An EM-Kalman method-based PT error online solving method, device and storage medium

Abstract

The application discloses a PT error online solving method and device based on an EM-Kalman method and a storage medium. First, secondary voltage data of the same-phase voltage mutual inductors connected to the same bus at multiple time points is collected, and amplitude, phase and other information is analyzed to construct an error parameter estimation model containing a basic physical model, a state transition equation and an observation equation. Model parameter initialization is completed through a truncated mean method and a robust statistic MAD, and then EM algorithm iteration optimization is performed. Kalman smoothing estimation of standard voltage and maximum likelihood function estimation of overall error offset parameters are alternately executed until iteration convergence, so that precise solution of the ratio difference and the angle difference in the mutual inductor error parameters is realized. The application does not need to rely on external standard sources, eliminates the influence of preset dynamic parameters through parameter self-learning, separates the cyclic dependence of standard values and error parameters, and improves the accuracy and reliability of PT error calculation in the online monitoring scene.

Description

Technical Field

[0001] This invention relates to the field of power measurement technology, specifically to an online method, device, and storage medium for solving PT errors based on the EM-Kalman method. Background Technology

[0002] Voltage transformers (PTs) are critical measurement devices in power systems, and their measurement accuracy directly impacts the metering accuracy, control reliability, and operational safety of the power system. In online PT monitoring, accurately obtaining the ratio difference and phase difference values—the error parameters of the transformer—is crucial for evaluating PT performance. However, traditional PT error detection methods rely on high-precision standard transformers to provide standard values. In online scenarios, these standard values ​​are difficult to calculate in real time, making it impossible to directly calculate PT errors. This has become a key bottleneck restricting the widespread adoption of online PT monitoring technology.

[0003] Traditional PT error detection primarily employs offline calibration. This method requires disassembling the PT under test from the system and transporting it to a laboratory or a temporary calibration platform set up on-site. A high-precision standard current transformer (with an error class typically of 0.01% or higher) provides a standard voltage signal, and the output difference between the PT under test and the standard current transformer is compared to calculate the error parameters. While this method can achieve high calibration accuracy, typically reaching 0.02%, it has significant limitations in practice:

[0004] 1. Offline detection requires interrupting the normal operation of the PT. For key scenarios such as hub substations and new energy grid-connected power stations, the shutdown of the PT may lead to metering interruption and protection mismatch in the corresponding area, which does not meet the core requirement of "uninterrupted power supply" of the power system.

[0005] 2. A single test takes 2-4 hours, resulting in a long offline testing cycle. The cost of renting standard instrument transformers and setting up on-site exceeds 10,000 yuan per test, making the actual usage cost high. It is difficult to achieve high-frequency condition assessment of a large number of PTs and cannot detect error drift caused by factors such as insulation aging, core magnetic saturation, and winding heating during PT operation in a timely manner. Studies have shown that in long-term operation of PTs for 5 years or more, the annual average drift of the ratio difference can reach 0.05% to 0.1%, and the annual average drift of the angle difference can reach 0.001 to 0.002 rad. If not monitored and corrected in time, it will gradually exceed the error limits specified in the national standard "GB1207-2020 Voltage Transformers", that is, the allowable error of the ratio difference of a 0.2 class PT is ±0.2%, and the allowable error of the angle difference is ±10', which can easily lead to measurement or control risks.

[0006] In existing technologies, some methods estimate errors based on the correlation of measurement data from multiple PTs on the same bus. However, since the dynamic offset parameters of PT errors (such as the rate of error change) are unknown in practical applications, the accuracy of the dynamic model constructed by traditional Kalman filtering methods is limited. Deviations between preset parameters and actual parameters can lead to distorted error estimation results, making it difficult to meet the requirements of high-precision online monitoring. Therefore, there is an urgent need for an online PT error solution method that does not rely on external standard sources and can adaptively optimize model parameters. Summary of the Invention

[0007] The purpose of this invention is to provide an online solution method, device, and storage medium for PT error based on the EM-Kalman method. In the process of online monitoring of voltage transformers (PTs) in power systems, this invention solves the problem that the standard values ​​used for transformer error calculation are difficult to measure, and that the errors of each transformer are difficult to calculate directly due to the difficulty in measuring the standard values.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An online method for solving PT error based on the EM-Kalman method includes the following steps:

[0010] Step S1: Set multiple time points, collect secondary voltage data of multiple in-phase voltage transformers with primary terminals connected to the same bus at each time point, and construct an initial dataset;

[0011] Step S2: Based on the initial dataset obtained in Step S1, construct a basic physical model, and then obtain the state transition equation and observation equation based on the basic physical model;

[0012] Step S3: Based on the initial dataset obtained in step S1, determine the initial estimated values ​​of the basic parameters, wherein the basic parameters include the standard voltage and the overall error offset parameter;

[0013] Step S4: Using the initial estimate of the standard voltage obtained in step S3 as the initial value, estimate the standard voltage using the Kalman smoothing method;

[0014] Step S5: Using the initial estimate of the overall error offset parameter obtained in step S3 as the initial value, estimate the overall error offset parameter using the maximum likelihood function;

[0015] Step S6: Alternately execute steps S4 and S5, iteratively update the standard voltage and overall error offset parameters until the preset termination condition is met, then stop the iteration and output the final overall error offset parameters, which are the transformer error parameters to be solved.

[0016] Furthermore, in step S2, the fundamental physical model is:

[0017] ;

[0018] in, Represented as the first The voltage transformer is in the first Secondary voltage data collected at each time point Represented as the first The ratio difference of each voltage transformer Represented as the first The angle difference value of each voltage transformer This is represented as the overall error offset parameter. This indicates that for each voltage transformer at the 1st The standard value of the secondary voltage at each moment. Represented as the first The voltage transformer is in the first The measurement noise at each time point conforms to a Gaussian distribution. and , .

[0019] Further, in step S2, the state transition equation includes:

[0020] (1) The true voltage state transition equation is as follows: ;

[0021] (2) Predict the covariance state transition equation, specifically: ;

[0022] in, It is expressed as the correlation coefficient between two adjacent measurements. This represents process noise that follows a zero-mean Gaussian distribution, i.e. Q represents the process noise covariance. Represented as the first The state covariance at each time step.

[0023] Further, in step S2, the observation equation is:

[0024] ;

[0025] in, Represented as a complex observation vector, , Represented as the overall error offset parameter vector of the mutual inductor group. , Represented as an observation noise vector, and each element satisfies , Represented as the first The observation noise variance of a voltage transformer.

[0026] Furthermore, in step S3, the process for determining the initial estimate of the basic parameters includes the following steps:

[0027] Step S3.1: Based on the initial dataset obtained in step S1, take the voltage amplitude and voltage phase of all in-phase voltage transformers measured at any time, sort all voltage amplitudes in ascending order to obtain a voltage amplitude sequence, and then sort all voltage phases according to the voltage transformer arrangement order corresponding to the voltage amplitude sequence to obtain a voltage phase sequence.

[0028] Step S3.2: Based on the voltage amplitude sequence and voltage phase sequence obtained in step S3.1, calculate and obtain the initial standard voltage amplitude using the truncated averaging method. Initial standard voltage phase ;

[0029] Step S3.3: Based on the initial standard voltage amplitude obtained in step S3.1, calculate and obtain the initial estimated value of the standard voltage. The calculation formula is as follows: ,in, Represented as the first The voltage transformer is in the first Voltage phase at each moment, This is represented as the counting index of the voltage transformer. Represented as the count index at time point;

[0030] Step S3.4: First, calculate the ratio difference and angle difference of all voltage transformers at each time step. Then, calculate and obtain the average value of all ratio differences and the average value of all angle differences at each time step.

[0031] Step S3.5: Using the average of all ratio differences and the average of all angle differences of all in-phase voltage transformers at each moment as the initial error estimation standard, calculate and obtain the initial estimate of the overall error offset parameter. The calculation formula is as follows: ,in, Represented as the first The average of all ratio differences of the voltage transformers at each time step. Represented as the first The average of all angle differences of the voltage transformers at each moment.

[0032] Furthermore, in step S4, the estimation process of the standard voltage based on the Kalman smoothing method specifically includes the following steps:

[0033] Step S4.1, Forward Kalman Filtering:

[0034] Step S4.1.1: Based on the first The estimated standard voltage at time n predicts the first... Standard voltage and state covariance at each moment;

[0035] Step S4.1.2: Construct the observation matrix and set its initial values. Calculate and obtain the Kalman gain based on the observation matrix.

