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

Abstract

The invention discloses an EM-Kalman method-based PT error online solving method and device and a storage medium, and the method comprises the steps: firstly collecting the secondary voltage data, measured at a plurality of moments, of a plurality of in-phase voltage transformers of which the primary ends are connected with the same bus, and analyzing the amplitude, phase and other information; an error parameter estimation model comprising a basic physical model, a state transition equation and an observation equation is constructed, model parameter initialization is completed through a truncation average method, robust statistics (MAD) and the like, iterative optimization is performed through an EM algorithm, Kalman smoothing is alternately executed to estimate standard voltage and a maximum likelihood function is alternately executed to estimate overall error offset parameters until iteration convergence is performed, and the overall error offset parameters are estimated. And accurate solving of the ratio difference value and the angle difference value in the error parameters of the mutual inductor is realized. The method does not need to depend on an external standard source, eliminates the influence of the preset dynamic parameter through parameter self-learning, separates the cyclic dependence of the standard value and the error parameter, and improves the accuracy and reliability of PT error calculation in an online monitoring scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric power measurement, in particular to a PT error online solving method based on an EM-Kalman method, a device and a storage medium. BACKGROUND

[0002] A voltage transformer, referred to as PT, as a key measurement device in a power system, the measurement accuracy of the PT directly affects the measurement accuracy, control reliability and operation safety of the power system. In the online monitoring process of the PT, the accurate acquisition of the ratio error value and the angle error value in the error parameters of the transformer is the core of evaluating the performance of the PT. However, the traditional PT error detection method needs to rely on a high-precision standard transformer to provide a standard value, and it is difficult to calculate the standard value in real time in an online scene, which leads to the fact that the PT error cannot be directly calculated, which becomes a key bottleneck restricting the popularization of the PT online monitoring technology.

[0003] The traditional PT error detection mainly adopts an offline calibration method, which needs to stop and disassemble the PT to be detected from the system, send it to a laboratory or temporarily build a calibration platform on site, provide a standard voltage signal by a high-precision standard transformer (the error level is usually 0.01 level and above), compare the output difference between the PT to be detected and the standard transformer, and then calculate the error parameters. Although this method can achieve high calibration accuracy, usually up to 0.02%, it has significant limitations in practice: 1. Offline detection needs to interrupt the normal operation of the PT, and for key scenes such as hub substations and new energy grid-connected power stations, the shutdown of the PT may lead to the interruption of measurement and the mismatch of protection in the corresponding area, which does not meet the core demand of "uninterrupted power supply" of the power system; 2. Single detection takes 2-4 hours, the offline detection period is long, the standard transformer rental and on-site construction cost is more than 10,000 yuan per time, the actual use cost is high, it is difficult to realize high-frequency state evaluation of a large number of PTs, and it is impossible to timely discover the error drift of the PT in the running process due to factors such as insulation aging, core magnetic saturation and winding heating; research shows that the annual drift of the ratio error value of the PT in the long-term operation of 5 years and above can reach 0.05%-0.1%, and the annual drift of the angle error value can reach 0.001-0.002 rad, if not timely monitored and corrected, it will gradually exceed the error limit value specified in the national standard "GB1207-2020 Voltage Transformer", i.e. the ratio error of 0.2 level PT is ±0.2%, and the angle error is ±10', which is easy to cause measurement or control risks.

[0004] 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

[0005] 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.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: An online method for solving PT error based on the EM-Kalman method includes the following steps: 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; 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; 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; 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; 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; 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.

[0007] Furthermore, in step S2, the fundamental physical model is: ; in, Represented as the first The voltage transformer is in the first the secondary voltage data collected at the kth time, the ratio error value of the kth voltage transformer, the angle error value of the kth voltage transformer, the overall error offset parameter of the voltage transformer group, the secondary voltage standard value of the kth voltage transformer at the kth time, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, the measurement noise of the kth voltage transformer at the kth time and conforming to Gaussian distribution, and , .

[0008] Further, in the step S2, the state transition equation comprises: (1) a voltage true value state transition equation, specifically: ; (2) a predicted covariance state transition equation, specifically: ; wherein, represents a correlation coefficient of adjacent two measurement data, represents a process noise satisfying 0 mean value Gaussian distribution, i.e. , Q represents a process noise covariance, represents a state covariance at the kth time.

[0009] Further, in the step S2, the observation equation is: ; wherein, represents a complex observation vector, , represents a voltage transformer group overall error offset parameter vector, , represents an observation noise vector and each element satisfies , represents an observation noise variance of the kth voltage transformer.

[0010] Further, in the step S3, the starting estimation value determination process of the basic parameter comprises the following steps: ​​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. 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 ; 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; 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. 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.

[0011] Furthermore, in step S4, the estimation process of the standard voltage based on the Kalman smoothing method specifically includes the following steps: Step S4.1, Forward Kalman Filtering: 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; Step S4.1.2: Construct the observation matrix and set its initial values. Calculate and obtain the Kalman gain based on the observation matrix. Step S4.1.3: Obtain the standard voltage and state covariance under the updated state through Kalman gain; Step S4.2, Kalman backward smoothing: Step S4.2.1: from t = T backward iteration to t = 1, construct Kalman backward gain, obtain the standard voltage based on the smoothing state estimation through the Kalman backward gain, and state covariance.

[0012] Further, in the step S5, the estimation process of the overall error offset parameter based on the maximum likelihood function, specifically comprising the following steps: Step S5.1: construct the likelihood function and the log-likelihood function; Step S5.2: solve the maximum likelihood estimation of the overall error offset parameter, obtain the 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.

[0013] Further, in the step S6, the preset termination condition comprises: (1) the change of the overall error offset parameter estimation of the previous and the next time is less than the preset convergence threshold; (2) the preset maximum iteration number is reached.

[0014] Further, the convergence threshold is set to ~ , and the maximum iteration number is set to 400.

[0015] The application also provides an electronic device, which comprises a memory and a processor, the memory is used for storing program code and transmitting the program code to the processor, and the processor is used for executing the PT error online solving method based on the EM-Kalman method according to the instructions in the program code.

[0016] The application also provides a computer readable storage medium, which is used for storing program code, and the program code is used for executing the PT error online solving method based on the EM-Kalman method.

[0017] The application has the following beneficial effects: 1. For multiple voltage transformers of the same phase connected to the same bus, the standard value of error calculation is consistent. The method is based on this characteristic, uses the correlation of the measurement data of multiple voltage transformers of the same phase, realizes joint estimation of the standard value and error parameters, constructs an error parameter estimation model related to the voltage transformer of the same phase and containing the basic physical model, state transition equation and observation equation, provides the required initial parameters for the subsequent Kalman smoothing method and expectation maximization algorithm, and through the hidden variable estimation of the to-be-solved variable and the dynamic model constraint, the estimation of the ratio difference value and the angle difference value can be roughly completed without the real voltage, the solving process does not need to rely on external standard source, and does not need to interrupt the normal operation of the voltage transformer, which meets the uninterrupted power supply requirement of the core demand of the power system, and effectively solves the problems of difficult acquisition of standard value in online scene, long offline detection period and high detection cost of standard transformer.

[0018] 2. The method can realize the parameter self-learning function, introduces the use of EM algorithm, that is, the combination of expectation maximization algorithm and Kalman filtering, separates the circular dependence of the standard value and error parameters, eliminates the influence of the preset dynamic parameters through iterative optimization, improves the adaptability of the basic physical model to the actual working condition, stably realizes the high-frequency state evaluation of a large number of voltage transformers, and timely discovers the error drift of the voltage transformer caused by insulation aging, core magnetic saturation, winding heating and other factors during operation.

[0019] 3. Combined with Kalman smoothing technology, the correlation of time series data is fully utilized, and robust methods such as truncated average method and robust statistic MAD are used to process abnormal data and noise, which effectively improves the estimation accuracy of the transformer error parameters, significantly improves the accuracy and reliability of the error estimation, avoids the risk of measurement interruption or error control risk caused by distorted error estimation results, meets the error limit value specified in the national standard, and effectively meets the high-precision online monitoring demand of the substation. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a flowchart of a PT error online solving method based on an EM-Kalman method. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor belong to the scope of protection of the present application. Embodiment 1

[0022] As Figure 1 As shown, an online method for solving PT error based on the EM-Kalman method includes the following steps: 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; 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; 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; 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; 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; Step S6: Alternately execute steps S4 and S5 to 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.

[0023] Furthermore, in step S2, the fundamental physical model is: ; 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 , .

[0024] Further, in step S2, the state transition equation includes: (1) The true voltage state transition equation is as follows: ; (2) The prediction covariance state transition equation is specifically as follows: wherein, represents the correlation coefficient of adjacent two measurement data, represents the process noise satisfying the 0 mean Gaussian distribution, that is, Q represents the process noise covariance, represents the state covariance at the k th moment.

[0025] Further, in the step S2, the observation equation is as follows: wherein, represents the complex observation vector, , represents the overall error offset parameter vector of the transformer group, , represents the observation noise vector and each element satisfies , represents the observation noise variance of the k th voltage transformer. It should be understood that the purpose of the method is to solve the problems that the standard value for transformer error calculation is difficult to measure and each transformer error is difficult to be directly calculated due to the difficulty in measuring the standard value in the process of online monitoring of the voltage transformer PT in the power system. The method is based on the introduction of the EM-Kalman method, that is, the combination of the expectation maximization algorithm (EM Algorithm) and Kalman filter, to quickly, effectively and stably realize the online detection and calculation processing of the voltage transformer PT.

[0026] It should be noted that the standard value for error calculation of multiple in-phase transformers connected to the same bus is consistent. Based on this feature, the error parameter estimation model of the voltage transformer can be constructed based on the Kalman smoothing method, and through the hidden variable estimation and dynamic model constraint of the to-be-solved variable, the estimation of the ratio difference and the angle difference can be roughly completed under the condition that the real voltage is unknown.

[0027]

[0028] ​​​​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

[0029] In step S3, the process for determining the initial estimates of the basic parameters includes the following steps: 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; 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: ; 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; 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: ; 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

[0030] In step S4, the estimation process for the standard voltage based on the Kalman smoothing method specifically includes the following steps: Step S4.1, Forward Kalman Filtering: 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, ; 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; 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; Step S4.2, Backward Kalman Smoothing: Step S4.2.1: Iterate backward from t = T to t = 1 to construct the Kalman backward gain: , the standard voltage based on the smoothed state estimation is obtained by Kalman backward gain, and the standard voltage based on the smoothed state estimation is: , and the state covariance based on the smoothed state estimation is: .

[0031] It should be noted that before the estimation of the standard voltage in the embodiment, the initial values required for the process noise covariance, the state covariance and the correlation coefficient of adjacent two measurement data are determined, and the specific steps include the following steps: Step S4.0.1: According to the obtained initial standard voltage amplitude, in combination with the fluctuation of the state quantity, the initial value of the process noise covariance is approximately calculated as: , wherein, represents the overall mean value of the voltage amplitude, , represents the maximum fluctuation of the voltage amplitude, , represents the maximum fluctuation of the voltage phase, ; Step S4.0.2: Since the state covariance reflects the uncertainty of the estimated quantity, the initial estimation of the true value of the voltage is not clear, and therefore has a large redundancy, the initial value of the state covariance is set to: ; Step S4.0.3: Since the fluctuation of the voltage amplitude in the large power grid is basically within 2%, and the stable phase relative value can be obtained by windowing when calculating FFT, the correlation coefficient of adjacent two measurement data is relatively stable, and the initial value can be directly set to: . Embodiment 4

[0032] In the step S5, the estimation process of the overall error offset parameter based on the maximum likelihood function, specifically includes the following steps: Step S5.1: Since each voltage transformer is independent, it is assumed that the measurement noise obeys the Gaussian distribution with mean value of 0 and variance of , that is, , the likelihood function is: , and the log-likelihood function is: ; Step S5.2: Since it is difficult to directly solve the maximum estimation of the likelihood function, the problem can be equivalent to minimizing the weighted error square sum, and the weight is set to 1 / , and the solving target is obtained as: ; 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.

[0033] 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: 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; 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 value of the observation noise covariance matrix is: ,in, This represents the median of all data. Example 5

[0034] In step S6, the preset termination condition includes: (1) The change in the overall error offset parameter estimate between the two consecutive times is less than the preset convergence threshold; (2) Reach the preset maximum number of iterations.

[0035] Furthermore, the convergence threshold is set to ~ The maximum number of iterations is set to 400.

[0036] It should be noted that the calculation process of the whole error offset parameter estimation change quantity before and after includes the following steps: Step S6.1: Based on the calculation formula of the whole error offset parameter estimation value: , the whole error offset parameter estimation value is decomposed into a difference value and an angle difference value . ; Step S6.2: Calculate the whole error offset parameter estimation change quantity before and after: .

[0037] The application also provides an electronic device, which comprises a memory and a processor, the memory is used for storing program codes and transmitting the program codes to the processor, and the processor is used for executing the PT error online solving method based on the EM-Kalman method according to the instructions in the program codes.

[0038] The application also provides a computer readable storage medium, which is used for storing program codes, and the program codes are used for executing the PT error online solving method based on the EM-Kalman method.

[0039] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system, device and unit described above can refer to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0040] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same and similar parts between each embodiment can be referred to.

[0041] Those skilled in the art should understand that the embodiments of the application can be provided as a method, device or computer program product. Therefore, the embodiments of the application can be in the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware aspects. Moreover, the embodiments of the application can be in the form of a computer program product 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 codes.

[0042] The embodiments of the present application are described with reference to the flowchart illustrations and / or block diagrams of the methods, terminal devices (systems) and computer program products according to the embodiments of the present application. 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 devices to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal devices, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0043] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal devices to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0044] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal devices, such that a series of operational steps are performed on the computer or other programmable terminal devices to produce a computer implemented process so that the instructions which execute on the computer or other programmable terminal devices provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0045] Although preferred embodiments of the present application have been described, those skilled in the art will be able to make additional modifications and variations to these embodiments without departing from the scope of the present application. Accordingly, the appended claims are intended to encompass all such modifications and variations as falling within the scope of the present application.

[0046] It should be noted that, in the present application, the relational terms such as "first" and "second", and the like, are used solely to distinguish one from another entity or action, without necessarily requiring or implying any actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0047] The foregoing is considered as illustrative only of the principles of the application. Numerous modifications and changes will readily occur to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without departing from the spirit or scope of the application. Accordingly, the scope of the application is intended to be defined only as set forth in the claims.

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.

2. The EM-Kalman method based PT error online solution method according to claim 1, characterized in that, 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 , .

3. The EM-Kalman method based PT error on-line solution method according to claim 2, 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 two adjacent measurement data, 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.

4. The EM-Kalman method based PT error online solution method according to claim 2, 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 bias 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.

5. The EM-Kalman method based PT error on-line solution method according to claim 1, characterized in that, 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 of the voltage transformers corresponding to 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 , the initial standard voltage phase are calculated and obtained by the truncated mean method. Step S3.3: Calculate and obtain the initial estimated value of the standard voltage according to the initial standard voltage amplitude obtained in step S3.1, the calculation formula is: wherein, represents the voltage phase of the first voltage transformer at the first time point, represents the counting index of the voltage transformer, represents the counting index of the 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: taking 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, the initial estimation value of the overall error offset parameter is calculated and obtained, and 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, 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.

6. The EM-Kalman method based PT error online solution method according to claim 3 or 5, 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.

7. The EM-Kalman method based PT error online solution method according to claim 4 or 5, 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.

8. 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.

9. The EM-Kalman method based PT error online solution method according to claim 8, characterized in that, The convergence threshold is set to ~ The maximum number of iterations is set to 400.

10. 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.

11. 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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