Line parameter identification method based on non-intrusive PMU prior error analysis and correction

Abstract

The invention belongs to the technical field of power system measurement and modeling, and particularly relates to a line parameter identification method based on non-intrusive PMU prior error analysis and correction, which comprises the following steps: calibrating a PMU through a synchronous standard source, obtaining measurement errors of a voltage amplitude, a phase angle and a current phase angle, and counting distribution characteristics of the measurement errors; establishing an error mapping relation between a true value known scene and an unknown scene to quantify the influence of the operation state on resistance, reactance and susceptance identification; and correcting the identification parameters according to the error distribution pattern, and adaptively selecting arithmetic mean, truncation mean, Huber estimation or GMM-EM weighted average methods to determine final parameters according to the error distribution pattern. According to the method, PMU measurement errors can be effectively compensated, and the precision and robustness of parameter identification in scenes such as a short circuit are remarkably improved.

Description

Technical Field

[0001] This application belongs to the field of power transmission line parameter measurement technology, specifically involving a line parameter identification method based on non-intrusive PMU prior error analysis and correction. Background Technology

[0002] Accurate power transmission line parameters are fundamental for power system power flow calculations, protection settings, stability analysis, and fault location. Inaccurate parameter settings can lead to a cascading risk of relay protection malfunctions / failures, inaccurate stability control, and distorted assessments of renewable energy absorption capacity, impacting the safe operation of the large power grid and the quality of power supply. With the advancement of new power system construction, the demand for model accuracy in power grid operation is shifting from static design values ​​to dynamic real-world values. This shift places higher demands on the real-time acquisition and dynamic tracking of parameters.

[0003] The methods for obtaining parameters of power transmission lines are divided into offline measurement methods and online measurement methods. Offline measurement methods require a long preparation time for each test, have high requirements for manpower and financial resources, and have poor test repeatability. They have been gradually replaced by online measurement methods.

[0004] Online measurement methods mainly include line parameter identification based on Supervisory Control and Data Acquisition (SCADA) systems and line parameter identification based on Phasor Units (PMUs). SCADA lacks measurement data with a common time scale, has low data accuracy, and lacks phase information, which leads to a sharp amplification of errors in scenarios such as load fluctuations and asymmetrical operation, making it unable to meet the requirements of high-precision modeling.

[0005] With the large-scale deployment of Wide Area Measurement Systems (WAMS), PMUs, with their microsecond-level synchronization accuracy, millisecond-level data refresh rate, and complete phasor data, have become a revolutionary tool for online identification. However, due to the inherent measurement errors of PMUs, PMU-based line parameter identification methods suffer from insufficient identification accuracy: insufficient identification accuracy means that there is a non-negligible deviation between the identified parameter values ​​and the true values, especially for short lines, where the identification results of this method are almost unusable. Summary of the Invention

[0006] This application provides a line parameter identification method based on non-intrusive PMU prior error analysis and correction, which solves the problem of insufficient identification accuracy of PMU-based line parameter identification methods.

[0007] The technical solution of this application is as follows: The line parameter identification method based on non-intrusive PMU prior error analysis and correction includes the following steps: S1. Connect the synchronization standard source to the PMU, use the parameter setting value of the synchronization standard source as the standard value, and record the difference between the parameter measurement value output by the PMU and the standard value as the measurement error of the PMU. S2. Calculate the mean and standard deviation of the measurement error, and obtain the distribution pattern of the measurement error based on the mean and standard deviation. The distribution pattern is described based on kurtosis, skewness, and bimodal coefficient. S3. Based on the PMU output value with measurement error, calculate the identification error in the simulation scene and the real scene. The difference between the simulation scene and the real scene is that the identification parameters of the simulation scene are known, while the identification parameters of the real scene are unknown. S4. Based on the principle that resistance is much smaller than reactance, the ratio of resistance to reactance in the formula for the identification error mapping relationship between real and simulated scenarios is simplified to approximately 0. Based on the law of large numbers, the random error term in the formula for the mapping relationship between the identification error of real scene and simulation scene is simplified. Based on the principle that the inherent error remains unchanged in the short time, the inherent error term in the formula for the mapping relationship between the identification error of the real scene and the simulation scene is simplified. S5. Calculate the corrected identification parameters based on the simplified formula for calculating identification parameters in the real scene; S6. Based on the distribution pattern of the measurement error, select the corresponding distribution center calculation method to calculate the distribution center of the corrected identification parameters, and use the distribution center as the identification result. in: When the distribution is uniform, the arithmetic mean method is used to calculate the distribution center; When the distribution pattern is multimodal, the GMM-EM weighted average method is used to calculate the distribution center; When the distribution is unimodal and symmetrical, the distribution center is calculated using the 20% truncated mean method. When the distribution is unimodal and skewed, the Huber estimation method is used to calculate the distribution center.

