Loss separation method of laminated iron core
The method addresses measurement errors in iron loss separation by calculating classical eddy current loss and using frequency selection and averaging to stabilize the determination of abnormal eddy current and hysteresis loss, achieving precise iron loss component separation.
Patent Information
- Application Number
- CN202411355048.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-27
- Publication Date
- 2024-12-13
AI Technical Summary
Existing methods for separating iron loss components in laminated cores, such as hysteresis, abnormal eddy current, and classical eddy current losses, are prone to measurement errors and require complex hardware or sensitive extrapolation, leading to inaccurate results.
A loss separation method that calculates classical eddy current loss, then selects frequencies to minimize the condition number of a coefficient matrix, uses linear equations to determine abnormal eddy current and hysteresis loss, and averages results to eliminate measurement errors.
The method provides stable, accurate separation of iron loss components by reducing the impact of measurement errors through frequency selection and arithmetic mean calculations.
Smart Images
Figure CN119128342A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of energy technology, in particular to a loss separation method for a laminated iron core. Background Art
[0002] Oriented and non-oriented silicon steel laminated cores are basic components of various types of electrical or electronic equipment such as motors, transformers, inductors, etc. Laminated cores are formed by stacking or winding processes, and are mainly used to construct the magnetic circuit of electromagnetic equipment, and occupy the largest volume and weight proportion in various electromagnetic equipment. Laminated core loss, referred to as iron loss, is a key energy consumption indicator of electromagnetic equipment such as motors and transformers, and is also an important parameter for performance prediction and optimal design of electromagnetic equipment.
[0003] Iron loss separation technology is to decompose iron loss into several loss components according to the loss generation mechanism. Iron loss separation is the basic work of iron loss prediction. Based on the loss separation principle and by studying the frequency dependence of loss components and their frequency domain or time domain representation, iron loss estimation can be accurately achieved. At present, the theory generally accepted by academia and engineering circles is the loss statistics theory proposed by Italian scholar Bertotti, that is, iron loss can be decomposed into three loss components: hysteresis loss, abnormal eddy current loss, and classical eddy current loss.
[0004] The only widely recognized method for separating the three components of iron loss is the experimental method. The first and key step of the experimental separation is to separate the hysteresis loss. There are two specific solutions: one is to measure the iron loss of the sample under extremely low frequency conditions (less than 1Hz) and assume that the iron loss values at this time are all hysteresis losses; the other is to obtain the hysteresis loss by fitting or interpolation extrapolation based on the iron loss measurement values under multiple frequency conditions. However, the iron loss measurement under extremely low frequency conditions has extremely demanding hardware requirements, and the measured iron loss data is usually very small and easily overwhelmed by errors; the extrapolation method calculates the hysteresis loss, and the calculation results are very sensitive to specific fitting or interpolation formulas, data point selection and other issues, and require a repeated demonstration process.
[0005] In summary, it is necessary to propose a new and simpler method for separating the three components of core loss of oriented and non-oriented silicon steel sheets laminates, which is both practical and accurate. Summary of the invention
[0006] The purpose of the present invention is to provide a loss separation method for a laminated core, which can eliminate the influence of measurement errors implied in iron loss data by reasonably selecting frequency combinations and calculating arithmetic mean values, thereby improving calculation stability. The present invention is implemented by the following technical solutions.
[0007] The present invention provides a loss separation method for a laminated core, which specifically comprises the following steps: S1, based on the traditional formula, calculates the classic eddy current loss of the laminated core or silicon steel sheet at a given frequency f0; S2, for a given frequency f0, select a suitable frequency f i The selection criteria are f0 and f i The condition number of the coefficient matrix of the loss linear equation system is less than the set threshold, where i=1, 2, ..., n, and n is the serial number of different frequencies; S3, based on two different frequencies (f0, f i ) and the classical eddy current loss at the given frequency f0, and calculating the abnormal eddy current loss and hysteresis loss at the given frequency f0 through a loss linear equation group or through an abnormal eddy current loss and hysteresis loss formula; S4, using different frequency combinations (f0, f1), (f0, f2), ..., (f0, f i ),…,(f0, f n ), repeat the calculation process of step S3 to obtain the calculation results of n abnormal eddy current losses and n hysteresis losses at a given frequency f0; S5, respectively calculating the arithmetic mean of the calculation results of the n abnormal eddy current losses and the n hysteresis losses obtained in step S4, and finally obtaining the actual abnormal eddy current loss and hysteresis loss at a given frequency f0.
