Fixed point iteration method for solving fast stability of hysteresis magnetic field under non-sine excitation

Abstract

The invention discloses a fast and stable fixed point iteration method for solving a hysteresis magnetic field under non-sine excitation, and belongs to the technical field of numerical simulation of motors and power electronics. Aiming at core loss increase and calculation convergence challenge caused by non-sinusoidal excitation, a time domain finite element method is combined with a fixed point iteration method to process hysteresis characteristics, and the hysteresis characteristics are analyzed through an inverse Preisach model; at a non-rotation point, a fixed point coefficient is set by using the differential magnetic resistance rate to accelerate iteration; at the rotation point, a global coefficient is set, and an Anderson acceleration method is introduced to ensure stable and rapid convergence of iteration; according to the method, on the basis of a traditional local coefficient method, a global coefficient and an Anderson acceleration method are combined, stable convergence at a rotation point and rapid iteration at a non-rotation point are achieved, the calculation efficiency is remarkably improved, meanwhile, the stability of overall calculation is guaranteed, and the method is suitable for large-scale popularization and application. The method has a wide application prospect in the aspects of electromagnet design, electrical equipment operation state prediction, loss evaluation and the like.

Description

Technical Field

[0001] The invention relates to the technical field of motor and power electronics numerical simulation, and in particular to a fixed point iteration method for solving a fast and stable hysteresis magnetic field under non-sinusoidal excitation. Background Art

[0002] In the field of motors and power electronics, non-sinusoidal excitation waveforms are often encountered during the operation of power equipment such as high-frequency transformers. This waveform characteristic leads to a significant increase in core loss. In order to improve the efficiency and performance of power equipment, it is particularly important to conduct in-depth electromagnetic performance analysis. Finite element analysis technology considering hysteresis characteristics is a key tool for analyzing the electromagnetic performance of power equipment, which can more accurately simulate the working state of the equipment under complex excitation conditions.

[0003] In the finite element calculation process of solving hysteresis characteristics, the handling of nonlinear problems is a critical and complex link. The complexity and non-monotonicity of the hysteresis phenomenon itself make it difficult to directly apply traditional linear methods. For this reason, a robust fixed-point iteration method is usually used to iteratively handle these nonlinear problems. The fixed-point iteration method gradually reduces the calculation error by gradually approaching the true solution, and finally converges to a solution that meets the accuracy requirements. However, this method has the disadvantage of slow convergence speed in practical applications, especially when dealing with multi-turning point problems under non-sinusoidal excitation, the convergence speed will be significantly affected, thereby greatly increasing the calculation time.

[0004] In order to speed up the calculation speed of the fixed-point iteration method, researchers have proposed a variety of improvement methods. Among them, a commonly used strategy is to adopt the local coefficient method, that is, to use the differential reluctance to set the fixed-point coefficient. This method can speed up the iteration speed and improve the calculation efficiency by optimizing the iteration coefficient at the non-turning point. However, for the turning point problem caused by the non-sinusoidal excitation waveform, due to the existence of non-monotonic nonlinearity, the differential reluctance cannot be accurately predicted, which makes the iterative calculation easy to diverge and the stability is affected.

[0005] In the prior art, a variety of alternative solutions have been proposed for the processing at the turning point. For example, the article "An enhanced implementation method of fixed-point iteration technique for solving magnetic hysteresis finite-element problems" at the 26th International Conference on Electrical Machines and Systems (ICEMS) in 2023 proposed to bypass the erroneous prediction value of the differential reluctance by adding a large number of parameters to be adjusted, but this method is complicated to implement and increases the computational burden. In addition, the article "A Fast Fixed-Point Method for Solving Magnetic Field Problems in Media of Hysteresis" in Volume 44, Issue 6 of "IEEE Transactions on Magnetics" uses a larger reluctance to predict the fixed coefficient of the turning point. Although this method can ensure iterative stability, it will significantly reduce the calculation speed at the turning point, thereby affecting the overall calculation efficiency. Although the above two existing solutions both propose improved methods for the problem of inaccurate prediction of differential reluctance at the turning point, they have failed to fully solve the problems of iterative stability and computational efficiency of hysteresis magnetic field problems under non-sinusoidal excitation.