[0008] Furthermore, in S3, let the true values ​​of resistance, reactance, and susceptance in the simulation scenario be denoted as follows: R ref1 , X ref1 , B ref1 ; The formula for calculating the identification error of the simulation scene is as follows: ; ; ; In the formula, , , These represent the simulation scenarios at the [number]th [year]. ti The resistance identification error, reactance identification error, and susceptance identification error at time points; , , These represent the values ​​after adding measurement error on the [number]th [day]. t i Resistance identification parameters, reactance identification parameters, and susceptance identification parameters at specific time points.

[0009] Furthermore, in S4, the simplified formula for calculating the recognition error of the real scene is as follows: ; ; ; In the formula, , , These represent the real-world scenarios at the [number]th [time]. t i The resistance identification error, reactance identification error, and susceptance identification error at time points; , These represent the voltage phase angle difference and the current phase angle difference at both ends of the line, respectively. f (·) represents the formula for calculating the distribution center; t i The subscripts 1 and 2 represent the simulation scene and the real scene, respectively.

[0010] Furthermore, in step S5, the corrected reactance identification parameters are as follows: ; The corrected susceptance identification parameters are as follows: ; The corrected resistor identification parameters are as follows: ; In the formula, , , These represent the corrected reactance identification parameters, susceptance identification parameters, and resistance identification parameters, respectively. , , These represent the uncorrected reactance identification parameters, susceptance identification parameters, and resistance identification parameters, respectively.

[0011] Furthermore, in S4, the method for calculating the distribution center in the simplified formula for calculating the identification error of the real scene is as follows: Based on the distribution pattern of the identification error in the simulation scene, the corresponding distribution center calculation method is selected to calculate the identification error of the simulation scene; in: When the distribution is uniform, the arithmetic mean method is used to calculate the distribution center; When the distribution pattern is multimodal, the GMM-EM weighted average method is used to calculate the distribution center; When the distribution is unimodal and symmetrical, the distribution center is calculated using the 20% truncated mean method. When the distribution is unimodal and skewed, the Huber estimation method is used to calculate the distribution center.

[0012] Due to the adoption of the above technical solution, the beneficial effects of this application are as follows: 1. This application obtains measured error data of voltage amplitude, voltage phase angle and current phase angle of a single PMU by non-invasively calibrating it in a controlled laboratory environment using a high-precision standard source. Based on statistical indicators (such as mean, standard deviation, skewness, kurtosis and bimodal coefficient), it comprehensively characterizes the distribution characteristics of its measurement error, providing reliable prior information for subsequent parameter identification.

[0013] 2. Constructing a simulation scenario with known truth values, combined with a real scenario with unknown truth values. This application establishes an error mapping bridge through the construction of two scenarios. That is, after injecting real PMU measurement errors into the simulation, the influence of known operating scenarios (such as voltage phase angle difference and current phase angle difference) on R / X / B identification errors is first quantified. Then, this influence is transferred to the actual scenario. Finally, usable identification parameters are obtained by relying only on measurable operating state quantities (no truth value required) – uncorrected identification parameters (unavailable).

[0014] 3. This application determines the distribution pattern of the corrected multi-time period identification result sequence. Based on the distribution pattern of the identification results, the optimal center estimation method is selected to ensure that the final output parameters have high robustness and statistical consistency. Attached Figure Description

[0015] The accompanying drawings, which are provided to further illustrate this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application.

