Power grid bad parameter identification and correction method based on synchronous phasor measurement

Abstract

The application provides a power grid bad parameter identification and correction method based on synchronous phasor measurement. State estimation based on PMU measurement can realize high-resolution real-time detection and state evaluation of the power grid. In view of the problem that parameter errors and bad measurement values are difficult to distinguish and identify in the PMU state estimation of the power system, the theory and method of unified identification and correction of bad parameters and bad measurement values are studied by using regularization Lagrange multipliers and residuals, and an improved strategy for improving the distinguishability of bad parameters is provided.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatch automation technology (including renewable energy), and particularly relates to a method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement. Background Technology

[0002] Power system state estimation (PSE) is a core engineering project of the power grid energy management system and a crucial support for power grid dispatch and operation. With the widespread application of power measurement units (PMUs), PMU-based state estimation enables high-resolution real-time monitoring of the power grid down to the millimeter level, supporting dynamic analysis and control of the power system. Correct network topology and model parameters are prerequisites for accurate PSE results and the foundation for advanced power system applications, providing network structure and parameter data for online power flow, state estimation, and security analysis. Modern power grid analysis and PMU-based state estimation place higher demands on the reliability and real-time performance of network topology analysis and parameter identification. However, parameter data obtained from offline measurements in the EMS database may contain significant errors, and sometimes even incorrect parameters, which can adversely affect the safe and stable operation and economic dispatch of the power system.

[0003] Whether based on RTU or PMU, current research widely employs least squares algorithms for state estimation. However, these algorithms are highly sensitive to bad data that does not conform to a normal distribution, thus most state estimation methods generally lack robustness to poor data. PMU measurements do not necessarily conform to a normal distribution, and bad measurements are difficult to completely avoid. To address the impact of bad data on state estimation, two types of methods have been proposed and extensively studied. The first type involves detecting and identifying bad data, removing bad measurements from the measurement set. In engineering, residual-based detection methods are more practical. In recent years, data mining and artificial intelligence-based methods have also been used to process bad PMU data; these methods can also be used for missing data recovery. The second type directly endows the state estimator with the ability to resist measurement data bias; this type of method is also called robust state estimation. Classic robust state estimation methods for power systems mainly include the M-estimation method, represented by minimum absolute value estimation, and its improved versions, which enhance the algorithm's robustness to bad data. In recent years, many new estimation methods and tools have been introduced into robust state estimation of power systems, such as uncertainty measure theory and Bayesian estimation methods. These methods obtain characteristics and information that are beneficial to robust estimation from different aspects, and improve the robustness of state estimation to bad data. However, the resulting increase in algorithm complexity restricts practicality and lacks consideration of the impact of model bias on state estimation.

[0004] In power system state estimation, parameter errors typically refer to model parameters embodied in the measurement equations, such as transformer tap positions and transmission line and transformer parameters. Line and transformer errors refer to errors in the series impedance or parallel admittance values ​​of the line, or the series impedance or tap positions of the transformer. These errors include unknown parameters or undetected parameter changes. Transformer tap measurements are primarily performed using the RTU device in the SCADA system. However, obtaining simulated line or transformer parameters during grid operation mainly relies on actual measurements, typically taken during equipment construction or power outage testing. Line parameters inevitably change with operational status and time. Therefore, line parameters are inherently prone to inaccuracies. Furthermore, with the development of Flexible Alternative Current Transmission Systems (FACTS), reactive power compensation equipment is often represented as parameters in PMU state estimation, potentially significantly increasing the uncertainty and inaccuracy of line parameters. Current methods for estimating and handling line and transformer parameter errors include augmented state estimation methods, methods based on residual analysis and residual sensitivity, and parameter estimation methods based on multiple cross-sectional data.

[0005] Residual analysis based on state estimation, especially residual sensitivity analysis, is a relatively effective method for identifying adverse parameters in power systems. Its basic principle is to obtain the sensitivity relationship between parameter deviation and residual values, and then identify and estimate erroneous model parameters based on the magnitude of the residual values. A more typical application is the two-step estimation method, which can utilize more measurement redundancy to further improve the accuracy of parameter estimation. On the other hand, another similar residual index—the Lagrange multiplier—is also widely used in the identification of adverse parameters in power systems. The NLM method is mainly applied to traditional state estimation methods based on SCADA measurements, with PMU only used to assist in improving measurement redundancy to enhance identification capabilities. Summary of the Invention

[0006] This invention enables high-resolution real-time detection and state assessment of the power grid based on PMU measurement. Addressing the difficulty in distinguishing between parameter errors and undesirable measurements in power system PMU state estimation, this invention studies the theory and method of using regularized Lagrange multipliers and residuals to achieve unified identification and correction of undesirable parameters and measurements, and proposes an improved strategy to enhance the identifiability of undesirable parameters.

[0007] The main innovations and contributions of this invention are summarized as follows:

[0008] This invention studies a method for detecting, identifying, and processing defective parameters and measurements after linear state estimation based on PMU. Addressing the difficulty in distinguishing and identifying defective parameters and measurements, a processing scheme based on Lagrange multipliers and measurement residuals is proposed. This scheme can detect problematic model parameters and measurement data in most cases, and obtain accurate parameter and measurement values ​​through further correction. It has high theoretical value and practical significance.

[0009] The present invention specifically adopts the following technical solution:

[0010] A method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, characterized by comprising the following steps:

[0011] Step S1: Initialize the program, obtain the power grid model parameters and network topology, and read the latest PMU measurement values;

[0012] Step S2: Perform linear state estimation based on PMU measurements;

[0013] Step S3: Calculate the regularized residuals corresponding to all measurements and the regularized Lagrange multipliers corresponding to all parameter values ​​respectively;

[0014] Step S4: Perform a unified comparison of all regularized residuals and regularized Lagrange multipliers and find the maximum value;

[0015] Step S5: If the maximum value is less than the threshold, it means that there are no bad parameters or bad measurements in the system, and the current state estimation ends.

[0016] Step S6: If the maximum value is greater than the threshold, find the corresponding defective data: if it is a defective parameter, correct it to obtain a new parameter value; if it is a defective measurement value, correct it to a new measurement value, or you can choose to directly remove the defective measurement value.

[0017] Step S7: Update the measurement set or parameter values, and return to step S2.

[0018] Furthermore, step S2 specifically includes the following steps:

[0019] Step S21: Linear state estimation based on PMU measurements:

[0020] PMUs can directly measure the current and voltage phasors of a line. Therefore, power system state estimation typically uses the column vector of voltage phasor values ​​of all topology nodes as the system state, denoted as U, and the column vector of branch current phasor values ​​with PMU measurements as denoted as I. b Based on the line impedance characteristics, we obtain:

[0021]

[0022] Among them, Y b The node-branch admittance matrix represents the direct relationship between node voltage and branch current.

[0023] Since the PMU measures the current phasors of all incoming and outgoing branches, including the injection volume within a plant, in addition to considering the branch characteristic equations, we further consider the node injection constraints based on KCL's law for each node. The injection constraints for all nodes in the network can be represented by a matrix as follows:

[0024]

[0025] It is the phasor vector of the injected current at the node. This is the node-branch correlation matrix. Injected current can be defined as the sum of the current phasors of the active current sources of a node. In actual transmission networks, it manifests as the current of the load or generator, and in measurement, it is the sum of the measured current values ​​of the transformer high-voltage side excluding the branch current. Simultaneously, there are some nodes in the power grid without load or power source, i.e., zero-injection nodes, whose injected current value is 0. Substituting equation (25) into equation (26) yields:

[0026]

[0027] The state estimation model considering node injection constraints is as follows:

[0028]

[0029] in, Let be the true value of the measured value. Since measurement errors are inevitable, let e denote the vector of measurement errors. And according to common practice, let x represent the state variable U and z represent the measured value. Then the measurement model can be rewritten as follows:

[0030]

[0031] It can be seen that the above estimation model is also a linear model, which is solved directly by minimizing the weighted sum of squares of the differences between the actual measured value and the estimated measured value:

[0032]

[0033] In state estimation, it is typically assumed that the measurement errors follow an independent and uncorrelated Gaussian probability distribution with a mean of zero, and the weights are the reciprocals of the variance R of the corresponding measurement errors. For the injection current value at a zero-injection node, its variance can be assumed to be a small value. The estimated state values ​​can be obtained as follows:

[0034]

[0035] in This is the gain matrix for the least squares method. As can be seen from the analysis, similar to ordinary linear state estimation, the state estimation model considering node injection constraints also remains linear and can be solved directly analytically with high computational efficiency.

[0036] Furthermore, step S3 specifically includes the following steps:

[0037] Step S31: Calculation of residuals and Lagrange multiplier method:

[0038] In state estimation, the measurement residual is defined as the difference between the measured value and the estimated value, as shown below:

[0039]

[0040] It can be proven that the relationship between residuals and errors is as follows:

[0041]

[0042] in The residual sensitivity matrix characterizes the relationship between measurement residuals and measurement errors. Further calculation of regularized residuals is used to identify defective data.

[0043]

[0044] in Let S be the diagonal elements of the residual sensitivity matrix S. The regularized residuals statistically follow a standard normal distribution; therefore, hypothesis testing is used to determine whether bad data has occurred.

[0045] Next, we consider identifying parameter errors in state estimation. Assume that parameter errors exist. ,in The error parameter values ​​are known and used when performing state estimation. This is the true value of the parameter.

[0046] Next, we will conduct a study on the characterization and quantitative analysis of model bias and measurement bias in state estimation. When performing state estimation, we assume that all parameters are correct, i.e., the parameter bias is zero, and we solve using the least squares method to obtain the system's state estimate. However, due to the presence of undesirable parameters, the solution in this case is erroneous. To further analyze the solution obtained in this case and study methods for identifying undesirable parameters, the result obtained from this solution process can be equivalent to solving the following problem regarding the state... and parameter deviation The optimal solution to the problem.

[0047]

[0048] In the above optimization problem, the system state and parameter deviation These are all optimization variables, but the solution process must satisfy parameter bias. To find the optimal solution to the constrained optimization problem above, we introduce the Lagrange multiplier λ to transform it into an unconstrained optimization problem, as shown below:

[0049]

[0050] Based on the first-order optimality condition for the existence of the optimal value. The following conditions must be met:

[0051]

[0052] in It is a measurement equation about The Jacobian matrix can be obtained from the above equation:

[0053]

[0054] The above formula gives the method for calculating the Lagrange multiplier. It can be seen that the Lagrange multiplier is directly related to the residual. Next, we need to further analyze the relationship between the measurement error of the Lagrange multiplier and the parameter deviation.

[0055] On the other hand, for measurement equations with erroneous parameters, the parameter deviation... After linear expansion, we get:

[0056]

[0057] in The estimated error state value can be obtained using the weighted least squares formula:

[0058]

[0059] Then, the estimated measurement value with errors can be obtained as follows:

[0060]

[0061] Subtracting equations (41) and (29) yields the measurement residual, as shown in the following equation. The measurement residual calculated in this way has a small linearization error, but since the error is low-order, it can be ignored. The residual can be solved as follows:

[0062]

[0063] Substituting the above equation into equation (38), we can obtain the error and Lagrange multipliers as shown below:

[0064]

[0065] The above equation illustrates the relationship between the Lagrange multipliers, parameter errors, and measurement errors. It can be seen that the value of the Lagrange multipliers mainly depends on the parameter deviation. It is also subject to measurement error. Impact. Further calculation of the Lagrange multiplier λ's deviation from the parameters. The sensitivity matrix can be obtained, and based on the above formula, improved Lagrange multipliers and residual indices can be introduced to characterize model bias and measurement bias.

[0066] The standard Lagrange multipliers (NLMs) are shown below and follow a normal distribution:

[0067]

[0068] Therefore, the NLM statistical test method can be used to determine whether there are undesirable parameters.

[0069] Step S32: Calculation of residuals and Lagrange multiplier method:

[0070] On the other hand, analysis of the calculation process of Lagrange multipliers and sensitivity matrices reveals that for multi-circuit transmission lines on the same tower, the identical start and end nodes and nearly identical line parameter values ​​lead to a linear correlation in the columns corresponding to the sensitivity matrix. Therefore, the standardized Lagrange multiplier values ​​for multi-circuit lines on the same tower will be very close. Thus, using only regularized Lagrange multipliers is insufficient to identify parameter errors in multi-circuit lines on the same tower. Since multi-circuit lines on the same tower are widespread in actual power grids, this embodiment proposes using regularized residuals to further identify instances of faulty parameters in multi-circuit lines on the same tower.

[0071] From equation (42), we can obtain:

[0072]

[0073] For normal measurements, i.e., measurements with small errors are not bad data, then:

[0074]

[0075] Therefore, the residuals can also reflect this, and the residuals of the current in the line with the faulty parameter will still be greater than those of the normal line on the same tower without parameter errors. Thus, the residual magnitude can be used to distinguish the lines on the same tower with faulty parameters. Each branch will have two measured values ​​of current in both directions, and therefore two residual values, which can further increase the reliability of the judgment.

[0076] In step S3, the present invention distinguishes multi-circuit lines on the same tower using the following method:

[0077] (1) Calculate and determine whether the maximum NLM is greater than the threshold of bad data hypothesis testing. If it is less than the threshold, the identification ends; otherwise, proceed to the next step.

[0078] (2) Determine whether there are multiple circuits on the same tower for the line corresponding to the maximum NLM. If not, directly determine that this parameter is a bad parameter and the identification ends; otherwise, proceed to the next step.

[0079] (3) Compare the differences of the same type of parameter NLM of the multi-circuit lines on the same tower. If the difference between the maximum NLM and the corresponding parameter NLM of other multi-circuit lines on the same tower is greater than 5%, then directly determine that the parameter corresponding to the maximum NLM is a bad parameter; otherwise, proceed to the next step.

[0080] (4) Compare the regularized residuals of the forward and reverse currents of multiple circuits on the same tower. If the two residuals of a certain circuit are both greater than the corresponding residual values ​​of other circuits, then the parameters of this circuit are judged to be bad parameters, and the identification ends.

[0081] (5) If such a line does not exist, it means that it cannot be determined by the residual size. Select the line with the largest NLM as the line where the bad parameter is located, and the identification ends.

[0082] Although the parameters of multiple circuits on the same tower are usually very similar, there are sometimes cases where the parameters differ significantly. In such cases, the NLM will have a large difference, so it can be directly judged, which is why step (2) is performed. In addition, based on the previous theoretical explanation and subsequent simulation verification, step (4) is usually sufficient to identify branches with bad parameters, and the probability of proceeding to step (5) is very small.

[0083] Furthermore, step S6 specifically includes the following steps:

[0084] Step S61: Correction of bad data and parameters:

[0085] When bad data is detected, the usual approach is to either remove or correct it, or use pseudo-measurements obtained through other methods as substitutes. However, due to the redundancy of the measurement set, the potentially large errors between corrected values ​​and pseudo-measurements, and the difficulty in estimating covariance, state estimation typically opts to remove bad data from the dataset. But the parameter set of the state estimation model must be complete; therefore, after detecting bad parameters, it is necessary to correct them and obtain more accurate parameters.

[0086] Defective measurement values ​​can be corrected using the following methods:

[0087]

[0088] Once the erroneous parameters are identified, NLM can be used to correct them.

[0089]

[0090] Once the undesirable parameters are corrected, the state estimation needs to be performed again until all NLM values ​​do not exceed the test threshold, meaning there are no undesirable parameters.

[0091] Compared to existing technologies, this invention and its preferred embodiment enable high-resolution real-time detection and state assessment of the power grid based on PMU measurements. Addressing the difficulty in distinguishing between parameter errors and undesirable measurements in power system PMU state estimation, this invention studies the theory and method of unified identification and correction of undesirable parameters and measurements using regularized Lagrange multipliers and residuals, and proposes improved strategies to enhance the identifiability of undesirable parameters. Testing has also demonstrated the effectiveness and accuracy of the proposed solution. Attached Figure Description

[0092] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0093] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention. Detailed Implementation

[0094] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0095] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0096] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0097] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0098] like Figure 1 As shown in the figure, an embodiment of the present invention proposes a method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, which includes the following steps:

[0099] Step 1: Initialize the program, obtain the power grid model parameters and network topology, and read the latest PMU measurement values;

[0100] Step 2: Perform linear state estimation based on PMU measurements;

[0101] Step 3: Calculate the regularized residuals for all measurements and the regularized Lagrange multipliers for all parameter values.

[0102] Step 4: Perform a unified comparison of all regularized residuals and regularized Lagrange multipliers and find the maximum value;

[0103] Step 5: If the maximum value is less than the threshold, it means that there are no bad parameters or bad measurements in the system, and the current state estimation ends.

[0104] Step 6: If the maximum value is greater than the threshold, find the corresponding defective data: if it is a defective parameter, correct it to obtain a new parameter value; if it is a defective measurement value, correct it to a new measurement value, or you can choose to directly remove the defective measurement value.

[0105] Step 7: Update the measurement set or parameter values, then return to Step 2.

[0106] For the above-mentioned method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, step 2 preferably includes the following steps:

[0107] 1) Linear state estimation based on PMU measurements:

[0108] PMUs can directly measure the current and voltage phasors of a line. Therefore, power system state estimation typically uses the column vector of voltage phasor values ​​of all topology nodes as the system state, denoted as U, and the column vector of branch current phasor values ​​with PMU measurements as denoted as I. b Based on the line impedance characteristics,

[0109]

[0110] Among them, Y b The node-branch admittance matrix represents the direct relationship between node voltage and branch current.

[0111] Since the PMU measures the current phasors of all incoming and outgoing branches, including the injection volume within a plant, in addition to considering the branch characteristic equations, we further consider the node injection constraints based on KCL's law for each node. The injection constraints for all nodes in the network can be represented by a matrix as follows:

[0112]

[0113] It is the phasor vector of the injected current at the node. This is the node-branch correlation matrix. Injected current can be defined as the sum of the current phasors of the active current sources of a node. In actual transmission networks, it manifests as the current of the load or generator, and in measurement, it is the sum of the measured current values ​​of the transformer high-voltage side excluding the branch current. Simultaneously, there are some nodes in the power grid without load or power source, i.e., zero-injection nodes, whose injected current value is 0. Substituting equation (49) into equation (50) yields:

[0114]

[0115] The state estimation model considering node injection constraints is as follows:

[0116]

[0117] in, Let be the true value of the measured value. Since measurement errors are inevitable, let e denote the vector of measurement errors. And according to common practice, let x represent the state variable U and z represent the measured value. Then the measurement model can be rewritten as follows:

[0118]

[0119] It can be seen that the above estimation model is also a linear model, which is solved directly by minimizing the weighted sum of squares of the differences between the actual measured value and the estimated measured value:

[0120]

[0121] In state estimation, it is typically assumed that the measurement errors follow an independent and uncorrelated Gaussian probability distribution with a mean of zero, and the weights are the reciprocals of the variance R of the corresponding measurement errors. For the injection current at zero-injection nodes, its variance can be assumed to be a small value. The estimated state values ​​can be obtained as follows:

[0122]

[0123] in This is the gain matrix for the least squares method. As can be seen from the analysis, similar to ordinary linear state estimation, the state estimation model considering node injection constraints also remains linear and can be solved directly analytically with high computational efficiency.

[0124] For the above-mentioned method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, step 3 includes the following steps:

[0125] 1) Calculation of residuals and Lagrange multiplier method:

[0126] In state estimation, the measurement residual is defined as the difference between the measured value and the estimated value, as shown below:

[0127]

[0128] It can be proven that the relationship between residuals and errors is as follows:

[0129]

[0130] in The residual sensitivity matrix characterizes the relationship between measurement residuals and measurement errors. Further calculation of regularized residuals is used to identify bad data.

[0131]

[0132] in Let S be the diagonal elements of the residual sensitivity matrix S. The regularized residuals statistically follow a standard normal distribution; therefore, hypothesis testing is used to determine whether bad data has occurred.

[0133] Next, we consider identifying parameter errors in state estimation. Assume that parameter errors exist. ,in The error parameter values ​​are known and used when performing state estimation. This is the true value of the parameter.

[0134] Next, we will conduct a study on the characterization and quantitative analysis of model bias and measurement bias in state estimation. When performing state estimation, we assume that all parameters are correct, i.e., the parameter bias is zero, and we solve using the least squares method to obtain the system's state estimate. However, due to the presence of undesirable parameters, the solution in this case is erroneous. To further analyze the solution obtained in this case and study methods for identifying undesirable parameters, the result obtained from this solution process can be equivalent to solving the following problem regarding the state... and parameter deviation The optimal solution to the problem.

[0135]

[0136] In the above optimization problem, the system state and parameter deviation These are all optimization variables, but the solution process must satisfy parameter bias. To solve the above constrained optimization problem with zero constraints, we introduce the Lagrange multiplier λ, transforming it into an unconstrained optimization problem, as shown below.

[0137]

[0138] Based on the first-order optimality condition for the existence of the optimal value. Need to meet

[0139]

[0140] in It is a measurement equation about The Jacobian matrix can be obtained from the above formula.

[0141]

[0142] The above formula gives the method for calculating the Lagrange multiplier. It can be seen that the Lagrange multiplier is directly related to the residual. Next, we need to further analyze the relationship between the measurement error of the Lagrange multiplier and the parameter deviation.

[0143] On the other hand, for measurement equations with erroneous parameters, the parameter deviation... After linear expansion, we can obtain

[0144]

[0145] in The value of the estimated error state can be obtained using the weighted least squares formula.

[0146]

[0147] This can then lead to an erroneous estimated measurement value.

[0148]

[0149] Subtracting equations (65) and (53) yields the measurement residual, as shown in the following equation. The measurement residual calculated in this way has a small linearization error, but since the error is low-order, it can be ignored. The residual can be solved as follows:

[0150]

[0151] Substituting the above equation into equation (62), we can obtain the error and Lagrange multipliers as shown below:

[0152]

[0153] The above equation illustrates the relationship between the Lagrange multipliers, parameter errors, and measurement errors. It can be seen that the value of the Lagrange multipliers mainly depends on the parameter deviation. It is also subject to measurement error. Impact. Further calculation of the Lagrange multiplier λ's deviation from the parameters. The sensitivity matrix can be obtained, and based on the above formula, improved Lagrange multipliers and residual indices can be introduced to characterize model bias and measurement bias.

[0154] The standard Lagrange multipliers (NLMs) are shown below and follow a normal distribution:

[0155]

[0156] Therefore, the NLM statistical test method can be used to determine whether there are undesirable parameters.

[0157] 2) Calculation of residuals and Lagrange multiplier method:

[0158] On the other hand, analysis of the calculation process of Lagrange multipliers and sensitivity matrices reveals that for multi-circuit transmission lines on the same tower, the identical start and end nodes and nearly identical line parameter values ​​lead to a linear correlation in the columns corresponding to the sensitivity matrix. Therefore, the standardized Lagrange multiplier values ​​for multi-circuit lines on the same tower will be very close. Thus, using only regularized Lagrange multipliers is insufficient to identify parameter errors in multi-circuit lines on the same tower. Since multi-circuit lines on the same tower are widespread in actual power grids, this embodiment proposes using regularized residuals to further identify instances of faulty parameters in multi-circuit lines on the same tower.

[0159] From equation (66), we can obtain:

[0160]

[0161] For normal measurements, i.e., measurements with small errors are not bad data, then:

[0162]

[0163] Therefore, the residuals can also reflect this, and the residuals of the current in the line with the faulty parameter will still be greater than those of the normal line on the same tower without parameter errors. Thus, the residual magnitude can be used to distinguish the lines on the same tower with faulty parameters. Each branch will have two measured values ​​of current in both directions, and therefore two residual values, which can further increase the reliability of the judgment.

[0164] This invention employs the following method to distinguish between multiple circuits on the same tower:

[0165] (1) Calculate and determine whether the maximum NLM is greater than the threshold of bad data hypothesis testing. If it is less than the threshold, the identification ends; otherwise, proceed to the next step.

[0166] (2) Determine whether there are multiple circuits on the same tower for the line corresponding to the maximum NLM. If not, directly determine that this parameter is a bad parameter and the identification ends; otherwise, proceed to the next step.

[0167] (3) Compare the differences of the same type of parameter NLM of the multi-circuit lines on the same tower. If the difference between the maximum NLM and the corresponding parameter NLM of other multi-circuit lines on the same tower is greater than 5%, then directly determine that the parameter corresponding to the maximum NLM is a bad parameter; otherwise, proceed to the next step.

[0168] (4) Compare the regularized residuals of the forward and reverse currents of multiple circuits on the same tower. If the two residuals of a certain circuit are both greater than the corresponding residual values ​​of other circuits, then the parameters of this circuit are judged to be bad parameters, and the identification ends.

[0169] (5) If such a line does not exist, it means that it cannot be determined by the residual size. Select the line with the largest NLM as the line where the bad parameter is located, and the identification ends.

[0170] Although the parameters of multiple circuits on the same tower are usually very similar, there are sometimes cases where the parameters differ significantly. In such cases, the NLM will have a large difference, so it can be directly judged, which is why step (2) is performed. In addition, based on the previous theoretical explanation and subsequent simulation verification, step (4) is usually sufficient to identify branches with bad parameters, and the probability of proceeding to step (5) is very small.

[0171] For the above-mentioned method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, step 6 includes the following steps:

[0172] 1) Correction of problematic data and parameters:

[0173] When bad data is detected, the usual approach is to either remove or correct it, or use pseudo-measurements obtained through other methods as substitutes. However, due to the redundancy of the measurement set, the potentially large errors between corrected values ​​and pseudo-measurements, and the difficulty in estimating covariance, state estimation typically opts to remove bad data from the dataset. But the parameter set of the state estimation model must be complete; therefore, after detecting bad parameters, it is necessary to correct them and obtain more accurate parameters.

[0174] Defective measurement values ​​can be corrected using the following methods:

[0175]

[0176] Once the erroneous parameters are identified, NLM can be used to correct them.

[0177]

[0178] Once the undesirable parameters are corrected, the state estimation needs to be performed again until all NLM values ​​do not exceed the test threshold, meaning there are no undesirable parameters.

[0179] Based on the above model and process design, this embodiment will be used for simulation testing on a 500kV transmission network of a power grid in China. The system has a total of 229 nodes and 486 lines. The modeling and solution process is as follows: Figure 1 As shown.

[0180] According to one embodiment of the present invention, single-parameter errors are identified by randomly adding a 20% error to a parameter and designating it as the erroneous parameter. During simulation, it was found that when a parameter error occurs with resistance r, its NLM (Neural Limiting Model) may be less than 3, but it is still the largest NLM among all parameters, and significantly larger than the NLM values ​​corresponding to other normal parameters by at least one order of magnitude. The main reason is that the resistance parameter r of the 500kV high-voltage transmission line used is relatively small, making it more easily overwhelmed by measurement errors. Therefore, through sufficient simulation observation and experience, the hypothesis test threshold for resistance parameters is adjusted to 1. A similar situation exists for ground susceptance, so the hypothesis test threshold is set to 2. The identification and correction results for some branch parameters are summarized in Table 1.

[0181] Table 1. Identification and correction results of line parameter errors in a power grid case.

[0182]

[0183] The simulation results in the table show that 11 out of 12 parameters were accurately identified as bad parameters, and the accuracy of the corrected parameter values ​​was high. The susceptance values ​​of branch 1 and branch 300 were corrected for 3 and 2 rounds respectively because the maximum NLM of the first round of correction was still greater than the threshold, and the accuracy was satisfactory.

[0184] On the other hand, the table shows that the resistance parameter of branch 200 was not identified. Its NLM value is small, and the largest NLM value is very small and points to the resistance parameter value of branch 197. After backtracking analysis, the resistance parameter value of branch 200 and its corresponding Lagrange multiplier sensitivity value are relatively small compared to other points, so they cannot be accurately identified and processed. As analyzed earlier, there may be individual parameters that cannot be identified and processed using NLM, but for a power system, most erroneous parameters can be identified.

[0185] According to one embodiment of the present invention, the method of improving the identifiability of multi-circuit lines on the same tower by using residuals is verified by simulation, that is, by using regularized residuals and NLM index to identify bad data on the same tower lines.

[0186] A simulation test was conducted using a full-network case study of a power grid to assess the identification of adverse parameters in multi-circuit lines on the same tower. Lines A and B are double-circuit lines on the same tower. The r-value of line A was set as the adverse parameter. Ten Monte Carlo simulations were performed. The regularized Lagrange multipliers and the regularized residuals of the forward and reverse currents of the two circuits were calculated. Identification was performed using NLM and the proposed method using both NLM and regularized residuals. The identification results are shown in Table 2.

[0187] Table 2. Identification of Adverse Parameters in Multi-Circuit Lines on the Same Tower in a Power Grid Case Study

[0188]

[0189] In Table 2, for ease of observation, the larger NLM values ​​and regularized residual values ​​for lines A and B are indicated by bold text. The table shows that the NLM values ​​of the resistance parameters of the two lines are very close, and the maximum NLM in the system also exists for the parameters corresponding to these two lines. Therefore, judging defective parameters solely based on the magnitude of NLM leads to misjudgments in 6 out of 10 cases. Since the difference in values ​​between the two lines is within 5%, further comparison of the regularized residuals of the forward and reverse current measurements of the two lines reveals that in all 10 cases, the regularized residuals of the forward and reverse currents of line A are greater than those of line B. Therefore, the resistance parameters of line A can be correctly identified as defective data in all cases. Simulation results for other multi-circuit lines on the same tower yielded the same conclusion. Therefore, for multi-circuit lines on the same tower, judging by both regularized residual values ​​and NLM can accurately identify defective parameters.

[0190] According to one embodiment of the present invention, a simulation verification was performed to identify the simultaneous existence of multiple parameters and defective data in a power grid. Four defective parameters {77r, 111x, 239b, 300x} and three defective measured values ​​(U20, Ift77, Itf165) were set, and some defective data were correlated. The identification process and results are recorded in Table 3.

[0191] Table 3. Identification and correction results of multiple adverse parameters and measurements in a power grid case.

[0192]

[0193] As can be seen from Table 3, after nine rounds of state estimation and correction identification, all defective parameters and defective measurements were identified and the accuracy after correction was also high. Among them, the susceptance value of branch 239 was identified and corrected in three rounds, and the accuracy gradually improved.

[0194] From the TVE (Total Value Estimation) index, the accuracy of state estimation generally increases with each calibration of parameters and measurements, ultimately reaching a TVE of 0.6826. While this doesn't reach the best level under conditions without any parameter or bad data errors, it primarily achieves the purpose of calibrating the state. Further analysis reveals that nodes with relatively inaccurate states are mainly concentrated at those associated with parameter errors and bad measurements, while the TVEs of other nodes are generally between 0.3 and 0.4, indicating that most nodes have obtained relatively good estimates. Without parameter and measurement correction, the overall TVE value exceeds 10, suggesting that directly estimating the state in the presence of bad data actually deviates further from the true value than the original measurements.

[0195] The simulation examples from this invention demonstrate that the unified bad data identification method using maximum Lagrange multipliers and measurement residuals can effectively and accurately identify and correct bad parameters and bad measurements in PMU-based linear state estimation, even if there is a direct correlation between bad parameters and unmeasured data. However, it should be noted that both the maximum residual method and the maximum Lagrange multiplier method are based on statistical hypothesis testing, and there is a small probability of identification failure. Furthermore, power systems may contain bad data with very low identifiability, making them difficult to detect. Nevertheless, overall, the maximum residual method and the maximum Lagrange multiplier method remain among the most effective methods for detecting, identifying, and correcting bad data.

[0196] This invention relates to a method for detecting, identifying, and processing defective parameters and measurements after linear state estimation using a PMU (Programmable Module Unit). Addressing the difficulty in distinguishing and identifying defective parameters and measurements, this invention proposes a processing scheme based on Lagrange multipliers and measurement residuals. This method can detect problematic model parameters and measurement data in most cases, and through further correction, obtain accurate parameter and measurement values. It possesses high theoretical value and practical significance.

[0197] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0198] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other various forms of methods for identifying and correcting faulty power grid parameters based on synchronous phasor measurement. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement, characterized in that, Includes the following steps: Step S1: Obtain the power grid model parameters and network topology, and read the latest PMU measurement values; Step S2: Perform linear state estimation based on PMU measurements; Step S3: Calculate the regularized residuals corresponding to all measurements and the regularized Lagrange multipliers corresponding to all parameter values ​​respectively; Step S4: Perform a unified comparison of all regularized residuals and regularized Lagrange multipliers and find the maximum value; Step S5: If the maximum value is less than the threshold, it means that there are no bad parameters or bad measurements in the system, and the current state estimation ends. Step S6: If the maximum value is greater than the threshold, find the corresponding defective data; if it is a defective parameter, correct it to obtain a new parameter value. If the measurement is defective, either correct it to a new measurement or choose to remove the defective measurement directly. Step S7: Update the measurement set or parameter values, and return to step S2; Step S2 specifically includes the following steps: Step S21: Linear state estimation based on PMU measurements: The column vector of voltage phasor values ​​of all topology nodes is taken as the system state, denoted as U, and the column vector of branch current phasor values ​​with PMU measurements is denoted as I. b Based on the line impedance characteristics, we obtain: Among them, Y b The node-branch admittance matrix represents the direct relationship between node voltage and branch current. The injection constraints for all nodes in the network are represented by a matrix as follows: It is the phasor vector of the injected current at the node. It is the node branch correlation matrix; the injected current is defined as the sum of the current phasors of the active current sources of the node, which is represented by the load or generator current in the actual transmission network, and in the measurement, it is the sum of the current measurements of the high-voltage side of the transformer excluding the branch; the injected current value of the zero-injection node is 0; substituting equation (1) into equation (2) yields: The state estimation model considering node injection constraints is as follows: in, Let be the true value of the measured value; let be the vector of the measurement error. Let x represent the state variable U and z represent the measured value. Then the measurement model can be rewritten as follows: Solve by minimizing the weighted sum of squares of the differences between the actual and estimated measurements: In state estimation, it is assumed that the measurement errors follow an independent and uncorrelated Gaussian probability distribution with zero mean, and the weights are the reciprocals of the variance R of the corresponding measurement errors. For the injection current value of the zero-injection node, the estimated state value is obtained as follows: in This is the gain matrix for the least squares method.

2. The method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement according to claim 1, characterized in that: Step S3 specifically includes the following steps: Step S31: Calculation of residuals and Lagrange multiplier method: In state estimation, the measurement residual is defined as the difference between the measured value and the estimated value, as shown below: The relationship between residuals and errors is as follows: in The residual sensitivity matrix characterizes the relationship between measurement residuals and measurement errors; Further calculation of regularized residuals is used to identify bad data: in The values ​​of the diagonal elements of the residual sensitivity matrix S are given. The regularized residuals statistically conform to the standard normal distribution, so hypothesis testing is used to determine whether bad data has occurred. Next, we consider identifying parameter errors in state estimation; assuming parameter errors exist... ,in The error parameter values ​​are known and used when performing state estimation. The true value of the parameter; Next, we will conduct a study on the characterization and quantitative analysis of model bias and measurement bias in state estimation. When performing state estimation, we assume the parameter bias is zero and solve using the least squares method to obtain the system's state estimate. However, due to the presence of undesirable parameters, the solution in this case is erroneous. To further analyze the solution obtained in this case and study methods for identifying undesirable parameters, the result obtained in this solution process is equivalent to solving the following conditions regarding the state... and parameter deviation The optimal solution to the problem; In the above optimization problem, the system state and parameter deviation These are all optimization variables, but the solution process must satisfy parameter bias. To find the optimal solution to the constrained optimization problem above, we introduce the Lagrange multiplier λ to transform it into an unconstrained optimization problem, as shown below: Based on the first-order optimality condition for the existence of the optimal value. The following conditions must be met: in It is a measurement equation about The Jacobian matrix is ​​obtained from the above equation: For measurement equations with erroneous parameters, the parameter deviation... After linear expansion, we get: in The estimated error state value is represented by the weighted least squares formula, which yields the error state estimate: Further, the estimated measurement value with errors was obtained as follows: Subtracting equation (17) from equation (5) yields the measurement residuals, and the resulting residuals are shown below: Substituting into equation (14), the error and Lagrange multipliers are obtained as follows: Further calculation of Lagrange multipliers Regarding parameter deviation The sensitivity matrix is ​​used to introduce improved Lagrange multipliers and residual indices to characterize model bias and measurement bias; The standard Lagrange multiplier NLM is shown below and follows a normal distribution: Use NLM statistical tests to determine if there are any undesirable parameters; Step S32: Calculation of residuals and Lagrange multiplier method: Regularized residuals are used to further identify cases where lines in multi-circuit lines on the same tower exhibit undesirable parameters. From equation (18), we get: For normal measurements, i.e., measurements with small errors are not bad data, then: 。 3. The method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement according to claim 2, characterized in that: In step S3, the following process is used to distinguish multiple circuits on the same tower: (1) Calculate and determine whether the maximum NLM is greater than the threshold for bad data hypothesis testing. If it is less than the threshold, the identification ends; otherwise, proceed to the next step. (2) Determine whether there are multiple circuits on the same tower for the line corresponding to the maximum NLM. If not, directly determine that this parameter is a bad parameter and the identification ends. Otherwise, proceed to the next step; (3) Compare the differences of the same type of parameter NLM of multi-circuit lines on the same tower. If the difference between the maximum NLM and the corresponding parameter NLM of other multi-circuit lines on the same tower is greater than 5%, then directly determine that the parameter corresponding to the maximum NLM is a bad parameter; otherwise, proceed to the next step. (4) Compare the regularized residuals of the forward and reverse currents of multiple circuits on the same tower. If the two residuals of a certain circuit are both greater than the corresponding residual values ​​of other circuits, then the parameters of this circuit are judged to be bad parameters, and the identification ends. (5) If such a line does not exist, it means that it cannot be determined by the residual size. Select the line with the largest NLM as the line where the bad parameter is located, and the identification ends.

4. The method for identifying and correcting faulty power grid parameters based on synchronous phasor measurement according to claim 2, characterized in that: In step S6, the correction of defective data and parameters specifically includes the following steps: Defective measurement values ​​are corrected using the following methods: Once the erroneous parameters are identified, use NLM to correct them: Once the undesirable parameters are corrected, the state estimation needs to be performed again until all NLM values ​​do not exceed the test threshold, meaning there are no undesirable parameters.

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