Online estimation method and system for ratio error of voltage transformer

Abstract

The invention provides a voltage transformer ratio error online estimation method and system, and the method comprises the steps: constructing a ratio error multi-objective optimization equation based on voltage measurement data collected by a transformer substation; randomly generating an initial population in a solution space of the multi-objective optimization equation, grouping the initial population, solving the multi-objective optimization equation through a coevolution algorithm, and selecting a subset with the maximum information entropy in the population to train an ARIMA model; generating an algorithm guide solution with a stable time sequence through the trained ARIMA model, adding the algorithm guide solution to the current population, and iteratively generating a non-dominated solution in a co-evolution algorithm; and when a preset maximum number of iterations is reached, calculating the ratio error estimation of the voltage transformer based on a non-dominated solution output by the coevolution algorithm. Through the scheme, the ratio error solving efficiency can be improved, and the accuracy of voltage transformer ratio error estimation is guaranteed.

Description

Technical Field

[0001] This invention belongs to the field of power equipment monitoring technology, and in particular relates to an online estimation method and system for voltage transformer ratio error. Background Technology

[0002] Voltage transformers (VTs) are key devices in power systems for achieving electrical isolation and voltage measurement. Their accuracy directly affects core aspects such as energy metering, reactive power and voltage control, and state estimation. Ratio error drift is one of the main types of voltage transformer faults, referring to the relative deviation between the measured voltage and the actual voltage. With the integration of a high proportion of new energy sources and power electronic equipment, the volatility of the power grid's operating state has increased, causing the ratio error of voltage transformers to exhibit significant time-varying characteristics. If it is not identified and compensated for in a timely and accurate manner, it will lead to long-term systematic deviations and instantaneous extreme errors, resulting in accumulated metering deviations, distortion of over-limit control, and safety and economic risks such as protection malfunctions / failures to operate.

[0003] In engineering practice, there are two main approaches to address voltage transformer errors: one is periodic calibration, which involves calibrating and correcting the voltage transformer by disconnecting it under power, injecting a standard source, or comparing it on-site. This type of method usually requires power outage operation. The other is data-driven online estimation, which relies on specific voltage transformer equivalent models or typified parameter priors to construct the estimator. This type of method is sensitive to model assumptions and device type and has poor versatility.

[0004] Currently, optimization-based online ratio error estimation methods are gradually maturing. These methods transform measurement truth estimation into a multi-objective optimization problem, simultaneously minimizing the sum of measurement deviation and time-varying ratio error changes at the objective level. Furthermore, they avoid reliance on specific types or models of voltage transformers in the modeling, significantly improving the versatility and portability of error estimation methods. However, existing optimization algorithms typically process decision variables independently at each time step, easily leading to discontinuous estimation trajectories and insufficient utilization of time-series information. This results in not only low accuracy in error estimation but also low solution efficiency. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide an online estimation method and system for voltage transformer ratio error, which is used to solve the problems of low accuracy and low efficiency in current voltage transformer error assessment.

[0006] In a first aspect of the present invention, a method for online estimation of voltage transformer ratio error is provided, comprising: Based on voltage measurement data collected from substations, a multi-objective optimization equation for ratio error is constructed; An initial population is randomly generated in the solution space of the multi-objective optimization equation. After grouping the initial population, the multi-objective optimization equation is solved by a co-evolutionary algorithm, and the subset with the largest information entropy in the population is selected to train the ARIMA model. The trained ARIMA model generates time-stable algorithm-guided solutions, which are then added to the current population and used in a co-evolutionary algorithm to iteratively generate non-dominated solutions. When the preset maximum number of iterations is reached, the ratio error estimate of the voltage transformer is calculated based on the non-dominated solution output by the co-evolutionary algorithm.

