Voltage sensor ratio error estimation method and device based on stage adaptive switching

Abstract

The invention discloses a stage adaptive switching voltage sensor ratio error estimation method and device, and relates to the technical field of power transmission system state monitoring, and the method comprises the steps: obtaining a historical real voltage value of a voltage sensor to be subjected to ratio error estimation and a historical measurement voltage value of the voltage sensor; constructing a multi-target ratio error estimation problem model of the voltage sensor based on the historical real voltage value and the historical measured voltage value; solving the multi-target ratio error estimation problem model by adopting an expensive constraint multi-target intelligent optimization method based on stage adaptive switching to obtain a real voltage estimation value of the voltage sensor; and performing calculation based on the real voltage estimation value and the historical real voltage value to obtain a ratio error estimation result. According to the method, the accuracy of voltage sensor ratio error estimation can be improved.

Description

Technical Field

[0001] This invention relates to the field of power transmission system condition monitoring technology, and in particular to a method and apparatus for estimating voltage sensor ratio error with stage adaptive switching. Background Technology

[0002] In the field of industrial power transmission, voltage transformers (VTs) are fundamental devices widely used in substations of power transmission systems to measure voltage values. Ratio error (RE) drift directly affects the accuracy of downstream applications such as relay protection and metering. Therefore, estimating the ratio error of voltage transformers plays a crucial role in power transmission systems. Field calibration techniques and data-driven RE estimation methods are the main RE estimation methods in modern power transmission systems. Field calibration involves disconnecting the power supply and manually comparing the VT to be calibrated with a high-precision standard VT. This method is accurate under standard conditions, but requires standard equipment far superior to the VT being measured, and repeated calibration of dozens of VTs within the substation is costly and inefficient, yielding only discrete, time-varying RE data. Data-driven estimation methods estimate RE by establishing a VT-specific model and utilizing electrical relationship constraints. While this method is less expensive, its accuracy and versatility are limited by the model itself, making it difficult to meet the complex and ever-changing actual operating conditions. To alleviate the problems of existing methods, this paper transforms the ratio error estimation problem into an expensive, constrained multi-objective optimization problem by considering the difference between the true voltage value and the VT measurement value, and uses an intelligent optimization method to estimate the true voltage value. This type of method is applicable to different models of VT, can provide real-time fault warnings, and can provide early warnings for VTs with potential faults, demonstrating significant application value.

[0003] Against this backdrop, constructing efficient and reliable intelligent optimization methods to find high-quality solutions that satisfy all constraints within a limited number of simulation evaluations has become the core challenge in solving this estimation problem. To address this challenge, Surrogate-Assisted Evolutionary Algorithms (SAEAs) have become the mainstream framework, replacing expensive simulations with inexpensive surrogate models and combining them with multi-stage optimization frameworks to guide the search. Despite the significant success of SAEAs and multi-stage frameworks, most current state-of-the-art methods suffer from a fundamental deficiency in their optimization strategies: a lack of awareness and adaptive response to the real-time search state. Existing methods often employ statically preset stage switching strategies (e.g., switching after a fixed number of evaluations). Static switching rules cannot dynamically adjust based on real-time changes in convergence, feasibility, and other metrics during the optimization process, leading to inaccurate stage switching timing and inefficient allocation of resources to reduce the number of expensive evaluations. Furthermore, the feasible domain structure and Pareto front morphology vary greatly among different optimization problems, making static switching rules difficult to adapt to diverse problem scenarios. Summary of the Invention

[0004] In view of this, the present invention provides a method and apparatus for estimating the ratio error of a voltage sensor with stage adaptive switching, the main purpose of which is to solve the problem of inaccurate ratio error estimation of voltage sensors with complex nonlinear constraints and unknown boundary structures.

[0005] To address the aforementioned problems, this application provides a method for estimating the ratio error of a voltage sensor with staged adaptive switching, comprising: Obtain the historical true voltage value of the voltage sensor to be used for ratio error estimation and the historical measured voltage value of the voltage sensor; A multi-objective ratio error estimation model for the voltage sensor is constructed based on the historical true voltage value and the historical measured voltage value. The expensive constraint multi-objective intelligent optimization method based on stage adaptive switching is used to solve the multi-objective ratio error estimation problem model to obtain the true voltage estimate of the voltage sensor. The ratio error estimation result is obtained by calculating based on the actual voltage estimate and the historical actual voltage value.

[0006] To address the aforementioned problems, this application provides a voltage sensor ratio error estimation device with staged adaptive switching, comprising: The acquisition module is used to acquire the historical true voltage value of the voltage sensor to be estimated for ratio error and the historical measured voltage value of the voltage sensor. The module is used to construct a multi-objective ratio error estimation problem model for the voltage sensor based on the historical true voltage value and the historical measured voltage value; The solution module is used to solve the multi-objective ratio error estimation problem model using an expensive constraint multi-objective intelligent optimization method based on stage adaptive switching, so as to obtain the true voltage estimate of the voltage sensor. The calculation module is used to calculate the ratio error estimation result based on the actual voltage estimate and the historical actual voltage value.

[0007] Beneficial effects of this application: The proposed method is lower in cost and achieves continuous estimation. Compared with data-driven estimation methods, the proposed method is not limited to a specific voltage sensor model and has greater versatility. Compared with existing intelligent optimization methods, this application designs an expensive constrained multi-objective intelligent optimization method based on stage adaptive switching. A stage adaptive switching strategy capable of sensing the current search state is constructed to replace the preset static switching rules. By analyzing the recent trends of these indicators to reveal the current search state, the method dynamically determines whether to execute the objective optimization stage or the constraint optimization stage. This method can accurately allocate a limited number of real evaluations to the most critical search stages, thereby achieving a balance between convergence, diversity, and enhanced feasibility, improving the efficiency and quality of problem solving. To improve the search efficiency of each stage, a stage-aware population update mechanism is proposed, ensuring targeted and efficient evolution at each stage, enhancing the adaptability of the method. In summary, the method proposed in this application can automatically respond to feasibility bottlenecks or convergence stagnation that occur during the search process, guide the population out of local regions through dynamic phase switching, and exhibit stronger robustness in complex constraint problems. It provides an efficient and automated solution for state monitoring and early fault warning of voltage sensors in power systems.

[0008] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0009] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1A schematic flowchart of a voltage sensor ratio error estimation method with stage adaptive switching provided in an embodiment of this application is shown. Figure 2 A schematic diagram of a voltage sensor in a power transmission system provided in an embodiment of this application is shown; Figure 3 A structural block diagram of a voltage sensor ratio error estimation device with stage adaptive switching provided in an embodiment of this application is shown. Detailed Implementation

[0010] Various embodiments and features of this application are described herein with reference to the accompanying drawings.

[0011] It should be understood that various modifications can be made to the embodiments described herein. Therefore, the above description should not be considered as limiting, but merely as an example of embodiments. Other modifications within the scope and spirit of this application will be apparent to those skilled in the art.

[0012] The accompanying drawings, which are included in and form part of this specification, illustrate embodiments of the present application and, together with the general description of the present application given above and the detailed description of the embodiments given below, serve to explain the principles of the present application.

[0013] These and other features of this application will become apparent from the following description of preferred forms of embodiments given as non-limiting examples, with reference to the accompanying drawings.

[0014] It should also be understood that although this application has been described with reference to some specific examples, those skilled in the art can certainly implement many other equivalent forms of this application.

[0015] The above and other aspects, features and advantages of this application will become more apparent when taken in conjunction with the accompanying drawings and in view of the following detailed description.

[0016] Specific embodiments of this application are described thereafter with reference to the accompanying drawings; however, it should be understood that the claimed embodiments are merely examples of this application, which can be implemented in various ways. Well-known and / or repeated functions and structures are not described in detail to avoid unnecessary or redundant details that could obscure the application. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely to teach those skilled in the art to use this application in a variety of substantially any suitable detailed structures.