[0036] Step S4.1.3: Obtain the standard voltage and state covariance under the updated state through Kalman gain;

[0037] Step S4.2, Backward Kalman Smoothing:

[0038] Step S4.2.1: Iterate backward from t = T to t = 1 to construct the Kalman backward gain, and obtain the standard voltage and state covariance based on smooth state estimation through the Kalman backward gain.

[0039] Furthermore, in step S5, the estimation process for the overall error offset parameter based on maximizing the likelihood function specifically includes the following steps:

[0040] Step S5.1: Construct the likelihood function and the log-likelihood function;

[0041] Step S5.2: Solve for the maximum likelihood estimate of the overall error offset parameter to obtain the objective.

[0042] Step S5.3: Perform nonlinear optimization on the solution objective obtained in step S5.2 to obtain the overall error offset parameters in the updated state.

[0043] Furthermore, in step S6, the preset termination condition includes:

[0044] (1) The change in the overall error offset parameter estimate between the two consecutive times is less than the preset convergence threshold;

[0045] (2) Reach the preset maximum number of iterations.

[0046] Furthermore, the convergence threshold is set to ~ The maximum number of iterations is set to 400.

[0047] The present invention also provides an electronic device, the electronic device including a memory and a processor, the memory being used to store program code and to transmit the program code to the processor, the processor being used to execute the online PT error solving method based on the EM-Kalman method according to the instructions in the program code.

[0048] The present invention also provides a computer-readable storage medium for storing program code for executing the online PT error calculation method based on the EM-Kalman method.

[0049] The beneficial effects of this invention are:

[0050] 1. For multiple in-phase voltage transformers connected to the same busbar, their error calculation standard values ​​are consistent. Based on this characteristic, this method utilizes the correlation of measurement data from multiple in-phase voltage transformers to achieve joint estimation of standard values ​​and error parameters. It constructs an error parameter estimation model related to the in-phase voltage transformers, which includes a basic physical model, state transition equations, and observation equations. This provides the necessary initial parameters for the subsequent Kalman smoothing method and expectation-maximization algorithm. Through the estimation of latent variables and dynamic model constraints, it can roughly estimate the ratio difference and angle difference even when the actual voltage is unknown. This solution process does not require external standard sources or interruption of the normal operation of voltage transformers, meeting the core requirement of uninterrupted power supply in power systems. It effectively solves the problems of difficulty in obtaining standard values ​​in online scenarios, long offline detection cycles, and high detection costs of standard transformers.

[0051] 2. This method can achieve parameter self-learning function. It introduces the EM algorithm, which is a combination of expectation maximization algorithm and Kalman filtering, to separate the cyclic dependence between standard value and error parameter. It eliminates the influence of preset dynamic parameters through iterative optimization, improves the adaptability of the basic physical model to actual working conditions, stably realizes high-frequency state assessment of a large number of voltage transformers, and timely detects error drift caused by factors such as insulation aging, core magnetic saturation, and winding heating during the operation of voltage transformers.

[0052] 3. By combining Kalman smoothing technology and making full use of the correlation of time series data, and by using robust methods such as truncated averaging and robust statistics MAD to handle abnormal data and noise, the estimation accuracy of instrument transformer error parameters is effectively improved, significantly enhancing the accuracy and reliability of error estimation. This avoids the risk of metering interruption or erroneous control caused by the distortion of error estimation results, meets the error limits specified in national standards, and effectively meets the high-precision online monitoring requirements of substations. Attached Figure Description

[0053] Figure 1 This is a flowchart of an online PT error calculation method based on the EM-Kalman method according to the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. Example 1

[0055] like Figure 1 As shown, an online method for solving PT error based on the EM-Kalman method includes the following steps:

[0056] Step S1: Set multiple time points, collect secondary voltage data of multiple in-phase voltage transformers with primary terminals connected to the same bus at each time point, and construct an initial dataset;

[0057] Step S2: Based on the initial dataset obtained in Step S1, construct a basic physical model, and then obtain the state transition equation and observation equation based on the basic physical model;

[0058] Step S3: Based on the initial dataset obtained in step S1, determine the initial estimated values ​​of the basic parameters, wherein the basic parameters include the standard voltage and the overall error offset parameter;

[0059] Step S4: Using the initial estimate of the standard voltage obtained in step S3 as the initial value, estimate the standard voltage using the Kalman smoothing method;

[0060] Step S5: Using the initial estimate of the overall error offset parameter obtained in step S3 as the initial value, estimate the overall error offset parameter using the maximum likelihood function;

[0061] Step S6: Alternately execute steps S4 and S5, iteratively update the standard voltage and overall error offset parameters until the preset termination condition is met, then stop the iteration and output the final overall error offset parameters, which are the transformer error parameters to be solved.

