A method for predicting the open-circuit impedance curve of a large hydro-generator by using an intelligent optimization algorithm

Abstract

The application discloses a method for predicting a large hydro-generator open-circuit impedance curve by using an intelligent optimization algorithm, collecting impedance points under a small amount of key angles when an open-circuit fault occurs, embedding sparse measured data into a high-dimensional phase space by using a chaotic time series phase space reconstruction technology and generating virtual samples to enhance the information quantity of a data set, establishing a composite circular curve model conforming to an open-circuit impedance trajectory form, constructing an improved particle swarm optimization algorithm fusing a simulated annealing mechanism, simultaneously introducing a curvature change smoothing regular term, and then searching for optimal model parameters, and finally substituting the equation to generate full-range impedance point coordinates according to fine angle steps to realize high-precision reconstruction from a small amount of measured points to a complete curve. The application breaks through the limitation of traditional methods which depend on a large amount of measured data, has high reconstruction curve precision and strong physical consistency, significantly reduces field test cost and engineering deployment difficulty, and improves real-time performance and economy of open-circuit fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of generator fault prediction technology, specifically relating to a method for predicting the loss-of-magnetic impedance curve of a large hydro-generator using an intelligent optimization algorithm. Background Technology

[0002] In the actual operation of a hydro-generator, its stator voltage With stator current The following relationship exists: its output power Its impedance .in Let U be the angle between voltage U and current I. Then the vector... This is called the measured impedance of the generator.

[0003] When a generator's excitation system malfunctions and causes the magnetic field to disappear, the generator will lose its ability to operate synchronously and will enter an asynchronous operating state. At this time, the generator will exhibit the following characteristics: 1. Stator current Increased: Due to the weakened magnetic field, the generator requires a larger current to maintain output voltage and power; 2. Reduced reactive power Q: After loss of excitation, the generator cannot provide sufficient reactive power to support the voltage stability of the power grid; 3. Voltage Decrease: As reactive power decreases, the voltage level in the power grid will also decrease accordingly.

[0004] Generator loss-of-excitation protection primarily determines whether a loss-of-excitation fault has occurred by monitoring changes in the generator's electrical quantities. Among these, impedance parameters... This is one of the important bases for judging loss-of-excitation faults; by comparing the difference in impedance characteristics between the generator under normal operating conditions and under loss-of-excitation conditions, accurate identification and protection actions for loss-of-excitation faults can be achieved. When the generator is operating normally, it generates active power and absorbs reactive power, with P being positive and Q being negative. Its measured impedance is as follows: Figure 5 As shown, point A is the location of the measured impedance in the impedance plane. Let OA be the angle between voltage and current, and the length of line segment OA be the magnitude of the impedance. When a fault occurs, voltage U decreases, current I increases, resulting in a decrease in Z, and the angle... This can also change, as seen at point B. Therefore, we need to determine an impedance range boundary for the relay protection device to determine whether a loss of excitation fault has occurred. This range is represented by the red curve in the coordinate system. When the coordinates of the impedance point fall within the red circle, a loss of excitation fault is identified; otherwise, it is considered normal.

[0005] In existing technologies, the generator loss-of-excitation impedance determination curve mainly relies on actual measurements. To obtain a complete impedance curve equation, a large amount of data needs to be measured. The impedance angle from 0° to 360° forms a closed-loop curve. This measurement method is time-consuming, labor-intensive, and very cumbersome. If an accuracy of 1° is required, 360 points need to be measured to obtain a complete curve, which is inefficient. However, if measurements are taken at 10° intervals, the amount of data is reduced, but the accuracy is still insufficient.

[0006] Therefore, it is necessary to design a method that uses intelligent optimization algorithms to predict the demagnetization impedance curve of large hydro-generators to solve the above problems. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm. This method aims to overcome the technical shortcomings of traditional methods, such as reliance on a large amount of measured data, low curve fitting accuracy, and high engineering deployment costs. It requires only a few measured impedance points to achieve full curve reconstruction, significantly improving the economy and real-time performance of demagnetization fault monitoring, and providing reliable technical support for rapid fault diagnosis of large hydro-generators.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm includes the following steps: Key impedance point acquisition: When a generator loss-of-excitation fault occurs, acquire the amplitude Z and angle of 3-5 key impedance points. ; Virtual sample generation: Using the theory of chaotic time series phase space reconstruction, key impedance points are arranged in angular order and embedded into a high-dimensional phase space. A set of virtual impedance points is generated through local linear mapping, which together with the key impedance points constitute an enhanced sample set. Curve Model Assumptions: Based on the approximate Cartesian cardioid characteristics of the loss-magnetic impedance curve on the complex plane, the mathematical model of the curve is assumed to be a composite circular curve equation, which includes amplitude-related parameters and phase offset. Hybrid intelligent optimization algorithm construction: An improved particle swarm optimization algorithm integrating simulated annealing mechanism is constructed. The composite objective function formed by the weighted sum of squared residuals of the measured impedance points and the enhanced sample set and the model predictions, plus the curve curvature change smoothing regularization term, is used as the optimization objective to establish a parameter optimization model. Model parameter optimization: The enhanced sample set is input into the hybrid intelligent optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination; the collected measured data is input into the particle swarm optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination. Full curve equation establishment and impedance point derivation: Substitute the optimal parameter combination into the assumed composite circular curve equation to obtain the final loss-of-magnetism impedance curve equation, and generate the full-range impedance point coordinates according to the preset angle step size to realize the reconstruction from a few points to the complete curve.

[0009] Preferably, in the critical impedance point acquisition step, the acquisition times are selected at the initial stage, development stage, and near-stable stage of simulated demagnetization, respectively, and the difference in impedance angle between adjacent acquired critical impedance points is not less than 30°; the acquired critical impedance points include impedance angles. There are four points: 0°, 90°, 180°, and 270°.

[0010] Preferably, the virtual sample generation step specifically includes: Collected The key impedance points are arranged in ascending order of impedance angle, and their impedance magnitudes are extracted to form a one-dimensional sequence. ,in Indicates the first The impedance amplitude at each measured point The number of measured points and ; Sequence determination using mutual information method Optimal delay time The calculation formula is as follows: ; in, For the delay steps, and They are respectively and Marginal probability distribution, For the joint probability distribution, take the mutual information function. When the local minimum is reached for the first time As the optimal delay time; The embedding dimension is determined using the Cao method. ; Based on the optimal delay time and embedding dimension The original one-dimensional amplitude sequence is reconstructed into a high-dimensional phase space to obtain the set of phase points. ; For each phase point Select within its neighborhood Using the nearest neighbor points, construct a local linear regression model to generate virtual phase points. The calculation formula is as follows: ; in, and To minimize The regression matrix and bias vector are obtained from the linear reconstruction error of the nearest neighbor in the neighborhood. For the first generated in phase space A virtual phase point; The generated virtual phase point The first dimension coordinate is extracted as the virtual impedance amplitude, and a corresponding angle value is assigned to form a virtual impedance point, which is then merged with the key impedance point to form an enhanced sample set.

[0011] Preferably, the embedding dimension is determined using the Cao method. The calculation formula is: ; in, For the embedding dimension, for The first in 3D phase space One phase point, In order to be in In 3D phase space and The nearest neighbor point, Represents Euclidean distance. and The corresponding phase points are at Extension in 3D space; taking Follow When the change tends to saturate The value is used as the optimal embedding dimension.

[0012] Preferably, in the curve model assumption step, the vector form of the assumed compound circular curve equation is: ; Where a, b, and c are amplitude-related parameters. , where is the phase offset, and are all unknown parameters to be optimized. t is a variable parameter in the parametric equation.

[0013] Preferably, in the hybrid intelligent optimization algorithm construction step, the improved particle swarm optimization algorithm, based on the introduction of nonlinear inertia weights and adaptive learning factors, further integrates a simulated annealing mechanism: after each particle position update, the fitness difference between the new position and the old position is calculated. ,like Then accept the new position; otherwise, accept the new position. The probability of accepting a new position, where temperature The decay gradually decreases with each iteration.

[0014] Preferably, the construction and execution of the hybrid intelligent optimization algorithm includes particle encoding and initialization: The combination of parameters to be optimized is encoded into a particle position vector. ,in , , , The first The amplitude parameters and phase shifts corresponding to each particle; random initialization. The position vector and velocity vector of each particle , Take 30 to 50.

[0015] Preferably, the construction and execution of the hybrid intelligent optimization algorithm further includes fitness calculation, and the calculated fitness value is used as the composite objective function: For each particle, its position vector components are substituted into the composite circular curve equation to obtain the predicted curve. Calculate the fitness value of the particle. : ; in, For the enhanced sample set, the first The coordinates of the impedance points To assign a value to the parameter corresponding to that point, To increase the number of points in the sample set, For the first The weighting coefficients of each sample point For particles The defined curve in the parameters curvature at that point This is a discrete approximation of the rate of change of curvature. and M is the preset balance coefficient, M is the number of discrete sampling points for curvature, and the curve curvature change smoothing regularization term is used to constrain the second-order smoothness of the fitted curve.

[0016] Preferably, for two-dimensional parametric equations The curvature formula is: ; Among them, the discrete approximation of the rate of change of curvature The calculation formula is: ; in, and These are the parameter values ​​corresponding to the discrete sampling points of curvature.

[0017] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes updating the inertia weights and learning factors: Calculate the current iteration number Corresponding nonlinear inertia weight and adaptive learning factor , : ; ; ; in, and These are the maximum and minimum values ​​of the inertia weight, respectively. The maximum number of iterations, It is a non-linear decay exponent. , As the initial learning factor, , To terminate the learning factor.

[0018] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes particle velocity and position updates, updating the velocity of each particle according to the following formula. and location : ; ; in, and A random number within the interval [0,1]. For particles The best historical position This is the current globally optimal position.

[0019] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes simulated annealing acceptance determination: Calculate new position relative to the original position fitness difference ;like If so, then accept the new position; if Then, based on probability Accepting the new position: ; in, Given the current temperature, follow the cooling strategy. renew, The initial temperature. The cooling coefficient, If accepted, then update. Otherwise, keep the original position.

[0020] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes global optimal update and termination judgment: After traversing all particles, update the global optimal position. and its fitness value ;like No significant decrease was observed after a fixed number of iterations, or the number of iterations reached... If the iteration terminates, the global optimal solution is output as the optimal parameter combination: , , , .

[0021] Preferably, in the model parameter optimization step, the particle dimension is 4, corresponding to a, b, c, Four parameters to be optimized, with the number of particles set to 30-50; the iteration termination condition is that the composite objective function value stabilizes for several consecutive generations or the maximum number of iterations is reached.

[0022] Preferably, in the steps of establishing the equation of the entire curve and deriving the impedance point, the preset angle step size is: traversal Substitute the values ​​into the final loss-of-magnetism impedance curve equation to calculate the impedance amplitude at the corresponding angle. Generate the full-range impedance point coordinates (| |, ).

[0023] Preferably, the method further includes a result verification step: using the root mean square error (S) to evaluate the deviation between the fitted curve and the measured points; when S≤0.02, the curve equation is determined to be valid; if the verification condition is not met, 1-2 measured points are added and the optimization process is re-executed.

[0024] Preferably, a system for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm is provided for executing the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm. The system includes: The acquisition module is used to obtain the amplitude and angle of several key impedance points when a generator loses excitation fault occurs; The phase space reconstruction module is used to sort the acquired key impedance points by angle and embed them into a high-dimensional phase space to generate virtual impedance points to form an enhanced sample set. The model building module is used to assume the composite circular curve equation of the loss-of-magnetism impedance curve; The hybrid optimization module is configured to execute an improved particle swarm optimization algorithm that incorporates simulated annealing mechanism, and optimizes the parameters of the composite circular curve equation using a composite objective function consisting of the weighted sum of squared residuals and the curvature change smoothing regularization term as the optimization criterion. The curve generation module is used to generate the final loss-of-magnetism impedance curve equation based on the optimized parameters, and output the coordinates of the full-range impedance points according to the preset angle step size.

[0025] Preferably, it also includes a computer device, including a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the method for predicting the loss-of-magnetic impedance curve of a large hydro-generator using an intelligent optimization algorithm.

[0026] Preferably, the method further includes a computer-readable storage medium storing computer instructions for causing a computer to execute the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm.

[0027] The beneficial effects of the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm provided by this invention are as follows: 1. This invention introduces chaotic time series phase space reconstruction technology to embed the limited number of 3 to 5 measured impedance points into a high-dimensional phase space and generate abundant virtual samples, effectively overcoming the bottleneck of traditional methods that rely on a large amount of field-collected data. This technology utilizes the inherent dynamic characteristics of the impedance amplitude sequence arranged angularly during demagnetization to expand the training sample set while maintaining the original curve topology, thus enabling stable reconstruction of the complete demagnetization impedance curve profile even under extremely sparse measured conditions. This approach fundamentally solves the problem of fitting divergence or severe local distortion caused by insufficient measured points in existing technologies, allowing this method to obtain reliable curve prediction results even in the early stages of faults and when data is extremely scarce.

[0028] 2. This invention constructs an improved particle swarm optimization algorithm that integrates simulated annealing and introduces a curvature change smoothing regularization term to construct a composite objective function. This elevates the curve fitting problem from a simple data approximation problem to a multi-objective optimization problem that considers both data fitting accuracy and the physical rationality of the curve. The hybrid optimization strategy retains the global collaborative search capability of the particle swarm algorithm while leveraging the probabilistic jump mechanism of simulated annealing to escape local optima traps, avoiding the premature convergence defects of traditional single algorithms. The geometric regularization term forces the fitted curve to maintain a smooth curvature transition, conforming to the inertial characteristics and electromagnetic change laws of the generator demagnetization process. This scheme significantly improves the ability of the curve equation to represent the real demagnetization impedance trajectory, and the fitting results are more physically consistent.

[0029] 3. This invention, through an integrated technology chain of "few-point acquisition—virtual enhancement—intelligent optimization—full-curve reconstruction," enables the automatic generation of a continuous impedance curve covering all angles by measuring impedance points at only four typical angles on-site. This fundamentally changes the cumbersome mode of traditional technology, which involves point-by-point measurement and repeated trial and error. This method eliminates the need for large-scale manual mapping of complete impedance diagrams, significantly reducing on-site testing workload and the long-term occupation of high-precision measuring equipment. Simultaneously, the provided high-precision curve can be directly embedded into the setting logic of relay protection devices, providing real-time and reliable technical support for rapid diagnosis of demagnetization faults and protection action decisions in large hydro-generators. It possesses extremely high engineering practicality and economic efficiency. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the system structure of the present invention; Figure 2 This is a schematic diagram of the method flow of the present invention; Figure 3 This is a schematic diagram of the Cartesian cardioid curve assumed in the schematic curve model of this embodiment of the invention; Figure 4 This is a schematic diagram showing the relative prediction error distribution of the method described in this invention compared to the traditional interpolation method and the standard PSO fitting method at 15 test angles in an embodiment of the invention. Figure 5 This is a schematic diagram illustrating the principle of generator impedance measurement in the background art of this invention; Figure 6 This is a point graph showing the output results of the generator demagnetization impedance curve equation in an embodiment of the present invention; Figure 7 This is a schematic diagram of the final result of impedance curve fitting in an embodiment of the present invention; Figure 8 This is a schematic diagram of the structure of a computer device in an embodiment of the present invention. Detailed Implementation

[0031] Example 1: like Figure 1 As shown, a method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm includes the following steps: Key impedance point acquisition: When a generator loss-of-excitation fault occurs, acquire the amplitude Z and angle of 3-5 key impedance points. ; Virtual sample generation: Using the theory of chaotic time series phase space reconstruction, key impedance points are arranged in angular order and embedded into a high-dimensional phase space. A set of virtual impedance points is generated through local linear mapping, which together with the key impedance points constitute an enhanced sample set. Curve Model Assumptions: Based on the approximate Cartesian cardioid characteristics of the loss-magnetic impedance curve on the complex plane, the mathematical model of the curve is assumed to be a composite circular curve equation, which includes amplitude-related parameters and phase offset. Hybrid intelligent optimization algorithm construction: An improved particle swarm optimization algorithm integrating simulated annealing mechanism is constructed. The composite objective function formed by the weighted sum of squared residuals of the measured impedance points and the enhanced sample set and the model predictions, plus the curve curvature change smoothing regularization term, is used as the optimization objective to establish a parameter optimization model. Model parameter optimization: The enhanced sample set is input into the hybrid intelligent optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination; the collected measured data is input into the particle swarm optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination. Full curve equation establishment and impedance point derivation: Substitute the optimal parameter combination into the assumed composite circular curve equation to obtain the final loss-of-magnetism impedance curve equation, and generate the full-range impedance point coordinates according to the preset angle step size to realize the reconstruction from a few points to the complete curve.

[0032] Preferably, in the critical impedance point acquisition step, the acquisition times are selected at the initial stage, development stage, and near-stable stage of simulated demagnetization, respectively, and the difference in impedance angle between adjacent acquired critical impedance points is not less than 30°; the acquired critical impedance points include impedance angles. There are four points: 0°, 90°, 180°, and 270°.

[0033] Preferably, the virtual sample generation step specifically includes: Collected The key impedance points are arranged in ascending order of impedance angle, and their impedance magnitudes are extracted to form a one-dimensional sequence. ,in Indicates the first The impedance amplitude at each measured point The number of measured points and ; Sequence determination using mutual information method Optimal delay time The calculation formula is as follows: ; in, For the delay steps, and They are respectively and Marginal probability distribution, For the joint probability distribution, take the mutual information function. When the local minimum is reached for the first time As the optimal delay time; The embedding dimension is determined using the Cao method. ; Based on the optimal delay time and embedding dimension The original one-dimensional amplitude sequence is reconstructed into a high-dimensional phase space to obtain the set of phase points. ; For each phase point Select within its neighborhood Using the nearest neighbor points, construct a local linear regression model to generate virtual phase points. The calculation formula is as follows: ; in, and To minimize The regression matrix and bias vector are obtained from the linear reconstruction error of the nearest neighbor in the neighborhood. For the first generated in phase space A virtual phase point; The generated virtual phase point The first dimension coordinate is extracted as the virtual impedance amplitude, and a corresponding angle value is assigned to form a virtual impedance point, which is then merged with the key impedance point to form an enhanced sample set.

[0034] Preferably, the embedding dimension is determined using the Cao method. The calculation formula is: ; in, For the embedding dimension, for The first in 3D phase space One phase point, In order to be in In 3D phase space and The nearest neighbor point, Represents Euclidean distance. and The corresponding phase points are at Extension in 3D space; taking Follow When the change tends to saturate The value is used as the optimal embedding dimension.

[0035] Preferably, such as Figure 3 As shown, in the curve model assumption step, the assumed equation of the compound circular curve is: ; This model integrates cosine square terms and sine terms, reflecting both the circular trend of the impedance curve and adapting to nonlinear variations; the vector form of the above equation is: ; Where a, b, and c are amplitude-related parameters. , where is the phase offset, and are all unknown parameters to be optimized. t is a variable parameter in the parametric equation.

[0036] Preferably, in the hybrid intelligent optimization algorithm construction step, the improved particle swarm optimization algorithm, based on the introduction of nonlinear inertia weights and adaptive learning factors, further integrates a simulated annealing mechanism: after each particle position update, the fitness difference between the new position and the old position is calculated. ,like Then accept the new position; otherwise, accept the new position. The probability of accepting a new position, where temperature The decay gradually decreases with each iteration.

[0037] Preferably, the construction and execution of the hybrid intelligent optimization algorithm includes particle encoding and initialization: The combination of parameters to be optimized is encoded into a particle position vector. ,in , , , The first The amplitude parameters and phase shifts corresponding to each particle; random initialization. The position vector and velocity vector of each particle , Take 30 to 50.

[0038] Preferably, the construction and execution of the hybrid intelligent optimization algorithm further includes fitness calculation, and the calculated fitness value is used as the composite objective function: For each particle, its position vector components are substituted into the composite circular curve equation to obtain the predicted curve. Calculate the fitness value of the particle. : ; in, For the enhanced sample set, the first The coordinates of the impedance points To assign a value to the parameter corresponding to that point, To increase the number of points in the sample set, For the first The weighting coefficients of each sample point For particles The defined curve in the parameters curvature at that point This is a discrete approximation of the rate of change of curvature. and M is the preset balance coefficient, M is the number of discrete sampling points for curvature, and the curve curvature change smoothing regularization term is used to constrain the second-order smoothness of the fitted curve.

[0039] Preferably, for two-dimensional parametric equations The curvature formula is: ; Among them, the discrete approximation of the rate of change of curvature The calculation formula is: ; in, and These are the parameter values ​​corresponding to the discrete sampling points of curvature.

[0040] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes updating the inertia weights and learning factors: Calculate the current iteration number Corresponding nonlinear inertia weight and adaptive learning factor , : ; ; ; in, and These are the maximum and minimum values ​​of the inertia weight, respectively. The maximum number of iterations, It is a non-linear decay exponent. , As the initial learning factor, , To terminate the learning factor.

[0041] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes particle velocity and position updates, updating the velocity of each particle according to the following formula. and location : ; ; in, and A random number within the interval [0,1]. For particles The best historical position This is the current globally optimal position.

[0042] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes simulated annealing acceptance determination: Calculate new position relative to the original position fitness difference ;like If so, then accept the new position; if Then, based on probability Accepting the new position: ; in, Given the current temperature, follow the cooling strategy. renew, The initial temperature. The cooling coefficient, If accepted, then update. Otherwise, keep the original position.

[0043] Preferably, the construction and execution of the hybrid intelligent optimization algorithm also includes global optimal update and termination judgment: After traversing all particles, update the global optimal position. and its fitness value ;like No significant decrease was observed after a fixed number of iterations, or the number of iterations reached... If the iteration terminates, the global optimal solution is output as the optimal parameter combination: , , , .

[0044] Preferably, in the model parameter optimization step, the particle dimension is 4, corresponding to a, b, c, Four parameters to be optimized, with the number of particles set to 30-50; the iteration termination condition is that the composite objective function value stabilizes for several consecutive generations or the maximum number of iterations is reached.

[0045] Preferably, in the steps of establishing the equation of the entire curve and deriving the impedance point, the preset angle step size is: traversal Substitute the values ​​into the final loss-of-magnetism impedance curve equation to calculate the impedance amplitude at the corresponding angle. Generate the full-range impedance point coordinates (| |, ).

[0046] Preferably, the method further includes a result verification step: using the root mean square error (S) to evaluate the deviation between the fitted curve and the measured points; when S≤0.02, the curve equation is determined to be valid; if the verification condition is not met, 1-2 measured points are added and the optimization process is re-executed.

[0047] like Figure 2 As shown, a system for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm is used to execute the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm. The system includes: The acquisition module is used to obtain the amplitude and angle of several key impedance points when a generator loses excitation fault occurs; The phase space reconstruction module is used to sort the acquired key impedance points by angle and embed them into a high-dimensional phase space to generate virtual impedance points to form an enhanced sample set. The model building module is used to assume the composite circular curve equation of the loss-of-magnetism impedance curve; The hybrid optimization module is configured to execute an improved particle swarm optimization algorithm that incorporates simulated annealing mechanism, and optimizes the parameters of the composite circular curve equation using a composite objective function consisting of the weighted sum of squared residuals and the curvature change smoothing regularization term as the optimization criterion. The curve generation module is used to generate the final loss-of-magnetism impedance curve equation based on the optimized parameters, and output the coordinates of the full-range impedance points according to the preset angle step size.

[0048] Preferably, it also includes a computer device, including a memory and a processor, which are interconnected. The memory stores computer instructions, and the processor executes the computer instructions to perform the method for predicting the loss-of-magnetic impedance curve of a large hydro-generator using an intelligent optimization algorithm.

[0049] Preferably, the method further includes a computer-readable storage medium storing computer instructions for causing a computer to execute the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm.

[0050] Example 2: This embodiment uses a 700MW turbine-generator unit at a large hydropower station in the Yangtze River basin as the application object. The generator model is SF700-80 / 19500, with a rated voltage of 20kV and a rated power factor of 0.9. To verify the effectiveness of the method under real operating conditions, a simulated demagnetization test was conducted during the unit's planned maintenance period, with the following operating conditions and parameters set: Operating conditions: The generator initially operates at 60% of its rated active power, i.e., 420MW, with a reactive power of -50Mvar. It is in leading phase operation, simulating a short circuit and loss of excitation in the excitation winding.

[0051] Data acquisition: A high-precision portable impedance measurement device with an accuracy class of 0.05 was used. The impedance amplitude Z at four key points with impedance angles φ of 0°, 90°, 180° and 270° were collected at 0.2s, 0.6s and 1.6s after the fault was triggered, respectively, to form four actual measurement points.

[0052] Parameter settings for this invention: In phase space reconstruction, the mutual information method is used to determine the optimal delay time. The Cao method determines the embedding dimension d=3, the local linear regression neighborhood points Q=5, and generates virtual points to augment the sample set with a total number of points N=60. In the hybrid optimization algorithm, the number of particles Np=30, the maximum number of iterations Gmax=200, and the inertia weight... Learning factors Simulated annealing initial temperature T0=1000, cooling coefficient 5; Balance coefficients of the composite objective function The number of discrete curvature sampling points is M=360.

[0053] Comparison method: Method 1: Traditional interpolation method, which uses the four measured points to directly perform cubic spline interpolation to obtain the full curve.

[0054] Method 2: Standard PSO fitting. Using the same four measured points, standard PSO (fixed inertia weight ω=0.7, fixed learning factor c1=c2=2.0) is used to perform single-objective least squares fitting of the cardioid equation parameters without regularization terms. The number of particles and the number of iterations are the same as in this invention.

[0055] Method 3: Actual measurement method. As a true reference benchmark, additionally measure 360 ​​impedance points from 0° to 360° in 1° increments to obtain a high-precision true value curve.

[0056] To quantitatively assess the prediction accuracy, this invention and two comparative methods predicted the impedance amplitude at 15 different angular positions: 0°, 24°, 48°, ..., 336°, and compared the predictions with the true values ​​obtained by the measured method to calculate the relative error percentage. All methods were independently repeated 20 times, and the error statistics are recorded as shown in Tables 1 and 2 below.

[0057] Table 1: Operating data of the method of the present invention;

[0058] Table 2: Comparison of the average relative error of the present invention and the comparative method at various angle points;

[0059] Figure 4This figure visually illustrates the relative error distribution of the proposed method, traditional interpolation, and standard PSO fitting method across 15 test angles. The width of each violin represents the probability density of error values ​​in 20 independent experiments, with the inner box bars indicating the median and interquartile range. It can be seen that the error distribution of the proposed method is extremely compact, all below 0.8%, with a median close to zero, demonstrating excellent regression accuracy and robustness. The traditional interpolation method not only has a high overall error level, with a peak value near 6%, but also a wide distribution range, indicating that relying solely on interpolation at a few points easily leads to structural biases. Although the standard PSO introduces a cardioid model, under sparse samples, due to the lack of a global escape mechanism and geometric constraints, the error is still scattered in the 1.5%–4.5% range, with outliers appearing at some angles. This figure strongly confirms that the phase space virtual enhancement and hybrid optimization fusion strategy proposed in this invention achieves high-fidelity curve reconstruction approaching high-density experimental methods at extremely low experimental cost.

[0060] As can be seen from the above comparative data, the method of this invention, under extremely sparse conditions with only 4 measured points, achieves an order-of-magnitude improvement in the accuracy of full curve reconstruction by virtue of its innovative three-in-one mechanism of "virtual enhancement of phase space reconstruction - hybrid optimization - geometric constraints," and the output results are as follows: Figure 6 and Figure 7 As shown, Figure 6 The full-range impedance point scatter plot output by the method of this invention generates 360 coordinate points with a step size of 1°. The curve is continuous, smooth, and completely covers the actual measured value trajectory. Figure 7 The complete demagnetization impedance curve formed by connecting the impedance points shows a complete closed heart-shaped outline, with a natural transition without distortion at the inflection point, which directly verifies the high-fidelity reconstruction capability of the method of the present invention.

[0061] Traditional interpolation methods rely entirely on simple connections of a small number of control points, failing to capture the nonlinear morphology of the loss-of-magnetic impedance curve. The maximum error reaches 4.95%, and significant deviations occur in regions of sharp curve curvature. While standard PSO fitting incorporates a cardioid model, its single optimization objective easily gets trapped in local optima under sparse data, leading to curve distortion in certain angle segments. The average error ranges from 1.38% to 3.55%, indicating insufficient robustness. This invention first utilizes chaotic phase space reconstruction technology to extract high-dimensional dynamic features from four measured points, generating 60 virtual samples to enrich the information and provide ample training support for the optimization algorithm. Then, an improved particle swarm optimization algorithm incorporating simulated annealing is employed, probabilistically escaping local minima. Combined with curvature change smoothing regularization, curve fitting is elevated from pure data approximation to multi-objective optimization that balances data accuracy and physical smoothness. This results in a highly consistent fitted impedance curve not only near the measured points but also maintaining a smooth inertial transition in unmeasured angle regions, significantly enhancing physical consistency. Twenty independent repeated tests showed that the average relative error predicted by this invention was consistently controlled below 0.6%, with a maximum of no more than 0.85%, and the standard deviation of the error was extremely low, demonstrating excellent stability and repeatability. This performance level is sufficient to meet the stringent requirements of relay protection setting for impedance boundary accuracy, truly achieving the engineering goal of obtaining a complete and high-precision loss-of-magnetism impedance characteristic curve with minimal on-site work.

[0062] Example 3: like Figure 8 As shown, embodiments of the present invention also provide a computer device. Figure 8 Taking a single processor 10 as an example, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other using different buses and can be mounted on a common motherboard or otherwise installed as needed. The processor can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices, such as display devices coupled to the interface. In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations, for example, as a server array, a group of blade servers, or a multiprocessor system.

[0063] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0064] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0065] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0066] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0067] The computer device also includes a communication interface 30 for communicating with other devices or communication networks.

[0068] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

Claims

1. A method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm, characterized in that, Includes the following steps: Key Impedance Point Acquisition: When a generator loses excitation, the amplitude Z and angle of several key impedance points are acquired. ; Virtual sample generation: Using the theory of chaotic time series phase space reconstruction, the key impedance points are arranged in angular order and embedded into a high-dimensional phase space. A set of virtual impedance points is generated through local linear mapping, which together with the key impedance points constitute an enhanced sample set. Curve Model Assumptions: Based on the approximate Cartesian cardioid characteristics of the loss-of-magnetic impedance curve in the complex plane, the mathematical model of the curve is assumed to be a composite circular curve equation, which includes amplitude-related parameters and phase offset. Hybrid intelligent optimization algorithm construction: An improved particle swarm optimization algorithm integrating simulated annealing mechanism is constructed. The composite objective function formed by the weighted sum of squared residuals of measured impedance points and enhanced sample sets and model predictions, plus the curve curvature change smoothing regularization term, is used as the optimization objective to establish a parameter optimization model. Model parameter optimization: The enhanced sample set is input into the hybrid intelligent optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination; the collected measured data is input into the particle swarm optimization algorithm to execute the parameter optimization process and obtain the optimal parameter combination. The equation for the entire curve is established and the impedance point is derived: the optimal combination of parameters is substituted into the assumed composite circular curve equation to obtain the final loss-of-magnetism impedance curve equation, and the coordinates of the full-range impedance points are generated according to the preset angle step size, so as to realize the reconstruction from a few points to the complete curve.

2. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, In the critical impedance point acquisition step, the acquisition time is selected at the initial stage, development stage and near-stable stage of simulated demagnetization, and the difference in impedance angle between adjacent critical impedance points is not less than 30°.

3. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, The virtual sample generation step specifically includes: Collected The key impedance points are arranged in ascending order of impedance angle, and their impedance magnitudes are extracted to form a one-dimensional sequence. ,in Indicates the first The impedance amplitude at each measured point This represents the number of measured points. Sequence determination using mutual information method Optimal delay time The calculation formula is as follows: ； in, For the delay steps, and They are respectively and Marginal probability distribution, For the joint probability distribution, take the mutual information function. When the local minimum is reached for the first time As the optimal delay time; The embedding dimension is determined using the Cao method. ; Based on the optimal delay time and embedding dimension The original one-dimensional amplitude sequence is reconstructed into a high-dimensional phase space to obtain the set of phase points. ; For each phase point Select within its neighborhood Using the nearest neighbor points, construct a local linear regression model to generate virtual phase points. The calculation formula is as follows: ； in, and To minimize The regression matrix and bias vector are obtained from the linear reconstruction error of the nearest neighbor in the neighborhood. For the first generated in phase space A virtual phase point; The generated virtual phase point The first dimension coordinate is extracted as the virtual impedance amplitude, and a corresponding angle value is assigned to form a virtual impedance point, which is then merged with the key impedance point to form an enhanced sample set.

4. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 3, characterized in that, The embedding dimension is determined using the Cao method. The calculation formula is: ； in, For the embedding dimension, for The first in 3D phase space One phase point, In order to be in In 3D phase space and The nearest neighbor point, Represents Euclidean distance. and The corresponding phase points are at Extension in 3D space; taking Follow When the change tends to saturate The value is used as the optimal embedding dimension.

5. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, In the curve model assumption step, the vector form of the assumed compound circular curve equation is: ； Where a, b, and c are amplitude-related parameters. , where is the phase offset, and are all unknown parameters to be optimized. t is a variable parameter in the parametric equation.

6. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, In the construction step of the hybrid intelligent optimization algorithm, the improved particle swarm optimization algorithm, based on the introduction of nonlinear inertia weights and adaptive learning factors, further integrates a simulated annealing mechanism: after each particle position update, the fitness difference between the new position and the old position is calculated. ,like Then accept the new position; otherwise, accept the new position. The probability of accepting a new position, where temperature The decay gradually decreases with each iteration.

7. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 6, characterized in that, The construction and execution of the hybrid intelligent optimization algorithm includes particle encoding and initialization: The combination of parameters to be optimized is encoded into a particle position vector. ,in , , , The first The amplitude parameters and phase shifts corresponding to each particle; random initialization. The position vector and velocity vector of each particle , Take 30 to 50.

8. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 7, characterized in that, The construction and execution of the hybrid intelligent optimization algorithm also includes fitness calculation, and the calculated fitness value is used as the composite objective function: For each particle, its position vector components are substituted into the composite circular curve equation to obtain the predicted curve. Calculate the fitness value of the particle. : ； in, For the enhanced sample set, the first The coordinates of the impedance points To assign a value to the parameter corresponding to that point, To increase the number of points in the sample set, For the first The weighting coefficients of each sample point For particles The defined curve in the parameters curvature at that point This is a discrete approximation of the rate of change of curvature. and M is the preset balance coefficient, M is the number of discrete sampling points for curvature, and the curve curvature change smoothing regularization term is used to constrain the second-order smoothness of the fitted curve.

9. A method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 8, characterized in that, For two-dimensional parametric equations The curvature formula is: ； Among them, the discrete approximation of the rate of change of curvature The calculation formula is: ； in, and These are the parameter values ​​corresponding to the discrete sampling points of curvature.

10. A method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 8, characterized in that, The construction and execution of the hybrid intelligent optimization algorithm also includes updating inertia weights and learning factors: Calculate the current iteration number Corresponding nonlinear inertia weight and adaptive learning factor , : ； ； ； in, and These are the maximum and minimum values ​​of the inertia weight, respectively. The maximum number of iterations, It is a non-linear decay exponent. , As the initial learning factor, , To terminate the learning factor.

11. A method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 10, characterized in that, The construction and execution of the hybrid intelligent optimization algorithm also includes particle velocity and position updates, with the velocity of each particle updated according to the following formula. and location : ； ； in, and A random number within the interval [0,1]. For particles The best historical position This is the current globally optimal position.

12. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 11, characterized in that, The construction and execution of the hybrid intelligent optimization algorithm also includes simulated annealing acceptance determination: Calculate new position relative to the original position fitness difference ;like If so, then accept the new position; if Then, based on probability Accepting the new position: ； in, Given the current temperature, follow the cooling strategy. renew, The initial temperature. The cooling coefficient, If accepted, then update. Otherwise, keep the original position.

13. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 12, characterized in that, The construction and execution of hybrid intelligent optimization algorithms also include global optimal updates and termination judgments: After traversing all particles, update the global optimal position. and its fitness value ;like No significant decrease was observed after a fixed number of iterations, or the number of iterations reached... If the iteration terminates, the global optimal solution is output as the optimal parameter combination: , , , .

14. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, In the model parameter optimization step, the particle dimension is 4, corresponding to a, b, c, ... Four parameters to be optimized; the iteration termination condition is that the composite objective function value stabilizes after several consecutive generations or reaches the maximum number of iterations.

15. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, wherein the preset angle step size in the steps of establishing the full curve equation and deriving the impedance point is... traversal Substitute the values ​​into the final loss-of-magnetism impedance curve equation to calculate the impedance amplitude at the corresponding angle. Generate the full-range impedance point coordinates (| |, ).

16. The method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm according to claim 1, characterized in that, The method also includes a result verification step: the root mean square error (S) is used to evaluate the deviation between the fitted curve and the measured points. When S ≤ a set threshold, the curve equation is determined to be valid. If the verification condition is not met, several measured points are added and the optimization process is re-executed.

17. A system for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm, for executing the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm as described in any one of claims 1-16, characterized in that, The system includes: The acquisition module is used to obtain the amplitude and angle of several key impedance points when a generator loses excitation fault occurs; The phase space reconstruction module is used to sort the acquired key impedance points by angle and embed them into a high-dimensional phase space to generate virtual impedance points to form an enhanced sample set. The model building module is used to assume the composite circular curve equation of the loss-of-magnetism impedance curve; The hybrid optimization module is configured to execute an improved particle swarm optimization algorithm that incorporates simulated annealing mechanism, and optimizes the parameters of the composite circular curve equation using a composite objective function consisting of the weighted sum of squared residuals and the curvature change smoothing regularization term as the optimization criterion. The curve generation module is used to generate the final loss-of-magnetism impedance curve equation based on the optimized parameters, and output the coordinates of the full-range impedance points according to the preset angle step size.

18. A computer device, characterized in that, It includes a memory and a processor, which are interconnected and communicate with each other. The memory stores computer instructions, and the processor executes the computer instructions to perform the method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm as described in any one of claims 1 to 16.

19. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute any one of claims 1 to 16, a method for predicting the demagnetization impedance curve of a large hydro-generator using an intelligent optimization algorithm.

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