； in for No. elements, for No. elements, for No. OK The elements of the column, , , , , ; Step S6.3: In the expectation maximization algorithm round, according to the estimated and , calculate the The mean and variance of the round: ， ； Step S6.4: Repeat steps S6.1 to S6.3 until the algorithm converges and obtains the estimated values ​​of the hyperparameter vector and error variance. and , thereby calculating the estimated value of the high-dimensional state variable, that is, the harmonic estimator: 。 9. A method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 8, characterized in that: In step S7, in each iteration, ensure that the loss function .

10. The method for estimating harmonic state of a power transmission system based on sparse Bayesian learning according to claim 8, characterized in that: In step S7, Based on the obtained harmonic estimate , obtain the harmonic current of each harmonic order , the relationship between all the operating states and state variables of the power transmission system is established by using the power flow calculation equation to obtain the operating state of the power transmission system, that is, the voltage of all nodes in the system: 。

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