[0006] Therefore, in order to solve the problems existing in the above-mentioned prior art, the present invention proposes a fixed point iteration method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation. This method combines the global coefficient and Anderson acceleration method on the basis of the traditional local coefficient method, and realizes stable convergence at the turning point and fast iteration at the non-turning point, thereby ensuring the stability and efficiency of the entire calculation process. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a fixed-point iteration method for solving the hysteresis magnetic field under non-sinusoidal excitation quickly and stably, so as to solve the problem of low calculation efficiency of nonlinear magnetic field problems caused by hysteresis characteristics in the field of motors and power electronics, especially in the field of high-frequency transformers and other equipment under non-sinusoidal excitation, where the core loss increases significantly and the calculation efficiency is low.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is to solve the fixed point iteration method of the hysteresis magnetic field under non-sinusoidal excitation to quickly stabilize the hysteresis magnetic field. The strategy includes the following steps: Step 1: The time-domain finite element method is used to calculate the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation, in which the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering hysteresis characteristics, and the inverse Preisach model is used to analyze the hysteresis characteristics; Step 2: Set the fixed point coefficient by differential magnetic reluctance, so as to speed up the iteration speed of solving the hysteresis magnetic field problem at the non-rotating point; Step 3: Record the iterative residual change. When the iterative residual change threshold is reached, the current time step is determined to be the turning point of iterative divergence. Step 4: At the turning point, the fixed point coefficient is set to the global coefficient to ensure stable convergence of the iteration; Step 5: At the turning point, the Anderson acceleration method is used to speed up the iterative convergence speed at the turning point.

[0009] In the preferred solution, the equation for calculating the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation by the time domain finite element method in Step 1 is: (1) In the formula, is the fixed point coefficient of the current time step, is the magnetic vector potential of the kth iteration step in the current time step, is the source matrix of the current time step, is the quasi-magnetization residual of the k-1th iteration step of the current time step, is the Hamiltonian operator; Among them, the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering the hysteresis characteristics, that is, the quasi-magnetization remainder of the right-hand term in the above formula. The nonlinear hysteresis relationship is divided into linear and nonlinear parts, and then the nonlinear part is continuously corrected in the iterative process to achieve convergence. The calculation formula is: (2) In the formula, represents the nonlinear relationship between magnetic field intensity H and magnetic flux density B, which can be calculated by the inverse Preisach model, is the fixed point coefficient, It is a magnetization margin, which is continuously corrected in the iterative calculation process. , when the magnetic flux density B obtained by iterative calculation meets the following conditions: (3) Then it is determined that the iteration converges at this time; where, is the magnetic flux density calculated at the kth iteration step, is the magnetic flux density calculated at the k-1th iteration step, is the convergence factor; Among them, the inverse Preisach model is to obtain the first-order rotation curve by analyzing the experimental data, and then obtain the inverse Everett function through the first-order rotation curve identification. Finally, the state and extreme value of the magnetization process are recorded through the program, and the magnetic field intensity H can be interpolated through the inverse Everett function. The model calculation formula is: (4) In the formula, is the magnetic field strength value of the current time step, is the magnetic field strength value of the latest extreme point, and are the minimum and maximum points of the magnetization history and their numbers, This is the magnetization state at this time, that is, whether the magnetization is in the rising branch or the falling branch. is the inverse Everett function value of the current ascending branch, is the inverse Everett function value of the current descending branch.

[0010] In the preferred solution, the fixed point coefficient is set by differential magnetic reluctance in Step 2 as: (5) In the formula, is the fixed point coefficient of the next time step. The formula uses the backward difference form to approximate the differential magnetic reluctance. C is the convergence coefficient. is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step, is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step.

[0011] In the preferred solution, the recorded iterative residual in Step 3 changes to , when the iterative residual becomes larger: (6) In the formula, Time step, is the calculation result of the current k-th iteration step, is the calculation result of the k-1th iteration step, are the calculation results of the first two iterations.

