CN118378576A - A three-dimensional time-domain hysteresis loop drawing method and system based on hysteresis model - Google Patents
A three-dimensional time-domain hysteresis loop drawing method and system based on hysteresis model Download PDFInfo
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Abstract
本发明公开了一种基于磁滞模型的三维时域磁滞回线描绘方法及系统,本发明方法包括如下步骤:构建目标铁芯对应的J‑A磁滞模型;获取目标铁芯不同时刻的动态杂散电流值,根据电流值计算磁场强度,将动态杂散磁场强度与正常交流磁场强度叠加作为J‑A磁滞模型的总输入;采用回溯搜索优化算法对J‑A磁滞模型进行参数辨识,基于目标磁场强度和实际磁化强度确定目标磁感应强度;对最终的磁场强度和磁感应强度进行曲线拟合,得到目标铁芯的三维磁滞回线;本发明将动态杂散电流产生的磁场强度与正常交流磁场强度叠加作为模型总输入,绘制考虑动态杂散电流持续性干扰的三维下的磁滞回线,展示了动态杂散电流在对磁滞回线影响的时变和无周期性。
The invention discloses a three-dimensional time-domain hysteresis loop drawing method and system based on a hysteresis model. The method of the invention comprises the following steps: constructing a J-A hysteresis model corresponding to a target iron core; obtaining dynamic stray current values of the target iron core at different times, calculating magnetic field strength according to the current value, and superimposing the dynamic stray magnetic field strength and the normal AC magnetic field strength as the total input of the J-A hysteresis model; using a backtracking search optimization algorithm to perform parameter identification on the J-A hysteresis model, and determining the target magnetic induction strength based on the target magnetic field strength and the actual magnetization strength; performing curve fitting on the final magnetic field strength and the magnetic induction strength, and obtaining the three-dimensional hysteresis loop of the target iron core; the invention superimposes the magnetic field strength generated by the dynamic stray current and the normal AC magnetic field strength as the total input of the model, draws a three-dimensional hysteresis loop considering the continuous interference of the dynamic stray current, and demonstrates the time-varying and non-periodicity of the dynamic stray current in affecting the hysteresis loop.
Description
技术领域Technical Field
本发明涉及铁芯磁化特性技术领域,具体为一种基于磁滞模型的三维时域磁滞回线描绘方法及系统。The invention relates to the technical field of iron core magnetization characteristics, and in particular to a three-dimensional time-domain hysteresis loop depiction method and system based on a hysteresis model.
背景技术Background technique
随着城市轨道交通的快速发展,因走行轨对地不完全绝缘而产生的动态杂散电流逐渐增多,其对变压器的影响日益增大。动态杂散电流即随时间动态变化的杂散电流在通过中性点流入变压器后会导致变压器出现振动噪声加剧,损耗增大,励磁电流谐波增加等一系列问题,因此对动态杂散电流干扰下变压器铁芯的磁特性进行探究非常重要。With the rapid development of urban rail transit, the dynamic stray current generated by the incomplete insulation of the running rails to the ground is gradually increasing, and its impact on the transformer is increasing. Dynamic stray current, that is, stray current that changes dynamically with time, will cause a series of problems such as increased vibration noise, increased losses, and increased harmonics of the excitation current after flowing into the transformer through the neutral point. Therefore, it is very important to explore the magnetic characteristics of the transformer core under the interference of dynamic stray current.
磁滞回线参数辨识作为研究铁芯磁特性的关键手段之一,现有的研究主要针对在正常工作条件、材料特性发生改变等工况下的磁滞回线进行参数辨识,从而使得磁滞回线的描绘更加准确。传统的磁滞回线用于表示磁性物质在周期变化的磁场强度下的磁滞现象,表明了磁性物质在反复磁化过程中磁感应强度B与磁场强度H的关系,具有明显的周期性。但动态杂散电流因其电流值随时间动态变化,产生的磁场强度也随时间动态变化,故而对铁芯磁特性造成的影响随时间变化而变化,不再具有周期性。由于传统的磁滞回线仅能表示二维层面上H与B的变化关系,忽视了时间域上H与B的变化关系,因此传统磁滞回线已经无法准确表述时间域上H与B的变化规律,也即无法准确表述动态杂散电流影响下磁性材料的磁滞特性。Hysteresis loop parameter identification is one of the key means to study the magnetic properties of the core. Existing research mainly focuses on parameter identification of hysteresis loops under normal working conditions and changes in material properties, so as to make the description of the hysteresis loop more accurate. The traditional hysteresis loop is used to represent the hysteresis phenomenon of magnetic materials under periodically changing magnetic field strength, indicating that the relationship between the magnetic induction intensity B and the magnetic field intensity H of magnetic materials during repeated magnetization has obvious periodicity. However, the dynamic stray current has a dynamic change in its current value over time, and the magnetic field intensity generated also changes dynamically over time, so the impact on the magnetic properties of the core changes with time and is no longer periodic. Since the traditional hysteresis loop can only represent the changing relationship between H and B on a two-dimensional level, and ignores the changing relationship between H and B in the time domain, the traditional hysteresis loop can no longer accurately describe the changing law of H and B in the time domain, that is, it cannot accurately describe the hysteresis characteristics of magnetic materials under the influence of dynamic stray currents.
