A method for adaptive state estimation of multi-machine power system under unknown noise

Abstract

This invention relates to the field of power system state calculation, and in particular to an adaptive method for estimating the state of a multi-machine power system under unknown noise. The method includes: constructing a state-space model of a random synchronous generator in a multi-machine power system, including the generator's state equations and the measurement equations of the generator's phasor measurement units; extracting unknown noise from the phasor measurement unit measurements and establishing a basic distribution for the unknown noise in the phasor measurement unit measurements based on a Gaussian mixture model; using a clustering algorithm to reduce the number of components in the basic distribution to obtain a simplified distribution; and constructing an adaptive state estimator that uses the obtained true distribution of unknown noise from the phasor measurement units and the synchronous generator model to adaptively estimate the state of the synchronous generator. Compared with existing technologies, this invention has advantages such as accurately calculating the state of a multi-machine power system under the influence of unknown measurement noise, and significantly reducing the computational burden in practical applications.

Description

Technical Field

[0001] This invention relates to the field of power system state calculation, and in particular to an adaptive multi-machine power system state estimation method under unknown noise. Background Technology

[0002] With the continuous expansion of the power system, the deep penetration of high-proportion new energy power generation, and the widespread application of new measurement equipment, the modern power system has gradually evolved into a highly complex and constantly changing system. Accurate and real-time perception of its operating status is of great significance for the monitoring, control, protection, and stable operation of the power system.

[0003] For synchronous generators, actual measurement data is often affected by noise from the equipment itself and complex noise during measurement data transmission. Current state estimation techniques generally assume that the distribution or statistical characteristics of the measurement noise are known. However, such assumptions obviously do not reflect the true situation of the measurement noise and will also affect the accuracy of the state estimation results.

[0004] Based on the above, in order to meet the needs of practical applications, there is an urgent need for a state estimation technique based on an adaptive method to solve the state estimation problem of multi-machine power systems under the influence of unknown measurement noise, thereby ensuring the accuracy of the state estimation results and the safe and stable operation of the power system. Therefore, this invention provides an adaptive state estimation method for multi-machine power systems under unknown noise. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide an adaptive multi-machine power system state estimation method under unknown noise.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] This invention provides an adaptive multi-machine power system state estimation method under unknown noise, comprising the following steps:

[0008] Step S1: Construct a model of a random synchronous generator in a multi-machine power system, including the generator's state equation and the generator phasor measurement unit's measurement equation, and obtain the synchronous generator's state and the phasor measurement unit's measurement values.

[0009] Step S2: Extract the unknown noise from the phasor measurement unit's measurement values, and establish a basic distribution for the unknown noise in the phasor measurement unit's measurement values ​​based on a Gaussian mixture model;

[0010] Step S3: Use a clustering algorithm to reduce the number of components in the basic distribution to obtain a simplified distribution;

[0011] Step S4: Construct an adaptive state estimator. Based on the phasor measurement unit measurements of the synchronous generator in Step S1, the basic distribution in Step S2, and the simplified distribution in Step S3, obtain the predicted state values ​​of the synchronous generator, the predicted values ​​of the phasor measurement unit measurements, the prediction error covariance matrix of the phasor measurement unit measurements, and the cross-covariance matrix of the prediction error between the synchronous generator state and the phasor measurement unit measurements. Eliminate unknown noise in the model of the synchronous generator to achieve adaptive state estimation of the synchronous generator.

[0012] The model of the synchronous generator is represented by the following formula:

[0013]

[0014] Where, x m,k+1 Let x represent the state of the m-th synchronous generator at time k+1. m,k This represents the state of the m-th synchronous generator at time k, including the generator speed and rotor angle; u m,k This represents the input of the synchronous generator, including mechanical torque and excitation voltage, g. m (·) is a nonlinear function used to characterize the physical mechanism of synchronous generators, w m,k This represents process noise with a known distribution; z m,k This represents the phasor measurement unit measurements of the m-th synchronous generator, including frequency, active power, and reactive power; h m (·) represents a nonlinear function that characterizes the relationship between the measured values ​​of the phasor measurement unit and the state and input, v m,k This represents the measurement noise of a phasor measurement unit whose statistical characteristics are unknown.

