JP5609376B2 - Method for estimating iron loss - Google Patents

Description

  The present invention relates to a method for estimating iron loss of a soft magnetic material used for a motor or the like under a magnetic flux density waveform in which carrier harmonics are superimposed.

  Due to recent environmental problems, high-efficiency motors with low energy loss are attracting attention. There are roughly three types of energy loss in motors: iron loss, copper loss, and mechanical loss, and various ideas have been proposed for reducing each of them. In order to devise such a technique, it is necessary to accurately grasp these loss values first. In particular, in order to reduce the number of prototypes of a motor and efficiently design an optimal motor, it is required to estimate the loss value as accurately as possible without actually performing trial manufacture and measurement.

However, among the above-mentioned losses, the iron loss greatly depends on the characteristics and use conditions of the soft magnetic material to be used, and it is difficult to accurately estimate the value. The actual measured value may be several times the actual iron loss calculated directly from the data listed in the catalog. Specific causes of such errors include (1) bias in the magnetic flux distribution inside the motor, (2) the influence of the rotating magnetic field, (3) superposition of harmonic components of the magnetic flux density, and (4) shrink fitting. It is considered that the material characteristics deteriorate due to the stress caused by the above and the distortion at the time of punching the core.
In particular, the superposition of harmonic components of magnetic flux density in (3) is strongly related to the use of inverters in recent years. That is, when an inverter is used, a component having a high frequency such as 10 kHz is superimposed on the magnetic flux density waveform and a large number of minor loops are formed on the BH plane, that is, a carrier generated in association with modulation such as PWM. Since the number of cases in which the motor is driven in a state where the harmonics are superimposed, it is necessary to devise a method for correcting the influence on the iron loss due to this.

  The simplest correction method is to perform Fourier transform on the magnetic flux density waveform to calculate the amplitude for each frequency, find the iron loss value for each frequency from the amplitude and catalog data, and correct the sum of these values. There is a method of using as. Such a method is based on the assumption that the iron loss of the component derived from the carrier harmonic is determined only by the amplitude and frequency regardless of the position of the minor loop. However, in fact, it has been known from magnetic property measurement in a demagnetized state that the iron loss is larger when the position of the minor loop is in the high magnetic flux density region than in the low magnetic flux density region. Yes. Therefore, such a method has an advantage that it is simple and has a short calculation time, but has a problem that the calculation accuracy is not so high.

  In contrast to this method, the following method can be considered as the simplest method for considering the position of the minor loop. First, the magnetic characteristics in the biased state are measured. Next, the amplitude for each frequency calculated by Fourier transforming the magnetic flux density waveform is obtained. Then, for each frequency, the center position of the minor loop is regarded as the amount of magnetic bias, the iron loss value of each minor loop is calculated from the magnetic characteristic measurement result in the magnetic bias state, and the sum thereof is obtained as a correction term.

  An example of such a method is proposed by Non-Patent Document 1. In this proposal, the iron loss value is calculated for the case where only one harmonic component is superimposed on the fundamental wave. However, in general, carrier harmonics are often composed of a plurality of frequency components, and when these frequencies are close, “interference” occurs. For example, if the fundamental frequency is 50 Hz and the carrier frequency is set to 10 kHz, the components 9950 Hz and 10050 Hz have a finite amplitude. In such a case, within one period of the fundamental wave, there are times when the components cancel each other and times when they are amplified ("interference"). An example of this interference is shown in FIG. In such a case, simply considering the position of the minor loop for each frequency does not capture the influence of this interference, and the calculation accuracy does not improve much.

Therefore, as a method of iron loss calculation that directly considers the position of the minor loop without using Fourier transform, a method according to Non-Patent Document 2 and a method according to Patent Document 1 have been proposed.
In the method according to Non-Patent Document 2, first, iron loss due to minor loops at various positions on the BH plane is measured using a step-down chopper circuit, and these are used as a database. Then, for each minor loop in the actual waveform, calculate the iron loss value from the database based on the amount of magnetic bias and amplitude, and calculate the iron loss that increases due to the carrier harmonic by taking the sum of those iron losses. doing.
On the other hand, in the method of Patent Document 1, the core loss increased due to carrier harmonics is calculated by applying a magnetic flux density waveform when the inverter is actually driven to the core and performing data analysis.
Note that the terms bias amount and bias amount have the same meaning, but in this specification, we use the expression bias amount in the iron loss function, and actually use the magnetic flux density waveform to estimate the iron loss. We will use the expression bias amount.