[0062] Furthermore, in step S2, the fundamental physical model is:

[0063] ;

[0064] in, Represented as the first The voltage transformer is in the first Secondary voltage data collected at each time point Represented as the first The ratio difference of each voltage transformer Represented as the first The angle difference value of each voltage transformer This is represented as the overall error offset parameter. This indicates that for each voltage transformer at the 1st The standard value of the secondary voltage at each moment. Represented as the first The voltage transformer is in the first The measurement noise at each time point conforms to a Gaussian distribution. and , .

[0065] Further, in step S2, the state transition equation includes:

[0066] (1) The true voltage state transition equation is as follows: ;

[0067] (2) Predict the covariance state transition equation, specifically: ;

[0068] in, It is expressed as the correlation coefficient between two adjacent measurements. This represents process noise that follows a zero-mean Gaussian distribution, i.e. Q represents the process noise covariance. Represented as the first The state covariance at each time step.

[0069] Further, in step S2, the observation equation is:

[0070] ;

[0071] in, Represented as a complex observation vector, , Represented as the overall error offset parameter vector of the mutual inductor group. , Represented as an observation noise vector, and each element satisfies , Represented as the first The observation noise variance of a voltage transformer.

[0072] It is important to understand that the purpose of this method is to address the problem of difficulty in calculating the standard values ​​used for voltage transformer (PT) error calculation during online monitoring of voltage transformers (PTs) in power systems. This problem stems from the difficulty in directly calculating the errors of each transformer due to the difficulty in calculating the standard values. Based on the introduction and use of the EM-Kalman method, which combines the Expectation-Maximization Algorithm (EM Algorithm) and Kalman Filter, the method can quickly, effectively and stably achieve online detection and calculation of voltage transformers (PTs).

[0073] It should be noted that for multiple voltage transformers connected to the same busbar, the standard values ​​for error calculation are consistent. Based on this characteristic, and using the Kalman smoothing method, an error parameter estimation model for voltage transformers can be constructed. By estimating the latent variables of the variables to be solved and constraining the dynamic model, the ratio difference and angle difference can be roughly estimated even when the actual voltage is unknown.

[0074] It should be noted that the accuracy of the dynamic model construction in the Kalman smoothing method directly affects the accuracy of the final estimation result. However, dynamic parameters such as the error offset rate are unknown in reality, leading to distortion in the estimation result due to the deviation between the preset value and the actual value. To further improve the accuracy of the calculation results, this method introduces an expectation-maximization approach, which can separate the cyclic dependence between the standard value and the error parameters. Furthermore, it eliminates the influence of the preset error dynamic parameters through parameter self-learning, achieving a joint optimal estimation. Example 2

[0075] In step S3, the process for determining the initial estimates of the basic parameters includes the following steps:

[0076] Step S3.1: Based on the initial dataset obtained in Step S1, take the voltage amplitude and voltage phase of all in-phase voltage transformers measured at time t, sort all voltage amplitudes in ascending order, and obtain the voltage amplitude sequence, denoted as . Then, all voltage phases are sorted according to the voltage transformer arrangement order corresponding to the voltage amplitude sequence to obtain the voltage phase sequence, denoted as... ,in, This is expressed as the number of voltage transformers;

[0077] Step S3.2: Based on the voltage amplitude sequence and voltage phase sequence obtained in step S3.1, the truncated averaging method is used to set the truncation ratio. The actual number of single-sided truncated tails The initial standard voltage amplitude and initial standard voltage phase are calculated and obtained, wherein the formula for calculating the initial standard voltage amplitude is: The formula for calculating the initial standard voltage phase is as follows: ;

[0078] Step S3.3: Based on the initial standard voltage amplitude obtained in step S3.1, calculate and obtain the initial estimated value of the standard voltage. The calculation formula is as follows: ,in, Represented as the first The voltage transformer is in the first Voltage phase at each moment, This is represented as the counting index of the voltage transformer. Represented as the count index at time point;