[0017] This specification may use the phrases “in one embodiment,” “in another embodiment,” “in yet another embodiment,” or “in other embodiments,” all of which may refer to one or more of the same or different embodiments according to this application.

[0018] This application provides a method for estimating the ratio error of a voltage sensor with phased adaptive switching, such as... Figure 1 As shown, it includes: Step S101: Obtain the historical true voltage value of the voltage sensor to be used for ratio error estimation and the historical measured voltage value of the voltage sensor; In practical implementation, a high-precision sampling device and a workstation can be installed in the central control room of the substation. The sampling device samples the analog signals of all voltage sensors in the substation and stores them as historical data in the workstation to obtain the historical true voltage values ​​and the historical measured voltage values ​​of the voltage sensors.

[0019] Step S102: Construct a multi-objective ratio error estimation model for the voltage sensor based on the historical true voltage value and the historical measured voltage value; In the specific implementation process, the historical ratio error of the voltage sensor is obtained by calculation based on the historical true voltage value and the historical measured voltage value; the ratio error change is obtained by calculation based on the historical ratio error; a model is constructed based on the historical true voltage value and the historical ratio error to obtain a first objective function that aims to minimize the sum of the time-varying ratio errors of the voltage sensor; a second objective function is constructed based on the historical true voltage value and the ratio error change to obtain a second objective function that aims to minimize the variance of the ratio error change of the voltage sensor; constraints are constructed, including a first topological constraint, a second topological constraint, and a time series constraint; a model is constructed based on the first topological constraint, the second topological constraint, the time series constraint, the first objective function, and the second objective function to obtain the multi-objective ratio error estimation problem model of the voltage sensor.

[0020] Step S103: The expensive constraint multi-objective intelligent optimization method based on stage adaptive switching is used to solve the multi-objective ratio error estimation problem model to obtain the true voltage estimate of the voltage sensor. In the specific implementation process, Step 1: A number of solutions are generated by uniformly sampling within a predetermined decision space using the Latin hypercube sampling method, and then evaluated using the multi-objective ratio error estimation problem model, and stored in an archive set. Step 2: Algorithm parameters and the current population are initialized. The algorithm parameters include the maximum number of iterations, the number of function evaluations consumed, and the initial evolutionary stage. Step 3: The evolutionary type of the current evolutionary stage is determined, and a determination result is obtained. Step 4: When the determination result indicates that the evolutionary type is the objective optimization stage, the NSGA-III algorithm is used to perform unconstrained evolutionary optimization on the current population in the current evolutionary stage, resulting in... The current candidate population and the current set of interpolation points; Step 5: When the judgment result indicates that the evolutionary type is in the constrained optimization stage, the NSGA-III algorithm combined with the constraint dominance criterion is used to perform constrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population and the current set of interpolation points; Step 6: Calculate the metric index of each solution in the current set of interpolation points to obtain the metric index value, and update the index vector based on the metric index value to obtain the current index vector. The metric index includes a convergence index, a constraint violation index, and a feasible solution ratio index; Step 7: Based on the current index vector and a predetermined... The stage switching rule determines the evolutionary stage of the next iteration round, which includes an objective optimization stage and a constraint optimization stage; Step 8: Use the environment selection method in the NSGA-III algorithm to obtain a predetermined number of solutions from the archive set to obtain the first population; Step 9: Update the current population based on the first population and the current interpolation point set; Step 10: Update the archive set based on the current interpolation point set to obtain the current archive set; Step 11: If the current iteration round is greater than the preset iteration round threshold, execute Step 12; If the current iteration round is less than or equal to the preset iteration round threshold... Step 12: Determine the evolutionary stage as the optimization stage for the next round, and repeat steps 3 to 10 to update the current candidate population, the current interpolation point set, the current index vector, the current population, and the current file set until the current iteration round is greater than a preset iteration round threshold. Then, determine the non-dominated solution in the updated current file set as the objective solution of the expensive constraint multi-objective optimization problem to obtain the true voltage estimate of the voltage sensor.

[0021] Step S104: Calculate the ratio error estimation result based on the actual voltage estimate and the historical actual voltage value.

[0022] In the specific implementation process, the ratio error estimation result is obtained based on the actual voltage estimate and the historical actual voltage value, and the fault voltage sensor is reported.

[0023] The method proposed in this application is lower in cost and achieves continuous estimation. Compared with data-driven estimation methods, the method proposed in this invention is not limited to a specific voltage sensor model and has greater versatility. Compared with existing intelligent optimization methods, this application designs an expensive constrained multi-objective intelligent optimization method based on stage adaptive switching. A stage adaptive switching strategy capable of sensing the current search state is constructed to replace the preset static switching rules. By analyzing the recent trends of these indicators to reveal the current search state, the method dynamically determines whether to execute the objective optimization stage or the constraint optimization stage. This method can accurately allocate a limited number of real evaluations to the most critical search stages, thereby achieving a balance between convergence, diversity, and enhanced feasibility, improving the problem-solving efficiency and solution quality. To improve the search efficiency of each stage, a stage-aware population update mechanism is proposed, ensuring targeted and efficient evolution at each stage, enhancing the adaptability of the method. In summary, the method proposed in this application can automatically respond to feasibility bottlenecks or convergence stagnation that occur during the search process, guide the population out of local regions through dynamic phase switching, and exhibit stronger robustness in complex constraint problems. It provides an efficient and automated solution for state monitoring and early fault warning of voltage sensors in power systems.

[0024] Another embodiment of this application provides a different method for estimating the ratio error of a voltage sensor with stage-adaptive switching, including: Step S201: Obtain the historical true voltage value of the voltage sensor to be estimated and the historical measured voltage value of the voltage sensor; In the specific implementation of this step, a high-precision sampling device and a workstation can be installed in the central control room of the substation. The sampling device samples the analog signals of all voltage sensors in the substation and stores them as historical data in the workstation to obtain the historical true voltage values ​​and the historical measured voltage values ​​of the voltage sensors. Figure 2 The diagram shows a voltage sensor in a power transmission system, specifically a 110 kV substation with four sets of three-phase VT sensors; , , as well as , , These represent the actual three-phase voltage values ​​on the primary and secondary sides, respectively.

[0025] Step S202: Construct a multi-objective ratio error estimation model for the voltage sensor based on the historical true voltage value and the historical measured voltage value; In the specific implementation process of this step, the historical ratio error of the voltage sensor is obtained by calculation based on the historical real voltage value and the historical measured voltage value; firstly, the mathematical expression of the decision variable is as shown in the following formula (1): (1) in, Indicates the first n Time of the first v The actual voltage value of the phase, , The number of decision variables is D = KT , K This indicates the total number of main voltage phases and / or secondary voltage phases. T This indicates the length of the measured time series data. Similarly, starting from the... p The historical voltage measurement data collected by the group of voltage sensors can be expressed by the following formula (2): (2) in, Indicates the first p Group voltage sensor at time n The v One measurement data, , This indicates the number of voltage sensors involved in the problem model. Then, the number of sensors is calculated. p The mathematical formula for calculating the historical ratio error of the group voltage sensor can be shown in the following formula (3): (3) The change in ratio error is obtained by calculation based on the historical ratio error; the mathematical formula for calculation can be shown in the following formula (4): (4) Based on the historical true voltage value and the historical ratio error, a model is constructed to obtain a first objective function that aims to minimize the sum of the time-varying ratio errors of the voltage sensors. The first objective is the total time-varying ratio error of all uncalibrated voltage sensors, which reflects the degree of matching between the true voltage value and the measured value. Therefore, the first objective needs to minimize the sum of the time-varying ratio errors of the voltage sensors, and the specific expression is shown in the following formula (5): (5) in, For the first p Group voltage sensor at time n Thev Historical ratio error of measurement data.

[0026] Based on the historical true voltage value and the change in ratio error, a model is constructed to obtain a second objective function that aims to minimize the variance of the change in voltage sensor ratio error. The second objective is the sum of the changes in ratio error over time, which reflects the time-varying relationship between the true voltage value and the measured value. Therefore, the second objective needs to minimize the variance of the change in ratio error of different voltage sensors, and the specific expression can be shown in the following formula (6): (6) in, This is the function for calculating standard deviation.