JP 2008-122210 A

MAG-05-43 Material of IEEJ Magnetics Study Group IEEJ Transactions Volume 127, Issue 3, P217-225

However, in the method of Non-Patent Document 2, for all the minor loops in the actual waveform, the start and end times of the minor loops are obtained and are obtained by referring to the database based on the amplitude within that time. Takes a lot of time.
Moreover, in the method of Patent Document 1, since the iron loss value can be obtained by a single measurement operation, the calculation time is shortened compared with the method of Non-Patent Document 2, but the main application is in a filter reactor of an inverter or the like. It is limited to the iron loss calculation, that is, the iron loss calculation in the case where the waveform may be considered uniform inside the core.
On the other hand, when the magnetic flux density waveform of each mesh part is calculated individually by electromagnetic field analysis, such as the iron loss calculation in the motor iron core, all the iron loss values for each mesh part must be calculated. . In such a case, it is practically difficult to calculate each of meshes exceeding several thousand, regardless of which method is used.

  An object of the present invention is to provide an iron loss estimation method capable of accurately estimating, in a short time, an iron loss occurring in a motor core or the like, omitting the above-described state.

In order to achieve the above object, in the present invention, an increase in calculation time is prevented by using Fourier transform, and high accuracy is achieved by taking into consideration the influence of interference between harmonics.
That is, the present invention is a method for estimating iron loss in an electrical device using a soft magnetic material, and uses a magnetic demagnetization amount, an amplitude, and a frequency based on magnetic characteristic data of the soft magnetic material under a magnetic demagnetization state. A step of setting an iron loss function, and a measured waveform of magnetic flux density in the soft magnetic material when the electric device is driven by a power conversion device that performs switching operation at a fundamental frequency and a carrier frequency higher than the fundamental frequency, or Fourier transforming the analysis calculation waveform to obtain amplitude values and phase angles for a plurality of frequency components including at least a fundamental frequency component and a carrier harmonic component, and from the amplitude value and phase angle in each frequency component, the carrier A step for generating a relational expression representing the magnetic flux density other than the harmonic component and the magnetic flux density of the carrier harmonic component. And dividing one period of the fundamental frequency by a predetermined unit time, and deriving a magnetic flux density value for each divided unit time by using the relational expression, the magnetic flux density value and the iron Obtaining a unit time iron loss value based on a loss function; and summing the unit time iron loss value by an integral multiple of a half cycle of the fundamental wave to obtain a time average value for one period, which is obtained as the soft magnetic material. And obtaining as a value of the carrier loss.

By including a low-order harmonic component in the plurality of frequency components, it is possible to estimate the iron loss with higher accuracy.
If necessary, the relational expression can include an absolute value term of the bias amount.

In the relational expression, the basic frequency in the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and n (n = 1, 2,..., K, where k is a natural number). On the other hand, the sum of the components of nf ₂ ± mf ₁ [Hz] for all m (m = 0, 1, 2,..., L, where l is a natural number) is expressed as B _n sin (2πf ₁ t + θ _{1, n} ) × sin (2πnf ₂ t + θ _{2, n} )
Where B _n is the amplitude of the above component, and θ _{1, n} and θ _{2, n} are the phase angles of the term that changes at the frequency f ₁ of the harmonic component and the term that changes at the frequency f ₂ with respect to the fundamental wave. It can be a thing.
The average value of the amplitudes of the two frequency components represented by nf ₂ ± mf ₁ [Hz] can be used as the time average value.

The basic frequency of the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and the sum of the components of nf ₂ ± mf ₁ [Hz] (m = 1, 3, 5) for all n Is expressed by the following equation (A), the amplitude of the magnetic flux density can be obtained by the following equation (B).

The basic frequency of the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and nf ₂ ± mf ₁ [Hz] (m = 1, 3, 5) [Hz] for n = 1, 3. ] Is expressed by the following formula (C), the amplitude of the magnetic flux density is obtained by the following formula (D), and for n = 2, 4, nf ₂ ± mf ₁ [Hz] (m = 0, 2, 4) When the sum of the components of [Hz] is expressed by the following equation (E), the amplitude of the magnetic flux density can be obtained by the following equation (F).

ただし、ａ（Ｂ_０）、ｂ（Ｂ_０）、ｃ（Ｂ_０）は、鉄損値をフィッティングして求めた任意関数である。 The soft magnetic material may have an iron loss value W that is uniquely derived from the amount of bias B ₀ , the frequency f, and the amplitude value B _{m according} to the following equation (G).

However, a (B ₀ ), b (B ₀ ), and c (B ₀ ) are arbitrary functions obtained by fitting iron loss values.

According to the present invention, the iron loss value at a certain time is calculated based on the magnetic characteristics (database) in the magnetically biased state, and the iron loss is calculated by taking the time average. Since the iron loss is defined as a function, the calculation at this time can be performed as a table calculation. Therefore, the amplitude for each minor loop is calculated one by one, and the iron loss value is obtained by referring to the database based on the amplitude. Compared with the conventional method to be obtained, the calculation time of the iron loss can be greatly shortened, and therefore, it is particularly effective as a method for obtaining the iron loss of the iron core of the motor driven by the inverter.
Further, according to the present invention, since the influence of interference between harmonics is taken into account, the calculation accuracy of iron loss can be increased.

It is a graph which shows the result of fitting the relationship between the amount-of-magnetism dependence function and the amount of magnetization by a cubic function. It is a graph which shows the 1st example of the FFT result (only an amplitude) of the magnetic flux density waveform when a carrier harmonic is superimposed. It is the graph which illustrated the FFT result (only the amplitude) of the magnetic flux density waveform when a low order harmonic and a carrier harmonic are superimposed. It is a graph which shows the 2nd example of the FFT result (amplitude and phase) of the magnetic flux density waveform when a carrier harmonic is superimposed. It is a graph which shows the 3rd example of the FFT result (amplitude and phase) of the magnetic flux density waveform when a carrier harmonic is superimposed. It is explanatory drawing which shows a mode that the iron loss calculation is performed by spreadsheet. 3 is a flowchart conceptually illustrating an iron loss estimation process according to the present invention. It is the graph which illustrated the interference form of the several high frequency components superimposed on the magnetic flux density waveform.

  The iron loss estimation method according to an embodiment of the present invention includes four processes (I) to (IV). Hereinafter, the best modes of these processes (I) to (IV) will be described.

[I] Creating a database of iron loss values in a biased state A specific example of this process is shown below.
First, the magnetic properties in the magnetic deviation state of an electric device including a soft magnetic material is measured by a magnetic characteristic measuring apparatus, on the basis of the measurement data (data about iron loss), polarized iron loss磁量B ₀ , Defined as a function of amplitude B _m and frequency f.
The above function is not particularly limited as long as the magnetic characteristics in the actual biased state can be expressed well, but from the viewpoint of shortening the calculation time, it is preferable that the function is expressed as one mathematical expression as described below.

をもとに表現する。ここで、ａ'，ｃ'は定数である。この式（１）において、第一項はヒステリシス損に対応し、第二項は渦電流損に対応する。
この式（１）を偏磁下でも適用できるようにするためには、下式（２）のように、定数を偏磁量Ｂ_０の関数として拡張することが考えられる。

この式（２）は、スタインメッツの式である式（１）にそのまま偏磁量依存性を持たせたものであり、圧粉磁心のように表皮効果があまり顕著でない素材に対して使用することができる。
ここで、ａ（Ｂ_０），ｂ（Ｂ_０），ｃ（Ｂ_０）は、上記測定データをフィッティングすることによって求めた関数であり、実際の測定結果をうまく表現できるような数式となっていれば何でもよい。この関数ａ（Ｂ_０），ｂ（Ｂ_０），ｃ（Ｂ_０）を多項式として近似した場合には、それぞれの多項式の係数を材料データとして保存しておけばよい。 In the first example, the iron loss is the Steinmetz equation

Express based on Here, a ′ and c ′ are constants. In this formula (1), the first term corresponds to the hysteresis loss, and the second term corresponds to the eddy current loss.
In order to be able to apply this formula (1) even under bias, it is conceivable to extend the constant as a function of the bias amount B ₀ as shown in the following formula (2).

This equation (2) is the Steinmetz equation (1), which is directly dependent on the amount of magnetization, and is used for a material whose skin effect is not so remarkable, such as a dust core. be able to.
Here, a (B ₀ ), b (B ₀ ), and c (B ₀ ) are functions obtained by fitting the measurement data, and are mathematical expressions that can express actual measurement results well. Anything is fine. When the functions a (B ₀ ), b (B ₀ ), and c (B ₀ ) are approximated as polynomials, the coefficients of the respective polynomials may be stored as material data.

のように表すことが考えられる。電磁鋼板のような磁性材料は、キャリア周波数が１０ｋＨｚ程度の場合、渦電流損の割合が高く、しかも表皮効果の影響が強い。この式（３）は、この電磁鋼板のような磁性材料に対してよく当てはまる。
図１に、周波数ｆと振幅Ｂ_ｍを固定した際の関数ａ（Ｂ_０）の偏磁量依存性を模式的に示す。関数ａ（Ｂ_０）の偏磁量依存性がこのような形状を示す場合、この偏磁量依存性については例えば３次関数で表現することが可能である。また、式（３）におけるγは、偏磁量にほとんど依存せず、１．６〜２．０程度の定数となる。この具体的数値についても、振幅依存性に対するフィッティングにより容易に求めることができる。 As a second example, iron loss

It is possible to express as follows. A magnetic material such as an electromagnetic steel sheet has a high eddy current loss ratio and a strong skin effect when the carrier frequency is about 10 kHz. This equation (3) applies well to magnetic materials such as this electrical steel sheet.
FIG. 1 schematically shows the dependence of the function a (B ₀ ) on the amount of magnetic bias when the frequency f and the amplitude B _m are fixed. In the case where the dependence of the function a (B ₀ ) on the amount of demagnetization shows such a shape, the dependence on the amount of demagnetization can be expressed by a cubic function, for example. Further, γ in the equation (3) hardly depends on the amount of demagnetization and is a constant of about 1.6 to 2.0. This specific numerical value can also be easily obtained by fitting to the amplitude dependency.

When the iron loss function is set as described above, the iron loss value at an arbitrary bias B ₀ , amplitude B _m , and frequency f is obtained by this iron loss function.
By creating such an iron loss function, it is possible to calculate an iron loss value at a time by a table calculation when a data string having an arbitrary bias B ₀ , amplitude B _m , and frequency f is given.

[II] Calculation of each frequency component by Fast Fourier Transform (hereinafter abbreviated as FFT) In this process, the electric device is driven by a power converter (inverter), and at that time, the soft component calculated by electromagnetic field analysis is calculated. FFT is performed on the magnetic flux density waveform in the magnetic material. The electromagnetic field analysis can be performed by inputting a shape, current conditions, etc. in general software such as JMAG.

When inverter driving is performed, the frequency of the carrier harmonic component having a significant amplitude is nf ₂ ± mf ₁ Hz. Here, f ₁ Hz is a fundamental frequency, f ₂ Hz is a set carrier frequency, n is a natural number, and m is an integer of 0 or more. As an example, among the results of performing FFT on the magnetic flux density waveform, the results for the amplitude are shown in FIG. This FIG. 2 is for the case of f ₁ = 50 Hz and f ₂ = 1000 Hz, and the combinations of (n, m) are (1,1), (1,3), (2,1), (2 , 3), there is a carrier harmonic component having a significant amplitude.

By the way, the magnetic flux density waveform in the soft magnetic material in an actual device is not composed of only the fundamental wave component and the carrier harmonic component as shown in FIG. 2, but includes a component of mf ₁ Hz as shown in FIG. May be. This is not derived from being driven by an inverter, but is called a low-order harmonic component. That is, this low-order harmonic component is a component of 150, 250, 350 Hz.

Here, the component of 100 Hz is considered. In the case of f ₁ = 50 Hz and f ₂ = 1000 Hz, the 100 Hz component satisfies the requirements as a low-order harmonic component when m = 2 in the mf ₁ Hz formula. However, if a negative sign is taken in the expression of nf ₂ ± mf ₁ Hz and n = 1 and m = 18, the component of 100 Hz also satisfies the requirement as a carrier harmonic component. As described above, there is a possibility that an ambiguity may arise as to whether a 100 Hz component should be handled as a low-order harmonic component or a carrier harmonic component. In order to avoid such ambiguity, the following may be performed.

For example, as shown in FIG. 3, when the amplitude of the component in the vicinity of 500 to 700 Hz is almost zero, the frequency component in this frequency region has little influence on the iron loss estimation calculation. This means that it is possible to divide the frequency component in this frequency domain into two frequency bands by assuming that the amplitude of the frequency component is zero and using one point in the frequency domain as a boundary.
Therefore, it is possible to determine the low-frequency component as the low-order harmonic component and the high-frequency component as the carrier harmonic component with respect to the boundary. Incidentally, by setting the carrier frequency f ₂ lower, the frequency domain amplitude is substantially zero is not almost exist, there may be cases where the distinction between low-order harmonic component and the carrier harmonics becomes difficult. In such a case, for example, determine the (f _2/2) one of the boundary frequency such Hz, the boundary of this, the low-frequency side components of low order harmonic components, the high frequency side of the component carrier harmonic components Then, it becomes possible to distinguish by deciding.

Of the above carrier harmonic components, those having a significant magnitude differ depending on whether the inverter is single-phase or three-phase.
In the case of a single phase, m = 1, 3, 5 for all n where n <5. In the case of three phases, m = 1, 3, 5 when n is odd and n = 0, and m = 0, 2, 4 when n is even. Therefore, the amplitude corresponding to these high frequency components is stored as waveform data. In this way, since the component having a significant amplitude differs depending on whether it is a single phase or a three-phase, in the next process [III], the single phase and the three phases must be considered separately.
The reason why n is set to n <5 is that the iron loss estimation target electric device in the present embodiment is an electric motor. In an electric motor, in general, even if n is set to n <5, the estimation result of iron loss is not greatly affected.

と表した場合について考える。ここで、Ｂ_１は基本波の振幅、ｆ_１は基本波の周波数、Ｂ_２は２つのキャリア高調波の振幅、ｆ_２＋ｆ_１、ｆ_２−ｆ_１は２つのキャリア高調波の周波数、θ_１、θ_２はこの２つのキャリア高調波の位相角である。 [III] Calculation of amount of magnetic bias and amplitude in a time range of about one cycle of nf ₂ Hz In this process, a mathematical expression used in process (IV) is specifically obtained.
(A) Simple example Simplify the equation of the waveform when carrier harmonics are superimposed, and change the magnetic flux density.

Consider the case where Here, B ₁ is the amplitude of the fundamental wave, f ₁ is the frequency of the fundamental wave, B ₂ is the amplitude of the two carrier harmonics, f ₂ + f ₁ and f ₂ −f ₁ are the frequencies of the two carrier harmonics, θ _1, theta ₂ is the phase angle of the two carrier harmonics.

4A and 4B respectively illustrate the amplitude characteristics and the phase characteristics obtained by performing the FFT process on the magnetic flux density waveform represented by Expression (4). Although the amplitudes of the second term and the third term on the right-hand side of Equation (4) are the same value, they are actually the same, but are not exactly the same. Therefore, among the FFT results, the average value of the amplitude of the component of the second term and the third term may be set to B _2. If such a change is made, it will be easier to expand the expression as shown below.

この式（５）の第二項は、周波数ｆ_１でゆっくり変化する項と周波数ｆ_２で早く変化する項との積で表現されている。第二項の一周期程度の時間領域において、第一項はほぼ一定とみなせるので、この第一項を第二項における「周波数ｆ_２で早く変化する項」の振幅と近似することができる。
ここで、高周波成分に対応する部分である

において、

と置き換えれば、Ｂ_nsin(２πｆ_１ｔ＋θ_１,n)×sin(２πｎｆ_２ｔ＋θ_２,ｎ)の式におけるｎ＝１の場合に対応していることが確認できる。
この近似のもとでの高調波成分の磁束密度は、時刻ｔの付近において以下のような振幅、周波数及び偏磁量を持つものとみなすことが可能である。

そして、この振幅、周波数及び偏磁量を例えば前記式（１）あるいは式（２）または式（３）に適用することによって鉄損をきわめて容易に算定することができる。 When two frequency components are included as in Expression (4), the two interfere with each other and the amplitude of the carrier harmonic component is not constant. Therefore, the equation (4) is modified as follows.

The second term of the equation (5) is expressed by the product of a term that slowly changes at the frequency f ₁ and a term that changes quickly at the frequency f ₂ . Since the first term can be regarded as almost constant in the time domain of about one cycle of the second term, the first term can be approximated with the amplitude of the “term that changes rapidly at the frequency f ₂ ” in the second term.
Here, it is the part corresponding to the high frequency component

In

It can be confirmed that this corresponds to the case of n = 1 in the formula B _n sin (2πf ₁ t + θ _{1, n} ) × sin (2πnf ₂ t + θ _{2, n} ).
The magnetic flux density of the harmonic component under this approximation can be regarded as having the following amplitude, frequency, and amount of bias near time t.

The iron loss can be calculated very easily by applying the amplitude, frequency, and amount of magnetic bias to, for example, the formula (1), the formula (2), or the formula (3).

と表される。そして、磁束密度波形がこの式（７）で表される場合は、式（６）に対して単純に偏磁量を下式(８)に示すように変更すればよい。

ここで、

は基本波に対する３次の高調波（低次高調波）である。 (B) Extension 1 -Bias amount and low-order harmonic capture-
The above example is a case where carrier harmonics are superimposed only on the fundamental wave, but in actuality, a bias amount or a low-order harmonic component is superimposed on the magnetic flux density waveform. In this case, the magnetic flux density waveform is, for example,

It is expressed. When the magnetic flux density waveform is expressed by this equation (7), the amount of bias can be simply changed as shown in the following equation (8) with respect to equation (6).

here,

Is a third-order harmonic (low-order harmonic) with respect to the fundamental wave.

となっている場合、すなわち、前記ｍ＝１，３，５であるｆ_２±ｆ_１,ｆ_２±３ｆ_１,ｆ_２±５ｆ_１の周波数成分が存在する場合を考える。図５の（ａ）、（ｂ）は、この場合の磁束密度波形をＦＦＴ処理することによって得られた振幅特性、位相特性をそれぞれ例示したものである。
この式（９）に対し前記と同様の式変形を行い、展開すると

となる。この式（１０）で表される波形は、前記と同様の時間領域においてほぼ正弦波であり、その振幅は

である。 (C) Extension 2 -Incorporation of all components with m <6-
The harmonic component of the waveform

In other words, the case where the frequency components of f ₂ ± f ₁ , f ₂ ± 3f ₁ , and f ₂ ± 5f ₁ where m = 1, 3, and 5 exist is considered. FIGS. 5A and 5B illustrate amplitude characteristics and phase characteristics obtained by performing FFT processing on the magnetic flux density waveform in this case.
If this equation (9) is transformed as described above and expanded,

It becomes. The waveform represented by this equation (10) is almost a sine wave in the same time domain as described above, and its amplitude is

It is.

とすれば、この波形も同様の時間領域においてほぼ正弦波であり、その振幅は

となる。
以上のことから、多数の周波数成分を含む場合には振幅の式を修正すればよいことがわかる。 Further, when the m = 0, 2, 4 a is _{f 2, f 2 ± 2f 1} , f 2 frequency components of the ± 4f ₁ is present, the harmonic component of the waveform

If this is the case, this waveform is almost sinusoidal in the same time domain, and its amplitude is

It becomes.
From the above, it can be seen that when a large number of frequency components are included, the amplitude equation may be corrected.

(D) Extension 3 -Incorporation of all components with n <5-
Since the frequency components with different n are separated by at least about f ₂ Hz, the influence of mutual interference is not so serious. Therefore, a plurality of n is dealt with by separately calculating the process [IV] described below.

と表す。この時、偏磁量は、

とすればよい。
次に、振幅は次のようにして求める。キャリア高調波成分は、

であり、この式は、式（４）を式（５）に変換したように、
Ｂ_nsin(２πｆ_１ｔ＋θ_１,n)×sin(２πｎｆ_２ｔ＋θ_２,ｎ)
の形に変形することができる。
ただし、Ｂ_nは上記成分の振幅、θ_１,n及びθ_２,ｎは基本波に対する、高調波成分の周波数ｆ_１で変化する項の位相角及び周波数ｆ_２で変化する項の位相角である。
そして、この形に変更した際の
Ｂ_nsin(２πｆ_１ｔ＋θ_１,n)
が、各nに対する振幅である。周波数は各ｎに対して、ｎｆ_２である。 (E) Extension 4 -Generalization-
The above is described in general terms as follows.
First, the magnetic flux density waveform is

It expresses. At this time, the amount of magnetic bias is

And it is sufficient.
Next, the amplitude is obtained as follows. Carrier harmonic component is

This equation is equivalent to converting equation (4) into equation (5),
B _n sin (2πf ₁ t + θ _{1, n} ) × sin (2πnf ₂ t + θ _{2, n} )
It can be transformed into a shape.
Where B _n is the amplitude of the above component, θ _{1, n} and θ _{2, n} are the phase angle of the term changing at the frequency f ₁ of the harmonic component and the phase angle of the term changing at the frequency f ₂ with respect to the fundamental wave. is there.
And when changing to this shape
B _n sin (2πf ₁ t + θ _{1, n} )
Is the amplitude for each n. The frequency is nf ₂ for each n.

[IV] Correlation of Iron Loss Value from Amount of Bias Magnetism and Amplitude and Time Average This process shows how to calculate the iron loss using the formula obtained in Process [III].
From the discussion in the previous section, it was found that for a certain n, a minor loop in the vicinity of a certain time may be regarded as a sine wave loop in which the amount of magnetization and the amplitude are expressed by mathematical expressions.
Therefore, the time corresponding to one period of the fundamental wave is engraved by a section having an equal time width of, for example, about 100 to 1000. Then, at each engraved time, the iron loss value is determined with reference to the material parameter (iron loss function) obtained in the process (I) based on the amount of magnetic bias, amplitude, and frequency nf ₂ Hz expressed by the mathematical formula. And take the sum of those iron loss values. Since the sum of the iron loss values can be the average value of the iron loss for one period, this may be performed for all n. Here, it should be noted that the equations used for the single-phase case and the three-phase case are different.
Here, the time width will be described. The time width can be determined on the basis of the time variation of the magnetic flux density. That is, for example, if the carrier frequency is 10 kHz, n is considered up to n <5, and therefore, a significant harmonic component whose magnetic flux density changes over time exists up to 40 kHz. Assuming that the frequency of the fundamental wave is 50 Hz, the frequency 40 kHz is 800 times the fundamental wave frequency 50 Hz. Therefore, if the time obtained by dividing the time of one period of the fundamental wave by 800 or a number larger than 800 is determined as the step time width, the change in magnetic flux density in one period of frequency 40 kHz can be included in the time width. Thereby, the estimation accuracy of the iron loss is increased to the limit.
The time required for the iron loss estimation calculation can be shortened as the time width is set larger. Therefore, the time width is appropriately set in consideration of the estimated calculation time, required iron loss estimation accuracy, and the like.