[0012] When the number of iterations is greater than or equal to 2, the above formula is judged after each iteration, and the iterative residual changes Initially 0, when the above formula is judged to be true, let At the same time, after each iteration, the iterative residual change is determined Is it greater than the iterative residual change threshold? If true, the current time step is determined to be the turning point of iterative divergence, and the iteration of the current step is restarted. A time step.

[0013] In the preferred solution, the fixed point coefficient is set at the turning point in Step 4. The global coefficients set to ensure iterative convergence are: (7) In the formula, is the vacuum reluctance. This fixed point coefficient can ensure that the iteration of the hysteresis magnetic field problem can converge stably.

[0014] In the preferred solution, in Step 5, at the turning point, the Anderson acceleration method is used to accelerate the iterative convergence speed at the turning point. First, the residual and residual interpolation are calculated by the magnetic flux density B obtained by each iteration: (8) In the formula, In a time step, is the residual value of the current iteration step, is the residual value of the previous iteration step, is the magnetic flux density calculated in the current iteration step, is the magnetic flux density calculated in the previous iteration step, is the residual difference of the current iteration step.

[0015] Then, the residual difference matrix can be obtained ,in , To accelerate the iteration space dimension of Anderson, the maximum storage size of the residual difference matrix is ​​limited residual difference; through the residual difference matrix and the residual value of the current iteration The least squares problem for this iteration can be obtained: (9) In the formula, is the least squares solution of the solution; finally, the least squares problem is solved by QR decomposition to obtain the final calculation result of the magnetic flux density of the current iteration step: (10) In the formula, is the relaxation factor, in In each time step, For the current The calculation results of the iteration step are It is the final calculation result after optimization by the least squares problem.

[0016] The fixed point iteration method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation provided by the present invention has the following beneficial effects: 1. The present invention solves the problem of significantly increased core loss and low computation efficiency of nonlinear magnetic field problems caused by hysteresis characteristics in the field of motors and power electronics, especially under non-sinusoidal excitation of high-frequency transformers and other equipment; 2. The present invention effectively accelerates the iterative convergence speed at the turning point by introducing the Anderson acceleration method, solving the problem that the traditional local coefficient method cannot accurately predict the differential magnetic reluctance at the turning point, and the iteration speed at the turning point is slow and unstable; 3. The present invention uses global coefficients at the turning point to ensure the stability of iteration, and uses local coefficients at the non-turning point to speed up the iteration speed, which not only ensures the stability of calculation, but also improves the calculation efficiency; 4. The present invention sets the fixed point coefficient at the non-rotating point by differential magnetic reluctance, speeds up the iteration speed, and uses the inverse Preisach model to analyze the hysteresis characteristics. This combination makes the method more accurate and efficient in dealing with hysteresis problems. 5. The present invention uses the inverse Preisach model to accurately analyze the hysteresis characteristics, solves the problem that the fixed point iteration method has a slow convergence speed and consumes a lot of computing time when dealing with nonlinear problems, and improves the processing accuracy of the nonlinear part; 6. The present invention records the change of iterative residuals. When the iterative residual change threshold is reached, the current time step is automatically determined to be the turning point of iterative divergence, and the iterative strategy is adjusted. This automated monitoring and adjustment mechanism makes the method more intelligent and stable in practical applications; 7. This method not only monitors the iteration process by the change of iterative residual, but also automatically adjusts the iteration strategy to deal with the iterative divergence problem. This perfect monitoring and feedback mechanism makes the method more reliable and stable in practical applications; 8. The present invention combines the local coefficients set by the differential magnetic reluctance and the Anderson acceleration method to accelerate the iterative convergence speed at both the non-turning point and the turning point, and the overall calculation efficiency is significantly improved; 9. The present invention takes into account the magnetization mechanism of the material, has a simple implementation method, is highly practical, and can ensure that the entire calculation process is stable and fast. By comparing the calculation efficiency of the proposed iterative method with that of the traditional iterative method, the stability and speed of the iterative method are verified; 10. The method of the present invention is of great significance in electromagnetic performance analysis such as refined electromagnet design, reasonable prediction of the operating status of electrical equipment, loss evaluation, and accurate calculation of transient electromagnetic characteristics of residual magnetism when transformers are switched on, and has broad prospects for engineering application. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below in conjunction with the accompanying drawings and implementation examples: Figure 1 is a flow chart of the iterative method of the present invention; Figure 2 A magnetic flux density distribution diagram obtained by numerical simulation using the invented method; Figure 3 is the specific unit in the Epstein square magnetic circuit BH Comparison of the calculation results of the curve in three iterative methods; Figure 4 The figure is a comparison chart of the number of iterations of the three iterative methods in each time step. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is further described below in conjunction with the embodiments and drawings: Example 1 A fixed point iteration method for solving the fast stabilization of the hysteresis magnetic field under non-sinusoidal excitation, the strategy comprises the following steps: Step 1: The time-domain finite element method is used to calculate the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation, in which the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering hysteresis characteristics, and the inverse Preisach model is used to analyze the hysteresis characteristics; Step 2: Set the fixed point coefficient by differential magnetic reluctance, so as to speed up the iteration speed of solving the hysteresis magnetic field problem at the non-rotating point; Step 3: Record the iterative residual change. When the iterative residual change threshold is reached, the current time step is determined to be the turning point of iterative divergence. Step 4: At the turning point, the fixed point coefficient is set to the global coefficient to ensure stable convergence of the iteration; Step 5: At the turning point, the Anderson acceleration method is used to speed up the iterative convergence speed at the turning point.