[0027] The constraints are constructed, including a first topological constraint, a second topological constraint, and a time series constraint. In a power transmission system, voltage sensors in the same substation are connected by wires, and voltage measurement is a long-term process. Therefore, the first topological constraint, the second topological constraint, and the time series constraint can be constructed to limit the feasible domain of the problem. The topological constraint is derived from the three-phase balance principle, which stipulates that when the power grid is controllable, the actual three-phase primary voltages must remain balanced. This balance is described by the voltage imbalance coefficient, which reflects the balance state of the three-phase impedance. Since the three-phase impedance remains balanced and changes slowly (especially in high-voltage power grids), the value of the voltage imbalance coefficient and its fluctuations are limited to a certain range. The mathematical expression of the first topological constraint can be expressed by the following formula (7): (7) in, , This represents the voltage imbalance coefficient for each phase. This represents the upper limit threshold for the allowable fluctuation of the voltage imbalance coefficient. This threshold is used to quantify the permissible deviation of the three-phase voltage under unbalanced conditions, ensuring that the estimated true voltage value meets the engineering requirements for stable operation. Furthermore, since the primary voltage value is proportional to the secondary voltage value, all ratios of the three-phase voltages should be the same. Therefore, the second constraint condition can be derived, and its mathematical expression can be shown in the following formula (8): (8) Where C2 represents the allowable fluctuation threshold for the consistency of the three-phase voltage ratio. This threshold is used to limit the degree of difference in the voltage ratio between different phases, ensuring that the estimated true voltage value meets the basic law that the primary side voltage is proportional to the secondary side voltage. The specific expression for the voltage imbalance coefficient can be shown in the following formula (9): (9) in, , .

[0028] Time series constraints primarily describe the time-varying relationship of the same decision variable. Their basic assumption is that the changes in the decision variable are slow and continuous, rather than abrupt. Decision vector. In the n The change in time can be represented by the following formula (10): (10) in, n ∈[1,2,..., T -1]. The corresponding time series constraints can be expressed as follows: (11) (11) in, This represents the allowable fluctuation threshold for voltage time-series stationarity. This threshold limits the dispersion of the rate of change of each phase voltage between different times, ensuring that the estimated true voltage value satisfies the fundamental physical law of slow and continuous voltage change over time. Note that... , , The value can be predetermined based on the operating experience of the power system, historical data statistics, or theoretical analysis.

[0029] Based on the first topological constraint, the second topological constraint, the time series constraint, the first objective function, and the second objective function, a model is constructed to obtain the multi-objective ratio error estimation problem model of the voltage sensor. The mathematical expression of the multi-objective ratio error estimation problem model can be expressed by the following formula (12): (12) in, Indicates a containing D The solution for each decision variable. Represents the decision-making space. express m A number of conflicting objective functions Indicates the first j Inequality constraints h This represents the number of constraint functions. In the voltage sensor ratio error estimation problem, it represents the number of optimization objectives. Number of constraint functions .

[0030] Step S203: Use the Latin hypercube sampling method to uniformly sample and generate several solutions in the predetermined decision space, and use the multi-objective ratio error estimation problem model to perform real evaluation and store them in the archive set; In the specific implementation process, this step uses Latin hypercube sampling to generate... NI Each solution undergoes an expensive real-world evaluation and is stored in an archive. Arc .

[0031] Step S204: Initialize algorithm parameters, including the maximum number of iterations, the number of function evaluations consumed, and the initial evolution stage; In the specific implementation process, this step involves starting from the archives. Arc Select N One solution is used as the initial population. ,and t =0. Set the maximum number of iterations during evolutionary optimization to 20; set the cost function evaluation ( FEs ) quantity is NI The initial optimization stage is set as the target optimization stage, i.e., Stage=1. In this invention, Stage=1 represents the target optimization stage, and Stage=2 represents the constraint optimization stage. Three index vectors are initialized. Con , CV , fr Empty, where vector Con Store the convergence index values ​​of the interpolation point set, in vector form. CV The constraint violation index values ​​of the interpolation point set are stored in a vector. fr The proportion of feasible solutions in the set of interpolation points.

[0032] Step S205: Determine the evolutionary type of the current evolutionary stage and obtain the determination result; In the specific implementation of this step, the evolution type includes the objective optimization stage and the constraint optimization stage; the judgment result is that the evolution type of the current evolution stage is the objective optimization stage or the judgment result is that the evolution type of the current evolution stage is the constraint optimization stage.

[0033] Step S206: When the judgment result is that the evolution type is the target optimization stage, the NSGA-III algorithm is used to perform unconstrained evolutionary optimization on the current population in the current evolution stage to obtain the current candidate population and the current interpolation point set. In the specific implementation of this step, when the judgment result indicates that the evolutionary type is the target optimization stage, the NSGA-III algorithm is used to perform unconstrained evolutionary optimization on the current population at the current evolutionary stage to obtain the current candidate population, including the following steps: Step 1: When the judgment result indicates that the evolutionary type is in the target optimization stage, for the current population... Crossover and mutation operations are performed to obtain the first generation population. population and The size isN ; Step 2: Merge the current population and the first offspring population to obtain the first target population; merge the parent population... and offspring population Merge to form a size of 2 N The first target population for merging .

[0034] Step 3: Perform non-dominated sorting on the first target population to obtain the first multi-level non-dominated solution set; For merged populations Perform non-dominated sorting and divide it into multiple non-dominated layers ( , , ...).in, This is the first-level non-dominated solution set, i.e., the Pareto optimal solution set; This is the second level of non-dominated solution set, and so on; Step 4: Extract a predetermined number of solutions starting from the first layer of the first multi-level non-dominated solution set to obtain the first generation population. ; Starting from the first non-dominated layer, the solution sets of each layer are sequentially added to the new generation population. In the middle, until a certain layer Until it cannot all be put in. (Assuming before...) All layers have been placed. And the first l The layers cannot all be placed at this time. The size is smaller than N And adding the first l The size after the layer exceeds N ;right The individuals in the dataset are normalized to scale their target values ​​to the same range. Then, the values ​​are... Each individual in the array is associated with the nearest reference point. These reference points are uniformly distributed on the unit hyperplane; from the th... l Select some individuals to join the layer , making The size equals N The selection criterion is to prioritize individuals associated with reference points that are associated with fewer individuals. Specifically, the number of individuals associated with each reference point is calculated. The number of individuals associated with a single reference point is determined, and then the individuals associated with the sparsest reference point are selected.

[0035] Step 5: If the current iteration count is greater than a preset iteration count threshold, proceed to Step 6; if the current iteration count is less than or equal to the preset iteration count threshold, replace the current population with the first new generation population, and repeat Steps 1 to 5 to update the first new generation population until the current iteration count is greater than the preset iteration count threshold. Then, update the first new generation population. Determined as the current candidate population ; Step six, transfer the first new generation population Determined as the current candidate population .

[0036] Generate a fixed set of uniformly distributed first reference vectors within the predetermined decision space. ; The current candidate population The solution in the first reference vector is associated with the first active reference vector to obtain the first active reference vector set; specifically, the current candidate population is... A solution is assigned to the nearest reference vector. If a reference vector has no associated solution, it is considered inactive. The first active reference vector set is clustered using the K-means clustering method to obtain... k A first reference vector cluster; based on a preset convergence and diversity function, a preset convergence and diversity improvement function, and a preset expected convergence and diversity improvement function, the solutions in the first candidate population are evaluated to obtain the expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population; the current candidate population is... The solutions are assigned to active reference vectors; the current candidate population is calculated using a pre-defined convergence and diversity function. The convergence and diversity indices of each solution in the equation; the mathematical expression can be shown in the following formula (13): (13) in, It is the first i The predicted value of each target, It is the predicted target vector. It is the selected reference vector. From arrive The vertical distance is calculated using a pre-defined convergence and diversity improvement function. The convergence and diversity improvement index of each solution can be calculated using the following formula (14): (14) in, It is an archive Arc The solution is calculated in Minimum value.