The iron loss can be calculated by the above process. In this method, the iron loss is obtained by performing the calculation using the formula obtained in the process (III) by the number of times of the period of one period of the fundamental wave, that is, the iron loss is calculated by a calculation process such as a table calculation. Loss can be determined. Such a calculation is shown in FIG.
The processing time for this calculation is instantaneous in a normal personal computer. On the other hand, it is known that the method according to Non-Patent Document 2 requires about several minutes as the calculation processing time. Therefore, the method according to the present invention greatly reduces the calculation time, and as a result, the calculation of the iron loss of an iron core such as a motor, which has conventionally required a lot of time, can be processed in a short time.
FIG. 7 is a flowchart conceptually showing the above-described process for determining the iron loss.

Claims (8)

A method for estimating iron loss in an electrical device using a soft magnetic material,
Based on the magnetic property data under the biased state of the soft magnetic material, setting the iron loss function using the bias value, amplitude value and frequency of the alternating magnetic field;
Fourier transform the measured waveform or analytical calculation waveform of the magnetic flux density in the soft magnetic material when the electric device is driven by a power converter that operates at a carrier frequency higher than the fundamental frequency and a carrier frequency higher than the fundamental frequency, Obtaining amplitude values and phase angles for a plurality of frequency components including at least a fundamental frequency component and a carrier harmonic component;
Generating a relational expression representing the magnetic flux density other than the carrier harmonic component and the magnetic flux density of the carrier harmonic component from the amplitude value and the phase angle in each frequency component;
One period of the fundamental frequency is divided by a predetermined unit time, and a magnetic flux density value for each divided unit time is derived using the relational expression. The magnetic flux density value and the iron loss function Obtaining a unit time iron loss value based on:
The unit time iron loss value is summed by an integral multiple of the fundamental wave half period to obtain a time average value for one period, and this is obtained as the value of the carrier loss of the soft magnetic material;
The iron loss estimation method characterized by including.   The iron loss estimation method according to claim 1, wherein a low-order harmonic component is included in the plurality of frequency components.   The iron loss estimation method according to claim 1, wherein a term of an absolute value of a bias amount is included in the relational expression. In the relational expression, the basic frequency in the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and n (n = 1, 2,..., K, where k is a natural number). On the other hand, the sum of the components of nf ₂ ± mf ₁ [Hz] for all m (m = 0, 1, 2,..., L, where l is a natural number) is expressed as B _n sin (2πf ₁ t + θ _{1, n} ) × sin (2πnf ₂ t + θ _{2, n} )
Where B _n is the amplitude of the above component, and θ _{1, n} and θ _{2, n} are the phase angles of the term that changes at the frequency f ₁ of the harmonic component and the term that changes at the frequency f ₂ with respect to the fundamental wave. The iron loss estimation method according to claim 1, wherein The iron loss estimation method according to claim 4 , wherein the time average value is an average value of amplitudes of two frequency components represented by nf ₂ ± mf ₁ [Hz]. The basic frequency of the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and the sum of the components of nf ₂ ± mf ₁ [Hz] (m = 1, 3, 5) for all n The iron loss estimation method according to any one of claims 2 to 3, wherein the amplitude of the magnetic flux density is obtained by the following equation (B) when represented by the following equation (A).

The basic frequency of the power converter is f ₁ [Hz], the carrier frequency is f ₂ [Hz], and nf ₂ ± mf ₁ [Hz] (m = 1, 3, 5) [Hz] for n = 1, 3. ] Is expressed by the following formula (C), the amplitude of the magnetic flux density is obtained by the following formula (D), and for n = 2, 4, nf ₂ ± mf ₁ [Hz] (m = 0, 2, 4) When the sum of the components of [Hz] is expressed by the following equation (E), the amplitude of the magnetic flux density is obtained by the following equation (F). The iron loss estimation method according to the above.

2. The iron loss estimation method according to claim 1, wherein the soft magnetic material has an iron loss value W that is unambiguously derived from the amount of bias B ₀ , the frequency f, and the amplitude value B _{m according} to the following expression (G). .

However, a (B ₀ ), b (B ₀ ), and c (B ₀ ) are arbitrary functions obtained by fitting iron loss values.

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