CN114242425B - Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading - Google Patents

Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading Download PDF

Info

Publication number
CN114242425B
CN114242425B CN202111231887.1A CN202111231887A CN114242425B CN 114242425 B CN114242425 B CN 114242425B CN 202111231887 A CN202111231887 A CN 202111231887A CN 114242425 B CN114242425 B CN 114242425B
Authority
CN
China
Prior art keywords
magnetic
traction transformer
magnetic circuit
core
iron core
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202111231887.1A
Other languages
Chinese (zh)
Other versions
CN114242425A (en
Inventor
周利军
李沃阳
陈家伟
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southwest Jiaotong University
Original Assignee
Southwest Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southwest Jiaotong University filed Critical Southwest Jiaotong University
Priority to CN202111231887.1A priority Critical patent/CN114242425B/en
Publication of CN114242425A publication Critical patent/CN114242425A/en
Application granted granted Critical
Publication of CN114242425B publication Critical patent/CN114242425B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01F—MAGNETS; INDUCTANCES; TRANSFORMERS; SELECTION OF MATERIALS FOR THEIR MAGNETIC PROPERTIES
    • H01F27/00—Details of transformers or inductances, in general
    • H01F27/34—Special means for preventing or reducing unwanted electric or magnetic effects, e.g. no-load losses, reactive currents, harmonics, oscillations, leakage fields
    • H01F27/341—Preventing or reducing no-load losses or reactive currents
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Analysis (AREA)
  • Power Engineering (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Data Mining & Analysis (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Operations Research (AREA)
  • Regulation Of General Use Transformers (AREA)
  • Measuring Magnetic Variables (AREA)

Abstract

本发明公开了一种计及铁心磁路分级的牵引变压器磁滞损耗求解方法，通过构建基于非线性媒质关系的硅钢片电磁感应方程，并引入非同频物理量功率积分可忽略的特性，针对铁心各级磁路磁效应互异的特点，提出了适用于磁铁心磁路分级的牵引变压器铁心磁滞损耗的简化计算模型。本发明的有益效果在于有助于提出一种更符合材料物性和运行工况的磁滞损耗评估方法，能为牵引变压器生产优化设计和服役性能测评提供必要的数据保障。

Figure 202111231887

The invention discloses a method for solving the hysteresis loss of a traction transformer considering the classification of the iron core magnetic circuit. By constructing the silicon steel sheet electromagnetic induction equation based on the nonlinear medium relationship, and introducing the characteristic that the power integral of the non-same-frequency physical quantity can be ignored, the iron core Due to the different characteristics of the magnetic effects of the magnetic circuits at different levels, a simplified calculation model for the hysteresis loss of the traction transformer core suitable for the classification of the magnetic circuit of the magnetic core is proposed. The invention has the beneficial effect of helping to propose a hysteresis loss evaluation method that is more in line with material properties and operating conditions, and can provide necessary data guarantee for traction transformer production optimization design and service performance evaluation.

Figure 202111231887

Description

一种计及铁心磁路分级的牵引变压器磁滞损耗求解方法A method for solving hysteresis loss of traction transformer considering core magnetic circuit classification

技术领域Technical Field

本发明属于电气设备电磁分析与数值计算领域，具体涉及一种计及铁心磁路分级的牵引变压器磁滞损耗求解方法。The invention belongs to the field of electromagnetic analysis and numerical calculation of electrical equipment, and in particular relates to a method for solving the hysteresis loss of a traction transformer taking into account the grading of the iron core magnetic circuit.

背景技术Background Art

牵引变压器作为牵引供电系统中的关键设备，具备短时冲击负荷大、空载时间长的运行特点，对其铁心能耗的评估与优化研究具有重要的工程价值。而磁滞损耗作为铁心能耗的重要组成部分，为对牵引变压器铁心损耗进行进一步研究，提出一种足够精确的牵引变压器磁滞损耗求解方法具有迫切的工程意义。As a key device in the traction power supply system, the traction transformer has the characteristics of large short-term impact load and long no-load time. The evaluation and optimization of its core energy consumption has important engineering value. As an important component of core energy consumption, hysteresis loss has urgent engineering significance to propose a sufficiently accurate method for solving hysteresis loss of traction transformer in order to further study the core loss of traction transformer.