[0037] The current candidate population is calculated using the expected convergence and diversity improvement function. The expected convergence and diversity improvement index of each solution can be calculated using the following formula (15): (15) in, It is the probability density function of the standard normal distribution. It is the first i The true function value of each objective. It is the first i Gaussian process prediction mean for each target It is the first i The standard deviation of the Gaussian process prediction for each objective yes m A real space. The integral calculations in the above formulas are explained. Improved function PDI The Gaussian posterior distribution. The term represents the joint probability density of the predicted target value. Therefore, the EPDI criterion essentially balances prediction performance and model uncertainty, promoting solutions with good performance, high uncertainty, or both. The solution with the highest expected convergence and diversity improvement index (EPDI) is selected from each of the first reference vector clusters to obtain the current interpolation point set. New The solution in the current interpolation point set is evaluated using the first objective function and the second objective function. This evaluation is expensive and requires a real evaluation.

[0038] Step S207: When the judgment result indicates that the evolutionary type is a constrained optimization stage, the NSGA-III algorithm combined with the constraint dominance criterion is used to perform constrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population and the current interpolation point set. Step 1: When the determination result indicates that the evolutionary type is in the constrained optimization stage, perform crossover and mutation operations on the current population to obtain a second offspring population; Step 2: Merge the current population and the second offspring population to obtain a second target population; Step 3: Perform non-dominated sorting on the second target population to obtain a second multi-level non-dominated solution set; Step 4: Extract a predetermined number of solutions from the first level of the second multi-level non-dominated solution set to obtain a second generation population; Step 5: If the current iteration count is greater than a preset iteration count threshold, proceed to Step 6; If the current iteration count is less than or equal to the preset iteration count threshold, replace the current population with the second generation population, and repeat Steps 1 to 5 to update the second generation population until the current iteration count is greater than the preset iteration count threshold, and determine the updated second generation population as the current candidate population; Step 6: Determine the second generation population as the current candidate population.

[0039] A fixed set of uniformly distributed second reference vectors is generated within the predetermined decision space. The solutions in the current candidate population are associated with the second reference vector to obtain a second active reference vector set; the second active reference vector set is clustered using the K-means clustering method to obtain... k A second reference vector cluster; Based on a preset convergence and diversity function, a preset improved convergence and diversity function, and a pre-predicted expected convergence and diversity improvement function, indices are calculated for the solutions in the current candidate population to obtain expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population. The calculation process for the expected convergence and diversity improvement indices is consistent with the method in the objective optimization stage and will not be repeated here. Based on a preset feasibility probability function, indices are calculated for the solutions in the current candidate population to obtain feasibility probability indices corresponding to the solutions in the current candidate population. The mathematical formula for calculation is shown in the following formula (16): (16) in, It is the cumulative distribution function. It is the first j The predicted distribution of each constraint function, It is the first j The mean of the Gaussian process with constraints is predicted. It is the first j Standard deviation of Gaussian process prediction under constraints; Perform a multiplication operation on the expected convergence and diversity improvement index and the feasibility probability index corresponding to the same solution in the current candidate population. The comprehensive index corresponding to the same solution is obtained; the solution with the largest comprehensive index is selected from each of the second reference vector clusters to obtain the current interpolation point set. The solution in the current interpolation point set is evaluated using the first objective function and the second objective function. This evaluation is expensive and requires a real evaluation.

[0040] Step S208: Calculate the metric index of each solution in the current interpolation point set, obtain the metric index value, and update the index vector based on the metric index value to obtain the current index vector. The metric index includes convergence index, constraint violation index and feasible solution ratio index. In the specific implementation process of this step, a stage adaptive switching strategy assisted by online search state awareness is proposed. This strategy aims to dynamically alternate between the objective optimization stage and the constraint optimization stage by analyzing the online feedback of the search state. In order to achieve online awareness of the search state, three key metrics are defined: the mathematical formula for calculating the convergence can be shown in the following formula (17): (17) in, Pop yes The population they belong to The calculation formula can be shown in the following formula (18): (18) Among them, when The smaller the value, the better the solution. The better the convergence, the better. To capture the convergence state of the search population, the average of the new interpolation points obtained in each iteration is used. The value serves as an indicator of population convergence. ; The mathematical expression for constraint violation (CV) can be shown by the following formula (19): (19) like ,but It is a feasible solution; otherwise... This is an infeasible solution. To capture the degree of constraint violation in the search population, the average CV value of the new interpolation points obtained in each iteration is used as an indicator of the degree of constraint violation in the population, denoted as: .

[0041] Feasible solution ratio index fr The proportion of feasible solutions is generally defined as the proportion of feasible solutions in the current population. The proportion of feasible solutions at each new interpolation point obtained in each iteration is expressed as... fr .

[0042] Step S209: Determine the evolution stage of the next iteration based on the current index vector and the predetermined stage switching rules. The evolution stage includes a target optimization stage and a constraint optimization stage. In this step, a predetermined sliding window is used to sample the current indicator vector for different indicator dimensions, obtaining sampling vectors corresponding to different indicator dimensions; the size of the predetermined sliding window is... ; The endpoint comparison method is used to compare the endpoint indicators of the sampling vector to obtain the trend comparison results corresponding to different indicator dimensions; using a size of Using a sliding window to generate the most recent The three index subsequences corresponding to the next iteration are represented as follows: , and The use of a sliding window ensures that trend detection remains sensitive to recent search dynamics while smoothly adapting to changes in search status, thus avoiding premature or unnecessary phase switching due to sudden fluctuations. A sliding window is used to record recent... The indicator sequence of the generation is analyzed to determine its changing trend (growth / decline). Specifically, this is to detect... and To determine the short-term direction of change, a simple endpoint comparison method is used. If the last value of the sequence is greater than the first value, the trend is classified as increasing; if it is less, it is classified as decreasing. This trend signal is based on convergence and constraint violation indices, combined with... fr The state triggers one of the following adaptive switching rules to complete the online search state-aware decision-making cycle of the strategy.

[0043] When the trend comparison result is the convergence index The decrease and the constraint violation index The process decreases, and the next iteration's evolutionary stage is determined as the target optimization stage; The decrease indicates that the new solution obtained has improved in terms of convergence. A decrease in feasibility implies an increase in feasibility. Simultaneous improvement in both indicates the effectiveness of the search. Since feasibility is no longer the current bottleneck, prioritizing objective optimization allows the method to leverage this momentum to further improve the quality of the solution.

[0044] When the trend comparison result is the convergence index Decrease, the constraint violation index The rate of decrease is greater than zero and the feasible solution ratio index is greater than zero. At this point, the evolutionary stage of the next iteration is determined as the objective optimization stage; the improvement in convergence indicates that the search is moving towards a space where the objective function value is better, which is a valuable trend. Although accompanied by The existence of feasible solutions, even with growth, still provides crucial stability and exploration guarantees, meaning the search has successfully located or at least approached the feasible region. Therefore, even if newly evaluated solutions cause fluctuations in constraint violations, this strategy ensures the entire process doesn't completely deviate from the feasible region and retains the ability to adjust within it. In this case, selecting objective optimization is a risk-controlled exploration strategy: utilizing information from existing feasible solutions as a guarantee, allowing for temporary increases in constraint violations, and prioritizing promising objective optimization directions.

[0045] When the trend comparison result is the convergence index Decrease, the constraint violation index The growth and the proportion of the feasible solution index equals zero. When this happens, the evolutionary stage of the next iteration is determined as the constrained optimization stage; Growth, and This indicates that the search process has completely deviated from the feasible region. Although convergence has improved, none of the new computed solutions satisfy the constraints, rendering the convergence improvement meaningless for solving the optimization problem. This typically occurs when overly aggressive objective optimization drives the population beyond the constraint boundaries into infeasible local regions. This rule is designed to pull the population back or towards the feasible region, prioritizing feasibility enhancement as the most urgent objective. Conversely, when the trend comparison result is the convergence index... Decrease, the constraint violation index The rate of decrease is greater than zero and the feasible solution ratio index is greater than zero. This allows for goal-driven exploration when a feasible foundation exists. This reflects a dynamic trade-off between exploring potential benefits and avoiding fundamental failure.