[0016] Figure 1 A flowchart of the line parameter identification method based on non-intrusive PMU prior error analysis and correction provided in this application; Figure 2 A comparison chart showing the results before and after correction with the true value. Detailed Implementation

[0017] Traditional power supply units (PMUs) are directly connected to the secondary output of the current transformer (CT). During PMU installation, maintenance, and replacement, the CT secondary circuit terminals must be short-circuited. For safety, the primary equipment must be de-energized, but this affects power supply reliability and user power supply, making periodic PMU calibration impossible. Different PMUs exhibit different error characteristics, and the error characteristics of the same PMU can change over long-term operation; therefore, it can only be assumed that the error follows a normal distribution. However, a single distribution characteristic cannot accurately reflect the characteristics of each device; a detailed analysis of the error distribution is necessary. Based on this, as shown in the attached... Figure 1 As shown, this application provides a line parameter identification method based on non-intrusive PMU prior error analysis and correction, including the following steps: S1. Connect the synchronization standard source to the PMU, use the parameter setting value of the synchronization standard source as the standard value, and record the difference between the parameter measurement value output by the PMU and the standard value as the measurement error of the PMU.

[0018] High-precision synchronization standard sources are widely used high-precision signal generation and measurement standard sources in power systems. In this embodiment, this application uses a relay protection tester (CMC series) manufactured by Omicron to connect to the PMU. The high-precision synchronization standard source directly provides the PMU with a known standard electrical signal (voltage and current) to calibrate the PMU's own measurement error. In metering or calibration scenarios, the output of the synchronization standard source is regarded as the "theoretical true value," i.e., the standard value of this application. The difference between the PMU's output of this standard value and the standard value is regarded as the measurement error. The measurement error includes inherent error and random error.

[0019] S2. Calculate the mean and standard deviation of the measurement error, and obtain the distribution pattern of the measurement error based on the mean and standard deviation. The distribution pattern is described based on kurtosis, skewness, and bimodal coefficient.

[0020] Before calculating measurement error, outliers should be removed. Outliers are observations that significantly deviate from the main subject of the dataset. The mean and standard deviation of the measurement error are used to describe the central tendency and dispersion of the error. The distribution shape is described based on kurtosis, skewness, and bimodal coefficient (BC). Specifically: ; ; ; In the formula, E [ ] represents the mathematical expectation operator. X Represents the indication error random variable, μ This represents the mean of the error distribution; The standard deviation represents the error distribution.

[0021] Kurtosis is a parameter that characterizes the kurtosis of the error distribution. The larger the value, the more significant the heavy-tailed distribution of the error data. Skewness is a parameter that characterizes the skewness of the error distribution. The larger the absolute value, the stronger the asymmetry of the error data. Bimodal coefficient is used as a criterion for multimodal distribution. It is generally believed that when BC ≥ 0.56, the error source can be determined to have multimodal distribution characteristics. When BC < 0.56, the error source can be determined to have unimodal distribution.

[0022] The measurement error distribution characteristics of the PMU will vary under different operating scenarios. Since voltage and current constantly change during actual power grid operation, the true values ​​of voltage and current over a long period cannot be determined, and therefore the distribution characteristics of measurement errors cannot be obtained. Therefore, methods that directly correct measurements ignore the influence of random errors; if the random error is large, the accuracy will be significantly reduced. This application is based on the premise that line parameters are generally considered to remain constant over a short period, and that the identification results at all time points within a short period can reflect the distribution of identification errors.

[0023] S3. Calculate the identification error in both the simulation scene and the real scene. The difference between the simulation scene and the real scene is that the identification parameters of the simulation scene are known, while the identification parameters of the real scene are unknown.

[0024] In simulation scenarios, the identified parameters are known quantities; in real-world scenarios, they are unknown quantities. The resistance, reactance, and susceptance identified parameters are denoted as follows: R est1 , X est1 , B est1 During implementation, the identification parameters are calculated using the PMU output value, which includes measurement error. ; Z=R+jX ; Y=jB ; In the formula, , For the line m Terminal voltage and current phasors , For the line n Terminal voltage and current phasors m and n Indicates the two ends of the line; Z For impedance, Y For admittance, X For reactance, R For resistance, j It is the imaginary unit.

[0025] Voltage phasors include both amplitude and voltage value. It also includes phase angle. .

[0026] In the simulation scenario, let the true values ​​of resistance, reactance, and susceptance be denoted as follows: R ref1 , X ref1 , B ref1 ; The formula for calculating the identification error of the simulation scene is as follows: ; ; ; In the formula, , , These represent the simulation scenarios at the [number]th [year]. t i The resistance identification error, reactance identification error, and susceptance identification error at time points; , , These represent the values ​​after adding measurement error on the [number]th [day]. t i Resistance identification parameters, reactance identification parameters, and susceptance identification parameters at specific time points.

