CN114242425A - Traction transformer hysteresis loss solving method considering iron core magnetic circuit grading - Google Patents
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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。
The invention discloses a method for solving the hysteresis loss of a traction transformer that takes into account the grading of the magnetic circuit of the iron core. By constructing a silicon steel sheet electromagnetic induction equation based on a nonlinear medium relationship, and introducing the characteristic that the power integral of non-same frequency physical quantities can be ignored, the iron core Due to the characteristics of different magnetic effects of different levels of magnetic circuits, a simplified calculation model of hysteresis loss of traction transformer iron cores suitable for the classification of magnetic circuits of magnetic cores is proposed. The beneficial effect of the invention is that it helps to propose a hysteresis loss evaluation method that is more in line with the material properties and operating conditions, and can provide necessary data guarantee for the production optimization design and service performance evaluation of the traction transformer.
Description
Technical Field
The invention belongs to the field of electromagnetic analysis and numerical calculation of electrical equipment, and particularly relates to a traction transformer hysteresis loss solving method considering iron core magnetic circuit grading.
Background
The traction transformer is used as a key device in a traction power supply system, has the operation characteristics of large short-time impact load and long dead time, and has important engineering value for evaluation and optimization research of iron core energy consumption. The hysteresis loss is an important component of the iron core energy consumption, and the method for solving the hysteresis loss of the traction transformer, which is accurate enough, is provided for further research on the iron core loss of the traction transformer, has urgent engineering significance.
The closed path through which magnetic flux passes in permanent magnets, ferromagnetic materials, and electromagnets is called the magnetic circuit, and the main purpose of magnetic circuit analysis is to determine the relationship between the excitation magnetomotive force and the magnetic flux it produces. Due to the winding process of the transformer, the different geometric sizes of the iron cores of all levels of the traction transformer cause different magnetic circuit reluctance of the iron cores of all levels, and further cause uneven distribution of the magnetic field intensity and the magnetic flux density of all levels of the iron cores of the transformer. In a traditional calculation formula, an iron core is generally regarded as a uniform whole in hysteresis loss calculation and is numerically proportional to an average magnetic field intensity and an average magnetic flux density, the formula cannot explain that the magnetic field distribution is uneven due to magnetic circuit grading, the calculation error is large, hysteresis loss at a certain point of the iron core cannot be accurately described, and the requirement of development of a traction transformer on higher loss calculation accuracy cannot be met. Therefore, it is important to provide a hysteresis loss calculation formula considering the magnetic circuit classification of the traction transformer.
Disclosure of Invention
The invention aims to provide a method for solving hysteresis loss of a traction transformer by taking iron core magnetic circuit grading into account, which is realized by the following technical means:
1) because the existence of power electronic equipment and the nonlinear characteristic of an iron core, the exciting current has obvious low-order harmonic component, because the exciting current function meets the Dirichlet sufficiency condition, Fourier transform is carried out on the exciting current function for analyzing the harmonic property of the exciting current function, and the expansion formula is as follows:
in the formula of exciting current IhIs decomposed into DC components
And fundamental wave and each subharmonic a orthogonal to each otherncosn ω t and bnsinn ω t. The current of the power supply system has no direct current component and has periodicityIn one period of the exciting current, the following equation can be simplified:
in the formula InCharacterised by the amplitude, I, of the fundamental and each harmonic of the exciting currentnThe values are found from the fourier decomposition properties:
because the power grid is a balanced three-phase system, even harmonics are mutually offset in the balanced three-phase system, the even harmonics of the exciting current can be approximately ignored, and the expression is simplified as follows:
in the formula, k belongs to {0,1,2,3 … }, since the harmonic amplitude is inversely proportional to the harmonic frequency and the higher harmonic amplitude is small, the calculation only considers the action of the fundamental wave and the third harmonic, the expression is further simplified:
Ih(t)≈I1cosωt+I3cos3ωt
considering that the magnetic hysteresis loss calculation needs to integrate the product of the magnetic field intensity and the magnetic flux density, the frequency of the magnetic field intensity is equal to the frequency of the exciting current, the frequency of the magnetic flux density is equal to the frequency of the exciting voltage, the exciting voltage is not distorted and is always the standard power frequency, and the integration of the product of physical quantities with different frequencies is equal to zero, so that only the fundamental component of the exciting current for determining the magnetic field intensity can be considered in the magnetic hysteresis loss calculation, and the exciting current expression is further simplified as follows:
Ih(t)≈I1cosωt
in the formula Ih(t) represents the excitation current of the traction transformer, I1、InRespectively representing the amplitude of the fundamental component and the nth harmonic component of the excitation current after Fourier decompositionAmplitude, ω is the angular frequency, which satisfies: ω is 2 pi f, f is the excitation frequency, t is the time;
2) because the silicon steel sheet adopted by the traction transformer iron core is in a cold-rolled orientation type, the silicon steel sheet is consistent with the optimal direction of the magnetic conductivity no matter in a core column, an iron yoke or a corner in the winding process, and the full current law can be realized
Normalized to
In the formula, H is the magnetic field intensity, N is the number of turns of the coil, and L is the length of a magnetic circuit where the geometric center of the cross section of the traction transformer iron core is located.