[0046] When the trend comparison result is the convergence index Growth and the constraint violation index When convergence declines, the evolutionary stage of the next iteration is determined to be the constrained optimization stage. When convergence deteriorates while constraint violation decreases, this indicates that the search trajectory is shifting from the unconstrained Pareto front region (superior objective value but infeasible solution) to the constrained Pareto front region (highly feasible but suboptimal objective value). Convergence degradation is an inevitable result of the population moving towards the feasible region. At this point, performing constrained optimization will guide the population towards the feasible space and eventually stabilize it on the constrained Pareto front, thus avoiding inefficient searches near the constraint boundaries.

[0047] When the trend comparison result is the convergence index Growth, the aforementioned constraint violation index The growth and the proportion of feasible solutions is greater than zero. When the convergence and cross-validation (CV) metrics deteriorate and feasible solutions exist, the search process stagnates, potentially falling into local optima or unfavorable search directions. Feasible solutions provide the basis for solving this problem. Switching to the objective optimization phase is not intended to immediately improve convergence. Instead, prioritizing objective optimization can encourage the population to move away from potentially overcrowded or stagnant areas, revitalize population diversity, and propel it towards more promising directions in the objective space. Objective optimization is more likely than constraint optimization to break stagnation.

[0048] When the trend comparison result is the convergence index Growth, the aforementioned constraint violation index The growth and the proportion of the feasible solution index equals zero. When the convergence and constraint violation indices deteriorate and no feasible solution exists, it means the search process is moving away from the unconstrained Pareto front and into the infeasible space, which is the worst-case scenario. This often happens when the population is trapped in complex infeasible regions or misled away from feasible regions. When the search process loses all positive feedback, it should return to the basic optimization objective: pull the population back to the constrained boundary and search for feasible solutions. Switching to the constrained optimization phase at this point avoids continuing to explore in infeasible directions and can trigger a phase switch to ensure that the search process converges to the constrained Pareto front even in the worst-case search scenario.

[0049] Step S210: Use the environment selection method in the NSGA-III algorithm to obtain a predetermined number of solutions from the archive set to obtain the first group; In the specific implementation process, this step uses the environment selection method in the NSGA-III algorithm from the archive set. Arc Select N The solutions form the first group. .

[0050] Step S211: Based on the first population and the current set of interpolation points Update the current population; In the specific implementation process of this step, an initial set with an empty solution set is constructed. Second set ; Calculate the first population First convergence index and the first feasibility indicator ; Calculate the second convergence index of the union of the first population and the current set of interpolation points. Second feasibility index For each solution in the set of interpolation points The potential impact on the population is assessed from the perspectives of convergence and feasibility. Specifically, the convergence metric of a population is defined as the average value of the solutions in the population. Con The feasibility index is defined as the minimum CV value for each solution in the population. Therefore, the first population... The two indicator values ​​are respectively expressed as: and Then, let Indicates the first group and candidate solutions The union of the two sets, and the corresponding index values ​​are expressed as follows: and .

[0051] When the second convergence index Less than the first convergence index Or, if the solution in the current interpolation point set is a non-dominated solution, then the current interpolation point set... The solution Add to the first set , for the first set Update the solution in the middle; When the second feasibility index Less than the first feasibility index Or the solution in the current set of interpolation points If a feasible solution is found, the solutions in the current interpolation point set are... Add to the second set , for the second set Update the solution in the middle; Given that the current stage is the objective optimization stage, based on the first population and the updated first set The solution in the algorithm updates the current population; to maintain a fixed population size. N Iteratively delete the solution with the worst convergence performance (i.e., the solution with the largest Con value). Given that the current stage is a constrained optimization stage, based on the first population... and the updated second set The current population is updated using solutions from the solution list. The population size is maintained by deleting the solution with the highest CV value. N Finally, the population for the next iteration is generated, with a size of [missing value]. NThis targeted population update strategy ensures that during the objective optimization phase, the search is actively guided towards the unconstrained Pareto front, while during the constrained optimization phase, the search is forcefully guided towards the feasible region. By tightly integrating population management mechanisms with the optimization phase, this mechanism guarantees that every accurate assessment directly contributes to achieving the pressing objective.

[0052] Step S212: Update the archive set based on the current interpolation point set to obtain the current archive set; In this step, the solutions in the current interpolation point set are inserted into the archive set to update the archive set and obtain the current archive set.

[0053] Step S213: If the current iteration round is greater than the preset iteration round threshold, execute step S214; if the current iteration round is less than or equal to the preset iteration round threshold, determine the evolutionary stage as the optimization stage of the next round, and repeat steps S205 to S212 to update the current candidate population, the current interpolation point set, the current index vector, the current population, and the current file set, until if the current iteration round is greater than the preset iteration round threshold, determine the non-dominated solution in the updated current file set as the objective solution of the expensive constraint multi-objective optimization problem, so as to obtain the true voltage estimate of the voltage sensor; Step S214: Determine the non-dominated solution in the updated current archive set as the objective solution of the expensive constrained multi-objective optimization problem to obtain the true voltage estimate of the voltage sensor.

[0054] Step S215: Calculate the ratio error estimation result based on the actual voltage estimate and the historical actual voltage value.

[0055] In the specific implementation process, the ratio error estimation result is obtained based on the actual voltage estimate and the historical actual voltage value, and the fault voltage sensor is reported.

[0056] The method proposed in this application is lower in cost and achieves continuous estimation. Compared with data-driven estimation methods, the method proposed in this invention is not limited to a specific voltage sensor model and has greater versatility. Compared with existing intelligent optimization methods, this application designs an expensive constrained multi-objective intelligent optimization method based on stage adaptive switching. A stage adaptive switching strategy capable of sensing the current search state is constructed to replace the preset static switching rules. By analyzing the recent trends of these indicators to reveal the current search state, the method dynamically determines whether to execute the objective optimization stage or the constraint optimization stage. This method can accurately allocate a limited number of real evaluations to the most critical search stages, thereby achieving a balance between convergence, diversity, and enhanced feasibility, improving the problem-solving efficiency and solution quality. To improve the search efficiency of each stage, a stage-aware population update mechanism is proposed, ensuring targeted and efficient evolution at each stage, enhancing the adaptability of the method. In summary, the method proposed in this application can automatically respond to feasibility bottlenecks or convergence stagnation that occur during the search process, guide the population out of local regions through dynamic phase switching, and exhibit stronger robustness in complex constraint problems. It provides an efficient and automated solution for state monitoring and early fault warning of voltage sensors in power systems.

[0057] Another embodiment of this application provides a voltage sensor ratio error estimation device 300 with staged adaptive switching, such as... Figure 3 As shown, it includes: The acquisition module 301 is used to acquire the historical true voltage value of the voltage sensor to be estimated for ratio error and the historical measured voltage value of the voltage sensor. Module 302 is used to construct a multi-objective ratio error estimation problem model for the voltage sensor based on the historical true voltage value and the historical measured voltage value; The solver module 303 is used to solve the multi-objective ratio error estimation problem model using an expensive constraint multi-objective intelligent optimization method based on stage adaptive switching, so as to obtain the true voltage estimate of the voltage sensor. The calculation module 304 is used to calculate the ratio error estimation result based on the actual voltage estimate and the historical actual voltage value.

[0058] In specific implementation, the construction module 302 is specifically used to: perform calculations based on the historical true voltage value and the historical measured voltage value to obtain the historical ratio error of the voltage sensor; perform calculations based on the historical ratio error to obtain the ratio error change; construct a model based on the historical true voltage value and the historical ratio error to obtain a first objective function that aims to minimize the sum of the time-varying ratio errors of the voltage sensor; construct a model based on the historical true voltage value and the ratio error change to obtain a second objective function that aims to minimize the variance of the ratio error change of the voltage sensor; construct constraints, including a first topological constraint, a second topological constraint, and a time series constraint; and construct a model based on the first topological constraint, the second topological constraint, the time series constraint, the first objective function, and the second objective function to obtain a multi-objective ratio error estimation problem model for the voltage sensor.