[0027] The formula for calculating the recognition error in real-world scenarios is as follows: ; ; ; In the formula, , , These represent the measurement errors of voltage amplitude, voltage phase angle, and current phase angle, respectively. This indicates the voltage phase angle difference between the two ends of the line. This indicates the phase angle difference of the currents at both ends of the line; the superscripts inh and rnd in the parameters represent inherent error and random error, respectively, and the subscripts... t i Indicates a point in time.

[0028] Based on the principle that resistance is much smaller than reactance, the ratio of resistance to reactance in the formula for mapping the identification error between real and simulated scenarios is simplified to approximately 0; that is, in the above formula... , For both items, when the resistance is much smaller than the reactance, the calculated value is 0.

[0029] Considering that in the identification of design line parameters, when the number of identifications is sufficiently large, the distribution of the two identifications will tend to stabilize, thus offsetting the impact of random errors; the inherent error of the PMU has short-term invariance characteristics, so its impact on the identification results also has short-term invariance characteristics. Therefore, based on the law of large numbers, the random error term in the formula for the mapping relationship between identification errors in real and simulated scenarios is simplified; based on the principle of short-term invariance of inherent errors, the inherent error term in the formula for the mapping relationship between identification errors in real and simulated scenarios is also simplified.

[0030] Based on the above, the formula for calculating the recognition error of the simplified real-world scene is as follows: ; ; ; In the formula, , , These represent the real-world scenarios at the [number]th [time]. t i The resistance identification error, reactance identification error, and susceptance identification error at time points; , These represent the voltage phase angle difference and the current phase angle difference at both ends of the line, respectively. f (·) represents the formula for calculating the distribution center; t i The subscripts 1 and 2 represent the simulation scene and the real scene, respectively.

[0031] In the above formula, the distribution center of the identification error in the simulation scenario is used to replace the specific value of the identification error. The calculation method of the distribution center here is the same as the calculation method of the measurement error distribution center in S6 below.

[0032] In S4, the calculation method for the distribution center in the simplified formula for calculating the recognition error of the real scene is as follows: Based on the distribution pattern of the identification error in the simulation scene, the corresponding distribution center calculation method is selected to calculate the identification error of the simulation scene; in: When the distribution is uniform, the arithmetic mean method is used to calculate the distribution center; When the distribution pattern is multimodal, the GMM-EM weighted average method is used to calculate the distribution center; When the distribution is unimodal and symmetrical, the distribution center is calculated using the 20% truncated mean method. When the distribution is unimodal and skewed, the Huber estimation method is used to calculate the distribution center.

[0033] S5. Calculate the corrected identification parameters based on the simplified formula for calculating identification parameters in the real scene; In step S5, the corrected reactance identification parameters are as follows: ; The corrected susceptance identification parameters are as follows: ; The corrected resistor identification parameters are as follows: ; In the formula, , , These represent the corrected reactance identification parameters, susceptance identification parameters, and resistance identification parameters, respectively. , , These represent the uncorrected reactance identification parameters, susceptance identification parameters, and resistance identification parameters, respectively. The uncorrected identification parameters are the identification parameters output by the actual PMU without error compensation. After the PMU outputs the identification parameters, each identification parameter is corrected according to the above formula.

[0034] S6. Based on the distribution pattern of the measurement error, select the corresponding distribution center calculation method to calculate the distribution center of the corrected identification parameters, and use the distribution center as the identification result. in: When the distribution is uniform, the arithmetic mean method is used to calculate the distribution center; When the distribution pattern is multimodal, the GMM-EM weighted average method is used to calculate the distribution center; When the distribution is unimodal and symmetrical, the distribution center is calculated using the 20% truncated mean method. When the distribution is unimodal and skewed, the Huber estimation method is used to calculate the distribution center.

[0035] This application was verified on a short 20km track, and the identification values ​​before and after the correction are shown in Table 1.

[0036] Table 1. Comparison of identification values ​​before and after correction for the 20km short track. As shown in Table 1 and appendix Figure 2 As shown, the simulation results indicate that the identification accuracy is significantly improved after error correction, and all errors are stably controlled below 5%. This error range meets the stringent requirements for line parameters in practical engineering applications such as power system planning, fault analysis, and operation simulation.

