Power transmission line parameter identification method and system based on differential evolution and double-layer optimization

Abstract

This invention relates to the field of power transmission line technology, providing a method and system for power transmission line parameter identification based on differential evolution and bi-layer optimization. The method includes constructing a lumped-parameter power transmission line model with a π-type equivalent circuit based on the transmission line topology; outer-layer optimization searches for optimal line parameter values ​​within a given range and outputs them to the inner layer; inner-layer optimization solves for the corresponding optimal error compensation amount under the given line parameter conditions from outer-layer optimization. This method can suppress the interference of measurement errors on weak signals, reduce the systematic bias of the line parameter identification results, and improve the stability and engineering applicability of the identification results.

Description

Technical Field

[0001] This invention relates to the field of power transmission line technology, and in particular to a method and system for identifying power transmission line parameters based on differential evolution and bi-layer optimization. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Synchronous phasor measurement units (PMUs) provide a highly synchronized data source for online identification of line parameters. However, PMU measurement data contains various errors, including transformer errors, synchronization clock errors, and algorithm fitting errors. These errors often exhibit complex statistical characteristics that are non-Gaussian and biased. For short-distance transmission lines, due to the low line impedance, the amplitude difference and phase angle difference of the voltage and current at both ends of the line are small during normal operation, resulting in a low signal-to-noise ratio. This makes the impact of measurement errors on the parameter identification results more significant, leading to difficulty in meeting engineering requirements for parameter identification accuracy.

[0004] Existing transmission line parameter identification methods typically make simplistic assumptions about PMU measurement errors or treat them as an unknown black box for overall estimation, failing to effectively utilize their true, device-dependent non-Gaussian statistical characteristics. When measurement phasors and errors are tightly coupled, achieving accurate decoupling and compensation becomes difficult. For short-distance transmission lines with low signal-to-noise ratios due to low impedance and weak signals, parameter identification methods are severely affected by inherent PMU measurement errors, and the identification accuracy is insufficient to meet engineering application requirements. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method and system for identifying transmission line parameters based on differential evolution and bi-layer optimization. This method can suppress the interference of measurement errors on weak signals, reduce the systematic deviation of the line parameter identification results, and improve the stability and engineering applicability of the identification results.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides a method for identifying transmission line parameters based on differential evolution and bi-layer optimization.

[0007] In one or more embodiments, a method for identifying transmission line parameters based on differential evolution and bi-level optimization is provided, including: A method for identifying transmission line parameters based on differential evolution and bi-level optimization, characterized by comprising: Based on the topology of the transmission line, a lumped parameter transmission line model of the π-type equivalent circuit is constructed; The lumped parameter transmission line model is optimized using a two-layer optimization model to identify the transmission line parameters; Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

[0008] As one implementation method, the process of optimizing the error compensation amount using the differential evolution algorithm during the inner layer optimization is as follows: An initial population was constructed using a hybrid initialization strategy; some individuals were generated according to a normal distribution based on the mean and standard deviation of the prior error, while the remaining individuals were obtained through random sampling. For each target vector, three distinct individuals are randomly selected, each containing a predetermined number of error compensation dimensions, to generate a mutation vector; Experimental vectors are generated through binomial crossover. The fitness of the experimental vector is compared with that of the current mutated vector, and the vector with smaller local loss is retained; where fitness is the amount of error compensation that minimizes the deviation between the estimated line parameters calculated by the compensated voltage and current phasors and the line parameters given by the outer layer. Record the optimal fitness value for each generation. If the improvement of the optimal fitness is less than the threshold or the maximum number of iterations is reached, terminate the iteration and output the optimal error compensation amount corresponding to the minimum local loss.

[0009] As one implementation method, in the inner-layer optimization process, minimizing the deviation between the estimated line parameters calculated from the compensated voltage and current phasors and the given line parameters in the outer layer constitutes the local loss. The calculation process of the corresponding local loss function is as follows: The ratio of the estimated line parameters calculated by compensation to the corresponding line parameters given by the outer layer is calculated. The squares of the differences between each ratio and 1 are then summed with the corresponding weighting coefficients to obtain the root mean square.