[0059] In the specific implementation process, the solution module 303 is specifically used for: Step 1, uniformly sampling and generating several solutions in a predetermined decision space using the Latin hypercube sampling method, and performing a real evaluation using the multi-objective ratio error estimation problem model, storing the results in an archive set; Step 2, initializing algorithm parameters and the current population, the algorithm parameters including the maximum number of iterations, the number of function evaluations consumed, and the initial evolutionary stage; Step 3, determining the evolutionary type of the current evolutionary stage and obtaining the determination result; Step 4, when the determination result indicates that the evolutionary type is the objective optimization stage, using the NSGA-III algorithm to perform a non-critical evaluation on the current population in the current evolutionary stage. Constrained evolutionary optimization is performed to obtain the current candidate population and the current set of interpolation points. Step 5: When the determination result indicates that the evolutionary type is in the constrained optimization stage, the NSGA-III algorithm combined with the constraint dominance criterion is used to perform constrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population and the current set of interpolation points. Step 6: The metric index of each solution in the current set of interpolation points is calculated to obtain the metric index value, and the index vector is updated based on the metric index value to obtain the current index vector. The metric index includes a convergence index, a constraint violation index, and a feasible solution ratio index. Step 7: Based on the current index... The vector and predetermined stage switching rules determine the evolutionary stage of the next iteration round, which includes an objective optimization stage and a constraint optimization stage; Step 8: Use the environment selection method in the NSGA-III algorithm to obtain a predetermined number of solutions from the file set to obtain the first population; Step 9: Update the current population based on the first population and the current interpolation point set; Step 10: Update the file set based on the current interpolation point set to obtain the current file set; Step 11: If the current iteration round is greater than the preset iteration round threshold, execute Step 12; if the current iteration round is less than or equal to the preset iteration round threshold... When the threshold is reached, the evolutionary stage is determined as the optimization stage for the next round. Steps three to ten are repeated to update the current candidate population, the current interpolation point set, the current index vector, the current population, and the current file set until the current iteration round is greater than the preset iteration round threshold. Then, the non-dominated solution in the updated current file set is determined as the objective solution of the expensive constraint multi-objective optimization problem to obtain the true voltage estimate of the voltage sensor. Step twelve: The non-dominated solution in the updated current file set is determined as the objective solution of the expensive constraint multi-objective optimization problem to obtain the true voltage estimate of the voltage sensor.

[0060] In the specific implementation process, the solution module 303 is further used for: Step 1, when the judgment result is that the evolution type is the target optimization stage, performing crossover and mutation operations on the current population to obtain a first offspring population; Step 2, merging the current population and the first offspring population to obtain a first target population; Step 3, performing non-dominated sorting on the first target population to obtain a first multi-level non-dominated solution set; Step 4, extracting a predetermined number of solutions from the first level of the first multi-level non-dominated solution set to obtain a first new generation population; Step 5, if the current iteration number is greater than a preset iteration number threshold, executing Step 6; if the current iteration number is less than or equal to the preset iteration number threshold, replacing the current population with the first new generation population, repeating Steps 1 to 5 to update the first new generation population until the current iteration number is greater than the preset iteration number threshold, and determining the updated first new generation population as the current candidate population; Step 6, determining the first new generation population as the current candidate population.

[0061] In specific implementation, the solution module 303 is further configured to: generate a fixed, uniformly distributed set of first reference vectors within the predetermined decision space; associate the solutions in the current candidate population with the first reference vectors to obtain a first active reference vector set; and cluster the first active reference vector set using the K-means clustering method to obtain... k A first reference vector cluster is defined; based on a preset convergence and diversity function, a preset convergence and diversity improvement function, and a preset expected convergence and diversity improvement function, indices are calculated for the solutions in the first candidate population to obtain expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population; the solution with the largest expected convergence and diversity improvement index is selected from each first reference vector cluster to obtain the current interpolation point set; the solutions in the current interpolation point set are subjected to expensive real evaluation using the first objective function and the second objective function.

[0062] In the specific implementation process, the solution module 303 is further used for: Step 1, when the judgment result is that the evolution type is a constrained optimization stage, performing crossover and mutation operations on the current population to obtain a second offspring population; Step 2, merging the current population and the second offspring population to obtain a second target population; Step 3, performing non-dominated sorting on the second target population to obtain a second multi-level non-dominated solution set; Step 4, extracting a predetermined number of solutions from the first level of the second multi-level non-dominated solution set to obtain a second generation population; Step 5, if the current iteration number is greater than a preset iteration number threshold, executing Step 6; if the current iteration number is less than or equal to the preset iteration number threshold, replacing the current population with the second generation population, repeating Steps 1 to 5 to update the second generation population until the current iteration number is greater than the preset iteration number threshold, and determining the updated second generation population as the current candidate population; Step 6, determining the second generation population as the current candidate population.

[0063] In specific implementation, the solution module 303 is further configured to: generate a fixed, uniformly distributed set of second reference vectors within the predetermined decision space; associate the solutions in the current candidate population with the second reference vectors to obtain a second active reference vector set; and cluster the second active reference vector set using the K-means clustering method to obtain... k A second reference vector cluster is defined; based on a preset convergence and diversity function, a preset convergence and diversity improvement function, and a preset expected convergence and diversity improvement function, indices are calculated for the solutions in the current candidate population to obtain expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population; based on a preset feasibility probability function, indices are calculated for the solutions in the current candidate population to obtain feasibility probability indices corresponding to the solutions in the current candidate population; the expected convergence and diversity improvement indices and feasibility probability indices corresponding to the same solution in the current candidate population are multiplied to obtain a comprehensive index corresponding to the same solution; the solution with the largest comprehensive index is selected from each second reference vector cluster to obtain the current interpolation point set; and the solutions in the current interpolation point set are subjected to expensive real evaluation using the first objective function and the second objective function.

[0064] In the specific implementation process, the solution module 303 is further configured to: sample the current index vector of different index dimensions using a predetermined sliding window to obtain sampled vectors corresponding to different index dimensions; compare the endpoint indices of the sampled vectors using the endpoint comparison method to obtain trend comparison results corresponding to different index dimensions; when the trend comparison result is that the convergence index decreases and the constraint violation index decreases, determine the evolution stage of the next iteration as the target optimization stage; when the trend comparison result is that the convergence index decreases, the constraint violation index decreases, and the feasible solution ratio index is greater than zero ... When the convergence index decreases, the constraint violation index increases, and the feasible solution ratio index equals zero, the evolutionary stage of the next iteration is determined to be the constraint optimization stage; when the trend comparison result shows that the convergence index increases and the constraint violation index decreases, the evolutionary stage of the next iteration is determined to be the constraint optimization stage; when the trend comparison result shows that the convergence index increases, the constraint violation index increases, and the feasible solution ratio index is greater than zero, the evolutionary stage of the next iteration is determined to be the objective optimization stage; when the trend comparison result shows that the convergence index increases, the constraint violation index increases, and the feasible solution ratio index equals zero, the evolutionary stage of the next iteration is determined to be the constraint optimization stage.

[0065] In specific implementation, the solution module 303 is further configured to: construct a first set and a second set with an initial empty solution set; calculate a first convergence index and a first feasibility index for the first population; calculate a second convergence index and a second feasibility index for the union of the first population and the current interpolation point set; when the second convergence index is less than the first convergence index or the solution in the current interpolation point set is a non-dominated solution, add the solution in the current interpolation point set to the first set to update the solution in the first set; when the second feasibility index is less than the first feasibility index or the solution in the current interpolation point set is a feasible solution, add the solution in the current interpolation point set to the second set to update the solution in the second set; when the current stage is the objective optimization stage, update the current population based on the first population and the updated solutions in the first set; when the current stage is the constraint optimization stage, update the current population based on the first population and the updated solutions in the second set.

[0066] The method proposed in this application is lower in cost and achieves continuous estimation. Compared with data-driven estimation methods, the method proposed in this invention is not limited to a specific voltage sensor model and has greater versatility. Compared with existing intelligent optimization methods, this application designs an expensive constrained multi-objective intelligent optimization method based on stage adaptive switching. A stage adaptive switching strategy capable of sensing the current search state is constructed to replace the preset static switching rules. By analyzing the recent trends of these indicators to reveal the current search state, the method dynamically determines whether to execute the objective optimization stage or the constraint optimization stage. This method can accurately allocate a limited number of real evaluations to the most critical search stages, thereby achieving a balance between convergence, diversity, and enhanced feasibility, improving the problem-solving efficiency and solution quality. To improve the search efficiency of each stage, a stage-aware population update mechanism is proposed, ensuring targeted and efficient evolution at each stage, enhancing the adaptability of the method. In summary, the method proposed in this application can automatically respond to feasibility bottlenecks or convergence stagnation that occur during the search process, guide the population out of local regions through dynamic phase switching, and exhibit stronger robustness in complex constraint problems. It provides an efficient and automated solution for state monitoring and early fault warning of voltage sensors in power systems.

[0067] The specific implementation process of the above method steps can be found in the embodiment of the voltage sensor ratio error estimation method with adaptive switching at any stage, which will not be repeated here.

[0068] The effectiveness of this invention will be further illustrated below in the context of voltage sensor ratio error estimation. In experimental verification, two test problems, denoted as TREE1 and TREE2, were constructed based on real substation data. Both TREE1 and TREE2 problems used a timing length of 40 (…). T The primary-side three-phase voltage time series (=40), decision variable dimensions. D =120, but the two simulated real-world scenarios are different in scale: TREE1 simulates a medium-sized hub station with 3 sets of voltage sensors; while TREE2 simulates a large critical substation with 12 sets of devices, forming a denser monitoring network. This setup results in different complexities for the two problems while maintaining the same search space dimension. TREE2, due to its increased device interactions and constraint relationships, is better suited to test the estimation robustness and scalability of the method in large-scale, highly coupled real-world power transmission systems.

[0069] To ensure a fair comparison, the maximum number of function evaluations for each method in the comparison test problem is set to 1440, and the initial sample size is [not specified]. NI All set to 11× D-1, each method is run independently 21 times on each test suite. Furthermore, for the method proposed in this invention, the population size is set to 100, the number of interpolation points is set to 5, and the sliding window size is set to 5.

[0070] To verify the superiority of the proposed Stage-Adaptive Switching Evolutionary Algorithm (SASEA) in solving the voltage sensor ratio error estimation problem, it is compared with five other advanced multi-objective optimization methods, including ANSGAIII, IBEA, GDE3, CMOPSO, and RECMO. Table 1 shows the objective and constraint values ​​for each method to obtain the optimal solution on the TREE1 and TREE2 problems. The '-' symbol in the table indicates that the method did not find a feasible solution.

[0071] Table 1: Objective function values ​​and constraint violation values ​​of each method for obtaining optimal solutions to the TREE1 and TREE2 problems.

[0072] As can be seen from the table, the method proposed in this invention can find feasible solutions for both TREE1 and TREE2 problems, and these solutions are Pareto optimal. Furthermore, Table 2 presents the Inverted Generation Distance (IGD) values ​​obtained by independently running the proposed method and other comparative methods 21 times on the TREE1 and TREE2 problems. A smaller IGD value indicates better convergence of the method.

[0073] Table 2: Comparison of IGD indices obtained by different methods on TREE1 and TREE2 problems

[0074] As shown in Table 2, the ANSGAIII, IBEA, and RECMO methods all failed to find a feasible solution, while the method proposed in this invention not only found a feasible solution but also demonstrated superior performance. Table 3 also presents the HV index values ​​obtained by each method on the TREE1 and TREE2 problems; a higher HV value indicates better method performance.

[0075] Table 3: Comparison of HV indices obtained by different methods on TREE1 and TREE2 problems

[0076] Similarly, as shown in Table 3, the method proposed in this invention achieves superior performance. This demonstrates that the stage-adaptive switching strategy and stage-aware population update mechanism employed in the proposed method can effectively balance convergence, diversity, and feasibility, thereby obtaining an optimal decision set that is closer to the true Pareto front within the feasible domain.

[0077] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. Those skilled in the art can make various modifications or equivalent substitutions to this application within the scope and nature of this application, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for estimating the ratio error of a voltage sensor with stage-adaptive switching, characterized in that, include: Obtain the historical true voltage value of the voltage sensor to be used for ratio error estimation and the historical measured voltage value of the voltage sensor; A multi-objective ratio error estimation model for the voltage sensor is constructed based on the historical true voltage value and the historical measured voltage value. The expensive constraint multi-objective intelligent optimization method based on stage adaptive switching is used to solve the multi-objective ratio error estimation problem model to obtain the true voltage estimate of the voltage sensor. The ratio error estimation result is obtained by calculating based on the actual voltage estimate and the historical actual voltage value.

2. The method as described in claim 1, characterized in that, The multi-objective ratio error estimation problem model for the voltage sensor, constructed based on the historical true voltage value and the historical measured voltage value, specifically includes: The historical ratio error of the voltage sensor is obtained by performing calculations based on the historical real voltage value and the historical measured voltage value. The change in ratio error is obtained by performing calculations based on the historical ratio error. A model is constructed based on the historical true voltage value and the historical ratio error, resulting in a first objective function that aims to minimize the sum of the time-varying ratio errors of the voltage sensor. Based on the historical true voltage value and the ratio error change, a model is constructed to obtain a second objective function that aims to minimize the variance of the voltage sensor ratio error change. Construct constraints, which include a first topological constraint, a second topological constraint, and a time series constraint; Based on the first topological constraint, the second topological constraint, the time series constraint, the first objective function, and the second objective function, a model is constructed to obtain the multi-objective ratio error estimation problem model of the voltage sensor.

3. The method as described in claim 1, characterized in that, The method employs an expensive constraint-based multi-objective intelligent optimization approach with stage-adaptive switching to solve the multi-objective ratio error estimation problem model, thereby obtaining the true voltage estimate of the voltage sensor. Specifically, this includes: Step 1: Use the Latin hypercube sampling method to uniformly sample and generate several solutions in the predetermined decision space, and use the multi-objective ratio error estimation problem model to perform real evaluation and store them in the archive set; Step 2: Initialize algorithm parameters and the current population. The algorithm parameters include the maximum number of iterations, the number of function evaluations consumed, and the initial evolutionary stage. Step 3: Determine the evolutionary type of the current evolutionary stage and obtain the determination result; Step 4: When the judgment result indicates that the evolutionary type is the target optimization stage, the NSGA-III algorithm is used to perform unconstrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population and the current interpolation point set. Step 5: When the judgment result indicates that the evolutionary type is in the constrained optimization stage, the NSGA-III algorithm combined with the constraint dominance criterion is used to perform constrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population and the current interpolation point set. Step 6: Calculate the metrics for each solution in the current interpolation point set, obtain the metric values, and update the metric vector based on the metric values ​​to obtain the current metric vector. The metric includes convergence metrics, constraint violation metrics, and feasible solution ratio metrics. Step 7: Determine the evolution stage of the next iteration based on the current indicator vector and the predetermined stage switching rules. The evolution stage includes the objective optimization stage and the constraint optimization stage. Step 8: Use the environment selection method in the NSGA-III algorithm to obtain a predetermined number of solutions from the archive set to obtain the first group; Step 9: Update the current population based on the first population and the current set of interpolation points; Step 10: Update the archive set based on the current set of interpolation points to obtain the current archive set; Step 11: If the current iteration round is greater than the preset iteration round threshold, proceed to Step 12; if the current iteration round is less than or equal to the preset iteration round threshold, determine the evolutionary stage as the optimization stage for the next round, and repeat Steps 3 to 10 to update the current candidate population, the current interpolation point set, the current index vector, the current population, and the current file set, until the current iteration round is greater than the preset iteration round threshold, and the non-dominated solution in the updated current file set is determined as the objective solution of the expensive constraint multi-objective optimization problem, so as to obtain the true voltage estimate of the voltage sensor. Step 12: Determine the non-dominated solution in the updated current archive set as the objective solution of the expensive constrained multi-objective optimization problem to obtain the true voltage estimate of the voltage sensor.