[0079] Step S3.4: First, calculate the ratio difference and angle difference of all voltage transformers at each time step. Then, calculate and obtain the average value of all ratio differences and the average value of all angle differences at each time step. The formula for calculating the ratio difference is as follows: The formula for calculating the average of all ratio differences at each time point is: The formula for calculating the angle difference is: The formula for calculating the average of all angle differences at each moment is: ;

[0080] Step S3.5: Using the average of all ratio differences and the average of all angle differences of all in-phase voltage transformers at each moment as the initial error estimation standard, calculate and obtain the initial estimate of the overall error offset parameter. The calculation formula is as follows: ,in, Represented as the first The average of all ratio differences of the voltage transformers at each time step. Represented as the first The average of all angle differences of the voltage transformers at each moment. Example 3

[0081] In step S4, the estimation process for the standard voltage based on the Kalman smoothing method specifically includes the following steps:

[0082] Step S4.1, Forward Kalman Filtering:

[0083] Step S4.1.1: Based on the first The estimated standard voltage at time n predicts the first... Standard voltage at any given moment: and state covariance: ,in, Represented as an iterative index, ;

[0084] Step S4.1.2: Construct the observation matrix The initial value of the observation matrix is ​​set to Based on the observation matrix, the Kalman gain is calculated and obtained: ,in, This is represented as the conjugate transpose of the observation matrix, used to ensure the positive definiteness of the covariance matrix. This is represented by adding a small number of diagonal matrices during matrix inversion to prevent singular matrices. , Represented as an identity matrix;

[0085] Step S4.1.3: Obtain the standard voltage and state covariance in the updated state through Kalman gain. The standard voltage in the updated state is: The state covariance in the updated state is: ,in, Represented as observation residuals, the weight of the residuals on state corrections is controlled using Kalman gain;

[0086] Step S4.2, Backward Kalman Smoothing:

[0087] Step S4.2.1: Iterate backward from t = T to t = 1 to construct the Kalman backward gain: The standard voltage and state covariance based on smoothed state estimation are obtained through Kalman backward gain. The standard voltage based on smoothed state estimation is: The state covariance based on smooth state estimation is: .

[0088] It should be noted that before the estimation of the standard voltage described in this embodiment begins, the initial values ​​required for the process noise covariance, state covariance, and correlation coefficient between two adjacent measurement data are determined, specifically including the following steps:

[0089] Step S4.0.1: Based on the obtained initial standard voltage amplitude and considering the fluctuation of state variables, the initial value of the process noise covariance is approximately calculated as follows:

[0090] ,

[0091] in, It is expressed as the overall average value of the voltage amplitude. , This represents the maximum fluctuation of the voltage amplitude. , This is expressed as the maximum value of the voltage phase fluctuation. ;

[0092] Step S4.0.2: Since the state covariance reflects the uncertainty of the estimator, and the initial estimate of the true voltage value is relatively unclear, a large redundancy is maintained. Therefore, the initial value of the state covariance is set as follows: ;

[0093] Step S4.0.3: Since the voltage amplitude fluctuation in a large power grid is generally within 2%, and stable phase relative values ​​can be obtained by windowing during FFT calculation, the correlation coefficient between two adjacent measurement data is relatively stable, and its initial value can be directly set as follows: . Example 4

[0094] In step S5, the estimation process for the overall error offset parameter based on maximizing the likelihood function specifically includes the following steps:

[0095] Step S5.1: Since each voltage transformer is independent, assume the measurement noise... The mean is 0 and the variance is 0. The Gaussian distribution, i.e. Then the likelihood function is: The log-likelihood function is: ;

[0096] Step S5.2: Since directly solving for the maximum estimate of the likelihood function is difficult, the problem can be equivalently transformed into minimizing the weighted sum of squared errors, with the weights set to 1 / The objective is then obtained as: ;

[0097] Step S5.3: For the nonlinear optimization problem of the objective obtained in step S5.2, the above minimum value problem can be transformed into: Let ,turn up , making closest The weighted average of the expression As a function, for complex conjugate Perform differentiation and solve for the case where the derivative is 0. The value of is then used to obtain the overall error offset parameter in the updated state: ,in, The standard voltage is represented by the Kalman smoothing method. Represented as the first The observation noise variance of a voltage transformer It is represented as complex conjugate.