[0019] In this embodiment, the equation for calculating the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation by the time domain finite element method in Step 1 is: (1) In the formula, is the fixed point coefficient of the current time step, is the magnetic vector potential of the kth iteration step in the current time step, is the source matrix of the current time step, is the quasi-magnetization residual of the k-1th iteration step of the current time step, is the Hamiltonian operator; Among them, the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering the hysteresis characteristics, that is, the quasi-magnetization remainder of the right-hand term in the above formula. The nonlinear hysteresis relationship is divided into linear and nonlinear parts, and then the nonlinear part is continuously corrected in the iterative process to achieve convergence. The calculation formula is: (2) In the formula, represents the nonlinear relationship between magnetic field intensity H and magnetic flux density B, which can be calculated by the inverse Preisach model, is the fixed point coefficient, It is a magnetization margin, which is continuously corrected in the iterative calculation process. , when the magnetic flux density B obtained by iterative calculation meets the following conditions: (3) Then it is determined that the iteration converges at this time; where, is the magnetic flux density calculated at the kth iteration step, is the magnetic flux density calculated at the k-1th iteration step, is the convergence factor; Among them, the inverse Preisach model is to obtain the first-order rotation curve by analyzing the experimental data, and then obtain the inverse Everett function through the first-order rotation curve identification. Finally, the state and extreme value of the magnetization process are recorded through the program, and the magnetic field intensity H can be interpolated through the inverse Everett function. The model calculation formula is: (4) In the formula, is the magnetic field strength value of the current time step, is the magnetic field strength value of the latest extreme point, and are the minimum and maximum points of the magnetization history and their numbers, This is the magnetization state at this time, that is, whether the magnetization is in the rising branch or the falling branch. is the inverse Everett function value of the current ascending branch, is the inverse Everett function value of the current descending branch.

[0020] Furthermore, in Step 2, the fixed point coefficient is set by using the differential magnetic reluctance as: (5) In the formula, is the fixed point coefficient of the next time step. The formula uses the backward difference form to approximate the differential magnetic reluctance. C is the convergence coefficient. is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step, is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step.

[0021] Furthermore, the recorded iterative residual in Step 3 changes to , when the iterative residual becomes larger: (6) In the formula, Time step, is the calculation result of the current k-th iteration step, is the calculation result of the k-1th iteration step, are the calculation results of the first two iterations.