Meanwhile, the lengths of magnetic circuits where the geometric centers of all levels of cross sections of the iron core of the traction transformer are located are different, the magnetic field strengths of all levels of the iron core are respectively calculated, and the excitation current expression is substituted to obtain the magnetic field strength expression of all levels of the iron core of the traction transformer:
in the formula, Hi(t) represents the magnetic field strength of the ith stage of the traction transformer core, a and b represent the magnetic path length and the magnetic path width of the traction transformer core, RiRepresents the radius of the ith-level magnetic circuit arc segment;
3) the electromotive force formula induced by the coil electromagnetism is
In the formula E1Is an effective value of the primary side induced voltage of the transformermRepresents the maximum value of the magnetic flux; due to the lower voltage drop at the primary side of the transformer, E is provided1And U is approximately equal to U, wherein U is the effective value of the excitation voltage of the transformer. The two formulas are combined and the magnetic induction intensity is related to the magnetic flux
Substituting to obtain:
in the formula, BmRepresenting the maximum value of the magnetic flux density of the traction transformer iron core, S representing the cross section area of a magnetic circuit, and w and d representing the width of each stage of the traction transformer iron core and the thickness of a silicon steel sheet respectively;
4) because the magnetomotive force F-NI of each stage of magnetic circuit of the iron core of the traction transformer is equal, the cold-rolled oriented silicon steel sheet has one-way magnetic permeability, an insulating layer is arranged between each stage of the iron core, and the topology of each stage of the iron core can be regarded as parallel connection on the surface of the magnetic circuit. Parallel magnetic circuit, magnetic flux and reluctance RmInversely proportional, the reluctance expression is:
in the formula, mu is the permeability of the transformer core material, and because the magnetic circuits at different levels are the same in material and equal in cross-sectional area, the magnetic flux at each level of the core can be regarded as being inversely proportional to the length of the magnetic circuit with the geometric center, namely:
in the formula Bi(t) is the magnetic flux density of each core stage, R1Representing the radius of the 1 st order magnetic circuit arc segment. The shortest primary magnetic circuit and the largest magnetic flux are considered, and the main magnetic flux lags behind the phase of the exciting current
The first stage magnetic circuit flux density may be expressed as:
further, substituting the first-stage magnetic circuit magnetic flux density expression into each-stage magnetic circuit magnetic flux density relational expression to obtain each-stage magnetic flux density expression of the traction transformer:
the magnetic flux density only has a fundamental frequency component because the magnetic flux density is determined by the excitation voltage, and the transformer excitation voltage is generally the power frequency voltage;
5) substituting the above formula into the definition of hysteresis loss of electromagnetism to obtain the average hysteresis loss P calculation formula of the traction transformer considering the grading of the iron core magnetic circuit under the high humidity environment:
the method has the advantages that a magnetic hysteresis loss calculation mode of the traction transformer considering magnetic circuit classification, which is more in line with material physical properties and operation conditions, is provided, and necessary data guarantee can be provided for the production optimization design and service performance evaluation of the traction transformer.
Drawings
Fig. 1 is a schematic diagram of a traction transformer core magnetic circuit in a grading manner.
Fig. 2 is a topological diagram of the parallel connection of the iron cores of the traction transformer in each stage.
Detailed Description
The following describes the process of the present invention in detail with reference to the accompanying drawings. Because the existence of power electronic equipment and the nonlinear characteristic of an iron core, the exciting current has obvious low-order harmonic component, because the exciting current function meets the Dirichlet sufficiency condition, Fourier transform is carried out on the exciting current function for analyzing the harmonic property of the exciting current function, and the expansion formula is as follows:
in the formula of exciting current IhIs decomposed into DC components
And fundamental wave and each subharmonic a orthogonal to each otherncosn ω t and bnsinn ω t. Because the current of the power supply system has no direct current component and has periodic property, in one period of the exciting current, the formula can be simplified as follows:
in the formula InCharacterised by the amplitude, I, of the fundamental and each harmonic of the exciting currentnThe values are found from the fourier decomposition properties:
because the power grid is a balanced three-phase system, even harmonics are mutually offset in the balanced three-phase system, the even harmonics of the exciting current can be approximately ignored, and the expression is simplified as follows:
in the formula, k belongs to {0,1,2,3 … }, since the harmonic amplitude is inversely proportional to the harmonic frequency and the higher harmonic amplitude is small, the calculation only considers the action of the fundamental wave and the third harmonic, the expression is further simplified:
Ih(t)≈I1cosωt+I3cos3ωt
the product of magnetic field strength and magnetic flux density is required to be integrated in consideration of hysteresis loss calculation, the frequency of the magnetic field strength is equal to the frequency of exciting current, the frequency of the magnetic flux density is equal to the frequency of exciting voltage, the exciting voltage is not distorted and is constant to standard power frequency, and the product integral of physical quantities with different frequencies is equal to zero, so that only the fundamental component of the exciting current for determining the magnetic field strength can be considered in the hysteresis loss calculation, and the exciting current expression is further simplified into Ih(t)≈I1cosωt
In the formula Ih(t) represents the excitation current of the traction transformer, I1、InRespectively represent the fundamental component amplitude and the nth harmonic component amplitude of the excitation current after Fourier decomposition, omega is angular frequency, and meets the following requirements: ω is 2 pi f, f is the excitation frequency, and t is the time.
Because the silicon steel sheet adopted by the traction transformer iron core is in a cold-rolled orientation type, the silicon steel sheet is consistent with the optimal direction of the magnetic conductivity no matter in a core column, an iron yoke or a corner in the winding process, and the full current law can be realized
Normalized to
In the formula, H is the magnetic field intensity, N is the number of turns of the coil, and L is the length of a magnetic circuit where the geometric center of the cross section of the traction transformer iron core is located.
Meanwhile, the magnetic field intensity of each level of the iron core is respectively calculated by considering the different lengths of the magnetic circuits of the geometric centers of the cross sections of each level of the iron core of the traction transformer.
Fig. 1 is a schematic diagram of a traction transformer core magnetic circuit in a hierarchical manner, wherein 8 levels are taken as an example in the diagram, and as can be seen from the diagram, each level of magnetic circuit is composed of four rectangles and four quarter circles, and the magnetic circuit length can be regarded as the sum of twice the core magnetic circuit length, twice the core magnetic circuit width and the circumference, so that an excitation current expression is substituted to obtain a magnetic field intensity expression of each level of the traction transformer core:
in the formula, Hi(t) represents the magnetic field strength of the ith stage of the traction transformer core, a and b represent the magnetic path length and the magnetic path width of the traction transformer core, RiRepresents the radius of the ith-order magnetic circuit arc segment.
The electromotive force formula induced by the coil electromagnetism is
In the formula E1Is an effective value of the primary side induced voltage of the transformermRepresents the maximum value of the magnetic flux; due to the lower voltage drop at the primary side of the transformer, E is provided1And U is approximately equal to U, wherein U is the effective value of the excitation voltage of the transformer. The two formulas are combined and the magnetic induction intensity is related to the magnetic flux
Substituting to obtain:
in the formula, BmThe maximum value of the magnetic flux density of the traction transformer iron core is represented, S represents the cross section area of a magnetic circuit, and w and d respectively represent the width of each stage of the traction transformer iron core and the thickness of a silicon steel sheet.
Because the magnetomotive force F-NI of each stage of magnetic circuit of the iron core of the traction transformer is equal, the cold-rolled oriented silicon steel sheet has one-way magnetic permeability, an insulating layer is arranged between each stage of the iron core, and the topology of each stage of the iron core can be regarded as parallel connection on the surface of the magnetic circuit. FIG. 2 is a topological diagram of the parallel connection of the iron core stages of the traction transformer in the invention, and the parallel magnetic circuit, the magnetic flux and the magnetic resistance R can be known from the diagrammInversely proportional, the reluctance expression is:
in the formula, mu is the permeability of the transformer core material, and because the magnetic circuits at different levels are the same in material and equal in cross-sectional area, the magnetic flux at each level of the core can be regarded as being inversely proportional to the length of the magnetic circuit with the geometric center, namely:
in the formula Bi(t) is the magnetic flux density of each core stage, R1Representing the radius of the 1 st order magnetic circuit arc segment. Considering the first stage with shortest magnetic path and maximum magnetic fluxMagnetic flux lag excitation current phase
The first stage magnetic circuit flux density may be expressed as:
further, substituting the first-stage magnetic circuit magnetic flux density expression into each-stage magnetic circuit magnetic flux density relational expression to obtain each-stage magnetic flux density expression of the traction transformer:
the only fundamental frequency component of the magnetic flux density is because the magnetic flux density is determined by the excitation voltage, which is generally the line frequency voltage.
Substituting the above formula into the definition of hysteresis loss of electromagnetism to obtain the average hysteresis loss P calculation formula of the traction transformer taking the iron core magnetic circuit grading into account:
the method has the advantages that a magnetic hysteresis loss calculation mode of the traction transformer considering magnetic circuit classification, which is more in line with material physical properties and operation conditions, is provided, and necessary data guarantee can be provided for the production optimization design and service performance evaluation of the traction transformer.
Claims (1)
1. A method for solving hysteresis loss of a traction transformer considering iron core magnetic circuit grading is characterized in that an iron core is made of high-permeability cold-rolled grain-oriented silicon steel sheets, and comprises the following steps:
1) considering that the magnetic flux density of the transformer core is a fundamental wave and the periodic integral of non-same-frequency physical quantities is zero, obtaining an exciting current expression of the traction transformer core:
in the formula Ih(t) is an excitation current, I1、InThe fundamental component amplitude and the nth component amplitude of the excitation current after Fourier decomposition are respectively adopted, omega is angular frequency, and the fundamental component amplitude and the nth component amplitude satisfy the following conditions: ω is 2 pi f, f is the excitation frequency, t is the time;
2) according to the full current law, magnetic circuit grading is considered, and the magnetic field intensity of each grade of the iron core of the traction transformer is expressed as follows:
in the formula, Hi(t) represents the magnetic field intensity of the ith level 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 represent the length and the width of the magnetic circuit of the traction transformer core respectively, and R isiRepresents the radius of the ith-level magnetic circuit arc segment;
3) obtaining an expression of the maximum value of the magnetic flux density in the iron core of the traction transformer according to a coil induced electromotive force formula and an approximate equal relation between primary side induced electromotive force of the transformer and excitation voltage:
in the formula, BmRepresenting the maximum value of the magnetic flux density of the core of the traction transformer, phimRepresenting the maximum value of magnetic flux, S representing the cross-sectional area of a magnetic circuit, U representing the effective value of excitation voltage of the transformer, w and d representing the width of each stage of the iron core of the traction transformer and the thickness of a silicon steel sheet respectively;
4) according to the parallel topology of each level of the magnetic circuit and the proportion relation of the magnetic resistance, obtaining the calculation formula of the magnetic flux density of each level of the iron core:
in the formula Bi(t) is the magnetic flux density of each core stage, R1Represents the radius of the arc segment of the 1 st order magnetic circuit,
lagging the phase of the exciting current for the main flux;
5) and (3) obtaining a calculation formula of the average hysteresis loss P of the traction transformer considering the iron core magnetic circuit grading according to the definitions of (2) and (4) and the electromagnetism on the hysteresis loss:
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| CN115656025A (en) * | 2022-11-22 | 2023-01-31 | 西南交通大学 | Evaluation method for corrosion resistance of iron core of offshore transformer |
| CN116127240A (en) * | 2022-11-22 | 2023-05-16 | 西南交通大学 | A method for evaluating the overload capacity of traction transformer wound cores |
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