[0010] As one implementation method, during the inner-layer optimization process, the error compensation amount of the calculated voltage and current phasors is compared with the prior error. The loss function corresponding to the total system loss reflecting the statistical consistency of the two is calculated as the weighted sum of the distribution characteristic difference loss and the mean deviation squared loss.

[0011] As one implementation method, a phased optimization strategy is adopted in the outer layer optimization process. First, the sensitivity of the line parameters relative to the total loss of the inner layer optimization is calculated, and the optimization order is determined according to the descending order of sensitivity. Then, single-parameter optimization is performed in this order to transform the three-dimensional problem into a one-dimensional problem and realize a large-scale coarse optimization of the line parameters. Finally, joint optimization of multiple line parameters is performed for fine optimization. When the convergence condition is met, the iteration is terminated and the optimal line parameters are output.

[0012] As one implementation method, the line parameters to be identified include: resistance, reactance, and susceptance.

[0013] A second aspect of the present invention provides a transmission line parameter identification system based on differential evolution and bi-layer optimization.

[0014] In one or more embodiments, a transmission line parameter identification system based on differential evolution and bi-level optimization includes: The model building module is used to construct a lumped parameter transmission line model of a π-type equivalent circuit based on the topology of the transmission line. The parameter identification module is used to optimize the lumped parameter transmission line model using a two-layer optimization model and identify the transmission line parameters. Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

[0015] A third aspect of the present invention provides a computer-readable storage medium.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the transmission line parameter identification method based on differential evolution and bi-level optimization as described above.

[0017] A fourth aspect of the present invention provides an electronic device.

[0018] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the transmission line parameter identification method based on differential evolution and bi-level optimization as described above.

[0019] A fifth aspect of the present invention provides a computer program product.

[0020] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps in the transmission line parameter identification method based on differential evolution and bi-level optimization as described above.

[0021] Compared with the prior art, the beneficial effects of the present invention are: This invention utilizes a two-layer optimization model to optimize the lumped-parameter transmission line model. The outer layer optimization uses line parameters as decision variables and minimizes the total system loss as the objective function, seeking a set of line parameters that maximizes the consistency between the statistical distribution of the calculation error output by the inner layer optimization and the pre-acquired prior error distribution. The inner layer optimization, given a set of line parameters by the outer layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to optimize it, minimizing the deviation between the compensated voltage and current phasor estimates and the line parameters given by the outer layer. The calculated error compensation amounts of the voltage and current phasors are compared with the prior errors to calculate the total system loss reflecting the statistical consistency between the two. This solves the problem that PMU measurement errors exhibit a complex non-Gaussian distribution and are difficult to directly separate during identification. By finding the optimal compensation error, effective separation and compensation of measurement errors are achieved at the algorithm level, improving the parameter identification accuracy of short lines under low signal-to-noise ratio conditions and providing a reliable data foundation for high-precision modeling and analysis of power grids. Attached Figure Description

[0022] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0023] Figure 1 This is a flowchart of the transmission line parameter identification method based on differential evolution and bi-layer optimization according to an embodiment of the present invention; Figure 2 This is a comparison diagram of the relationship between global loss and line parameters in an embodiment of the present invention; Figure 3 This is a single-parameter optimized parameter transfer relationship according to an embodiment of the present invention; Figure 4(a) shows the two-step iterative convergence process of global parameter optimization based on distribution consistency test in an embodiment of the present invention; Figure 4(b) shows the multi-step iterative convergence process of global parameter optimization based on distribution consistency test in an embodiment of the present invention. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0025] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0026] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0027] With the increasing proportion of renewable energy connected to the grid and the widespread adoption of power electronic equipment, the complexity of power grid operation and the requirements for safety and stability are rising, placing higher demands on the accuracy of power grid models. The resistance, reactance, and susceptance parameters of transmission lines are fundamental to advanced applications such as relay protection setting, power flow calculation, state estimation, and stability analysis; their accuracy directly affects the reliability of power grid analysis and control decisions. However, actual line parameters are often affected by factors such as environmental temperature and humidity, conductor aging, and sag changes, resulting in deviations from design values ​​or offline measurements. Therefore, developing technologies capable of accurately identifying the true parameters of power lines online is of great significance for ensuring the safe, reliable, and economical operation of new power systems.