[0098] It should be noted that before estimating the overall error offset parameter as described in this embodiment, the initial values ​​for the observation noise variance and observation noise covariance matrix are determined, specifically including the following steps:

[0099] Step S5.0.1: Calculate the initial residual of each voltage transformer. The calculation formula is as follows: ,in, Represented as the first The secondary voltage data collected by each voltage transformer at an initial time, where the initial time refers to a time other than the multiple times set in step S1. This represents the initial estimate of the overall error offset parameter. The value is assigned to the initial estimate of the obtained standard voltage;

[0100] Step S5.0.2: Estimate the noise standard deviation using the robust statistic MAD: The initial value of the observation noise variance is: The initial values ​​of the observation noise covariance matrix are: ,in, This represents the median of all data. Example 5

[0101] In step S6, the preset termination condition includes:

[0102] (1) The change in the overall error offset parameter estimate between the two consecutive times is less than the preset convergence threshold;

[0103] (2) Reach the preset maximum number of iterations.

[0104] Furthermore, the convergence threshold is set to ~ The maximum number of iterations is set to 400.

[0105] It should be noted that the calculation process for the change in the overall error offset parameter estimate between the two iterations includes the following steps:

[0106] Step S6.1: Calculation formula based on the estimated value of the overall error offset parameter: ,Will Decomposed into ratio difference sum of angle difference ;

[0107] Step S6.2: Calculate the estimated change in the overall error offset parameter between the two steps: .

[0108] The present invention also provides an electronic device, the electronic device including a memory and a processor, the memory being used to store program code and to transmit the program code to the processor, the processor being used to execute the online PT error solving method based on the EM-Kalman method according to the instructions in the program code.

[0109] The present invention also provides a computer-readable storage medium for storing program code for executing the online PT error calculation method based on the EM-Kalman method.

[0110] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0111] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0112] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, embodiments of the present invention can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0117] It should be noted that in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0118] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. An EM-Kalman method-based PT error online solution method, characterized in that, The method comprises the following steps: Step S1: setting multiple time points, collecting secondary voltage data of multiple primary side voltage transformers connected to the same bus at each time point, and constructing an initial data set; Step S2: constructing a basic physical model according to the initial data set obtained in step S1, and then obtaining a state transition equation and an observation equation based on the basic physical model; Step S3: determining a starting estimation value of a basic parameter according to the initial data set obtained in step S1, wherein the basic parameter comprises a standard voltage and an overall error offset parameter; Step S4: taking the starting estimation value of the standard voltage obtained in step S3 as an initial value, and estimating the standard voltage by using a Kalman smoothing method; Step S5: taking the starting estimation value of the overall error offset parameter obtained in step S3 as an initial value, and estimating the overall error offset parameter by using a maximum likelihood function; Step S6: alternately performing step S4 and step S5, iteratively updating the standard voltage and the overall error offset parameter, stopping iteration when a preset termination condition is met, and outputting the finally obtained overall error offset parameter as the required transformer error parameter; In the step S2, the basic physical model is: ； wherein, represents the secondary voltage data collected by the i-th voltage transformer at the j-th time point, represents the secondary voltage data collected by the i-th voltage transformer at the j-th time point, represents the ratio difference value of the i-th voltage transformer, represents the ratio difference value of the i-th voltage transformer, represents the angle difference value of the i-th voltage transformer, represents the angle difference value of the i-th voltage transformer, represents the overall error offset parameter, represents the secondary voltage standard value of each voltage transformer at the j-th time point, represents the measurement noise of the i-th voltage transformer at the j-th time point and conforms to Gaussian distribution, represents the measurement noise of the i-th voltage transformer at the j-th time point and conforms to Gaussian distribution, represents the measurement noise of the i-th voltage transformer at the j-th time point and conforms to Gaussian distribution, represents the measurement noise of the i-th voltage transformer at the j-th time point and conforms to Gaussian distribution, represents the measurement noise of the i-th voltage transformer at the j-th time point and conforms to Gaussian distribution, and , ; In the step S3, the starting estimation value determination process of the basic parameter comprises the following steps: Step S3.1: according to the initial data set obtained in step S1, taking the voltage amplitude and the voltage phase of all the voltage transformers measured at any time point, sorting all the voltage amplitudes in ascending order to obtain a voltage amplitude sequence, and then sorting all the voltage phases in the order corresponding to the voltage transformer arrangement order of the voltage amplitude sequence to obtain a voltage phase sequence; Step S3.2: According to the voltage amplitude sequence and the voltage phase sequence obtained in step S3.1, the initial standard voltage amplitude is calculated and obtained by the truncated mean method , the initial standard voltage phase ; Step S3.3: Based on the initial standard voltage amplitude obtained in step S3.2, calculate and obtain the initial estimated value of the standard voltage. The calculation formula is as follows: ,in, Represented as the first The voltage transformer is in the first Voltage phase at each moment, This is represented as the counting index of the voltage transformer. Represented as the count index at time point; Step S3.4: first, calculating the ratio difference value and the angle difference value of all the voltage transformers at each time point, and then calculating and obtaining the average value of all the ratio difference values at each time point and the average value of all the angle difference values at each time point; Step S3.5: Take the average of all the ratio difference values and the average of all the angle difference values of all the voltage transformers at each time as the initial error estimation criterion, calculate and obtain the initial estimated value of the overall error offset parameter, the calculation formula is: Wherein, represents the average of all the ratio difference values of the first voltage transformer at each time, represents the average of all the angle difference values of the first voltage transformer at each time.