发明内容Summary of the invention
针对现有技术的不足,本发明的目的在于提供一种能够准确描述磁性材料的磁滞特性在动态杂散电流影响下的变化情况的方法及系统,为后续磁滞损耗和磁性材料工作温度的研究提供帮助。In view of the deficiencies in the prior art, the purpose of the present invention is to provide a method and system that can accurately describe the changes in the hysteresis characteristics of magnetic materials under the influence of dynamic stray currents, so as to provide assistance for subsequent research on hysteresis losses and the operating temperature of magnetic materials.
为实现上述目的,本发明提供如下技术方案:一种基于磁滞模型的三维时域磁滞回线描绘方法,包括:To achieve the above object, the present invention provides the following technical solution: a three-dimensional time-domain hysteresis loop drawing method based on a hysteresis model, comprising:
构建目标铁芯对应的J-A磁滞模型;Construct the J-A hysteresis model corresponding to the target core;
获取目标铁芯多个不同时刻的动态杂散电流的电流值,根据获取的电流值计算动 态杂散电流产生的磁场强度,将动态杂散电流产生的磁场强度与正常工频交流电流在目标 铁芯内部产生的交流磁场强度叠加得到的目标磁场强度作为J-A磁滞模型的总输入; The current values of the dynamic stray current of the target core at multiple different times are obtained, and the magnetic field strength generated by the dynamic stray current is calculated based on the obtained current values. The target magnetic field strength is obtained by superimposing the magnetic field strength generated by the dynamic stray current with the AC magnetic field strength generated by the normal power frequency AC current inside the target core. As the total input of JA hysteresis model;
采用回溯搜索优化算法对输入目标磁场强度后的J-A磁滞模型进行参数辨 识,将参数辨识后得到J-A磁滞模型的模型参数代入J-A磁滞模型,并在此基础上基于目标 磁场强度得到对应的实际磁化强度,利用目标磁场强度和实际磁化强度得到目标磁感应强度B(t); The backtracking search optimization algorithm is used to input the target magnetic field strength The JA hysteresis model is then identified, and the model parameters of the JA hysteresis model obtained after parameter identification are substituted into the JA hysteresis model. The corresponding actual magnetization intensity , using the target magnetic field strength and the actual magnetization Obtain the target magnetic induction intensity B(t);
对目标磁场强度和目标磁感应强度进行曲线拟合,得到目标铁芯的三维磁滞回线。The target magnetic field intensity and the target magnetic induction intensity are curve fitted to obtain the three-dimensional hysteresis loop of the target core.
进一步的,所述目标铁芯对应的J-A磁滞模型表示为:Furthermore, the J-A hysteresis model corresponding to the target core is expressed as:
(1); (1);
式中,表示实际磁化强度对目标磁场强度的微分;表示微分 算子;为防止出现非物理解而引出的系数;为可逆磁化系数;为不可逆损耗系数; 为方向系数,当目标磁场强度的变化率dH(t)/dt>0时,,当dH(t)/dt<0时,;t 表示时间;为无磁滞效应磁化强度,为畴壁相互作用系数。 In the formula, Indicates the actual magnetization Target magnetic field strength The differential of represents a differential operator; The coefficient introduced to prevent non-physical solutions; is the reversible magnetic susceptibility; is the irreversible loss coefficient; is the directional coefficient. When the rate of change of the target magnetic field strength dH(t)/dt>0, , when dH(t)/dt<0, ; t represents time; is the magnetization intensity without hysteresis effect, is the domain wall interaction coefficient.
进一步的,所述无磁滞效应磁化强度表示为: Furthermore, the hysteresis-free magnetization Expressed as:
(2); (2);
式中,为饱和磁化强度;为无磁滞效应磁化强度形状系数;表示有效磁场强度,其中,为畴壁相互作用系数。 In the formula, is the saturation magnetization; is the magnetization intensity shape factor without hysteresis effect; represents the effective magnetic field strength, where is the domain wall interaction coefficient.
进一步的,根据获取的电流值计算动态杂散电流产生的磁场强度的具体过程为: 基于安培环路定律求解动态杂散电流产生的磁场强度: Furthermore, the specific process of calculating the magnetic field strength generated by the dynamic stray current based on the acquired current value is as follows: Solving the magnetic field strength generated by the dynamic stray current based on Ampere's loop law :
(3); (3);
式中,为绕组线圈匝数;为动态杂散电流;为有效磁路长度。 In the formula, is the number of turns of the winding coil; is the dynamic stray current; is the effective magnetic path length.
进一步的,将动态杂散电流产生的磁场强度与正常工频交流电流在目标铁 芯内部产生的交流磁场强度叠加得到的目标磁场强度作为J-A磁滞模型的总 输入由式(4)表示: Furthermore, the magnetic field strength generated by the dynamic stray current The AC magnetic field strength generated by the normal power frequency AC current inside the target core The superimposed target magnetic field strength The total input of the JA hysteresis model is expressed by equation (4):
(4)。 (4).
进一步的,采用回溯搜索优化算法对J-A磁滞模型进行参数辨识,将参数辨识后得 到的模型参数代入J-A磁滞模型,并在此基础上基于目标磁场强度得到对应的实际磁 化强度,利用目标磁场强度和实际磁化强度得到目标磁感应强度B(t)的 具体过程为: Furthermore, the backtracking search optimization algorithm is used to identify the parameters of the JA hysteresis model, and the model parameters obtained after parameter identification are substituted into the JA hysteresis model, and on this basis, the target magnetic field intensity is used to The corresponding actual magnetization intensity , using the target magnetic field strength and the actual magnetization The specific process of obtaining the target magnetic induction intensity B(t) is:
对回溯搜索优化算法的参数初始化;Initialize the parameters of the backtracking search optimization algorithm;
设置回溯搜索优化算法的种群大小和种群迭代次数,同时,给定步长因子γ和随 机扰动因子r,并在约束条件内初始化产生满足约束条件的个体,其中,每个个体由、、、、共五个J-A磁滞模型内的参数组成,、、、、的取值范围组成约束条件;Set the population size and number of iterations of the backtracking search optimization algorithm. At the same time, give the step size factor γ and the random perturbation factor r, and initialize the individuals that meet the constraints within the constraints. Each individual is , , , , There are five parameters in the JA hysteresis model. , , , , The value range of constitutes the constraint condition;
对回溯搜索优化算法的种群内个体进行迭代更新;Iteratively update individuals in the population of the backtracking search optimization algorithm;
通过式(5)改变个体包含的、、、、参数,实现种群内个体的迭代更新; By changing the individual inclusion , , , , Parameters, to achieve iterative update of individuals within the population;
(5); (5);
式中,为种群内个体包含的、、、、参数的变化步长,其 中,为约束条件的上界,为约束条件的下界;为第代种群;为第代种 群;表示产生由0~1之间均匀分布的随机数组成的数组;表示获取目标矩阵的行数 和列数; In the formula, The number of individuals in a population , , , , The step size of the parameter change, where is the upper bound of the constraint condition, is the lower bound of the constraint; For the Generation population; For the Generation population; It means to generate an array of random numbers uniformly distributed between 0 and 1; Indicates obtaining the number of rows and columns of the target matrix;
对超出约束条件的个体包含的、、、、参数按式(6)和式(7)进行上下限 控制: For individuals exceeding the constraints , , , , The parameters are controlled by upper and lower limits according to equations (6) and (7):
超出上限:(6); Exceeding the limit: (6);
超出下限:(7); Exceeded lower limit: (7);
式中,表示个体中第m个包含的、、、、参数;表示上限的第 m个、、、、参数;表示下限的第m个、、、、参数; In the formula, Represents an individual The mth one contained in , , , , parameter; The mth upper limit , , , , parameter; The mth lower limit , , , , parameter;
将更新后的所有种群内个体代入J-A磁滞模型,得到每个时刻的实际磁化强度,基于每个时刻的目标磁场强度和每个时刻的实际磁化强度确定每个时刻的目标磁 感应强度B(t); Substitute all updated individuals in the population into the JA hysteresis model to obtain the actual magnetization intensity at each moment , determine the target magnetic induction intensity B(t) at each moment based on the target magnetic field intensity at each moment and the actual magnetization intensity at each moment;
使用适应度函数计算每次迭代更新后的种群内每个个体的适应度值,适应度函数F表示为:The fitness function is used to calculate the fitness value of each individual in the population after each iterative update. The fitness function F is expressed as:
(8); (8);
式中,为通过J-A磁滞模型计算得到的目标磁感应强度数据中的第个值;为基准磁感应强度数据中的第j个值;为数据点的个数; In the formula, is the target magnetic flux density data calculated by the JA hysteresis model. Values; is the jth value in the reference magnetic induction intensity data; is the number of data points;
判断是否达到终止条件,当达到终止条件时,选择适应度值最小的个体作为最优输出,否则判断迭代更新次数是否为规定值,当迭代更新次数为规定值则重新初始化,否则开始下一次种群内个体的迭代更新。Determine whether the termination condition is reached. When the termination condition is reached, select the individual with the smallest fitness value as the optimal output. Otherwise, determine whether the number of iterative updates is the specified value. When the number of iterative updates is the specified value, reinitialize. Otherwise, start the next iterative update of individuals in the population.