[0022] When the number of iterations is greater than or equal to 2, the above formula is judged after each iteration, and the iterative residual changes Initially 0, when the above formula is judged to be true, let At the same time, after each iteration, the iterative residual change is determined Is it greater than the iterative residual change threshold? If true, the current time step is determined to be the turning point of iterative divergence, and the iteration of the current step is restarted. A time step.

[0023] Furthermore, in Step 4, at the turning point, the fixed point coefficient The global coefficients set to ensure iterative convergence are: (7) In the formula, is the vacuum magnetic resistivity. The fixed point coefficient set in this way can ensure that the iteration of the hysteresis magnetic field problem can converge stably.

[0024] Furthermore, in Step 5, at the turning point, the Anderson acceleration method is used to accelerate the iterative convergence speed at the turning point. First, the residual and residual interpolation are calculated by the magnetic flux density B obtained by each iteration: (8) In the formula, In a time step, is the residual value of the current iteration step, is the residual value of the previous iteration step, is the magnetic flux density calculated in the current iteration step, is the magnetic flux density calculated in the previous iteration step, is the residual difference of the current iteration step.

[0025] Then, the residual difference matrix can be obtained ,in , To accelerate the iteration space dimension of Anderson, the maximum storage size of the residual difference matrix is ​​limited residual difference; through the residual difference matrix and the residual value of the current iteration The least squares problem for this iteration can be obtained: (9) In the formula, is the least squares solution of the solution; finally, the least squares problem is solved by QR decomposition to obtain the final calculation result of the magnetic flux density of the current iteration step: (10) In the formula, is the relaxation factor, in In each time step, For the current The calculation results of the iteration step are It is the final calculation result after optimization by the least squares problem.

[0026] Example 2 In another preferred embodiment, based on the above embodiment 1, Figure 1 As shown, based on the fixed point iteration method of differential reluctance and global coefficient, this embodiment aims to elaborate on how to apply the method of the present invention to solve the hysteresis magnetic field problem under non-sinusoidal excitation through specific steps and parameter settings.

[0027] Step 1: Time domain finite element method calculation First, we use the time-domain finite element method to construct a mathematical model of the magnetic field problem considering the hysteresis characteristics under non-sinusoidal excitation. The specific equation form is as follows: (1) In the formula, is the fixed point coefficient of the current time step, is the magnetic vector potential of the kth iteration step in the current time step, is the source matrix of the current time step, is the quasi-magnetization residual of the k-1th iteration step of the current time step, is the Hamiltonian operator; In order to deal with nonlinear hysteresis characteristics, we use the fixed point iteration method to divide the nonlinear relationship into linear and nonlinear parts, and gradually correct the nonlinear part through iteration to achieve convergence. The specific calculation formula is: (2) In the formula, represents the nonlinear relationship between magnetic field intensity H and magnetic flux density B, which can be calculated by the inverse Preisach model, is the fixed point coefficient, It is a magnetization margin, which is continuously corrected in the iterative calculation process. , when the magnetic flux density B obtained by iterative calculation meets the following conditions: (3) Then it is determined that the iteration converges at this time; where, is the magnetic flux density calculated at the kth iteration step, is the magnetic flux density calculated at the k-1th iteration step, is the convergence factor. In this embodiment, ; Among them, the inverse Preisach model is to obtain the first-order rotation curve by analyzing the experimental data, and then obtain the inverse Everett function through the first-order rotation curve identification. Finally, the state and extreme value of the magnetization process are recorded through the program, and the magnetic field intensity H can be interpolated through the inverse Everett function. The model calculation formula is: (4) In the formula, is the magnetic field strength value of the current time step, is the magnetic field strength value of the latest extreme point, and are the minimum and maximum points of the magnetization history and their numbers, This is the magnetization state at this time, that is, whether the magnetization is in the rising branch or the falling branch. is the inverse Everett function value of the current ascending branch, is the inverse Everett function value of the current descending branch.

[0028] Step 2: Differential reluctance setting fixed point coefficient At the non-rotating point, we use the differential reluctance to set the fixed point coefficient to speed up the iteration. The specific formula is: (5) in, is the fixed point coefficient of the next time step. The formula uses the backward difference form to approximate the differential reluctance. is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step, is the magnetic field strength at the current time step, is the magnetic field intensity of the previous time step, C is the convergence coefficient, which is 1 in this embodiment; the formula uses the backward difference form to approximately calculate the differential reluctance.

[0029] Step 3: Record the changes in iterative residuals We record the residual change at each iteration , to detect whether the turning point of iterative divergence has been reached. The specific judgment conditions are: (6) In the formula, Time step, is the calculation result of the current k-th iteration step, is the calculation result of the k-1th iteration step, are the calculation results of the first two iterations.

[0030] When the number of iterations is greater than or equal to 2, the above formula is judged after each iteration, and the iterative residual changes Initially 0, when the above formula is judged to be true, let At the same time, after each iteration, the iterative residual change is determined Is it greater than the iterative residual change threshold? If true, the current time step is determined to be the turning point of iterative divergence, and the iteration of the current step is restarted. A time step.

[0031] Step 4: Set the global coefficient at the turning point After detecting the turning point, we fix the point coefficients Set as a global coefficient to ensure stable iteration convergence. The global coefficient is set to half of the vacuum magnetic resistivity. ,Right now: (7) Step 5: Anderson acceleration method At the turning point, the Anderson acceleration method is used to speed up the iterative convergence. First, the residual and residual interpolation of the current iteration step are calculated: (8) In the formula, In a time step, is the residual value of the current iteration step, is the residual value of the previous iteration step, is the magnetic flux density calculated in the current iteration step, is the magnetic flux density calculated in the previous iteration step, is the residual difference of the current iteration step; Then the residual difference matrix is ​​constructed, and the least squares problem is solved by QR decomposition to obtain the optimized magnetic flux density calculation result. : (10) In the formula, is the relaxation factor, in In each time step, For the current The calculation result of the iteration step.

[0032] In order to verify the effectiveness of this embodiment, we performed numerical simulation calculations and compared them with the global coefficient method GCM and the local coefficient method LCM. Specifically, the inverse Preisach model was established by analyzing the measured data of B30P105 electrical steel sheet, and then the finite element numerical calculations were performed in the self-programming program by the following three fixed-point iteration methods: the global coefficient method (Global-Coefficient Method, GCM), the local coefficient method (Local-Coefficient Method, LCM), and the iterative method combining the local coefficient method and Anderson acceleration (LCM-AA, Local-Coefficient Method-Aderson Acceleration) proposed in the present invention. The calculation results of the numerical simulation were compared to verify the stability and rapidity of the proposed iterative method; Figure 2 A magnetic flux density distribution diagram obtained by numerical simulation using the invented method; Figure 3 is the specific unit in the Epstein square magnetic circuit BH Comparison of the calculation results of the curve in three iterative methods; Figure 4 The comparison chart of the number of iterations of the three iterative methods in each time step can be obtained from Figure 3 It can be seen that the numerical calculation results of the three are basically consistent. Figure 4 It can be seen that due to the increase in turning points caused by non-sinusoidal excitation, the number of iterations of LCM at the turning points is too large, resulting in a smaller reduction in the overall calculation time compared to GCM using global coefficients. The proposed LCM-AA can ensure stable iterations at the turning points while reducing a lot of calculation time at non-turning points compared to GCM, and also reduces a lot of calculation time at turning points compared to LCM. Finally, it is achieved that in the entire calculation process under non-sinusoidal excitation, the calculation can always be carried out stably and quickly.

[0033] In the numerical simulation calculation, the excitation frequency is set to 50 Hz, and each magnetization cycle is divided into 200 time steps. The three iterative methods are numerically calculated on a 3.20 GHz AMD Ryzen 7 5800H CPU computer. The final calculation efficiency results are shown in Table 1. Comparison results of the calculation efficiency of the three iterative methods: Table 1 Comparison results of the calculation efficiency of three iterative methods

[0034] It can be seen that the stable and fast fixed-point iterative method for solving the hysteresis magnetic field problem under non-sinusoidal excitation proposed in the present invention can speed up the calculation speed through the differential magnetic reluctance at the non-turning point compared with the global coefficient method GCM, and can ensure convergence stability through the global coefficient at the turning point compared with the local coefficient method LCM, and combined with Anderson acceleration, it ensures the rapid progress of iterative calculation at the turning point, so that the stability and speed of the calculation can always be guaranteed in the overall calculation, especially in the case of multiple turning points under non-sinusoidal excitation, the acceleration effect is more significant.

[0035] In summary, the present invention proposes a fixed-point iteration method for solving the hysteresis magnetic field under non-sinusoidal excitation, which solves the problem that the core loss increases significantly and the nonlinear magnetic field problem caused by hysteresis characteristics is inefficient in calculation in the field of motors and power electronics, especially under non-sinusoidal excitation of high-frequency transformers and other equipment; the present invention uses a global coefficient at the turning point to ensure the stability of the iteration, and uses a local coefficient at the non-turning point to speed up the iteration speed, which not only ensures the stability of the calculation, but also improves the calculation efficiency; further introduces Anderson acceleration into the iterative calculation of the hysteresis magnetic field. Although the Anderson acceleration method has been widely used in the field of optimization, it is rarely used in the iterative calculation of the hysteresis magnetic field. The present method creatively introduces Anderson acceleration into the iterative calculation of the hysteresis magnetic field, accelerates the iteration process by using historical iteration information, and significantly improves the iteration convergence speed; the present method sets the fixed-point coefficient at the non-turning point by differential reluctance to speed up the iteration speed, and uses the inverse Pr The eisach model analyzes the hysteresis characteristics. This combination makes the method more accurate and efficient in dealing with hysteresis problems. This method records the change of iterative residuals. When the threshold of iterative residual change is reached, the current time step is automatically determined to be the turning point of iterative divergence, and the iteration strategy is adjusted. This automated monitoring and adjustment mechanism makes the method more intelligent and stable in practical applications. This method not only monitors the iteration process by the change of iterative residuals, but also automatically adjusts the iteration strategy to deal with the problem of iterative divergence. This perfect monitoring and feedback mechanism makes the method more reliable and stable in practical applications. The research results show that this method can effectively handle the multi-turning point situation under non-sinusoidal excitation, ensuring that the entire calculation process can always remain stable and fast, which is conducive to the operation of finite element numerical calculation programs considering hysteresis characteristics under non-sinusoidal excitation, and has broad engineering application prospects. It is of great significance in electromagnetic performance analysis such as refined electromagnet design, reasonable prediction of the operating status of electrical equipment, loss evaluation, and accurate calculation of transient electromagnetic characteristics of residual magnetism of transformer closing.

Claims

1. A fixed point iterative method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation, characterized in that: The method comprises the following steps: Step 1: The time-domain finite element method is used to calculate the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation, in which the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering hysteresis characteristics, and the inverse Preisach model is used to analyze the hysteresis characteristics; Step 2: Set the fixed point coefficient by differential magnetic reluctance, so as to speed up the iteration speed of solving the hysteresis magnetic field problem at the non-rotating point; Step 3: Record the iterative residual change. When the iterative residual change threshold is reached, the current time step is determined to be the turning point of iterative divergence. Step 4: At the turning point, the fixed point coefficient is set to the global coefficient to ensure stable convergence of the iteration; Step 5: At the turning point, the Anderson acceleration method is used to speed up the iterative convergence speed at the turning point.