[0015] The phasor measurement unit specifically obtains the measurement value through the w-th measurement window of length S.

[0016] The fundamental distribution of phasor measurement units is characterized by using estimates of phasor measurement units from several previous time points and the Kernel density estimation method.

[0017] Step S3 specifically includes the following steps:

[0018] Step S31: Initialize the parameters in the basic distribution based on the fuzzy clustering algorithm;

[0019] Step S32: Set the Wasserstein distance between any two components to be minimized, solve for the Gaussian density, and use it to merge two candidate components and reduce one of the components;

[0020] Step S33: Repeat the above steps until the number of reduced components reaches the preset reduction component threshold, and a simplified distribution is obtained.

[0021] The fuzzy clustering algorithm includes the fuzzy c-means clustering algorithm.

[0022] The Wasserstein distance between the two components is determined based on the location of the cluster centroid.

[0023] Furthermore, the centroid of each cluster is determined recursively.

[0024] In a second aspect, the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the steps of any of the methods described above.

[0025] Thirdly, the present invention provides a storage medium having a program stored thereon, which, when executed, implements the steps of any of the methods described above.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1) To address the problem of power system state estimation under the influence of unknown measurement noise, this invention proposes a state estimation method for multi-machine power systems based on adaptive principles under unknown noise. This method includes an online implementation of a sliding window-based statistical model for unknown measurement noise. Based on this method, the distribution of unknown noise can be extracted and estimated. The noise distribution is removed in the initial state. Moreover, this method only requires a small number of Gaussian mixture components and can accurately calculate the state of multi-machine power systems, which can greatly reduce the computational burden in practical applications.

[0028] 2) Based on the statistical model of the acquired unknown measurement noise, this invention proposes an adaptive state estimation algorithm with a sliding window within the framework of capacitive Kalman filtering and Gaussian filtering. This algorithm not only has good estimation performance but is also suitable for online implementation. Therefore, this invention can effectively meet the needs of practical applications and provide a reliable guarantee for the accuracy and stable operation of state estimation in multi-machine power systems.

[0029] 3. In traditional synchronous generator state estimation, it is always assumed that the PMU measurement noise distribution is known and that the parameters characterizing this distribution are always constant. However, this assumption not only fails to consider the actual PMU measurement noise distribution, but also results in synchronous generator state estimation that cannot reflect the true situation. This invention obtains the true distribution of PMU measurement noise based on steps S2 and S3, and the parameters characterizing this distribution are updated as the sliding window moves, enabling adaptive matching with the true distribution of PMU measurement noise. Attached Figure Description

[0030] Figure 1 This is a flowchart of a method for state estimation using an adaptive algorithm under unknown measurement noise according to an embodiment of the present invention;

[0031] Figure 2 This is a distribution estimation result of unknown PMU measurement noise under the influence of a Gaussian distribution characterized by constant parameters according to an embodiment of the present invention;

[0032] Figure 3 According to an embodiment of the present invention Figure 2 The adaptive state estimation result of a synchronous generator in a multi-machine power system under the influence of unknown PMU measurement noise is shown.

[0033] Figure 4 This is a distribution estimation result of unknown PMU measurement noise under the influence of a non-Gaussian distribution characterized by random parameters, according to an embodiment of the present invention;

[0034] Figure 5 According to an embodiment of the present invention Figure 4 The adaptive state estimation result of a synchronous generator in a multi-machine power system under the influence of unknown PMU measurement noise is shown.

[0035] Figure 6 This is a distribution estimation result of unknown PMU measurement noise under the influence of a complex non-Gaussian distribution characterized by random parameters, according to an embodiment of the present invention.