2. The EM-Kalman method based PT error online solution method according to claim 1, characterized in that, In the step S2, the state transition equation comprises: (1) The voltage true value state transition equation is specifically as follows: ; (2) The prediction covariance state transition equation is specifically as follows: ; wherein, is a correlation coefficient of the data of the two adjacent measurements, is a process noise satisfying a 0-mean Gaussian distribution, i.e. Q is a process noise covariance, is a state covariance at the th time point.

3. The EM-Kalman method based PT error on-line solution method according to claim 1, characterized in that, In the step S2, the observation equation is: ； wherein, is represented as a complex observation vector, , is represented as a whole error offset parameter vector of the transformer set, , is represented as an observation noise vector and each element satisfies , is represented as an observation noise variance of the th voltage transformer.

4. The EM-Kalman method based PT error online solution method according to claim 1 or 2, characterized in that, In the step S4, the estimation process of the standard voltage based on the Kalman smoothing method comprises the following steps: Step S4.1, forward Kalman filtering: Step S4.1.1: predicting the standard voltage, state covariance at the second time instant based on the estimated standard voltage at the first time instant Step S4.1.2: predicting the standard voltage, state covariance at the second time instant based on the estimated standard voltage at the first time instant​ Step S4.1.2: constructing an observation matrix and setting an initial value for the observation matrix, calculating and obtaining a Kalman gain according to the observation matrix; Step S4.1.3: obtaining the standard voltage and the state covariance in the updated state through the Kalman gain; Step S4.2, backward Kalman smoothing: Step S4.2.1: iteratively constructing a Kalman backward gain from t = T to t = 1, and obtaining the standard voltage and the state covariance estimated based on the smoothing state through the Kalman backward gain.

5. The EM-Kalman method based PT error online solution method according to claim 1 or 3, characterized in that, In the step S5, the estimation process of the overall error offset parameter based on the maximum likelihood function comprises the following steps: Step S5.1: constructing a likelihood function and a log-likelihood function; Step S5.2: solving the maximum likelihood estimation of the overall error offset parameter to obtain a solution target; Step S5.3: Nonlinear optimization is performed on the solution target obtained in step S5.2 to obtain the overall error offset parameter in the updated state.

6. The EM-Kalman method based PT error on-line solution method according to claim 1, characterized in that, In the step S6, the preset termination condition includes: (1) the variation of the overall error offset parameter estimation between the previous and the current time is less than a preset convergence threshold; (2) the preset maximum iteration number is reached.

7. The EM-Kalman method based PT error online solution method according to claim 6, characterized in that, The convergence threshold is set to ~ The maximum number of iterations is set to 400.

8. An electronic device, comprising: The electronic device includes a memory and a processor, the memory is used to store program codes and transmit the program codes to the processor, and the processor is used to execute the PT error online solving method based on the EM-Kalman method according to the instructions in the program codes.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium is used to store program codes, and the program codes are used to execute the PT error online solving method based on the EM-Kalman method.

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