进一步的,对目标磁场强度和目标磁感应强度进行曲线拟合,得到目标铁芯的三 维磁滞回线的具体过程为:构建以x轴、y轴、z轴为坐标轴的三维直角坐标系,将目标磁场强 度和目标磁感应强度分别作为三维直角坐标系的x轴和y轴数据,将时间t作为三 维直角坐标系的z轴数据绘制目标铁芯的三维磁滞回线。 Furthermore, the target magnetic field intensity and the target magnetic induction intensity are curve fitted to obtain the three-dimensional hysteresis loop of the target iron core. The specific process is as follows: construct a three-dimensional rectangular coordinate system with the x-axis, y-axis, and z-axis as coordinate axes, and transform the target magnetic field intensity and target magnetic induction intensity The three-dimensional hysteresis loop of the target core is drawn by taking the x-axis and y-axis data of the three-dimensional rectangular coordinate system respectively and the time t as the z-axis data of the three-dimensional rectangular coordinate system.
一种基于磁滞模型的三维时域磁滞回线描绘系统,包括:A three-dimensional time-domain hysteresis loop drawing system based on a hysteresis model, comprising:
构建模块,用于构建目标铁芯对应的J-A磁滞模型;A construction module is used to construct a J-A hysteresis model corresponding to the target core;
计算模块,用于获取目标铁芯多个不同时刻的动态杂散电流的电流值,根据获取的电流值计算动态杂散电流产生的磁场强度,将动态杂散电流产生的磁场强度与正常工频交流电流在目标铁芯内部产生的交流磁场强度叠加得到的目标磁场强度作为J-A磁滞模型的总输入;A calculation module is used to obtain the current values of the dynamic stray current of the target iron core at multiple different times, calculate the magnetic field strength generated by the dynamic stray current according to the obtained current value, and superimpose the magnetic field strength generated by the dynamic stray current with the AC magnetic field strength generated by the normal power frequency AC current inside the target iron core to obtain the target magnetic field strength as the total input of the J-A hysteresis model;
辨识模块,用于采用回溯搜索优化算法对输入目标磁场强度后的J-A磁滞模型进行参数辨识,将参数辨识后得到J-A磁滞模型的模型参数代入J-A磁滞模型,并在此基础上基于目标磁场强度得到对应的实际磁化强度,利用目标磁场强度和实际磁化强度得到目标磁感应强度;An identification module is used to perform parameter identification on the J-A hysteresis model after inputting the target magnetic field strength by using a backtracking search optimization algorithm, substitute the model parameters of the J-A hysteresis model obtained after the parameter identification into the J-A hysteresis model, and obtain the corresponding actual magnetization intensity based on the target magnetic field strength on this basis, and obtain the target magnetic induction intensity by using the target magnetic field strength and the actual magnetization intensity;
拟合模块,用于对目标磁场强度和目标磁感应强度进行曲线拟合,得到目标铁芯的三维磁滞回线。The fitting module is used to perform curve fitting on the target magnetic field intensity and the target magnetic induction intensity to obtain the three-dimensional hysteresis loop of the target iron core.