永久磁铁、铁磁性材料，以及电磁铁中，磁通经过的闭合路径叫做磁路，磁路分析的主要目的是要确定励磁磁通势和它所产生的磁通的关系。由于变压器卷绕工艺，牵引变压器各级铁心几何尺寸不同，将造成铁心各级磁路磁阻不同，进而使得变压器铁心各级磁场强度、磁通密度分布不均。在传统计算公式中，磁滞损耗计算通常将铁心视为均一化整体，数值上正比于平均磁场强度和平均磁通密度，这种公式无法解释由于磁路分级造成的磁场分布不均，计算误差较大且无法精确描述铁心某点的磁滞损耗，不能满足牵引变压器发展对损耗计算精度更高的要求。为此，提出一种考虑牵引变压器磁路分级的磁滞损耗计算公式显得尤为重要。In permanent magnets, ferromagnetic materials, and electromagnets, the closed path through which magnetic flux passes is called a magnetic circuit. The main purpose of magnetic circuit analysis is to determine the relationship between the excitation magnetic flux potential and the magnetic flux it generates. Due to the transformer winding process, the geometric dimensions of the cores at each level of the traction transformer are different, which will cause different magnetic resistances at each level of the core magnetic circuit, and thus make the magnetic field strength and flux density at each level of the transformer core unevenly distributed. In the traditional calculation formula, the hysteresis loss calculation usually regards the core as a homogenized whole, and the value is proportional to the average magnetic field strength and average flux density. This formula cannot explain the uneven magnetic field distribution caused by the magnetic circuit grading, the calculation error is large, and it cannot accurately describe the hysteresis loss at a certain point in the core, and cannot meet the requirements of the development of traction transformers for higher loss calculation accuracy. For this reason, it is particularly important to propose a hysteresis loss calculation formula that takes into account the magnetic circuit grading of traction transformers.

发明内容Summary of the invention

本发明的目的是提供一种计及铁心磁路分级的牵引变压器磁滞损耗求解方法，并通过如下技术手段实现：The purpose of the present invention is to provide a method for solving the hysteresis loss of a traction transformer taking into account the iron core magnetic circuit classification, and the method is achieved by the following technical means:

1)由于电力电子设备的存在与铁心自身的非线性特征，导致励磁电流存在显著低次谐波分量，由于励磁电流函数满足狄利克雷充分条件，为分析其谐波性质对其进行傅里叶变换，展开式为：1) Due to the presence of power electronic equipment and the nonlinear characteristics of the core itself, the excitation current has significant low-order harmonic components. Since the excitation current function satisfies the Dirichlet sufficient condition, a Fourier transform is performed to analyze its harmonic properties. The expansion is:

Figure SMS_1
Figure SMS_1

式中励磁电流Ih被分解为直流分量

Figure SMS_2
和相互正交的基波与各次谐波ancosnωt和bnsinnωt。由于供电系统电流不存在直流分量，并具有周期性质，在励磁电流一个周期内，可将上式简化为：Where the excitation current Ih is decomposed into the DC component
Figure SMS_2
And mutually orthogonal fundamental wave and harmonics a n cosnωt and b n sinnωt. Since there is no DC component in the power supply system current and it has a periodic nature, within one cycle of the excitation current, the above formula can be simplified to:

Figure SMS_3
Figure SMS_3

式中In表征为励磁电流基波与各次谐波的幅值，In数值依据傅里叶分解性质求得：In the formula, In represents the amplitude of the fundamental wave and each harmonic of the excitation current. The value of In is obtained based on the Fourier decomposition property:

Figure SMS_4
Figure SMS_4

由于电网为平衡的三相系统，在平衡的三相系统中，偶次谐波互相抵消，可近似忽略励磁电流的偶次谐波，将其表达式简化为：Since the power grid is a balanced three-phase system, in a balanced three-phase system, the even harmonics cancel each other out, and the even harmonics of the excitation current can be approximately ignored, and its expression can be simplified to:

Figure SMS_5
Figure SMS_5

式中k∈{0,1,2,3…}，由于谐波幅值与谐波次数呈反比，高次谐波幅值较小，计算仅考虑基波与三次谐波作用，故进一步简化表达式得：Where k∈{0,1,2,3…}, since the harmonic amplitude is inversely proportional to the harmonic order, the high-order harmonic amplitude is small, and the calculation only considers the fundamental and third harmonic effects, so the expression is further simplified to:

Ih(t)≈I1cosωt+I3cos3ωtI h (t)≈I 1 cosωt+I 3 cos3ωt

考虑磁滞损耗计算需对磁场强度和磁通密度的乘积进行积分，磁场强度频率等于励磁电流频率，磁通密度频率等于励磁电压频率，由于励磁电压不畸变，恒为标准工频，且不同频率物理量乘积积分等于零，故在磁滞损耗计算中对于决定磁场强度的励磁电流可仅考虑其基波分量，励磁电流表达式进一步简化为：Considering the hysteresis loss calculation, the product of magnetic field intensity and magnetic flux density needs to be integrated. The frequency of magnetic field intensity is equal to the frequency of excitation current, and the frequency of magnetic flux density is equal to the frequency of excitation voltage. Since the excitation voltage is not distorted and is always the standard power frequency, and the product integral of physical quantities of different frequencies is equal to zero, in the calculation of hysteresis loss, only the fundamental component of the excitation current that determines the magnetic field intensity can be considered. The excitation current expression is further simplified to:

Ih(t)≈I1cosωtI h (t)≈I 1 cosωt

式中，Ih(t)代表牵引变压器的励磁电流，I1、In分别代表励磁电流经傅里叶分解后的基波分量幅值和n次谐波分量幅值，ω为角频率，它满足：ω＝2πf，f 为励磁频率，t为时间；Where, I h (t) represents the excitation current of the traction transformer, I 1 and In represent the amplitude of the fundamental component and the amplitude of the nth harmonic component of the excitation current after Fourier decomposition, ω is the angular frequency, which satisfies: ω＝2πf, f is the excitation frequency, and t is the time;

2)由于牵引变压器铁心所采用的硅钢片是冷轧取向型，其在卷绕过程中无论是在心柱、铁轭还是拐角，都与导磁性能最佳的方向保持一致，可将全电流定律

Figure SMS_6
标量化为
Figure SMS_7
式中H为磁场强度、N为线圈匝数、L为牵引变压器铁心横截面的几何中心所在磁路的长度。2) Since the silicon steel sheets used in the traction transformer core are cold-rolled oriented, during the winding process, whether in the core column, iron yoke or corner, they are consistent with the direction with the best magnetic conductivity, so the full current law can be
Figure SMS_6
Scalarization
Figure SMS_7
Where H is the magnetic field strength, N is the number of coil turns, and L is the length of the magnetic circuit where the geometric center of the traction transformer core cross section is located.

同时，考虑牵引变压器铁心各级横截面几何中心所在磁路长度不同，对铁心各级磁场强度分别计算，由此将励磁电流表达式代入得到牵引变压器铁心各级磁场强度表达式：At the same time, considering that the length of the magnetic path where the geometric center of each cross section of the traction transformer core is located is different, the magnetic field strength of each level of the core is calculated separately, and the expression of the magnetic field strength of each level of the traction transformer core is substituted into it:

Figure SMS_8
Figure SMS_8

式中，Hi(t)代表牵引变压器铁心第i级的磁场强度，a和b分别代牵引变压器铁心磁路长度和磁路宽度，Ri代表第i级磁路弧段半径；Where, Hi (t) represents the magnetic field intensity of the traction transformer core at the i-th level, a and b represent the magnetic path length and magnetic path width of the traction transformer core, respectively, and Ri represents the radius of the arc segment of the i-th magnetic path;

3)由线圈电磁感应电动势公式有

Figure SMS_9
式中E1为变压器一次侧感应电压有效值，φm代表磁通最大值；由于变压器一次侧电压降较低，有E1≈U，式中U为变压器励磁电压有效值。联立以上二式，并将磁感强度与磁通关系
Figure SMS_10
代入，得：3) The formula for the electromagnetic induction electromotive force of the coil is:
Figure SMS_9
Where E1 is the effective value of the transformer primary induced voltage, φm represents the maximum value of the magnetic flux; due to the low voltage drop on the transformer primary side, E1 ≈U, where U is the effective value of the transformer excitation voltage. Combining the above two equations, and the relationship between magnetic induction intensity and magnetic flux
Figure SMS_10
Substituting in, we get:

Figure SMS_11
Figure SMS_11

式中，Bm代表牵引变压器铁心磁通密度最大值，S代表磁路横截面积，w 和d分别代牵引变压器铁心各级宽度和硅钢片厚度；Where, Bm represents the maximum value of the magnetic flux density of the traction transformer core, S represents the cross-sectional area of the magnetic circuit, w and d represent the width of each level of the traction transformer core and the thickness of the silicon steel sheet respectively;

4)由于牵引变压器铁心各级磁路的磁动势F＝NI相等，冷轧取向型硅钢片具有单向导磁性且铁心各级间存在绝缘层，在磁路层面，可将铁心各级拓扑视为并联。并联磁路，磁通与磁阻Rm成反比，磁阻表达式为：4) Since the magnetomotive force F=NI of each level of the traction transformer core is equal, the cold-rolled oriented silicon steel sheet has unidirectional magnetic conductivity and there is an insulating layer between each level of the core, at the magnetic circuit level, the topology of each level of the core can be regarded as parallel. In the parallel magnetic circuit, the magnetic flux is inversely proportional to the magnetic resistance Rm , and the magnetic resistance expression is:

Figure SMS_12
Figure SMS_12

式中μ为变压器铁心材质磁导率，由于各级磁路材质相同、横截面积相等，铁心各级磁通可视为与其几何中心所在磁路的长度成反比，即有：Where μ is the magnetic permeability of the transformer core material. Since the materials and cross-sectional areas of the magnetic circuits at each level are the same, the magnetic flux at each level of the core can be regarded as inversely proportional to the length of the magnetic circuit where its geometric center is located, that is:

Figure SMS_13
Figure SMS_13

式中Bi(t)为铁心各级的磁通密度，R1代表第1级磁路弧段半径。由于第一级磁路最短、磁通最大，考虑主磁通滞后励磁电流相位

Figure SMS_14
第一级磁路磁通密度可表示为：Where Bi (t) is the magnetic flux density of each level of the core, and R1 represents the radius of the arc segment of the first-level magnetic circuit. Since the first-level magnetic circuit is the shortest and the magnetic flux is the largest, the main magnetic flux lags behind the excitation current phase.
Figure SMS_14
The magnetic flux density of the first-stage magnetic circuit can be expressed as:

Figure SMS_15
Figure SMS_15

进一步，将第一级磁路磁通密度表达式代入各级磁路磁通密度关系式中，得到牵引变压器各级磁通密度表达式：Furthermore, the expression of the first-stage magnetic circuit flux density is substituted into the relationship between the flux density of each stage of the magnetic circuit to obtain the expression of the flux density of each stage of the traction transformer:

Figure SMS_16
Figure SMS_16

磁通密度仅有基频分量是因为磁通密度由励磁电压决定，变压器励磁电压一般为工频电压；The reason why the magnetic flux density has only the fundamental frequency component is that the magnetic flux density is determined by the excitation voltage, and the transformer excitation voltage is generally the power frequency voltage;

5)将上式代入电磁学对磁滞损耗的定义中，得到高湿度环境下计及铁心磁路分级的牵引变压器平均磁滞损耗P计算式：5) Substituting the above formula into the definition of hysteresis loss in electromagnetics, the calculation formula for the average hysteresis loss P of the traction transformer taking into account the core magnetic circuit classification in a high humidity environment is obtained:

Figure SMS_17
Figure SMS_17

本发明的有益效果在于提出了一种更符合材料物性和运行工况的考虑磁路分级的牵引变压器磁滞损耗计算方式，能为牵引变压器生产优化设计和服役性能测评提供必要的数据保障。The beneficial effect of the present invention is that a method for calculating the hysteresis loss of a traction transformer that takes into account magnetic circuit classification and is more in line with material properties and operating conditions is proposed, which can provide necessary data guarantee for the production optimization design and service performance evaluation of traction transformers.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明中所述牵引变压器铁心磁路分级示意图。FIG1 is a schematic diagram of the magnetic circuit classification of the traction transformer core described in the present invention.

图2为本发明中所述牵引变压器铁心各级并联拓扑图。FIG. 2 is a topological diagram of the parallel connection of each level of the traction transformer core according to the present invention.

具体实施方式DETAILED DESCRIPTION

下面结合附图对本发明的实施流程作进一步的详述。由于电力电子设备的存在与铁心自身的非线性特征，导致励磁电流存在显著低次谐波分量，由于励磁电流函数满足狄利克雷充分条件，为分析其谐波性质对其进行傅里叶变换，展开式为：The implementation process of the present invention is further described in detail below in conjunction with the accompanying drawings. Due to the presence of power electronic equipment and the nonlinear characteristics of the core itself, the excitation current has significant low-order harmonic components. Since the excitation current function satisfies the Dirichlet sufficient condition, a Fourier transform is performed to analyze its harmonic properties, and the expansion is:

Figure SMS_18
Figure SMS_18

式中励磁电流Ih被分解为直流分量

Figure SMS_19
和相互正交的基波与各次谐波 ancosnωt和bnsinnωt。由于供电系统电流不存在直流分量，并具有周期性质，在励磁电流一个周期内，可将上式简化为：Where the excitation current Ih is decomposed into the DC component
Figure SMS_19
And mutually orthogonal fundamental wave and harmonics a n cosnωt and b n sinnωt. Since there is no DC component in the power supply system current and it has a periodic nature, within one cycle of the excitation current, the above formula can be simplified to:

Figure SMS_20
Figure SMS_20

式中In表征为励磁电流基波与各次谐波的幅值，In数值依据傅里叶分解性质求得：In the formula, In represents the amplitude of the fundamental wave and each harmonic of the excitation current. The value of In is obtained based on the Fourier decomposition property:

Figure SMS_21
Figure SMS_21

由于电网为平衡的三相系统，在平衡的三相系统中，偶次谐波互相抵消，可近似忽略励磁电流的偶次谐波，将其表达式简化为：Since the power grid is a balanced three-phase system, in a balanced three-phase system, the even harmonics cancel each other out, and the even harmonics of the excitation current can be approximately ignored, and its expression can be simplified to:

Figure SMS_22
Figure SMS_22

式中k∈{0,1,2,3…}，由于谐波幅值与谐波次数呈反比，高次谐波幅值较小，计算仅考虑基波与三次谐波作用，故进一步简化表达式得：Where k∈{0,1,2,3…}, since the harmonic amplitude is inversely proportional to the harmonic order, the high-order harmonic amplitude is small, and the calculation only considers the fundamental and third harmonic effects, so the expression is further simplified to:

Ih(t)≈I1cosωt+I3cos3ωtI h (t)≈I 1 cosωt+I 3 cos3ωt

考虑磁滞损耗计算需对磁场强度和磁通密度的乘积进行积分，磁场强度频率等于励磁电流频率，磁通密度频率等于励磁电压频率，由于励磁电压不畸变，恒为标准工频，且不同频率物理量乘积积分等于零，故在磁滞损耗计算中对于决定磁场强度的励磁电流可仅考虑其基波分量，励磁电流表达式进一步简化为 Ih(t)≈I1cosωtConsidering the hysteresis loss calculation, the product of magnetic field intensity and magnetic flux density needs to be integrated. The frequency of magnetic field intensity is equal to the frequency of excitation current, and the frequency of magnetic flux density is equal to the frequency of excitation voltage. Since the excitation voltage is not distorted and is always the standard power frequency, and the product integral of physical quantities of different frequencies is equal to zero, in the calculation of hysteresis loss, only the fundamental component of the excitation current that determines the magnetic field intensity can be considered. The excitation current expression is further simplified to I h (t) ≈ I 1 cosωt

式中，Ih(t)代表牵引变压器的励磁电流，I1、In分别代表励磁电流经傅里叶分解后的基波分量幅值和n次谐波分量幅值，ω为角频率，它满足：ω＝2πf，f 为励磁频率，t为时间。Where, Ih (t) represents the excitation current of the traction transformer, I1 and In represent the amplitude of the fundamental component and the amplitude of the nth harmonic component of the excitation current after Fourier decomposition, ω is the angular frequency, which satisfies: ω＝2πf, f is the excitation frequency, and t is the time.

由于牵引变压器铁心所采用的硅钢片是冷轧取向型，其在卷绕过程中无论是在心柱、铁轭还是拐角，都与导磁性能最佳的方向保持一致，可将全电流定律

Figure SMS_23
标量化为
Figure SMS_24
式中H为磁场强度、N为线圈匝数、L为牵引变压器铁心横截面的几何中心所在磁路的长度。Since the silicon steel sheets used in the traction transformer core are cold-rolled oriented, during the winding process, whether in the core column, iron yoke or corner, they are consistent with the direction with the best magnetic conductivity, and the full current law can be
Figure SMS_23
Scalarization
Figure SMS_24
Where H is the magnetic field strength, N is the number of coil turns, and L is the length of the magnetic circuit where the geometric center of the traction transformer core cross section is located.

同时，考虑牵引变压器铁心各级横截面几何中心所在磁路长度不同，对铁心各级磁场强度分别计算。At the same time, considering the different lengths of the magnetic circuits at the geometric centers of the cross sections of the traction transformer core at each level, the magnetic field strength of each level of the core is calculated separately.