4. The method as described in claim 3, characterized in that, When the determination result indicates that the evolutionary type is the target optimization stage, the NSGA-III algorithm is used to perform unconstrained evolutionary optimization on the current population at the current evolutionary stage to obtain the current candidate population, specifically including: Step 1: When the judgment result indicates that the evolutionary type is in the target optimization stage, perform crossover and mutation operations on the current population to obtain the first generation population; Step 2: Merge the current population and the first offspring population to obtain the first target population; Step 3: Perform non-dominated sorting on the first target population to obtain the first multi-level non-dominated solution set; Step 4: Extract a predetermined number of solutions from the first layer of the first multi-layer non-dominated solution set to obtain the first generation population; Step 5: If the current iteration count is greater than the preset iteration count threshold, proceed to Step 6; If the current iteration count is less than or equal to the preset iteration count threshold, replace the current population with the first new generation population, and repeat Steps 1 to 5 to update the first new generation population until the current iteration count is greater than the preset iteration count threshold, and determine the updated first new generation population as the current candidate population. Step six: The first new generation population is identified as the current candidate population.

5. The method as described in claim 4, characterized in that, The step of using the NSGA-III algorithm to perform unconstrained evolutionary optimization on the current population at the current evolutionary stage to obtain the current set of interpolation points specifically includes: Generate a fixed set of uniformly distributed first reference vectors within the predetermined decision space; The solutions in the current candidate population are associated with the first reference vector to obtain the first active reference vector set; The first active reference vector set is clustered using the K-means clustering method to obtain... k A first reference vector cluster; Based on the preset convergence and diversity function, the preset convergence and diversity improvement function, and the preset expected convergence and diversity improvement function, the indices of the solutions in the first candidate population are calculated to obtain the expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population. From each of the first reference vector clusters, select the solution that maximizes the expected convergence and diversity improvement index to obtain the current interpolation point set; The solutions in the current set of interpolation points are evaluated using the first objective function and the second objective function. This is an expensive real evaluation.

6. The method as described in claim 3, characterized in that, When the determination result indicates that the evolutionary type is in the constrained optimization stage, the NSGA-III algorithm combined with the constraint dominance criterion is used to perform constrained evolutionary optimization on the current population in the current evolutionary stage to obtain the current candidate population, specifically including: Step 1: When the judgment result indicates that the evolutionary type is in the constrained optimization stage, perform crossover and mutation operations on the current population to obtain the second generation population; Step 2: Merge the current population and the second offspring population to obtain the second target population; Step 3: Perform non-dominated sorting on the second target population to obtain the second multi-level non-dominated solution set; Step 4: Extract a predetermined number of solutions starting from the first layer of the second multi-layer non-dominated solution set to obtain the second generation population; Step 5: If the current iteration count is greater than the preset iteration count threshold, proceed to Step 6; If the current iteration count is less than or equal to the preset iteration count threshold, replace the current population with the second new generation population, and repeat Steps 1 to 5 to update the second new generation population until the current iteration count is greater than the preset iteration count threshold, and determine the updated second new generation population as the current candidate population. Step six: The second generation population is identified as the current candidate population.

7. The method as described in claim 6, characterized in that, The NSGA-III algorithm, incorporating a constraint dominance criterion, is used to perform constrained evolutionary optimization on the current population at the current evolutionary stage, resulting in the current set of interpolation points, specifically including: A fixed set of uniformly distributed second reference vectors is generated within the predetermined decision space; The solutions in the current candidate population are associated with the second reference vector to obtain the second active reference vector set; The second active reference vector set is clustered using the K-means clustering method to obtain... k A second reference vector cluster; Based on the preset convergence and diversity function, the preset convergence and diversity improvement function, and the preset expected convergence and diversity improvement function, the indices of the solutions in the current candidate population are calculated to obtain the expected convergence and diversity improvement indices corresponding to the solutions in the current candidate population, respectively. Based on a preset feasibility probability function, the solutions in the current candidate population are evaluated to obtain feasibility probability indices corresponding to the solutions in the current candidate population. Multiply the expected convergence and diversity improvement index and the feasibility probability index corresponding to the same solution in the current candidate population to obtain the comprehensive index corresponding to the same solution. The solution with the largest comprehensive index is selected from each of the second reference vector clusters to obtain the current set of interpolation points; The solutions in the current set of interpolation points are evaluated using the first objective function and the second objective function. This is an expensive real evaluation.

8. The method as described in claim 3, characterized in that, The process of determining the evolutionary stage of the next iteration based on the current indicator vector and the predetermined stage switching rules specifically includes: A predetermined sliding window is used to sample the current indicator vector for different indicator dimensions to obtain the sampling vectors corresponding to different indicator dimensions. The endpoint comparison method is used to compare the endpoint indicators of the sampling vector to obtain the trend comparison results corresponding to different indicator dimensions. When the trend comparison result shows that the convergence index decreases and the constraint violation index decreases, the evolutionary stage of the next iteration round is determined to be the target optimization stage. When the trend comparison results show that the convergence index decreases, the constraint violation index decreases, and the feasible solution ratio index is greater than zero, the evolution stage of the next iteration round is determined to be the target optimization stage. When the trend comparison result shows that the convergence index decreases, the constraint violation index increases, and the feasible solution ratio index is equal to zero, the evolution stage of the next iteration round is determined to be the constraint optimization stage. When the trend comparison result shows that the convergence index increases and the constraint violation index decreases, the evolution stage of the next iteration round is determined to be the constraint optimization stage. When the trend comparison results show that the convergence index increases, the constraint violation index increases, and the feasible solution ratio index is greater than zero, the evolution stage of the next iteration round is determined to be the target optimization stage. When the trend comparison results show that the convergence index increases, the constraint violation index increases, and the feasible solution ratio index is equal to zero, the evolution stage of the next iteration round is determined to be the constraint optimization stage.

9. The method as described in claim 3, characterized in that, The step of updating the current population based on the first population and the current interpolation point set specifically includes: Construct a first set and a second set with empty initial solution sets; Calculate the first convergence index and the first feasibility index for the first population; Calculate the second convergence index and the second feasibility index of the union of the first population and the current set of interpolation points; When the second convergence index is less than the first convergence index or the solution in the current interpolation point set is a non-dominated solution, the solution in the current interpolation point set is added to the first set to update the solution in the first set; When the second feasibility index is less than the first feasibility index or when the solution in the current interpolation point set is a feasible solution, the solution in the current interpolation point set is added to the second set to update the solution in the second set; When the current stage is the objective optimization stage, the current population is updated based on the first population and the solutions in the updated first set; when the current stage is the constraint optimization stage, the current population is updated based on the first population and the solutions in the updated second set.

10. A voltage sensor ratio error estimation device with stage-adaptive switching, characterized in that, include: The acquisition module is used to acquire the historical true voltage value of the voltage sensor to be estimated for ratio error and the historical measured voltage value of the voltage sensor. The module is used to construct a multi-objective ratio error estimation problem model for the voltage sensor based on the historical true voltage value and the historical measured voltage value; The solution module is used to solve the multi-objective ratio error estimation problem model using an expensive constraint multi-objective intelligent optimization method based on stage adaptive switching, so as to obtain the true voltage estimate of the voltage sensor. The calculation module is used to calculate the ratio error estimation result based on the actual voltage estimate and the historical actual voltage value.

Images