进一步的,所述目标铁芯对应的J-A磁滞模型表示为:Furthermore, the J-A hysteresis model corresponding to the target core is expressed as:
; ;
式中,表示实际磁化强度对目标磁场强度的微分;表示微分 算子;为防止出现非物理解而引出的系数;为可逆磁化系数;为不可逆损耗系数; 为方向系数,当目标磁场强度的变化率dH(t)/dt>0时,,当dH(t)/dt<0时,;t 表示时间;为无磁滞效应磁化强度,为畴壁相互作用系数; In the formula, Indicates the actual magnetization Target magnetic field strength The differential of represents a differential operator; The coefficient introduced to prevent non-physical solutions; is the reversible magnetic susceptibility; is the irreversible loss coefficient; is the directional coefficient. When the rate of change of the target magnetic field strength dH(t)/dt>0, , when dH(t)/dt<0, ; t represents time; is the magnetization intensity without hysteresis effect, is the domain wall interaction coefficient;
所述无磁滞效应磁化强度表示为: The hysteresis-free magnetization Expressed as:
; ;
式中,为饱和磁化强度;为无磁滞效应磁化强度形状系数;表示有效磁场强度,其中,为畴壁相互作用系数。 In the formula, is the saturation magnetization; is the magnetization intensity shape factor without hysteresis effect; represents the effective magnetic field strength, where is the domain wall interaction coefficient.
一种计算机可读存储介质,存储有计算机程序,所述计算机程序被处理器执行时实现基于磁滞模型的三维时域磁滞回线描绘方法。A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a three-dimensional time-domain hysteresis loop drawing method based on a hysteresis model.
与现有的技术相比,本发明具备以下有益效果:本发明将动态杂散电流产生的磁场强度与正常交流磁场强度叠加作为模型总输入,绘制考虑动态杂散电流持续性干扰的三维下的磁滞回线,展示了动态杂散电流在对磁滞回线影响的时变和无周期性,同时,通过三维下的磁滞回线可以观测每个正常交流磁场强度变化周期内磁滞回线的变化情况,进而评估磁性材料工作时磁滞损耗及温度变化。Compared with the existing technology, the present invention has the following beneficial effects: the present invention superimposes the magnetic field intensity generated by the dynamic stray current and the normal AC magnetic field intensity as the total input of the model, draws a three-dimensional hysteresis loop considering the continuous interference of the dynamic stray current, and shows the time-varying and non-periodicity of the influence of the dynamic stray current on the hysteresis loop. At the same time, through the three-dimensional hysteresis loop, the change of the hysteresis loop in each normal AC magnetic field intensity change cycle can be observed, and the hysteresis loss and temperature change of the magnetic material when working can be evaluated.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明在动态杂散电流干扰下对J-A磁滞模型进行参数辨识的流程图。FIG1 is a flow chart of the present invention for parameter identification of the J-A hysteresis model under dynamic stray current interference.
图2为本发明智能算法参数辨识流程图。FIG. 2 is a flow chart of parameter identification of the intelligent algorithm of the present invention.
图3为本发明实测变电站中性点电流波形图。FIG3 is a diagram showing the measured neutral point current waveform of a substation according to the present invention.
图4为本发明动态杂散电流磁场强度与交流磁场强度叠加后的波形图。FIG4 is a waveform diagram of the dynamic stray current magnetic field intensity and the AC magnetic field intensity superimposed on each other according to the present invention.
图5为本发明J-A磁滞模型参数辨识的三维时域对比图。FIG5 is a three-dimensional time domain comparison diagram of the J-A hysteresis model parameter identification of the present invention.
图6为本发明的系统结构示意图。FIG6 is a schematic diagram of the system structure of the present invention.
具体实施方式Detailed ways
如图1所示,本发明提供技术方案:一种基于磁滞模型的三维磁滞回线描绘方法,包括如下步骤:As shown in FIG1 , the present invention provides a technical solution: a three-dimensional hysteresis loop drawing method based on a hysteresis model, comprising the following steps:
步骤S1:构建目标铁芯对应的J-A磁滞模型:Step S1: Construct the J-A hysteresis model corresponding to the target core:
(1); (1);
式中,表示实际磁化强度对目标磁场强度的微分;表示微分 算子;为防止出现非物理解而引出的系数;为可逆磁化系数;为不可逆损耗系数; 为方向系数,当目标磁场强度的变化率dH(t)/dt>0时,,当dH(t)/dt<0时,;t 表示时间;为畴壁相互作用系数;为无磁滞效应磁化强度,表示为: In the formula, Indicates the actual magnetization Target magnetic field strength The differential of represents a differential operator; The coefficient introduced to prevent non-physical solutions; is the reversible magnetic susceptibility; is the irreversible loss coefficient; is the directional coefficient. When the rate of change of the target magnetic field strength dH(t)/dt>0, , when dH(t)/dt<0, ; t represents time; is the domain wall interaction coefficient; is the magnetization intensity without hysteresis effect, expressed as:
(2); (2);
式中,为饱和磁化强度;为无磁滞效应磁化强度形状系数;表示有效磁场强度,其中,为畴壁相互作用系数。 In the formula, is the saturation magnetization; is the magnetization intensity shape factor without hysteresis effect; represents the effective magnetic field strength, where is the domain wall interaction coefficient.
步骤S2:获取目标铁芯多个不同时刻的动态杂散电流的电流值,如图3所示,根据 获取的电流值计算动态杂散电流产生的磁场强度,将动态杂散电流产生的磁场强度与正常 工频交流电流在目标铁芯内部产生的交流磁场强度叠加得到的目标磁场强度作为J- A磁滞模型的总输入。 Step S2: Obtain the current values of the dynamic stray current of the target core at multiple different times, as shown in Figure 3, calculate the magnetic field strength generated by the dynamic stray current based on the obtained current value, and superimpose the magnetic field strength generated by the dynamic stray current with the AC magnetic field strength generated by the normal power frequency AC current inside the target core to obtain the target magnetic field strength As the total input of the J-A hysteresis model.
步骤S3:采用回溯搜索优化算法对输入目标磁场强度后的J-A磁滞模型进行 参数辨识,将参数辨识后得到J-A磁滞模型的模型参数代入J-A磁滞模型,并在此基础上基 于目标磁场强度得到对应的实际磁化强度,利用目标磁场强度和实际磁 化强度得到目标磁感应强度B(t),如图2所示。 Step S3: Use the backtracking search optimization algorithm to input the target magnetic field strength The JA hysteresis model is then identified, and the model parameters of the JA hysteresis model obtained after parameter identification are substituted into the JA hysteresis model. The corresponding actual magnetization intensity , using the target magnetic field strength and the actual magnetization The target magnetic induction intensity B(t) is obtained, as shown in FIG2 .
步骤S4:对目标磁场强度和目标磁感应强度进行曲线拟合,得到目标铁芯的三维磁滞回线。Step S4: performing curve fitting on the target magnetic field intensity and the target magnetic induction intensity to obtain a three-dimensional hysteresis loop of the target core.
其中,根据获取的电流值计算动态杂散电流产生的磁场强度的具体过程为:基于 安培环路定律求解动态杂散电流产生的磁场强度: The specific process of calculating the magnetic field strength generated by the dynamic stray current based on the acquired current value is as follows: Based on Ampere's loop law, the magnetic field strength generated by the dynamic stray current is solved. :
(3); (3);
式中,为绕组线圈匝数;为动态杂散电流;为有效磁路长度。 In the formula, is the number of turns of the winding coil; is the dynamic stray current; is the effective magnetic path length.
其中,将动态杂散电流产生的磁场强度与正常工频交流电流产生的交流磁 场强度叠加得到的目标磁场强度作为J-A磁滞模型的总输入如式(4)所示,计 算所得目标磁场强度的波形图如图4所示; Among them, the magnetic field strength generated by the dynamic stray current is The AC magnetic field strength generated by the normal power frequency AC current The superimposed target magnetic field strength The total input of the JA hysteresis model is shown in formula (4), and the waveform of the calculated target magnetic field strength is shown in Figure 4;
(4); (4);
步骤S3的具体过程为:The specific process of step S3 is:
步骤S3.1:对回溯搜索优化算法的参数初始化;Step S3.1: Initialize the parameters of the backtracking search optimization algorithm;
设置回溯搜索优化算法的种群大小和种群迭代次数,同时,给定步长因子γ和随 机扰动因子r,并在约束条件内初始化产生满足约束条件的个体,其中,每个个体由、、 k、a、c共五个J-A磁滞模型内的参数组成,、、k、a、c的取值范围组成了约束条件。 Set the population size and number of iterations of the backtracking search optimization algorithm. At the same time, give the step size factor γ and the random perturbation factor r, and initialize the individuals that meet the constraints within the constraints. Each individual is , , k, a, c, a total of five parameters in the JA hysteresis model, , The value ranges of k, a, and c constitute the constraints.
步骤S3.2:对回溯搜索优化算法的种群内个体进行迭代更新;Step S3.2: iteratively update the individuals in the population of the backtracking search optimization algorithm;
通过式(5)改变个体包含的、、、、参数实现种群内个体的迭代更新; By changing the individual inclusion , , , , Parameters realize iterative updates of individuals within the population;
(5); (5);
式中,为种群内个体包含的、、、、参数的变化步长,其 中,为约束条件的上界,为约束条件的下界;为第代种群;为第代种 群;表示产生由0~1之间均匀分布的随机数组成的数组;表示获取目标矩阵的行数 和列数。 In the formula, The number of individuals in a population , , , , The step size of the parameter change, where is the upper bound of the constraint condition, is the lower bound of the constraint; For the Generation population; For the Generation population; It means to generate an array of random numbers uniformly distributed between 0 and 1; Indicates getting the number of rows and columns of the target matrix.
步骤S3.3:对超出约束条件的个体包含的、、、、参数按式(6)和式(7)进 行上下限控制: Step S3.3: For individuals that exceed the constraints , , , , The parameters are controlled by upper and lower limits according to equations (6) and (7):
超出上限:(6); Exceeding the limit: (6);
超出下限:(7); Exceeded lower limit: (7);
式中,表示个体中第m个包含的、、、、参数;表示上限的第 m个、、、、参数;表示下限的第m个、、、、参数。 In the formula, Represents an individual The mth one contained in , , , , parameter; The mth upper limit , , , , parameter; The mth lower limit , , , , parameter.
步骤S3.4:将更新后的所有种群内个体代入J-A磁滞模型,得到每个时刻的实际磁化强度M,基于每个时刻的目标磁场强度和每个时刻的实际磁化强度确定每个时刻的目标磁感应强度B(t);Step S3.4: Substitute all the updated individuals in the population into the J-A hysteresis model to obtain the actual magnetization intensity M at each moment, and determine the target magnetic induction intensity B(t) at each moment based on the target magnetic field intensity at each moment and the actual magnetization intensity at each moment;
使用适应度函数计算每次迭代更新后的种群内每个个体的适应度值,适应度值越小的个体越优秀,适应度函数F表示为:The fitness function is used to calculate the fitness value of each individual in the population after each iteration. The smaller the fitness value, the better the individual. The fitness function F is expressed as:
(8); (8);
式中,为通过J-A磁滞模型计算得到的目标磁感应强度数据中的第个值;为基准磁感应强度数据中的第j个值;为数据点的个数;适应度函数F的值越小,则 表明回溯搜索优化算法辨识的J-A磁滞模型参数与真实值越接近。 In the formula, is the target magnetic flux density data calculated by the JA hysteresis model. Values; is the jth value in the reference magnetic induction intensity data; is the number of data points; the smaller the value of the fitness function F is, the closer the JA hysteresis model parameters identified by the backtracking search optimization algorithm are to the true values.
步骤S3.5:判断是否达到终止条件,当达到终止条件时,选择适应度值最小的个体作为最优输出,否则判断迭代更新次数是否为5的整倍数,当迭代更新次数为5的整倍数则重新初始化,否则开始下一次种群内个体的迭代更新。Step S3.5: Determine whether the termination condition is met. When the termination condition is met, select the individual with the smallest fitness value as the optimal output. Otherwise, determine whether the number of iterative updates is an integer multiple of 5. If the number of iterative updates is an integer multiple of 5, reinitialize. Otherwise, start the next iterative update of individuals in the population.
步骤S4的具体过程为:构建以x轴、y轴、z轴为坐标轴的三维直角坐标系,将目标磁 场强度和目标磁感应强度分别作为三维直角坐标系的x轴和y轴数据,将时间t作 为三维直角坐标系的z轴数据绘制目标铁芯的三维磁滞回线。 The specific process of step S4 is: construct a three-dimensional rectangular coordinate system with x-axis, y-axis and z-axis as coordinate axes, and convert the target magnetic field intensity and target magnetic induction intensity The three-dimensional hysteresis loop of the target core is drawn by taking the x-axis and y-axis data of the three-dimensional rectangular coordinate system respectively and the time t as the z-axis data of the three-dimensional rectangular coordinate system.
使用回溯搜索优化算法对J-A磁滞模型进行参数辨识得到的目标铁芯的三维磁滞回线如图5所示,从图5中可以看出,使用回溯搜索优化算法对J-A磁滞模型进行参数辨识得到的目标铁芯的三维磁滞回线与基准值相近,采用本方案可以取得较好的效果。The three-dimensional hysteresis loop of the target core obtained by using the backtracking search optimization algorithm to identify the parameters of the J-A hysteresis model is shown in Figure 5. It can be seen from Figure 5 that the three-dimensional hysteresis loop of the target core obtained by using the backtracking search optimization algorithm to identify the parameters of the J-A hysteresis model is close to the benchmark value, and this scheme can achieve better results.
如图6所示,一种基于磁滞模型的三维时域磁滞回线描绘系统,包括:As shown in FIG6 , a three-dimensional time-domain hysteresis loop drawing system based on a hysteresis model includes:
构建模块,用于构建目标铁芯对应的J-A磁滞模型;A construction module is used to construct a J-A hysteresis model corresponding to the target core;
计算模块,用于获取目标铁芯多个不同时刻的动态杂散电流的电流值,根据获取的电流值计算动态杂散电流产生的磁场强度,将动态杂散电流产生的磁场强度与正常工频交流电流在目标铁芯内部产生的交流磁场强度叠加得到的目标磁场强度作为J-A磁滞模型的总输入;A calculation module is used to obtain the current values of the dynamic stray current of the target iron core at multiple different times, calculate the magnetic field strength generated by the dynamic stray current according to the obtained current value, and superimpose the magnetic field strength generated by the dynamic stray current with the AC magnetic field strength generated by the normal power frequency AC current inside the target iron core to obtain the target magnetic field strength as the total input of the J-A hysteresis model;
辨识模块,用于采用回溯搜索优化算法对输入目标磁场强度后的J-A磁滞模型进行参数辨识,将参数辨识后得到J-A磁滞模型的模型参数代入J-A磁滞模型,并在此基础上基于目标磁场强度得到对应的实际磁化强度,利用目标磁场强度和实际磁化强度得到目标磁感应强度;An identification module is used to perform parameter identification on the J-A hysteresis model after inputting the target magnetic field strength by using a backtracking search optimization algorithm, substitute the model parameters of the J-A hysteresis model obtained after the parameter identification into the J-A hysteresis model, and obtain the corresponding actual magnetization intensity based on the target magnetic field strength on this basis, and obtain the target magnetic induction intensity by using the target magnetic field strength and the actual magnetization intensity;
拟合模块,用于对目标磁场强度和目标磁感应强度进行曲线拟合,得到目标铁芯的三维磁滞回线。The fitting module is used to perform curve fitting on the target magnetic field intensity and the target magnetic induction intensity to obtain the three-dimensional hysteresis loop of the target iron core.
其中,所述目标铁芯对应的J-A磁滞模型表示为:Among them, the J-A hysteresis model corresponding to the target core is expressed as:
; ;
式中,表示实际磁化强度对目标磁场强度的微分;表示微分 算子;为防止出现非物理解而引出的系数;为可逆磁化系数;为不可逆损耗系数; 为方向系数,当目标磁场强度的变化率dH(t)/dt>0时,,当dH(t)/dt<0时,;t 表示时间;为无磁滞效应磁化强度,为畴壁相互作用系数。 In the formula, Indicates the actual magnetization Target magnetic field strength The differential of represents a differential operator; The coefficient introduced to prevent non-physical solutions; is the reversible magnetic susceptibility; is the irreversible loss coefficient; is the directional coefficient. When the rate of change of the target magnetic field strength dH(t)/dt>0, , when dH(t)/dt<0, ; t represents time; is the magnetization intensity without hysteresis effect, is the domain wall interaction coefficient.
其中,所述无磁滞效应磁化强度表示为: Wherein, the hysteresis-free magnetization intensity Expressed as:
; ;
式中,为饱和磁化强度;为无磁滞效应磁化强度形状系数;表示有效磁场强度,其中,为畴壁相互作用系数。 In the formula, is the saturation magnetization; is the magnetization intensity shape factor without hysteresis effect; represents the effective magnetic field strength, where is the domain wall interaction coefficient.
一种计算机可读存储介质,存储有计算机程序,所述计算机程序被处理器执行时实现基于磁滞模型的三维时域磁滞回线描绘方法。A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a three-dimensional time-domain hysteresis loop drawing method based on a hysteresis model.
本领域内的技术人员应明白,本申请的实施例可提供为方法、系统、或计算机程序产品。因此,本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。本申请实施例中的方案可以采用各种计算机语言实现,例如,面向对象的程序设计语言Java和直译式脚本语言JavaScript等。Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The schemes in the embodiments of the present application may be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present application is described with reference to the flowcharts and/or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and/or box in the flowchart and/or block diagram, as well as the combination of the processes and/or boxes in the flowchart and/or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate a device for implementing the functions specified in one process or multiple processes in the flowchart and/or one box or multiple boxes in the block diagram.
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.
尽管已描述了本申请的优选实施例,但本领域内的技术人员一旦得知了基本创造性概念,则可对这些实施例作出另外的变更和修改。所以,所附权利要求意欲解释为包括优选实施例以及落入本申请范围的所有变更和修改。Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.
显然,本领域的技术人员可以对本申请进行各种改动和变型而不脱离本申请的精神和范围。这样,倘若本申请的这些修改和变型属于本申请权利要求及其等同技术的范围之内,则本申请也意图包含这些改动和变型在内。Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.
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