[0028] In traditional power supply units (PMUs), the current sensing element is directly integrated inside the device and fixedly connected to the secondary circuit of the current transformer (CT). This built-in design makes it physically an inseparable node in the secondary circuit. To obtain the error distribution characteristics of its current measurement channel, the CT secondary circuit terminals must be shorted. For safety reasons, the primary equipment must be de-energized. This process is complex, costly, and can affect power supply reliability.

[0029] With the development of non-invasive PMUs, it has become possible to systematically obtain the statistical distribution characteristics of their measurement errors. Non-invasive PMUs can use external clamp-on current transformers, directly clamped to the secondary conductors of a running current transformer (CT). This design allows for the disassembly, assembly, and verification of the PMU without disconnecting or altering existing electrical connections, enabling the acquisition of measurement data and the establishment of a priori database of measurement errors. This provides a reliable data foundation for subsequent error modeling and parameter compensation.

[0030] PMU measurement errors have become a major challenge restricting high-precision parameter identification based on PMU data, and short transmission lines with low signal-to-noise ratios account for a significant proportion of these lines. Therefore, it is urgent to study effective theoretical methods and technical means that can fully utilize prior knowledge of error distribution to effectively suppress or compensate for the impact of these errors, thereby improving the accuracy, stability, and reliability of short-line parameter identification.

[0031] Therefore, it is necessary to establish a robust parameter identification method that is resistant to interference, suppress the interference of measurement errors on weak signals, reduce the systematic deviation of line parameter identification results, and improve the stability and engineering applicability of the identification results.

[0032] according to Figure 1 The transmission line parameter identification method based on differential evolution and bi-layer optimization in this embodiment may include the following steps S1 to S2.

[0033] The specific implementation process of steps S1 to S2 is as follows: Step S1: Based on the topology of the transmission line, construct a lumped parameter transmission line model of the π-type equivalent circuit; Step S2: Optimize the lumped parameter transmission line model using a two-layer optimization model to identify the transmission line parameters; Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

[0034] In this embodiment, the line parameters to be identified include: resistance. R Reactance X and susceptance B.

[0035] Figure 1 The explanations of M1, M2, and M3 are as follows: M1: Given several sets of test parameters as input, call the inner layer optimization to calculate the total loss, and calculate the sensitivity of resistance, reactance, and susceptance to the total loss based on the changes in total loss of different parameters.

[0036] M2: Takes the single parameter to be optimized and two other fixed parameters as input, calls the inner optimization layer, and calculates the single parameter corresponding to the minimum total loss.

[0037] M3: Given three parameters to be optimized as input, call the inner optimization layer to calculate the three parameters corresponding to the minimum total loss.

[0038] In the inner layer optimization process, this embodiment uses the error compensation value based on the differential evolution algorithm for optimization.

[0039] In the measurement errors of a PMU, amplitude error is generally considered a multiplicative error, while phase error is an additive error. Therefore, the compensation methods for these two types of errors are different. The specific compensation formula is as follows: (1) In the formula, superscript comp This indicates the quantity measured after compensation. mea This indicates the actual measurement of the PMU. err Indicates the amount of error compensation; subscript U , I They represent voltage and current, respectively. t i Indicates the first t i A specific point in time.

[0040] Based on the obtained error compensation amount, the parameter identification result of the measured phasor after error compensation can be calculated. The calculation formula is as follows: (2) In the formula, the subscripts m and n represent the PMU measurements at both ends of the line, and est represents the identification value; and These represent voltage phasors and current phasors, respectively.

[0041] In the inner-layer optimization process, the local loss is defined as minimizing the deviation between the estimated line parameters calculated from the compensated voltage and current phasors and the line parameters given in the outer layer. The calculation process of the corresponding local loss function is as follows: The ratio of the estimated line parameters calculated by compensation to the corresponding line parameters given by the outer layer is calculated. The squares of the differences between each ratio and 1 are then summed with the corresponding weighting coefficients to obtain the root mean square.

[0042] For example, the identification parameters obtained after error compensation are compared with the outer layer optimized output parameters. R opt , X opt , B opt The difference between them is the local loss, and the local loss is used to calculate the loss. Minimization is the optimization objective, and the loss function is calculated using the following formula: (3) In the formula, α 1 、α 2 、α 3 represents the weighting coefficients for resistance, reactance, and susceptance, respectively. α 1 、α 2 、α 3. All three have the same value, which is 1 / 3.

[0043] The three-phase voltage amplitude error, voltage phase angle error, and current phase angle error of the dual-ended PMU are set as variables to be optimized, totaling 18 dimensions, with dimension index sequence number as follows: k Because the error parameters to be identified have high dimensionality and there are coupling relationships between variables, the optimization algorithm may get stuck in a local optimum.

[0044] To efficiently solve high-dimensional optimization problems, a differential evolution algorithm is used to optimize the error compensation amount, thereby minimizing local loss. J local This algorithm maintains population diversity through differential mutation and crossover operations, which helps avoid getting trapped in local optima and effectively alleviates the search performance degradation caused by dimensionality increase, thus achieving robust estimation of error parameters.

[0045] The process of optimizing the error compensation amount using the differential evolution algorithm is as follows: An initial population was constructed using a hybrid initialization strategy; some individuals were generated according to a normal distribution based on the mean and standard deviation of the prior error, while the remaining individuals were obtained through random sampling. For each target vector, three distinct individuals are randomly selected, each containing a predetermined number of error compensation dimensions, to generate a mutation vector; Experimental vectors are generated through binomial crossover. The fitness of the experimental vector is compared with that of the current mutated vector, and the vector with smaller local loss is retained; where fitness is the amount of error compensation that minimizes the deviation between the estimated line parameters calculated by the compensated voltage and current phasors and the line parameters given by the outer layer. Record the optimal fitness value for each generation. If the improvement of the optimal fitness is less than the threshold or the maximum number of iterations is reached, terminate the iteration and output the optimal error compensation amount corresponding to the minimum local loss.

[0046] In the inner-layer optimization process, the error compensation of the calculated voltage and current phasors is compared with the prior error. The loss function corresponding to the total system loss that reflects the statistical consistency of the two is calculated as the weighted sum of the distribution characteristic difference loss and the mean deviation squared loss.

[0047] For example, based on the obtained optimal error compensation amount, it is compared with the prior error distribution. The statistical distribution of the error compensation sequence at all time points is calculated to ensure consistency with the known prior error distribution, and this consistency is used as the global loss function. J total This loss will be used to guide the updating of global circuit parameters in the outer layer optimization. With the goal of minimizing this loss, the loss function is calculated as follows: (4) loss function loss 1 and loss The formula for calculating 2 is: (5) (6) In the formula, N Indicates the number of measurement time sections. and Let the first and second errors be the prior error distribution and the optimized error distribution, respectively. k The cumulative distribution function of each component; λ 1 and λ 2 is the weighting coefficient, which can be set according to the actual situation. The sum of the two is 1. error_opt This represents the error compensation amount obtained through optimization. error_prior This represents the PMU prior error; x A pre-defined constant.

[0048] loss function loss The 1 represents the distributional characteristic difference loss, used to quantify the difference between the computational error and the prior error in the overall statistical distribution. It exhibits strong robustness when the parameters are close to the true value, effectively suppressing the influence of noise and local disturbances, thus ensuring the accuracy of the final output parameter identification. However, when the parameter values ​​deviate significantly from the true value, the computational error often undergoes severe distortion, leading to loss. loss The response to parameters with different degrees of deviation tends to be flat, making it difficult to provide sufficient discrimination to form an effective optimization gradient.