[0008] Optionally, in step S1, the classical eddy current loss of the laminated core or a single silicon steel sheet at a given frequency is calculated based on the traditional formula, which is specifically obtained by the following formula: , Where P cl (f0) is the classical eddy current loss at a given frequency f0, and the variable , is the thickness of a single silicon steel sheet, and are the electrical conductivity and magnetic permeability of silicon steel sheet materials, B m is the amplitude of the sinusoidal magnetic flux density, sinh and cosh represent the hyperbolic sine function and hyperbolic cosine function respectively, sin and cos represent the sine function and cosine function respectively.
[0009] Optionally, in step S2, the coefficient matrix of the loss linear equation group is: , Among them, the frequency f i The selection criteria are that for a given frequency f0, the frequency f i The choice should make the condition number of the coefficient matrix A of the loss linear equation group less than the specified data.
[0010] Optionally, in step S3, the loss linear equation group is: , Where P hy (f0) and P ex (f0) are the hysteresis loss and abnormal eddy current loss at a given frequency f0, respectively, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i The iron loss measurement data under and The iron loss measurement data P tot (f0) and P tot (f i ) contains the measurement error.
[0011] Optionally, in step S3, the calculation formula of abnormal eddy current loss at the given frequency f0 is: , Where P i ex (f0) is the frequency combination of the i-th group (f0,f i ) under abnormal eddy current loss, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i Iron loss measurement data, f0 and f i are respectively given frequencies, i=1, 2,…, n, where n is the serial number of the given frequency.
[0012] Optionally, in step S3, the hysteresis loss calculation formula at the given frequency f0 is: , Where P i hy (f0) is the frequency combination of the i-th group (f0,f i ) under hysteresis loss, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i Iron loss measurement data, f0 and f i are respectively given frequencies, i=1, 2,…, n, where n is the serial number of the given frequency.
[0013] Optionally, in step S5, the arithmetic mean of the n abnormal eddy current losses obtained in step S4 is calculated to finally obtain the actual abnormal eddy current loss at a given frequency f0, which is specifically calculated by the following formula: , In the formula, is the actual abnormal eddy current loss at a given frequency f0, is the i-th frequency combination (f0,f i ) under abnormal eddy current loss.
[0014] Optionally, in step S5, the arithmetic mean of the n hysteresis losses obtained in step S4 is calculated to finally obtain the actual hysteresis loss at a given frequency f0, which is specifically calculated by the following formula: , In the formula, is the actual hysteresis loss at a given frequency f0, is the i-th frequency combination (f0,f i ) under hysteresis loss.
[0015] Beneficial Effects This iron loss separation method can directly use the formula or solve the linear equations to calculate the hysteresis loss, abnormal eddy current loss and classical eddy current loss. During the implementation of the algorithm, the arithmetic mean value is used to eliminate the possible impact of the measurement error implicit in the iron loss data, and the calculation stability problem is taken into account by reasonably selecting the frequency combination. It is simple, fast and accurate. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Figure 1 The figure shows a schematic diagram of the process of separating the three components of the laminated core loss of the present invention; Figure 2 The figure shows the comparison of the iron loss separation results of the laminated core I at a given frequency of 50 Hz; Figure 3 The figure shows the comparison of the iron loss separation results of the laminated core II at a given frequency of 50 Hz. DETAILED DESCRIPTION
[0017] The invention is further described below with reference to the accompanying drawings and specific embodiments.
[0018] Embodiment 1: This embodiment introduces a loss separation method of a laminated core, which specifically includes the following contents:
[0019] S1, based on the traditional formula, calculates the classic eddy current loss of the laminated core or silicon steel sheet at a given frequency f0; S2, for a given frequency f0, select a suitable frequency f iThe selection criteria are f0 and f i The condition number of the coefficient matrix of the loss linear equation system is less than the set threshold, where i=1, 2, ..., n, and n is the serial number of different frequencies; S3, based on two different frequencies (f0, f i ) and the classical eddy current loss at the given frequency f0, and calculating the abnormal eddy current loss and hysteresis loss at the given frequency f0 through a loss linear equation group or through an abnormal eddy current loss and hysteresis loss formula; S4, using different frequency combinations (f0, f1), (f0, f2), ..., (f0, f i ),…,(f0, f n ), repeat the calculation process of step S3 to obtain the calculation results of n abnormal eddy current losses and n hysteresis losses at a given frequency f0; S5, respectively calculating the arithmetic mean of the calculation results of the n abnormal eddy current losses and the n hysteresis losses obtained in step S4, and finally obtaining the actual abnormal eddy current loss and hysteresis loss at a given frequency f0.
[0020] In practical applications, the laminated core is composed of multiple silicon steel sheets stacked together. The iron loss separation calculation method proposed in the present invention is applicable to both the overall loss separation of the laminated core and the loss separation of a single silicon steel sheet. Figure 1 The figure shows the calculation flow of abnormal eddy current loss and hysteresis loss of the present invention. In actual calculation, the classical eddy current loss of the laminated core or a single silicon steel sheet at a given frequency f0 is first calculated by the traditional formula, and then the different frequencies f0, f1, ..., f are measured by experimental instruments. i , …, f n The iron loss measurement data under two different frequencies are obtained, and then multiple combinations of (f0, f1), (f0, f2), ..., (f0, f i ),…,(f0, f n ) and the classical eddy current loss data, the abnormal eddy current loss and hysteresis loss formula proposed by the present invention, or the proposed loss linear equation group, are used to calculate the abnormal eddy current loss and hysteresis loss under the corresponding frequency combination, and the arithmetic mean value of the calculation results is calculated to calculate the actual abnormal eddy current loss and hysteresis loss under the frequency f0. The calculation method proposed by the present invention eliminates the possible influence of the measurement error implied in the iron loss data by reasonably selecting the frequency combination and calculating the arithmetic mean value.
[0021] Embodiment 2: Based on Embodiment 1, this embodiment further introduces a loss separation method for a laminated core, which specifically includes the following contents.
[0022] The laminated core I selected in this embodiment is rolled from oriented silicon steel sheets, and the laminated core II is stacked from non-oriented silicon steel sheets, and its main parameters are shown in Table 1. During the experiment, a programmable power supply was used for excitation, and a power analyzer was used to measure electrical parameters such as voltage, current, and power. During the iron loss separation calculation process, the selected frequency combination and the corresponding loss linear equation coefficient matrix condition number are shown in Table 2.
[0023] Table 1 Laminated core parameters parameter Laminated core I (made of oriented silicon steel sheets) Laminated core II (non-oriented silicon steel sheets stacked) Total width (mm) Total height (mm) Total thickness (mm) Width of single silicon steel sheet (mm) Thickness of single silicon steel sheet (mm) Electrical conductivity of silicon steel sheet (MS / m) Overall mass of core (kg) Number of turns of excitation coil Number of turns of measurement coil Excitation coil resistance (Ω) 13020430500.272.226.20330900.051 20024072400.52.7815.865552200.136 Table 2 Frequency combination table <![CDATA[f0]]> <![CDATA[f i (i=1,2,3)]]> Coefficient matrix condition number 50 152030 30.829.434.9 The calculation process of the experiment is as follows: Step 1: Calculate the classic eddy current loss of the laminated core or a single silicon steel sheet at a given frequency based on the traditional formula, which is calculated by the following formula: , Where P cl (f0) is the classical eddy current loss at a given frequency f0, Represents a variable, , is the thickness of silicon steel sheet, and are the electrical conductivity and magnetic permeability of silicon steel sheet materials, B m is the amplitude of the sinusoidal magnetic flux density, sinh and cosh represent the hyperbolic sine function and the hyperbolic cosine function respectively, sin and cos represent the sine function and the cosine function respectively. In this embodiment, f0 is 50 Hz.