2. The fixed point iteration method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation according to claim 1 is characterized in that: The equation for calculating the magnetic field problem considering hysteresis characteristics under non-sinusoidal excitation by the time domain finite element method in Step 1 is: （1） In the formula, is the fixed point coefficient of the current time step, is the magnetic vector potential of the kth iteration step in the current time step, is the source matrix of the current time step, is the quasi-magnetization residual of the k-1th iteration step of the current time step, is the Hamiltonian operator; Among them, the fixed point iteration method is used to deal with the nonlinear part of the magnetic field problem considering the hysteresis characteristics, that is, the quasi-magnetization remainder of the right-hand term in the above formula. The nonlinear hysteresis relationship is divided into linear and nonlinear parts, and then the nonlinear part is continuously corrected in the iterative process to achieve convergence. The calculation formula is: （2） In the formula, represents the nonlinear relationship between magnetic field intensity H and magnetic flux density B, which can be calculated by the inverse Preisach model, is the fixed point coefficient, It is a magnetization margin, which is continuously corrected in the iterative calculation process. , when the magnetic flux density B obtained by iterative calculation meets the following conditions: （3） Then it is determined that the iteration converges at this time; where, is the magnetic flux density calculated at the kth iteration step, is the magnetic flux density calculated at the k-1th iteration step, is the convergence factor; Among them, the inverse Preisach model is to obtain the first-order rotation curve by analyzing the experimental data, and then obtain the inverse Everett function through the first-order rotation curve identification. Finally, the state and extreme value of the magnetization process are recorded through the program, and the magnetic field intensity H can be interpolated through the inverse Everett function. The model calculation formula is: （4） In the formula, is the magnetic field strength value of the current time step, is the magnetic field strength value of the latest extreme point, and are the minimum and maximum points of the magnetization history and their numbers, This is the magnetization state at this time, that is, whether the magnetization is in the rising branch or the falling branch. is the inverse Everett function value of the current ascending branch, is the inverse Everett function value of the current descending branch.

3. The fixed point iteration method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation according to claim 1 is characterized in that: In Step 2, the fixed point coefficient is set by differential magnetic reluctance as: （5） In the formula, is the fixed point coefficient of the next time step. The formula uses the backward difference form to approximate the differential magnetic reluctance. C is the convergence coefficient. is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step, is the magnetic field strength at the current time step, is the magnetic field strength at the previous time step.

4. The fixed point iteration method for solving the fast and stable hysteresis magnetic field under non-sinusoidal excitation according to claim 1 is characterized in that: The recorded iterative residual change in Step 3 is: , when the iterative residual becomes larger: （6） In the formula, Time step, is the calculation result of the current k-th iteration step, is the calculation result of the k-1th iteration step, are the calculation results of the first two iterations. When the number of iterations is greater than or equal to 2, the above formula is judged after each iteration, and the iterative residual changes Initially 0, when the above formula is judged to be true, let At the same time, after each iteration, the iterative residual change is determined Is it greater than the iterative residual change threshold? If true, the current time step is determined to be the turning point of iterative divergence, and the iteration of the current step is restarted. A time step.

5. The fixed point iteration method for solving the fast stabilization of the hysteresis magnetic field under non-sinusoidal excitation according to claim 1 is characterized in that: In Step 4, at the turning point, the fixed point coefficient is set to a global coefficient to ensure iterative convergence: （7） In the formula, is the vacuum magnetic resistivity. The fixed point coefficient set in this way can ensure that the iteration of the hysteresis magnetic field problem can converge stably.

6. The fixed point iteration method for solving the fast stabilization of the hysteresis magnetic field under non-sinusoidal excitation according to claim 1 is characterized in that: In Step 5, the Anderson acceleration method is used to accelerate the iterative convergence speed at the turning point. First, the magnetic flux density calculated by each iteration is B Compute residuals and interpolate residuals: （8） In the formula, In a time step, is the residual value of the current iteration step, is the residual value of the previous iteration step, is the magnetic flux density calculated in the current iteration step, is the magnetic flux density calculated in the previous iteration step, is the residual difference of the current iteration step. Then, the residual difference matrix can be obtained ,in , To accelerate the iteration space dimension of Anderson, the maximum storage size of the residual difference matrix is ​​limited residual difference; Through the residual difference matrix and the residual value of the current iteration The least squares problem for this iteration can be obtained: （9） In the formula, is the least squares solution of the solution; finally, the least squares problem is solved by QR decomposition to obtain the final calculation result of the magnetic flux density of the current iteration step: （10） In the formula, is the relaxation factor, in In each time step, For the current The calculation results of the iteration step are It is the final calculation result after optimization by the least squares problem.

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