[0049] loss function loss The 2 represents the mean deviation sum of squares loss, used to measure the degree of deviation of the error sample from the center of the prior error distribution. When the parameter is far from the true value, this loss value has a clear monotonic relationship with the degree of parameter deviation, thus providing a clear gradient direction for the optimization process and driving the parameter to converge towards the true value. However, since this loss depends only on the mean information of the prior error, it is extremely sensitive to data fluctuations when the parameter is close to the true value, and its robustness is weak. If used alone, it can easily lead to instability in the optimization process or convergence to a local optimum.

[0050] When the parameters deviate significantly from the true value, the loss based on the distribution consistency test... loss1. The response is smooth and the value is small, while the loss is based on the mean deviation. loss The value 2 is relatively large, therefore it accounts for a larger proportion in the weighted loss, providing a clear gradient guide for parameter optimization and accelerating parameter convergence; while when the parameters are close to the true value, loss 2 approaches 0, at which point the distribution characteristics differ. loss 1. This mechanism is primary, ensuring the accuracy and stability of the algorithm during the convergence phase. A dual-loss weighted structure guarantees that the optimization process, globally, balances convergence efficiency and identification accuracy. The global loss corresponds to the line parameters as follows: Figure 2 As shown.

[0051] To improve the robustness and efficiency of the optimization process, a phased optimization strategy is adopted in the outer layer optimization process. First, the sensitivity of the line parameters relative to the total loss of the inner layer optimization is calculated, and the optimization order is determined according to the descending order of sensitivity. Then, single-parameter optimization is performed in this order to transform the three-dimensional problem into a one-dimensional problem and realize a large-scale coarse optimization of the line parameters. Finally, joint optimization of multiple line parameters is performed for fine optimization. When the convergence condition is met, the iteration is terminated and the optimal line parameters are output.

[0052] Considering the coupling of resistance, reactance, and susceptance parameters during parameter optimization, even if a parameter approaches its true value during iteration, the global loss function may remain high if other parameters still deviate significantly from the true value. This makes it difficult for the optimization algorithm to effectively identify and retain the locally correct information already obtained for that parameter. Since the global objective function is not significantly improved, the algorithm may continue to adjust all parameters in the wrong direction, causing parameters that were already close to the true value to deviate from it again. Therefore, this embodiment employs a staged optimization strategy to optimize the line parameters.

[0053] 1) Sensitivity calculation ( Figure 1 (M1) When the initial parameter values ​​are unknown, they can be set within a reasonable range based on typical engineering experience. Based on the initial parameter values, the sensitivity of the three parameters—resistance, reactance, and susceptance—to the total loss is calculated. Parameters with higher sensitivity have a more significant impact on the total loss; prioritizing their optimization can effectively improve convergence efficiency. Therefore, the three parameters are ranked according to the sensitivity calculation results to determine the subsequent optimization order for individual parameters. The sensitivity calculation formula is: (7) (8) (9) In the formula, the subscript init This indicates the initial value of the corresponding parameter. , , These are the sensitivities of resistance, reactance, and susceptance, respectively. L 1. L 2 represents two low-magnification test points, with values ​​less than 1. H 1. H 2 represents two high-magnification test points, with values ​​greater than 1. To ensure that the parameter values ​​at the low-magnification test points are less than the true values ​​and those at the high-magnification test points are greater than the true values, in practical applications, a set of smaller values ​​should be selected for the low-magnification test points (e.g., 0.2, 0.4), and a set of larger values ​​should be selected for the high-magnification test points (e.g., 5, 6).

[0054] In the sensitivity ranking calculation, equation (3) represents the local loss. J local All three weighting coefficients are taken to have the same value.

[0055] 2) Single-parameter search optimization ( Figure 1 (M2) Based on the descending order of sensitivity, the single-parameter optimization process for the three parameters is divided into three stages with a determined optimization order: first, the line parameter corresponding to the highest sensitivity is optimized, and the optimization result is used as the input parameter for the next stage; finally, the parameter with the lowest sensitivity is optimized. In each stage, the other two parameters are fixed, thus transforming the three-dimensional optimization problem into a one-dimensional search problem, such as... Figure 3 As shown.

[0056] The parameter optimization process is as follows: First, a grid search method is used to initially explore the parameter space. The parameters to be optimized are discretized within their upper and lower bounds, with each parameter being evenly divided into several parts, thus forming a grid set in the parameter space. Then, the global loss function value corresponding to each parameter in the grid is calculated by traversing the grid, and the parameter corresponding to the minimum global loss is retained by comparison.

[0057] Then, within the range of the left and right adjacent points of the minimum global loss point, the golden section algorithm is used to find the optimal value, which quickly converges to a parameter value with relatively high accuracy. During this process, the local loss of equation (3) can be increased. J local The weight coefficients corresponding to the current parameter to be optimized are used to strengthen the optimization guidance of that parameter and improve its optimization efficiency. The resulting output parameters will be used as inputs for the next parameter optimization, thereby making the resistance, reactance, and susceptance parameters continuously approach their true values.

[0058] 3) Joint optimization of three parameters ( Figure 1 (M3) The line parameters optimized by a single parameter are used as the initial values ​​of the parameters in this stage. Considering that the total loss function is calculated from the inner optimization results, the analytical gradient is difficult to obtain. However, Nelder-Mead guides the search by comparing the function values ​​of the simplex vertices, which does not require gradients and is suitable for low-dimensional joint search. Therefore, Nelder-Mead simplex method is used for joint optimization.

[0059] Based on single-parameter optimization results y Construct an initial simplex centered at 0. Since there are three parameters to be optimized, four vertices are constructed, and the calculation formula is shown below: (10) Where α is the initial step size factor. These represent the optimized resistance, reactance, and susceptance, respectively.

[0060] Calculate the total loss function of the four vertices mentioned above. f ( y )= J total ( R , X , B And sort the vertices according to the function size as follows: f ( x l )< f ( x s )< f ( x m )< f ( x h Then, remove the vertex with the largest loss function value. y h And calculate the mean of the remaining three vertices as the centroid of the simplex. y c Next, using the center of gravity as a reference, reflect the worst vertex to obtain the reflection point. y r Based on the loss function value corresponding to the reflection point, the simplex vertices are updated through expansion, contraction, or shrinkage operations, and the original worst vertex is replaced with the new vertex. This process is repeated iteratively until the algorithm converges, ultimately yielding the line parameters corresponding to the minimum loss function value.

[0061] 4) Iterative convergence judgment; Sensitivity analysis, single-parameter optimization, and joint optimization constitute one main iteration. After each iteration, the global loss corresponding to the current optimal parameter is calculated and compared with the global loss of the previous main iteration. If the difference between the global losses corresponding to the optimal parameters in two consecutive iterations is less than a preset threshold, the algorithm is considered to have converged, and the iteration terminates; if it has not converged, the current optimal parameter is used as a new initial point, sensitivity analysis is performed again, and the next main iteration begins until the convergence condition is met. The iterative convergence process of the algorithm is as follows: Figure 3 As shown.

[0062] Figure 4(a) illustrates an ideal, efficient convergence scenario: the algorithm optimizes the line parameters in the first iteration, and the second iteration serves as a verification iteration, confirming that the result has stably converged to the optimal solution. Figure 4(b) shows a more common multi-step convergence process: the algorithm significantly optimizes the parameters in the first iteration, but does not reach the optimal value, providing a better starting point for the next iteration. This design reduces the dependence on the precise initial values ​​of the parameters, and through a finite number of iterations of gradual approximation, ultimately ensures that the algorithm stably converges from a wide range of initial values ​​to the global optimum.

[0063] The method described in this invention exhibits excellent engineering adaptability and robustness. By designing a phased optimization strategy, the sensitivity to initial parameter values ​​is significantly reduced. Through a dual-loss function weighting mechanism, the algorithm can balance optimization efficiency and accuracy, avoiding getting trapped in local optima. Furthermore, this method is independent of specific operating conditions or line lengths, flexibly adapting to various changing conditions in actual power grid operation. Compared to traditional methods, it significantly enhances the stability and reliability of the algorithm while improving the accuracy of parameter identification.

[0064] In one or more embodiments, a transmission line parameter identification system based on differential evolution and two-layer optimization is provided, which can be implemented in software. The transmission line parameter identification system based on differential evolution and two-layer optimization includes the following software modules: The model building module is used to construct a lumped parameter transmission line model of a π-type equivalent circuit based on the topology of the transmission line. The parameter identification module is used to optimize the lumped parameter transmission line model using a two-layer optimization model and identify the transmission line parameters. Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

[0065] It should be noted that each module in the transmission line parameter identification system based on differential evolution and bi-layer optimization in this embodiment corresponds one-to-one with each step in the transmission line parameter identification method based on differential evolution and bi-layer optimization in the above embodiment, and their specific implementation processes are the same, so they will not be repeated here.

[0066] The structure of the electronic device according to embodiments of the present invention is described in detail below. The electronic device provided in embodiments of the present invention includes: at least one processor, a memory, a user interface, and at least one network interface. The various components in the transmission line parameter identification system based on differential evolution and two-layer optimization are coupled together through a bus system. It can be understood that the bus system is used to realize the connection and communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus. The user interface may include a display, keyboard, mouse, trackball, click wheel, buttons, a touchpad, or a touch screen, etc.

[0067] It is understood that the memory can be volatile memory or non-volatile memory, or both. The memory in this embodiment of the invention is capable of storing data to support the operation of the terminal. Examples of this data include any computer programs used to operate on the terminal, such as operating systems and applications. The operating system includes various system programs, such as the framework layer, core library layer, driver layer, etc., used to implement various basic services and handle hardware-based tasks. Applications can include various applications.

[0068] In some embodiments, the transmission line parameter identification system based on differential evolution and two-layer optimization provided in this invention can be implemented using a combination of hardware and software. For example, the transmission line parameter identification system based on differential evolution and two-layer optimization provided in this invention can be a processor in the form of a hardware decoding processor, which is programmed to execute the transmission line parameter identification method based on differential evolution and two-layer optimization provided in this invention. For instance, the processor in the form of a hardware decoding processor can employ one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0069] As an example, a processor can be an integrated circuit chip with signal processing capabilities, such as a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., where a general-purpose processor can be a microprocessor or any conventional processor, etc.

[0070] As an example of the hardware implementation of the transmission line parameter identification system based on differential evolution and two-layer optimization provided in this embodiment of the invention, the device provided in this embodiment of the invention can be directly executed by a processor in the form of a hardware decoding processor. For example, it can be executed by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components to implement the transmission line parameter identification method based on differential evolution and two-layer optimization provided in this embodiment of the invention.

[0071] The memory in this embodiment of the invention is used to store various types of data to support the operation of the transmission line parameter identification system based on differential evolution and two-level optimization, or to store data for execution. Figure 1The program code for the method shown. Examples of this data include: any executable instructions for operation on a transmission line parameter identification system based on differential evolution and two-level optimization, such as executable instructions that can be included in the executable instructions to implement the transmission line parameter identification method based on differential evolution and two-level optimization of the present invention.

[0072] Specifically, according to embodiments of this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program including functions for executing... Figure 1 The program code for the method shown. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by the central processing unit, it performs the various functions defined in the apparatus of this application.