[0024] Step 2: For a given frequency f0, select a suitable frequency f i The selection criteria are f0 and f i The condition number of the coefficient matrix of the loss linear equation system is small enough, where i=1, 2, ..., n, and n is the serial number of different frequencies. Generally, the condition number of the coefficient matrix is made less than 35.
[0025] In this embodiment, n=3, f0=50Hz, f1=15Hz, f2=20Hz, f3=30Hz are selected. From Table 2, it can be obtained that the condition numbers of the coefficient matrices of the loss linear equations corresponding to the frequency combinations (50,15), (50,20), and (50,30) are 30.8, 29.4, and 34.9, respectively, all less than 35.
[0026] Step 3, based on two different frequencies (f0, f i) and the classical eddy current loss at the given frequency f0, and calculate the abnormal eddy current loss and hysteresis loss through the loss linear equation group or through the abnormal eddy current loss and hysteresis loss formula.
[0027] Wherein, the loss linear equation group is: , Where P hy (f0) and P ex (f0) are the hysteresis loss and abnormal eddy current loss at a given frequency f0, respectively, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i The iron loss measurement data under and The iron loss measurement data P tot (f0) and P tot (f i ) contains measurement errors. , It will be eliminated by arithmetic mean calculation in subsequent processing. Therefore, when using the loss linear equation group to calculate the hysteresis loss and abnormal eddy current loss, it can be temporarily set to .
[0028] The formula for abnormal eddy current loss at a given frequency f0 is: , Where P i hy (f0) is the frequency combination of the i-th group (f0,f i ) under hysteresis loss, P cl f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i Iron loss measurement data, f0 and f i are given frequencies respectively, i=1, 2, ..., n, n is the serial number of the given frequency. In this embodiment, n is 3, and i is 1, 2, 3.
[0029] In this embodiment, the frequency combinations are (50, 15), (50, 20), and (50, 30). The instrument can measure the iron loss values at frequencies of 50 Hz, 15 Hz, 20 Hz, and 30 Hz, namely, P tot (50Hz), P tot(15Hz), P tot (20Hz) and P tot (30Hz) value.
[0030] Step 4: Use different frequency combinations (f0, f1), ..., (f0, f n ) under the condition of iron loss measurement data, repeat the calculation process of step S3 to obtain the calculation results of n abnormal eddy current losses and n hysteresis losses.
[0031] Step 5, respectively calculate the arithmetic mean of the n abnormal eddy current losses and n hysteresis losses calculated in step S4, and finally obtain the actual abnormal eddy current loss and hysteresis loss at a given frequency f0, which are specifically obtained by the following formula: ,
[0032] , In the formula, and are the actual abnormal eddy current loss and hysteresis loss at a given frequency f0, P i ex (f0) and P i hy (f0) are the frequency combinations of the i-th group (f0,f i ) under abnormal eddy current loss and hysteresis loss. In this embodiment, n is 3, and i is 1, 2, and 3.
[0033] Based on the laminated core loss separation method proposed in the present invention, this embodiment plots the obtained calculation results into a bar graph, specifically: the loss separation of laminated core I and laminated core II is performed at a given frequency of 50 Hz and different magnetic flux densities, the hysteresis loss and abnormal eddy current loss are calculated by the calculation model proposed in this patent, and the separation results are compared with the experimental results. The comparison results are shown in FIG. Figure 2 and Figure 3 .in, Figure 2 This is a comparison chart of the loss separation results of the laminated core I. Figure 3 This is a comparison chart of the loss separation results of laminated core II. Figure 2 , Figure 3 In the data, the hysteresis loss and abnormal eddy current loss calculated based on the loss separation method proposed in the present invention are marked as hysteresis loss (this patent) and abnormal loss (this patent), respectively, and the experimental method results are marked as hysteresis loss (measurement) and abnormal loss (measurement). Determination of classical eddy current loss, Figure 2 , Figure 3 The algorithm used in the experimental method is consistent with that used in the method of the present invention. Figure 2 , Figure 3As shown, the calculation results of the iron loss separation method proposed in the present invention are very close to the experimental data, which verifies the effectiveness and accuracy of the present invention.
[0034] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.
Claims
1. A loss separation method for a laminated core, characterized in that: include: S1, based on the traditional formula, calculates the classic eddy current loss of the laminated core or silicon steel sheet at a given frequency f0; S2, for a given frequency f0, select a suitable frequency f i The selection criteria are f0 and f i The condition number of the coefficient matrix of the loss linear equation system is less than the set threshold, where i=1, 2, ..., n, and n is the serial number of different frequencies; S3, based on two different frequencies (f0, f i ) and the classical eddy current loss at the given frequency f0, and calculating the abnormal eddy current loss and hysteresis loss at the given frequency f0 through a loss linear equation group or through an abnormal eddy current loss and hysteresis loss formula; S4, using different frequency combinations (f0, f1), (f0, f2), ..., (f0, f i ),…,(f0, f n ), repeat the calculation process of step S3 to obtain the calculation results of n abnormal eddy current losses and n hysteresis losses at a given frequency f0; S5, respectively calculating the arithmetic mean of the calculation results of the n abnormal eddy current losses and the n hysteresis losses obtained in step S4, and finally obtaining the actual abnormal eddy current loss and hysteresis loss at a given frequency f0.
2. The loss separation method according to claim 1, characterized in that: In step S1, the classical eddy current loss of the laminated core or a single silicon steel sheet at a given frequency is calculated based on the traditional formula, which is specifically obtained by the following formula: ， Where P cl (f0) is the classical eddy current loss at a given frequency f0, and the variable , is the thickness of a single silicon steel sheet, and are the electrical conductivity and magnetic permeability of silicon steel sheet materials, B m is the amplitude of the sinusoidal magnetic flux density, sinh and cosh represent the hyperbolic sine function and hyperbolic cosine function respectively, sin and cos represent the sine function and cosine function respectively.
3. The loss separation method according to claim 1, characterized in that: In step S2, the coefficient matrix of the loss linear equation system is: ， Among them, the frequency f i The selection criteria are that for a given frequency f0, the frequency f i The choice should make the condition number of the coefficient matrix A of the loss linear equation group less than the specified data.
4. The loss separation method according to claim 1, characterized in that: In step S3, the loss linear equation group is: , Where P hy (f0) and P ex (f0) are the hysteresis loss and abnormal eddy current loss at a given frequency f0, respectively, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i The iron loss measurement data under and The iron loss measurement data P tot (f0) and P tot (f i ) contains measurement errors.
5. The loss separation method according to claim 1, characterized in that In step S3, the calculation formula of abnormal eddy current loss at the given frequency f0 is: ， Where P i ex (f0) is the frequency combination of the i-th group (f0,f i ) under abnormal eddy current loss, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i Iron loss measurement data, f0 and f i are respectively given frequencies, i=1, 2,…, n, where n is the serial number of the given frequency.
6. The loss separation method according to claim 1, characterized in that In step S3, the hysteresis loss calculation formula at the given frequency f0 is: ， Where P i hy (f0) is the frequency combination of the i-th group (f0,f i ) under hysteresis loss, P cl (f0) is the classical eddy current loss at a given frequency f0, P tot (f0) and P tot (f i ) are respectively at given frequencies f0 and f i Iron loss measurement data, f0 and f i are respectively given frequencies, i=1, 2,…, n, where n is the serial number of the given frequency.
7. The loss separation method according to claim 1, characterized in that: In step S5, the arithmetic mean of the n abnormal eddy current losses obtained in step S4 is calculated to finally obtain the actual abnormal eddy current loss at a given frequency f0, which is specifically calculated by the following formula: , In the formula, is the actual abnormal eddy current loss at a given frequency f0, is the i-th frequency combination (f0,f i ) under abnormal eddy current loss.
8. The loss separation method according to claim 1, characterized in that: In step S5, the arithmetic mean of the n hysteresis losses obtained in step S4 is calculated to finally obtain the actual hysteresis loss at a given frequency f0, which is specifically calculated by the following formula: , In the formula, is the actual hysteresis loss at a given frequency f0, is the i-th frequency combination (f0,f i ) under hysteresis loss.