[0037] For any parts not mentioned in this application, existing technologies may be used or referenced.

[0038] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A line parameter identification method based on non-intrusive PMU prior error analysis and correction, characterized in that, The method comprises the following steps: S1, connecting a synchronous standard source to a PMU, taking the parameter setting value of the synchronous standard source as a standard value, and recording the difference between the parameter measurement value output by the PMU and the standard value as the measurement error of the PMU; S2, calculating the average value and the standard deviation of the measurement error, and obtaining the distribution form of the measurement error based on the average value and the standard deviation, the distribution form being described based on kurtosis, skewness, and bimodal coefficient; S3, calculating the identification error in a simulation scenario and a real scenario based on the PMU output value with the measurement error, the difference between the simulation scenario and the real scenario being that the identification parameter of the simulation scenario is known and the identification parameter of the real scenario is unknown; S4, approximating 0 to simplify the resistance-to-reactance ratio in the identification error mapping relationship formula of the real scenario and the simulation scenario based on the principle that the resistance is much smaller than the reactance; Based on the law of large numbers, the random error term in the identification error mapping relationship formula of the real scenario and the simulation scenario is divided; Based on the inherent error short-time invariance principle, the inherent error term in the identification error mapping relationship formula of the real scenario and the simulation scenario is divided; S5, calculating the corrected identification parameter based on the simplified identification parameter calculation formula of the real scenario; S6, calculating the distribution center of the corrected identification parameter by selecting a corresponding distribution center calculation method according to the distribution form of the measurement error, and taking the distribution center as the identification result; Wherein: When the distribution form is uniform distribution, the arithmetic mean method is used to calculate the distribution center; When the distribution form is multimodal distribution, the GMM-EM weighted average method is used to calculate the distribution center; When the distribution form is unimodal distribution and symmetric distribution, the 20% truncated mean method is used to calculate the distribution center; When the distribution form is unimodal distribution and skewed distribution, the Huber estimation method is used to calculate the distribution center.

2. The line parameter identification method based on non-intrusive PMU prior error analysis and correction according to claim 1, wherein the identification error calculation formula of the simulation scenario is as follows: In S3, the resistance true value, the reactance true value, and the susceptance true value of the simulation scene are recorded as R ref1 , X ref1 , B ref1 ; 3. The line parameter identification method based on non-intrusive PMU prior error analysis and correction according to claim 2, wherein in S4, the identification error calculation formula of the real scenario after simplification is as follows: ； ； ； In the formula, , , respectively represent the resistance identification error, the reactance identification error, and the susceptance identification error of the simulation scene at the t i time point. , , respectively represent the resistance identification parameter, the reactance identification parameter, and the susceptance identification parameter after adding the measurement error at the t i time point.

4. The line parameter identification method based on non-intrusive PMU prior error analysis and correction according to claim 3, wherein in step S5, the corrected reactance identification parameter is as follows: The corrected susceptance identification parameter is as follows: ； ； ； In the formula, , , respectively represent the resistance recognition error, the reactance recognition error, and the susceptance recognition error of the real scene at the t i time point; , respectively represent the phase angle difference of the voltage and the phase angle difference of the current at both ends of the line, f (·) represents the distribution center calculation formula; t i represent the time point, and the subscript 1 and the subscript 2 respectively represent the simulation scene and the real scene. The corrected resistance identification parameter is as follows:

5. The line parameter identification method based on non-intrusive PMU prior error analysis and correction according to claim 3, wherein in S4, the calculation method of the distribution center in the identification error calculation formula of the real scenario after simplification is as follows: ； According to the identification error distribution form of the simulation scenario, a corresponding distribution center calculation method is selected to calculate the identification error of the simulation scenario; ； Wherein: ； In the formula, , , respectively represent the corrected reactance identification parameter, the susceptance identification parameter, and the resistance identification parameter; , , respectively represent the uncorrected reactance identification parameter, the susceptance identification parameter, and the resistance identification parameter. When the distribution form is uniform distribution, the arithmetic mean method is used to calculate the distribution center; When the distribution form is multimodal distribution, the GMM-EM weighted average method is used to calculate the distribution center; ​ ​ ​ ​ When the distribution form is unimodal distribution and symmetric distribution, the distribution center is calculated by using 20% truncated mean method; When the distribution form is unimodal distribution and skew distribution, the distribution center is calculated by using Huber estimation method.

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