[0073] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0074] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying transmission line parameters based on differential evolution and bi-level optimization, characterized in that, include: Based on the topology of the transmission line, a lumped parameter transmission line model of the π-type equivalent circuit is constructed; The lumped parameter transmission line model is optimized using a two-layer optimization model to identify the transmission line parameters; Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

2. The transmission line parameter identification method based on differential evolution and bi-level optimization as described in claim 1, characterized in that, In the inner layer optimization process, the process of using the differential evolution algorithm to optimize the error compensation amount is as follows: An initial population was constructed using a hybrid initialization strategy; some individuals were generated according to a normal distribution based on the mean and standard deviation of the prior error, while the remaining individuals were obtained through random sampling. For each target vector, three distinct individuals are randomly selected, each containing a predetermined number of error compensation dimensions, to generate a mutation vector; Experimental vectors are generated through binomial crossover. The fitness of the experimental vector is compared with that of the current variant vector, and the vector with smaller local loss is retained; where fitness is the amount of error compensation that minimizes the deviation between the estimated line parameters calculated by the compensated voltage and current phasors and the line parameters given by the outer layer. Record the optimal fitness value for each generation. If the improvement of the optimal fitness is less than the threshold or the maximum number of iterations is reached, terminate the iteration and output the optimal error compensation amount corresponding to the minimum local loss.

3. The transmission line parameter identification method based on differential evolution and bi-level optimization as described in claim 1, characterized in that, In the inner-layer optimization process, the local loss is defined as minimizing the deviation between the estimated line parameters calculated from the compensated voltage and current phasors and the line parameters given in the outer layer. The calculation process of the corresponding local loss function is as follows: The ratio of the estimated line parameters calculated by compensation to the corresponding line parameters given by the outer layer is calculated. The squares of the differences between each ratio and 1 are then summed with the corresponding weighting coefficients to obtain the root mean square.

4. The transmission line parameter identification method based on differential evolution and bi-level optimization as described in claim 1, characterized in that, In the inner-layer optimization process, the error compensation of the calculated voltage and current phasors is compared with the prior error. The loss function corresponding to the total system loss that reflects the statistical consistency of the two is calculated as the weighted sum of the distribution characteristic difference loss and the mean deviation squared loss.

5. The transmission line parameter identification method based on differential evolution and bi-level optimization as described in claim 1, characterized in that, In the outer layer optimization process, a phased optimization strategy is adopted. First, the sensitivity of the line parameters relative to the total loss of the inner layer optimization is calculated, and the optimization order is determined according to the descending order of sensitivity. Then, single parameter optimization is performed in this order to transform the three-dimensional problem into a one-dimensional problem and realize a large-scale coarse optimization of the line parameters. Finally, joint optimization of multiple line parameters is performed for fine optimization. When the convergence condition is met, the iteration is terminated and the optimal line parameters are output.

6. The method for identifying transmission line parameters based on differential evolution and bi-level optimization as described in claim 1, characterized in that, The circuit parameters to be identified include: resistance, reactance, and susceptance.

7. A transmission line parameter identification system based on differential evolution and bi-level optimization, characterized in that, The transmission line parameter identification method based on differential evolution and bi-level optimization as described in any one of claims 1-6 includes: The model building module is used to construct a lumped parameter transmission line model of a π-type equivalent circuit based on the topology of the transmission line. The parameter identification module is used to optimize the lumped parameter transmission line model using a two-layer optimization model and identify the transmission line parameters. Among them, the outer optimization of the two-layer optimization model takes the line parameters as decision variables and minimizes the total system loss as the objective function. It seeks a set of line parameters that make the statistical distribution characteristics of the calculation error output of the inner optimization have the highest consistency with the pre-acquired error prior distribution. The inner-layer optimization, given a set of line parameters by the outer-layer optimization, uses the measurement error compensation amount at each PMU data sampling time as the optimization variable and employs a differential evolution algorithm to find the optimal value, so that the estimated values ​​of line parameters calculated by the compensated voltage and current phasors have the smallest deviation from the line parameters given by the outer layer. The calculated error compensation amount of the voltage and current phasors is compared with the prior error, and the total system loss reflecting the statistical consistency between the two is calculated.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the transmission line parameter identification method based on differential evolution and bi-level optimization as described in any one of claims 1-6.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the transmission line parameter identification method based on differential evolution and bi-layer optimization as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the transmission line parameter identification method based on differential evolution and bi-level optimization as described in any one of claims 1-6.

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