图1为本发明中所述牵引变压器铁心磁路分级示意图，图中以8级为例，由图可见，各级磁路均由四个矩形和四个四分之一圆构成，磁路长度可视为两倍铁心磁路长度、两倍铁心磁路宽度和圆周长之和，由此将励磁电流表达式代入得到牵引变压器铁心各级磁场强度表达式：FIG1 is a schematic diagram of the grading of the core magnetic circuit of the traction transformer in the present invention. The figure takes level 8 as an example. It can be seen from the figure that each level of the magnetic circuit is composed of four rectangles and four quarter circles. The length of the magnetic circuit can be regarded as the sum of twice the length of the core magnetic circuit, twice the width of the core magnetic circuit and the circumference. Therefore, the excitation current expression is substituted into the expression to obtain the magnetic field strength expression of each level of the traction transformer core:

Figure SMS_25
Figure SMS_25

式中，Hi(t)代表牵引变压器铁心第i级的磁场强度，a和b分别代牵引变压器铁心磁路长度和磁路宽度，Ri代表第i级磁路弧段半径。Where Hi (t) represents the magnetic field intensity of the traction transformer core at the i-th level, a and b represent the magnetic path length and magnetic path width of the traction transformer core, respectively, and Ri represents the radius of the arc segment of the i-th magnetic path.

由线圈电磁感应电动势公式有

Figure SMS_26
式中E1为变压器一次侧感应电压有效值，φm代表磁通最大值；由于变压器一次侧电压降较低，有 E1≈U，式中U为变压器励磁电压有效值。联立以上二式，并将磁感强度与磁通关系
Figure SMS_27
代入，得：The formula for the electromagnetic induction electromotive force of the coil is:
Figure SMS_26
Where E1 is the effective value of the transformer primary induced voltage, φm represents the maximum value of the magnetic flux; due to the low voltage drop on the transformer primary side, E1 ≈U, where U is the effective value of the transformer excitation voltage. Combining the above two equations, and the relationship between magnetic induction intensity and magnetic flux
Figure SMS_27
Substituting in, we get:

Figure SMS_28
Figure SMS_28

式中，Bm代表牵引变压器铁心磁通密度最大值，S代表磁路横截面积，w 和d分别代牵引变压器铁心各级宽度和硅钢片厚度。Where Bm represents the maximum value of the magnetic flux density of the traction transformer core, S represents the cross-sectional area of the magnetic circuit, and w and d represent the width of each level of the traction transformer core and the thickness of the silicon steel sheet, respectively.

由于牵引变压器铁心各级磁路的磁动势F＝NI相等，冷轧取向型硅钢片具有单向导磁性且铁心各级间存在绝缘层，在磁路层面，可将铁心各级拓扑视为并联。图2为本发明中所述牵引变压器铁心各级并联拓扑图，由图可知并联磁路，磁通与磁阻Rm成反比，磁阻表达式为：Since the magnetomotive force F=NI of each level of the traction transformer core magnetic circuit is equal, the cold-rolled oriented silicon steel sheet has unidirectional magnetic conductivity and there is an insulating layer between each level of the core, the topology of each level of the core can be regarded as parallel at the magnetic circuit level. Figure 2 is a parallel topology diagram of each level of the traction transformer core in the present invention. It can be seen from the figure that in the parallel magnetic circuit, the magnetic flux is inversely proportional to the magnetic resistance R m , and the magnetic resistance expression is:

Figure SMS_29
Figure SMS_29

式中μ为变压器铁心材质磁导率，由于各级磁路材质相同、横截面积相等，铁心各级磁通可视为与其几何中心所在磁路的长度成反比，即有：Where μ is the magnetic permeability of the transformer core material. Since the materials of the magnetic circuits at each level are the same and the cross-sectional areas are equal, the magnetic flux at each level of the core can be regarded as inversely proportional to the length of the magnetic circuit where its geometric center is located, that is:

Figure SMS_30
Figure SMS_30

式中Bi(t)为铁心各级的磁通密度，R1代表第1级磁路弧段半径。由于第一级磁路最短、磁通最大，考虑主磁通滞后励磁电流相位

Figure SMS_31
第一级磁路磁通密度可表示为：Where Bi (t) is the magnetic flux density of each level of the core, and R1 represents the radius of the arc segment of the first-level magnetic circuit. Since the first-level magnetic circuit is the shortest and the magnetic flux is the largest, the main magnetic flux lags behind the excitation current phase.
Figure SMS_31
The magnetic flux density of the first-stage magnetic circuit can be expressed as:

Figure SMS_32
Figure SMS_32

进一步，将第一级磁路磁通密度表达式代入各级磁路磁通密度关系式中，得到牵引变压器各级磁通密度表达式：Furthermore, the expression of the first-stage magnetic circuit flux density is substituted into the relationship between the flux density of each stage of the magnetic circuit to obtain the expression of the flux density of each stage of the traction transformer:

Figure SMS_33
Figure SMS_33

磁通密度仅有基频分量是因为磁通密度由励磁电压决定，变压器励磁电压一般为工频电压。The magnetic flux density has only a fundamental frequency component because the magnetic flux density is determined by the excitation voltage, and the transformer excitation voltage is generally an industrial frequency voltage.