[0036] Figure 7 According to an embodiment of the present invention Figure 6 The figure shows the adaptive state estimation result of a synchronous generator in a multi-machine power system under the influence of unknown PMU measurement noise. Detailed Implementation

[0037] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0038] This embodiment is implemented based on the technical solution of the present invention, and provides detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiment.

[0039] This embodiment provides an adaptive multi-machine power system state estimation method under unknown noise conditions, such as... Figure 1 As shown, it includes the following steps:

[0040] Step S1: Establish a model of the m-th synchronous generator in a multi-machine power system, including the state equation of the synchronous generator and the measurement equation of the generator phasor measurement unit (PMU). Obtain the state of the synchronous generator and the measurement values ​​of the phasor measurement unit (PMU), expressed by the following formula:

[0041]

[0042] Where, x m,k This represents the state of the m-th synchronous generator at time k, including the generator speed, rotor angle, etc., u m,k This represents the input of a synchronous generator, including mechanical torque, excitation voltage, etc., g m (·) is a nonlinear function used to characterize the physical mechanism of synchronous generators, w m,k z represents process noise whose true distribution is known; m,k This represents the PMU measurements of the m-th synchronous generator, including frequency, active power, and reactive power, h. m (·) represents a nonlinear function that characterizes the relationship between PMU measurements and state and input, v m,k This represents PMU measurement noise with unknown statistical characteristics.

[0043] Step S2: Extract the unknown noise from the phasor measurement unit measurements and establish a basic distribution for the unknown noise in the phasor measurement unit measurements based on the Gaussian mixture model (GMM).

[0044] Specifically, for the m-th synchronous generator, consider the w-th measurement window that contains historical measurement data of S PMUs.

[0045] A PMU measurement window of length S is established, expressed by the following formula:

[0046]

[0047] Among them, Z m,w express……, This represents the w-th sliding window.

[0048] The fundamental distribution of PMU measurement noise can be characterized using estimates from measurements taken in previous time steps and the kernel density estimation method. Specifically, let... The state estimate of the m-th synchronous generator in the w-th sliding window is expressed by the following formula:

[0049]

[0050] The PMU measurement noise corresponding to the w-th sliding window can be expressed as follows:

[0051]

[0052] in,

[0053] Let V m,w For v m,w If the sample set is v, then v m,w The basic Gaussian mixture density can be expressed as:

[0054]

[0055] Among them, K H This represents the Gaussian kernel function with bandwidth matrix H, where S represents the total number of samples, and the parameters are... It should be noted that the parameter is v m,w The fundamental probability density function, i.e., the fundamental distribution, can be represented by the GMM as:

[0056]

[0057] Where, the total sample size S represents the number of components of the basic distribution represented by the GMM, and the parameters... The detailed expression is:

[0058]

[0059] in, The mean is variance is Let S be the s-th component of the GMM (s = 1, 2, ..., S). In the GMM representation of the basic distribution, the weights of each component are denoted as... and

[0060] Step S3: Based on the clustering algorithm, reduce the Gaussian mixture components of the basic distribution to obtain a simplified distribution.

[0061] Specifically, fuzzy c-means clustering algorithm is used, combined with the Wasserstein distance criterion, to reduce the number of components in the basic distribution in step S2, thereby deriving a simplified Gaussian mixture density, i.e., a simplified distribution, expressed by the following formula:

[0062]

[0063] The number of components is L3S. and

[0064] Initialize the Gaussian Mixture Components algorithm based on fuzzy clustering. For simplicity, let the component in the i-th (i=1,2,…,S) basic distribution GMM representation shown in formula (6) be denoted as . Then the two GMM components and The Wasserstein distance between them is expressed as:

[0065]

[0066] The distance between GMM components in any two basic distributions is calculated using the Wasserstein distance criterion.

[0067] Assuming the Wasserstein distance given in formula (9) is minimized, then the Gaussian density... This can be achieved by minimizing the following formula:

[0068]

[0069] The result is used to merge candidate components p. i (v m,w ) and p j (v m,w ),in W D (·) represents the Wasserstein distance, and its definition is given in Equation (9).

[0070] Once the Wasserstein distance is found, the Gaussian density can be solved. Then it can replace component p i (v m,w ) and p j (v m,w This means that the number of components in the basic distribution can be reduced by one. The solution to formula (10) is as follows:

[0071]

[0072]

[0073] Repeat the above process until the preset number of reduction components L is reached, thus completing the parameter calculation. Initialization.

[0074] Next, the parameters are updated using the fuzzy c-means clustering algorithm. The initial values ​​are then determined. Specifically, each component of the reduced basic distribution obtained from the initialization is first treated as a cluster, and then a new centroid for each cluster is found using an objective function based on Wasserstein distance. For simplicity, assume that the l-th (l = 1, 2, ..., L) component of the simplified GMM is... for There is an objective function:

[0075]

[0076] in, For the l-th cluster The membership degree and d∈[1,∞] are parameters that control the ambiguity. represent and The Wasserstein distance between them. It should be noted that... Depending on the location of the new cluster centroids, the cluster centroids must be found recursively until the objective function J is reached. m The difference between the current value and the previous value is lower than a predefined threshold.

[0077] J m For u il Taking the partial derivative and setting it to zero, we have:

[0078]

[0079] in, and The cluster centroids can be obtained using the data from the previous iteration. Similarly, the new weights, mean, and covariance of each cluster can be obtained using the following formulas:

[0080]

[0081]

[0082]

[0083] The simplified Gaussian mixture density is finally obtained, which is Equation (8).

[0084] like Figure 2 As shown, Figure 2 The first sub-figure shows the measured noise w of the m-th synchronous generator in step S1. m,k The true distribution of the noise w is represented by a Gaussian distribution characterized by constant parameters; the second sub-figure shows the noise w measured in step S1. m,kThe active power measurement curve under the influence; the green curve in the third sub-figure is the basic distribution of the phasor measurement unit in the 16th sliding window established based on the Gaussian mixture model in step S2, and the blue curve is the estimate of the distribution obtained by the cluster-based Gaussian mixture component reduction algorithm proposed in step S3.

[0085] Figure 4 The first sub-figure shows the measured noise w of the m-th synchronous generator in step S1. m,k The true distribution of the noise w is represented by a Gaussian distribution characterized by random parameters; the second sub-figure shows the noise w measured in step S1. m,k The active power measurement curve under the influence; the green curve in the third sub-figure is the basic distribution of the phasor measurement unit in the 13th sliding window established based on the Gaussian mixture model in step S2, and the blue curve is the estimate of the distribution obtained by the cluster-based Gaussian mixture component reduction algorithm proposed in step S3.

[0086] Figure 6 The first sub-figure shows the measured noise w of the m-th synchronous generator in step S1. m,k The true distribution of the noise w is represented by a complex Gaussian distribution characterized by random parameters; the second sub-figure shows the noise w measured in step S1. m,k The active power measurement curve under the influence; the green curve in the third sub-figure is the basic distribution of the phasor measurement unit in the 13th sliding window established based on the Gaussian mixture model in step S2, and the blue curve is the estimate of the distribution obtained by the cluster-based Gaussian mixture component reduction algorithm proposed in step S3.

[0087] Step S4: Construct an adaptive state estimator to perform adaptive state estimation of the synchronous generator state.

[0088] Specifically, firstly, state prediction is performed. For w+1 windows, based on the estimated value of the m-th synchronous generator at time s-1, the expression for the τ-th volumetric point can be obtained as follows:

[0089]

[0090] Where S m,w+1,s-1|s-1 Representation matrix P xx,m,w+1,s-1|s-1 The square root in the Cholesky decomposition sense, i.e. χ τ Represents a scalar parameter, which is defined as follows:

[0091] Where e τ It is a unit vector.

[0092] After obtaining the volume point, the state equation g of the synchronous generator in step S1 is used.m (·) Propagate each point to generate a new set of transformation volume points, in the following form:

[0093]

[0094] For w+1 windows, the predicted state value of the m-th synchronous generator at time s-1 in step S1 and the prediction error covariance are calculated as follows:

[0095]

[0096]

[0097] in

[0098] The PMU measurement function h is used in step S1. m (·) To find the τ-th predicted volume point with respect to the measured value, we have

[0099]

[0100] in, S m,w+1,s|s-1 Representation matrix P xx,m,w+1,s|s-1 Square root in the Cholesky decomposition sense.

[0101] Based on the true distribution of PMU measurement noise obtained in steps S2 and S3, namely the basic distribution in step S2 and the simplified distribution in step S3, the predicted value of PMU measurement, the covariance matrix of PMU measurement prediction error, and the cross-covariance matrix of synchronous generator state-PMU measurement prediction error are calculated respectively, and expressed by formulas (21) to (23) respectively, so that these variables can adaptively match the true distribution of PMU measurement noise:

[0102]

[0103]

[0104]

[0105] in, This represents the l-th (l = 1, 2, ..., L) reduced GMM component of the PMU measurement noise obtained in step S3, which is obtained using historical PMU measurements contained in the w-th sliding window.

[0106] In traditional synchronous generator state estimation, it is always assumed that the PMU measurement noise distribution is known and that the parameters characterizing this distribution remain constant. However, this assumption not only fails to consider the actual PMU measurement noise distribution, but also results in synchronous generator state estimation that cannot reflect the true situation. To overcome this deficiency, this invention obtains the true distribution of PMU measurement noise based on steps S2 and S3, and the parameters characterizing this distribution are updated as the sliding window moves. This allows the predicted PMU measurement values, the PMU measurement prediction error covariance matrix, and the synchronous generator state-PMU measurement prediction error cross-covariance matrix to adaptively change with the distribution parameters of the PMU measurement noise.

[0107] Based on the PMU measurement values ​​obtained in step S1, the true distribution of PMU measurement noise obtained in steps S2 and S3, and the synchronous generator state prediction values, PMU measurement prediction values, PMU measurement prediction error covariance matrix, and synchronous generator state-PMU measurement prediction error cross-covariance matrix obtained by the aforementioned formula (18), the synchronous generator state is adaptively estimated, that is, the estimated value of the synchronous generator state in step S1 and its corresponding estimation error covariance are calculated:

[0108]

[0109]

[0110] in,

[0111] The gain matrix is:

[0112] This step utilizes the PMU measurements from step S1 and the continuously updated true distribution of PMU measurement noise obtained from steps S2 and S3, thereby achieving adaptive estimation of the multi-machine power system state in step S1 under unknown noise.

[0113] Figure 3 The red curve represents the synchronous generator model shown in step S1. Figure 2 The measurement noise w is shown in the first sub-figure. m,k The actual state trajectory under the influence; the green curve represents the assumed measurement noise w. m,k The state estimation result obtained by the traditional cubature Kalman filter (CKF) under the condition that the distribution is known; the blue dashed line represents... Figure 2 The blue curve in the third subfigure shows the estimated trajectory of the state obtained in step S4 under the estimated distribution.

[0114] Figure 5The red curve represents the synchronous generator model shown in step S1. Figure 4 The measurement noise w is shown in the first sub-figure. m,k The actual state trajectory under the influence; the green curve represents the assumed measurement noise w. m,k The state estimation result obtained by the traditional cubature Kalman filter (CKF) under the condition that the distribution is known; the blue dashed line represents... Figure 4 The blue curve in the third subfigure shows the estimated trajectory of the state obtained in step S4 under the estimated distribution.

[0115] Figure 7 The red curve represents the synchronous generator model shown in step S1. Figure 6 The measurement noise w is shown in the first sub-figure. m,k The actual state trajectory under the influence; the green curve represents the assumed measurement noise w. m,k The state estimation result obtained by the traditional cubature Kalman filter (CKF) under the condition that the distribution is known; the blue dashed line represents... Figure 6 The blue curve in the third subfigure shows the estimated trajectory of the state obtained in step S4 under the estimated distribution.

[0116] Secondly, this embodiment provides an electronic device, including a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the steps of the method provided in this embodiment.

[0117] Thirdly, this embodiment provides a storage medium on which a program is stored, and when the program is executed, it implements the steps of the method provided in this embodiment. The storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0118] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for state estimation of a multi-machine power system based on adaptive noise under unknown conditions, characterized in that, Includes the following steps: Step S1: Construct a model of a random synchronous generator in a multi-machine power system, including the state equation of the synchronous generator and the measurement equation of the generator phasor measurement unit, and obtain the state of the synchronous generator and the measurement values ​​of the phasor measurement unit. Step S2: Extract the unknown noise from the phasor measurement unit's measurement values, and establish a basic distribution for the unknown noise in the phasor measurement unit's measurement values ​​based on a Gaussian mixture model; Step S3: Use a clustering algorithm to reduce the number of components in the basic distribution to obtain a simplified distribution; Step S4: Construct an adaptive state estimator. Based on the phasor measurement unit measurements of the synchronous generator in Step S1, the basic distribution in Step S2, and the simplified distribution in Step S3, obtain the predicted state values ​​of the synchronous generator, the predicted values ​​of the phasor measurement unit measurements, the prediction error covariance matrix of the phasor measurement unit measurements, and the cross-covariance matrix of the prediction error between the synchronous generator state and the phasor measurement unit measurements. Eliminate unknown noise in the model of the synchronous generator to achieve adaptive state estimation of the synchronous generator. The model of the synchronous generator is represented by the following formula: in, Indicates the first m A synchronous generator in k+ The state at time 1 Indicates the first m A synchronous generator in k The state at any given moment, including the synchronous generator speed and rotor angle; This represents the input of the synchronous generator, including mechanical torque and excitation voltage. The nonlinear function is used to characterize the physical mechanism of synchronous generators. This represents process noise with a known distribution; Indicates the first m The phasor measurement unit of a synchronous generator measures the frequency, active power and reactive power. The nonlinear function characterizes the relationship between the measured values ​​of the phasor measurement unit and the state and input. This refers to the measurement noise of a phasor measurement unit whose statistical characteristics are unknown. Step S3 specifically includes the following steps: Step S31: Initialize the parameters in the basic distribution based on the fuzzy clustering algorithm; Step S32: Set the Wasserstein distance between any two components to be minimized, solve for the Gaussian density, and use it to merge two candidate components and reduce one of the components; Step S33: Repeat the above steps until the number of reduced components reaches the preset reduction component threshold, and a simplified distribution is obtained.

2. The adaptive multi-machine power system state estimation method under unknown noise as described in claim 1, characterized in that, The phasor measurement unit measures values ​​specifically through the... The measurement window of length S is obtained.

3. The adaptive multi-machine power system state estimation method under unknown noise as described in claim 1, characterized in that, The fundamental distribution of phasor measurement units is characterized by using estimates of phasor measurement units from several previous time points and the Kernel density estimation method.

4. The adaptive multi-machine power system state estimation method under unknown noise as described in claim 1, characterized in that, The fuzzy clustering algorithm includes the fuzzy c-means clustering algorithm.

5. The adaptive multi-machine power system state estimation method under unknown noise as described in claim 4, characterized in that, The Wasserstein distance between the two components is determined based on the location of the cluster centroid.

6. The adaptive multi-machine power system state estimation method under unknown noise as described in claim 5, characterized in that, The centroid of each cluster is determined recursively.

7. An electronic device comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-6.

8. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the steps of the method as described in any one of claims 1-6.

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