[0007] In a second aspect of the present invention, an online estimation system for voltage transformer ratio error is provided, comprising: The equation construction module is used to construct a multi-objective optimization equation for the ratio error based on voltage measurement data collected from substations. The objective solution module is used to randomly generate an initial population in the solution space of the multi-objective optimization equation, and after grouping the initial population, solve the multi-objective optimization equation through a co-evolutionary algorithm. The subset selection module is used to select the subset with the highest information entropy in the population for training the ARIMA model. The iterative update module is used to generate time-stable algorithm-guided solutions from the trained ARIMA model, add the algorithm-guided solutions to the current population, and iteratively generate non-dominated solutions in the co-evolutionary algorithm. The error estimation module is used to calculate the ratio error of the voltage transformer based on the non-dominated solution output by the co-evolutionary algorithm when the preset maximum number of iterations is reached.

[0008] In a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor executes the computer program to implement the steps of the method as described in the first aspect of the present invention.

[0009] In a fourth aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method provided in the first aspect of the present invention.

[0010] In this embodiment of the invention, a multi-objective optimization equation for the ratio error is constructed, and the multi-objective optimization equation is solved using a co-evolutionary algorithm. The subset with the largest information entropy is selected to train the ARIMA model, generating an algorithm-guided solution with time-stationarity. This solution participates in environmental selection and evolutionary updates together with the current population to obtain the ratio error estimate. This not only improves the solution efficiency of the co-evolutionary algorithm in the minimum tree problem, but also ensures the accuracy of voltage transformer error estimation. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 A flowchart illustrating an online estimation method for voltage transformer ratio error according to an embodiment of the present invention; Figure 2 This is a schematic diagram of an online voltage transformer ratio error estimation system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of an electronic device provided in one embodiment of the present invention. Detailed Implementation

[0013] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below 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.

[0014] It should be understood that the terms "comprising" and other similar expressions in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, or apparatus that includes a series of steps or units and is not limited to the listed steps or units. Furthermore, "first" and "second" are used to distinguish different objects and are not intended to describe a specific order.

[0015] Please see Figure 1 The present invention provides a flowchart illustrating an online estimation method for voltage transformer ratio error, comprising: S101. Based on the voltage measurement data collected from the substation, construct a multi-objective optimization equation for the ratio error; By acquiring measurement data from each voltage transformer within the substation and using the actual voltage of the voltage transformer as the decision variable, a multi-objective optimization equation for the ratio error can be constructed based on the voltage measurement data and the actual voltage characterizing the ratio error.

[0016] For example, voltage measurement data is collected within a substation. , It can be represented as: ; In the formula, Indicates the first Group of voltage transformers, Indicates the first Time of the first One measurement data.

[0017] The corresponding decision variables are: ; In the formula, Indicates the first Time of the first The actual voltage value of the phase.

[0018] The ratio error multi-objective optimization equation is an optimization equation composed of multiple objective functions constructed based on the ratio error.

[0019] The construction of the multi-objective optimization equation for the ratio error includes: Construct the total time-varying ratio error of all uncalibrated voltage transformers, construct the sum of the changes in ratio error over time, and construct the phase angle relationship between the true voltage value, the measured phase angle value, and the measured voltage value.

[0020] The multi-objective optimization equation for the ratio error can be represented by the following three objective functions: The first objective function is the total time-varying ratio error of all uncalibrated voltage transformers, expressed as: ; In the formula, , indicating the ratio error; The second objective function is the sum of the changes in the ratio error over time, expressed as:

[0021] In the formula,

[0022] The third objective function reflects the phase angle relationship between the true voltage value, the measured phase angle value, and the measured voltage value, and its expression is:

[0023] In the formula, This indicates the total number of phases of the primary and / or secondary voltages.

[0024] S102. Randomly generate an initial population in the solution space of the multi-objective optimization equation. After grouping the initial population, solve the multi-objective optimization equation through a co-evolutionary algorithm, and select the subset with the largest information entropy in the population to train the ARIMA model. The initial population is a set of initial, randomized candidate solutions of size n generated in the search space or solution space of the problem; that is, it is obtained through random initialization. Grouping is based on the variable relationships of the initial population, used to decompose complex problems into multiple subproblems, which can improve optimization efficiency and accuracy. In this embodiment, the grouping strategy of the initial population adopts a hybrid strategy, that is, different strategies complement each other to improve the decomposition effect.

[0025] Co-evolutionary algorithm is an optimization algorithm that simulates the interactions between biological populations. It constructs competitive or cooperative relationships among multiple populations, leveraging the mutual selection pressure to drive adaptive evolution and achieve the desired optimization goal. Co-evolutionary algorithm can be used to solve multi-objective optimization equations with contrast errors. Each iteration generates offspring, from which a representative subset of a fixed size and the highest information entropy is selected and input into the ARIMA model for training.

[0026] The maximum information entropy is calculated according to the following formula:

[0027] In the formula, Represents the subset information entropy. S To represent a subset, For this generation of the population, For subset size, Indicates the total number of voltage phases. Indicates the weighting coefficient. For unit array, , This represents the total number of voltage phases for individuals a and b. The feature vectors of individuals a and b are represented.

[0028] ARIMA (Autoregressive Integrated Moving Average model) is a comprehensive forecasting model that integrates autoregressive (AR) and moving average (MA) methods to eliminate the non-stationarity of time series through differencing operations.

[0029] The mathematical form of the ARIMA model is as follows:

[0030] In the formula, For lag operators, defined as ; , indicating the autoregressive (AR) component; , representing the moving average (MA) portion; For difference operators, eliminate trend terms; It is white noise; This is a constant term.

[0031] S103. Generate time-stable algorithm-guided solutions using the trained ARIMA model, add the algorithm-guided solutions to the current population, and iteratively generate non-dominated solutions in the co-evolutionary algorithm. Subset selection is performed in each generation of the population, and this process is repeated until any generation of the population is reached. At that time, a representative subset is selected from the population to train the ARIMA model. The ARIMA model trained on this subset generates time-stationary algorithm-guided solutions that participate in environmental selection and evolutionary updates alongside the current population. For example, the ARIMA model generates an auxiliary candidate solution set Q, which is then compared with the current population... The union environment selects the next generation of population with a population size of n. EnvironmentalSelection Therefore, guided solutions can improve the efficiency and quality of co-evolutionary algorithms.

[0032] S104. When the preset maximum number of iterations is reached, the ratio error estimate of the voltage transformer is calculated based on the non-dominated solution output by the co-evolutionary algorithm.

[0033] After reaching the maximum number of iterations, the co-evolutionary algorithm outputs the non-dominated solution of the decision variables, which can be regarded as the true voltage values ​​of each phase at each time step that best fit the objective function. Based on the true voltage values ​​and the measured voltage of the voltage transformer, the ratio error of the voltage transformer can be calculated.

[0034] In this process, the non-dominated solution output by the co-evolutionary algorithm is used as the true voltage value. The ratio of the difference between the true voltage value and the measured voltage value of the transformer to the true voltage value is calculated to obtain the transformer ratio error.

[0035] In this embodiment, the concept of subset information entropy is introduced when training the ARIMA model, which can reduce training overhead while maintaining sample diversity and representativeness. By generating algorithm-guided solutions with time-stationarity through the ARIMA model, the efficiency and quality of co-evolutionary algorithms in solving multi-objective optimization problems can be improved, and the accuracy of voltage transformer ratio error estimation can be increased.

[0036] In one embodiment, the initial population grouping in step S102 includes: For the decision variables of the initial population, after coarse grouping based on the sensitivity of the target-aware decision variables to the objective function, the decision variables are further subdivided using a difference grouping method.

[0037] The decision variables are grouped using a hybrid grouping strategy of goal awareness and differential grouping. First, low-cost goal awareness is used to coarsely group the decision variables based on their sensitivity to the objective function, and then differential grouping is used to refine the grouping.

[0038] Preferably, in the feasible region Internal selection sample set For each variable in the sample set With the goal Calculate the sensitivity of the forward finite difference estimation:

[0039]

[0040] Normalization yields:

[0041] In the formula, This represents the sensitivity corresponding to the m-th objective function in the i-th phase at time j. Represents variables, Indicates the step size. This represents the target value of variable x. For unit basis vectors, Indicates the upper and lower bounds of a variable. This is the step size scaling factor. Indicates normalization sensitivity. This represents the sensitivity corresponding to the m-th objective function in the p-th phase at time q. This represents the maximum value of the normalized sensitivity. All are count variables, where m represents the m-th objective function. There are a total of three objective functions, m∈{1,2,3}. Variables are placed into the target bucket based on normalization sensitivity and pre-defined multi-label bucketing rules. And coarse groups are obtained by clustering the sensitivity images by cosine similarity; The default rules for adding multiple tags to the bucket can be: If and ,but ; In the formula, This is a relative threshold. This is the absolute threshold.

[0042] The sensitivity image is an image formed by the sensitivity curves of each objective function, using the sensitivity image... Cosine similarity clustering yields coarse groupings:

[0043] In the formula, Representing variables The sensitivity vector; Representing variables respectively The normalization sensitivity to the first, second, and third objective functions. Representing variables With variables cosine similarity, It indicates the degree of overlap between vectors in a direction. The 2-norm of the sensitivity vector is represented by the formula: ; Represents the initial coarse grouping set, for example, This represents the first group under target m. Within each target bucket... Within the process, the four-point difference interaction of candidate variables is calculated. When the difference value is greater than the adaptive threshold, the group is further subdivided using the connected component algorithm.

[0044] Four-point difference is a numerical method for solving partial differential equations. It discretizes the equation over the solution domain, transforming it into a system of algebraic equations for solution. This method uses the values ​​at four grid points to approximate the derivative term, forming a rectangular region for computation.

[0045] For candidate variables Calculate the four-point difference interaction according to the formula: ; In the formula, Indicates the first Under one objective function, the variables pair The four-point difference interaction values, Represents the feasible region Selected sample points within, , Representing variables and The perturbation step size, , This is the proportionality coefficient. upper and lower bounds of the variable, , Representing variables and The unit vector of direction; like , If an adaptive threshold is used, the system is divided into smaller subgroups using a connected component algorithm.

[0046] In this embodiment, a hybrid grouping strategy based on target perception and differential grouping is adopted. First, low-cost target perception is used to coarsely group the variables based on their sensitivity to the objective function. Then, differential grouping is used to refine the grouping. This approach can effectively maintain the coupling characteristics between variables while controlling the grouping overhead. It can also improve the accuracy and efficiency of the co-evolutionary algorithm.

[0047] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0048] Figure 2 This invention provides a schematic diagram of an online voltage transformer ratio error estimation system, comprising: Equation building module 210 is used to build a multi-objective optimization equation for ratio error based on voltage measurement data collected from substations; The construction of the multi-objective optimization equation for the ratio error includes: Construct the total time-varying ratio error of all uncalibrated voltage transformers, construct the sum of the changes in ratio error over time, and construct the phase angle relationship between the true voltage value, the measured phase angle value, and the measured voltage value.

[0049] The objective solution module 220 is used to randomly generate an initial population in the solution space of the multi-objective optimization equation, and after grouping the initial population, solve the multi-objective optimization equation through a co-evolutionary algorithm. Optionally, the target solving module 220 includes: The variable grouping unit is used to coarsely group the decision variables of the initial population based on their sensitivity to the objective function, and then further subdivide the decision variables using a difference grouping method.

[0050] Preferably, in the feasible region Internal selection sample set For each variable in the sample set With the goal Calculate the sensitivity of the forward finite difference estimation:

[0051]

[0052] Normalization yields:

[0053] In the formula, This represents the sensitivity corresponding to the m-th objective function in the i-th phase at time j. Represents the actual voltage. Indicates the step size. Indicates voltage The target value, For unit basis vectors, These represent the upper and lower bounds of the variable, respectively. This is the step size scaling factor. Indicates normalization sensitivity. This represents the sensitivity corresponding to the m-th objective function in the p-th phase at time q. This represents the maximum normalization sensitivity, and m represents the m-th objective function. Variables are placed into the target bucket based on normalization sensitivity and pre-defined multi-label bucketing rules. And coarse groups are obtained by clustering the sensitivity images by cosine similarity; In each target bucket Within the process, the four-point difference interaction of candidate variables is calculated. When the difference value is greater than the adaptive threshold, the group is further subdivided using the connected component algorithm.

[0054] Subset selection module 230 is used to select the subset with the highest information entropy in the population for training the ARIMA model; The maximum information entropy is calculated according to the following formula:

[0055] In the formula, Represents the subset information entropy. S To represent a subset, For this generation of the population, For subset size, Indicates the total number of voltage phases. Indicates the weighting coefficient. For unit array, , This represents the total number of voltage phases for individuals a and b. The feature vectors of individuals a and b are represented.

[0056] The iterative update module 240 is used to generate time-stable algorithm-guided solutions through the trained ARIMA model, add the algorithm-guided solutions to the current population, and iteratively generate non-dominated solutions in the co-evolutionary algorithm. Error estimation module 250 is used to calculate the ratio error of voltage transformer based on the non-dominated solution output by the co-evolutionary algorithm when the preset maximum number of iterations is reached.

[0057] Optionally, the non-dominated solution output by the co-evolutionary algorithm is used as the true voltage value, and the ratio of the difference between the true voltage value and the measured voltage value of the transformer to the true voltage value is calculated to obtain the transformer ratio error.

[0058] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and modules described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0059] Figure 3 This is a schematic diagram of an electronic device according to an embodiment of the present invention. The electronic device is used for estimating the ratio error of a voltage transformer. Figure 3 As shown, the electronic device 3 in this embodiment includes: a memory 310, a processor 320, and a system bus 330. The memory 310 includes an executable program 3101 stored thereon. As those skilled in the art will understand, Figure 3 The electronic device structure shown does not constitute a limitation on the electronic device and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0060] The following is combined with Figure 3 A detailed introduction to each component of the electronic device: The memory 310 can be used to store software programs and modules. The processor 320 executes various functional applications and data processing of the electronic device by running the software programs and modules stored in the memory 310. The memory 310 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for at least one function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the electronic device (such as cached data), etc. In addition, the memory 310 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0061] The memory 310 contains an executable program 3101 for a ratio error evaluation method. This executable program 3101 can be divided into one or more modules / units, which are stored in the memory 310 and executed by the processor 320 to perform functions such as voltage transformer error evaluation. Each module / unit can be a series of computer program instruction segments capable of performing a specific function, describing the execution process of the executable program 3101 in the electronic device 3. For example, the executable program 3101 can be divided into functional modules such as an equation construction module, an objective solution module, a subset selection module, an iterative update module, and an error estimation module.

[0062] The processor 320 is the control center of the electronic device. It connects various parts of the electronic device via various interfaces and lines. By running or executing software programs and / or modules stored in the memory 310, and by calling data stored in the memory 310, it performs various functions and processes data, thereby monitoring the overall status of the electronic device. Optionally, the processor 320 may include one or more processing units; preferably, the processor 320 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, application programs, etc., and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into the processor 320.

[0063] The system bus 330 is used to connect various functional components within the computer, transmitting data, address, and control information. Its type can be, for example, a PCI bus, an ISA bus, or a CAN bus. Instructions from the processor 320 are transmitted to the memory 310 via the bus, and the memory 310 sends data back to the processor 320. The system bus 330 is responsible for data and instruction exchange between the processor 320 and the memory 310. Of course, the system bus 330 can also connect to other devices, such as network interfaces and display devices.

[0064] In this embodiment of the invention, the executable program executed by the processor 320 included in the electronic device includes: Based on voltage measurement data collected from substations, a multi-objective optimization equation for ratio error is constructed; An initial population is randomly generated in the solution space of the multi-objective optimization equation. After grouping the initial population, the multi-objective optimization equation is solved by a co-evolutionary algorithm, and the subset with the largest information entropy in the population is selected to train the ARIMA model. The trained ARIMA model generates time-stable algorithm-guided solutions, which are then added to the current population and used in a co-evolutionary algorithm to iteratively generate non-dominated solutions. When the preset maximum number of iterations is reached, the ratio error estimate of the voltage transformer is calculated based on the non-dominated solution output by the co-evolutionary algorithm.

[0065] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0066] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0067] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for online estimation of the ratio error of a voltage transformer, characterized in that, include: Based on voltage measurement data collected from substations, a multi-objective optimization equation for ratio error is constructed; An initial population is randomly generated in the solution space of the multi-objective optimization equation. After grouping the initial population, the multi-objective optimization equation is solved by a co-evolutionary algorithm, and the subset with the largest information entropy in the population is selected to train the ARIMA model. The trained ARIMA model generates time-stable algorithm-guided solutions, which are then added to the current population and used in a co-evolutionary algorithm to iteratively generate non-dominated solutions. When the preset maximum number of iterations is reached, the ratio error estimate of the voltage transformer is calculated based on the non-dominated solution output by the co-evolutionary algorithm.

2. The method according to claim 1, characterized in that, The constructed ratio error multi-objective optimization equation includes: Construct the total time-varying ratio error of all uncalibrated voltage transformers, construct the sum of the changes in ratio error over time, and construct the phase angle relationship between the true voltage value, the measured phase angle value, and the measured voltage value.

3. The method according to claim 1, characterized in that, The initial population grouping includes: For the decision variables of the initial population, after coarse grouping based on the sensitivity of the target-aware decision variables to the objective function, the decision variables are further subdivided using a difference grouping method.

4. The method according to claim 3, characterized in that, After the initial grouping of the target-aware decision variables based on their sensitivity to the objective function, the decision variables are further subdivided using a difference grouping method, including: In the feasible region Internal selection sample set For each variable in the sample set With the goal Calculate the sensitivity of the forward finite difference estimation: Normalization yields: In the formula, This represents the sensitivity corresponding to the m-th objective function in the i-th phase at time j. Represents the actual voltage. Indicates the step size. Indicates voltage The target value, For unit basis vectors, These represent the upper and lower bounds of the variable, respectively. This is the step size scaling factor. Indicates normalization sensitivity. This represents the sensitivity corresponding to the m-th objective function in the p-th phase at time q. This represents the maximum normalization sensitivity, and m represents the m-th objective function. Variables are placed into the target bucket based on normalization sensitivity and pre-defined multi-label bucketing rules. And coarse groups are obtained by clustering the sensitivity images by cosine similarity; In each target bucket Within the process, the four-point difference interaction of candidate variables is calculated. When the difference value is greater than the adaptive threshold, the group is further subdivided using the connected component algorithm.

5. The method according to claim 1, characterized in that, The step of selecting the subset with the highest information entropy in the population for training the ARIMA model includes: The maximum information entropy is calculated using the following formula: In the formula, Represents the subset information entropy. S To represent a subset, For this generation of the population, For subset size, Indicates the total number of voltage phases. Indicates the weighting coefficient. Represents a unit array.

6. The method according to claim 1, characterized in that, The ratio error estimation of the voltage transformer calculated based on the non-dominated solution output by the co-evolutionary algorithm includes: The non-dominated solution output by the co-evolutionary algorithm is used as the true voltage value. The ratio of the difference between the true voltage value and the measured voltage value of the transformer to the true voltage value is calculated to obtain the transformer ratio error.

7. An online estimation system for voltage transformer ratio error, characterized in that, include: The equation construction module is used to construct a multi-objective optimization equation for the ratio error based on voltage measurement data collected from substations. The objective solution module is used to randomly generate an initial population in the solution space of the multi-objective optimization equation, and after grouping the initial population, solve the multi-objective optimization equation through a co-evolutionary algorithm. The subset selection module is used to select the subset with the highest information entropy in the population for training the ARIMA model. The iterative update module is used to generate time-stable algorithm-guided solutions from the trained ARIMA model, add the algorithm-guided solutions to the current population, and iteratively generate non-dominated solutions in the co-evolutionary algorithm. The error estimation module is used to calculate the ratio error of the voltage transformer based on the non-dominated solution output by the co-evolutionary algorithm when the preset maximum number of iterations is reached.

8. The system according to claim 7, characterized in that, The objective solving module includes: The variable grouping unit is used to coarsely group the decision variables of the initial population based on their sensitivity to the objective function, and then further subdivide the decision variables using a difference grouping method.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the online estimation method for voltage transformer ratio error as described in any one of claims 1 to 6.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed, it implements the steps of the online estimation method for voltage transformer ratio error as described in any one of claims 1 to 6.

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