将上式代入电磁学对磁滞损耗的定义中，得到计及铁心磁路分级的牵引变压器平均磁滞损耗P计算式：Substituting the above formula into the definition of hysteresis loss in electromagnetics, we can obtain the calculation formula for the average hysteresis loss P of the traction transformer taking into account the core magnetic circuit classification:

Figure SMS_34
Figure SMS_34

本发明的有益效果在于提出了一种更符合材料物性和运行工况的考虑磁路分级的牵引变压器磁滞损耗计算方式，能为牵引变压器生产优化设计和服役性能测评提供必要的数据保障。The beneficial effect of the present invention is that a method for calculating the hysteresis loss of a traction transformer that takes into account magnetic circuit classification and is more in line with material properties and operating conditions is proposed, which can provide necessary data guarantee for the production optimization design and service performance evaluation of traction transformers.

Claims (1)

1. A method for solving hysteresis loss of a traction transformer considering the grading of an iron core magnetic circuit is characterized in that the iron core is made of high-permeability cold-rolled grain-oriented silicon steel sheets, and comprises the following steps:
1) According to the hysteresis calculation principle, the exciting current for determining the magnetic field strength only considers the fundamental component and the periodic integral of the non-common frequency physical quantity is zero, so that an exciting current expression is obtained:
Figure FDA0004119680530000011
wherein I is h (t) is excitation current, I 1 、I n The fundamental component amplitude and the n-time component amplitude of exciting current after Fourier decomposition are respectively, ω is angular frequency, and the method meets the following conditions: ω=2pi f, f is excitation frequency, t is time;
2) According to the full current law, considering the magnetic circuit classification, the magnetic field intensity of each stage of the traction transformer iron core is expressed as:
Figure FDA0004119680530000012
wherein H is i (t) represents the magnetic field intensity of the ith stage of the traction transformer core, N represents the total number of turns of the exciting winding coil, L is the length of a magnetic circuit where the geometric center of the cross section of the traction transformer core is located, a and b respectively represent the length and the width of the magnetic circuit of the traction transformer core, R i Represents the radius of the arc section of the ith magnetic circuit;
3) According to the coil induced electromotive force formula and the approximate equal relation between the primary side induced electromotive force of the transformer and the exciting voltage, the expression of the maximum value of the magnetic flux density in the traction transformer core is obtained:
Figure FDA0004119680530000013
wherein B is m Represents the maximum value of the magnetic flux density phi of the traction transformer core m Representing the maximum value of magnetic flux, S representing the cross section area of a magnetic circuit, U representing the effective value of exciting voltage of the transformer, w and d respectively representing the widths of all stages of the traction transformer iron core and the thickness of the silicon steel sheet;
4) According to the parallel topology and the magnetic resistance proportional relation of each level of the magnetic circuit, the magnetic flux density calculation formula of each level of the iron core is obtained:
Figure FDA0004119680530000014
in B of i (t) is the magnetic flux density of each stage of the iron core, R 1 Represents the radius of the arc section of the level 1 magnetic circuit,
Figure FDA0004119680530000016
retarding the exciting current phase for the main magnetic flux;
5) According to (2) (4) and the definition of hysteresis loss by electromagnetism, the calculation formula of the average hysteresis loss P of the traction transformer considering the grading of the iron core magnetic circuit is obtained:
Figure FDA0004119680530000015
CN202111231887.1A 2021-10-22 2021-10-22 Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading Active CN114242425B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111231887.1A CN114242425B (en) 2021-10-22 2021-10-22 Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111231887.1A CN114242425B (en) 2021-10-22 2021-10-22 Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading

Publications (2)

Publication Number Publication Date
CN114242425A CN114242425A (en) 2022-03-25
CN114242425B true CN114242425B (en) 2023-06-02

Family

ID=80743199

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111231887.1A Active CN114242425B (en) 2021-10-22 2021-10-22 Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading

Country Status (1)

Country Link
CN (1) CN114242425B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115656025B (en) * 2022-11-22 2024-03-12 西南交通大学 Evaluation method for corrosion resistance of offshore transformer core
CN116127240B (en) * 2022-11-22 2023-12-05 西南交通大学 Evaluation method for overload capacity of wound core of traction transformer

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108647382A (en) * 2018-04-02 2018-10-12 西南交通大学 A kind of assessment method of rewinding material tractive transformer eddy-current loss
CN110399693A (en) * 2019-07-31 2019-11-01 西南交通大学 A calculation method for eddy current loss of transformer wound core under inter-chip short circuit
JP2019204269A (en) * 2018-05-23 2019-11-28 日本製鉄株式会社 Electromagnetic field analysis system, electromagnetic field analysis method, and program

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6873239B2 (en) * 2002-11-01 2005-03-29 Metglas Inc. Bulk laminated amorphous metal inductive device
EP2320439A4 (en) * 2008-09-03 2018-05-02 Hitachi Industrial Equipment Systems Co., Ltd. Wound iron core for static apparatus, amorphous transformer and coil winding frame for transformer
JP2017040002A (en) * 2015-08-21 2017-02-23 日本金属株式会社 Nonoriented electrical steel sheet for high frequency and method for producing the same
JP2018084940A (en) * 2016-11-23 2018-05-31 吉川工業株式会社 Design method, manufacturing method, and design program of iron core
DE102017205004B4 (en) * 2017-03-24 2022-12-08 Siemens Aktiengesellschaft circuit breaker
CN111270064B (en) * 2020-01-23 2020-10-02 西南交通大学 A method for controlling the annealing process of a wound iron core and a method for evaluating the annealing effect
CN112016204B (en) * 2020-08-27 2022-04-26 西南交通大学 Eddy current loss analysis method considering nonlinear magnetic property of autotransformer wound core material
CN111931310B (en) * 2020-08-28 2021-08-13 西南交通大学 An evaluation method of short-circuit eddy current loss between layers of wound iron core considering different magnetic boundary values

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108647382A (en) * 2018-04-02 2018-10-12 西南交通大学 A kind of assessment method of rewinding material tractive transformer eddy-current loss
JP2019204269A (en) * 2018-05-23 2019-11-28 日本製鉄株式会社 Electromagnetic field analysis system, electromagnetic field analysis method, and program
CN110399693A (en) * 2019-07-31 2019-11-01 西南交通大学 A calculation method for eddy current loss of transformer wound core under inter-chip short circuit

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
高洁，杨富尧等.0.23 mm薄规格取向硅钢谐波损耗与磁致伸缩研究.功能材料.2019,12132-12136. *

Also Published As

Publication number Publication date
CN114242425A (en) 2022-03-25

Similar Documents

Publication Publication Date Title
Rezaei-Zare Enhanced transformer model for low-and mid-frequency transients—Part I: Model development
CN110008645A (en) A kind of transformer loss calculation method
CN112632458B (en) Traction transformer eddy current loss solving method considering iron core magnetic saturation
CN114242425B (en) Hysteresis loss solving method for traction transformer considering iron core magnetic circuit grading
Najafi et al. Comparison of core loss and magnetic flux distribution in amorphous and silicon steel core transformers
Wang et al. Estimation model of core loss under DC bias
CN111931310A (en) Method for evaluating eddy current loss of wound core interlayer short circuit in consideration of boundary conditions of different magnetic fields
Li et al. Analytical loss model for magnetic cores based on vector magnetic circuit theory
Magdaleno-Adame et al. Electromagnetic finite element analysis of electrical steels combinations in lamination core steps of single-phase distribution transformers
Li et al. Numerical model for eddy-current loss of wound core in single-phase transformer
Hane et al. Dynamic hysteresis modeling taking skin effect into account for magnetic circuit analysis and validation for various core materials
Zhao et al. A dynamic model for prediction of hysteresis and loss property of soft material under multiple harmonic magnetizations
Wang et al. A higher-order loss-separation model for fast estimation of core loss in high-frequency transformers
Cheng et al. Engineering-oriented benchmarking of problem 21 family and experimental verification
Dawood et al. Numerical and experimental comparison of the no-load losses in the different grain-oriented electrical steel materials
Potgieter et al. Effects observed in the characterization of soft magnetic composite for high frequency, high flux density applications
Qin et al. Compatibility analysis among vector magnetic circuit theory, electrical circuit theory, and electromagnetic field theory
Wang et al. Magnetic shunt design and their effects on transformer winding electromagnetic forces
Deželak et al. Usage of a simplified and Jiles–Atherton model when accounting for the hysteresis losses within a welding transformer
CN114168887B (en) Traction transformer eddy current loss solving method considering iron core magnetic circuit classification
Li et al. Core form transformer topological duality based transient model validation for exciting current calculation within DC bias
Carrander Magnetizing currents in power transformers: Measurements, simulations, and diagnostic methods
Zirka et al. Modelling losses in electrical steel laminations
Elhaminia et al. Magnetic flux density determination in 3D wound core transformer using H-balance equation
Moses et al. Power loss of non oriented electrical steel under square wave excitation

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant