MEASUREMENT METHOD FOR B-H CURVE OF MAGNETIC MATERIAL BASED ON MAGNETIC-INDUCTANCE

Abstract

The present invention discloses a measurement method for a B-H curve of magnetic material based on a magnetic-inductance principle, and relates to the field of electric engineering. A measurement apparatus includes an Epstein frame, an alternating power supply, a power analyzer, and an oscilloscope. The core content of the present invention is to perform electromagnetic coupling modeling on an Epstein frame based on a vector model of a magnetic circuit, where an iron core of the Epstein frame is formed by laminating a silicon steel sheet to be measured, and an excitation coil and a detection coil with the same turns number are wound around the iron core. The measurement process is to first obtain a reference B-H curve that only considers a nonlinear reluctance of the iron core, and then to derive a B-H curve considering an eddy current effect in a magnetic field at any frequency from the reference B-H curve. The present invention provides a measurement and simulation method for deriving a B-H curve at any frequency by only measuring a B-H curve at a certain frequency. The method, applicable to a measurement for B-H curves at middle and high frequencies, may obtain much higher accuracy.

Claims

1. A measurement method for a B-H curve of magnetic material, wherein electromagnetic coupling modeling is performed on an Epstein frame based on a vector model of a magnetic circuit, an iron core of the Epstein frame is formed by laminating a silicon steel sheet to be measured, and an excitation coil and a detection coil with the same turns number are wound around the iron core, the measurement method comprising: (1) a measurement process of a reference B-H curve: S1, a voltage {dot over (U)}.sub.E with a reference frequency f is applied to the excitation coil, generating an exciting current İ.sub.E, then an induced voltage {dot over (U)}.sub.D is generated on the detection coil, and a magnetic flux {dot over (Φ)} in the iron core of the Epstein frame can be derived as {dot over (Φ)}={dot over (U)}.sub.D/(2πfN.sub.2), wherein N.sub.2 is the turns number of the detection coil; S2, active power fed to the excitation coil is measured by a power analyzer with copper loss of the excitation coil being removed, then a magnetic-inductance L.sub.mc can be obtained according to a relationship of P=ω.sup.2L.sub.mc∥{dot over (Φ)}∥.sup.2 between the active power and the magnetic-inductance, wherein ω is an angular frequency of a magnetic flux varied in the magnetic circuit; S3, a maximum value of the exciting current İ.sub.E is measured corresponding to each induced voltage {dot over (U)}.sub.D by using an oscilloscope to obtain a magnetomotive force (MMF) {dot over (F)} and the magnetic flux {dot over (Φ)} of the magnetic circuit of the iron core of the Epstein frame, then a magnetic impedance Ż.sub.m2c of the whole iron core can be derived, and next, a reluctance R.sub.mc of the iron core under the action of the exciting current İ.sub.E can be derived based on a formula ∥Ż.sub.mc∥=√{square root over (R.sub.mc.sup.2+(ωL.sub.mc).sup.2)} and the magnetic-inductance L.sub.mc; S4, a magnetic flux density {dot over (b)} of the iron core can be derived from the magnetic flux {dot over (Φ)} and a cross-sectional area S of the iron core, then a magnetic permeability μ of the iron core can be obtained by a formula R.sub.mc=L/(μS), and next a magnetic field strength corresponding to the magnetic flux density {dot over (B)} can be obtained, wherein l is an average length of the magnetic circuit of the iron core; and the exciting voltage {dot over (U)}.sub.E is adjusted and the measurement process is repeated to obtain a reference B-H curve which only considers a nonlinear reluctance of the iron core; (2) a B-H curve considering an eddy current effect at any frequency of magnetic field can be derived from the reference B-H curve, wherein the specific process is as follows: a reluctance R.sub.mc can be obtained from the reference B-H curve when any magnetic flux density ∥{dot over (B)}∥ is known, the magnetic impedance Ż.sub.mc of the magnetic circuit can be obtained under the condition that the magnetic-inductance L.sub.mc is known corresponding to an eddy current reaction at any frequency, then the MMF {dot over (F)} can be derived in this case by {dot over (F)}=Ż.sub.mc.Math.{dot over (Φ)}, next the magnetic field strength {dot over (H)} can be obtained by {dot over (H)}={dot over (F)}/l, and the B-H curve considering the eddy current effect can be drawn.

2. The measurement method for a B-H curve of magnetic material according to claim 1, wherein values of the magnetic-inductance L.sub.mc at different frequencies f.sub.1 and f.sub.2 satisfy a relationship equation $\frac{L_{\mathrm{mc}\_1}}{L_{\mathrm{mc}\_2}}=\sqrt{\frac{f_2}{f_1}},$ and according to the relationship equation, the value of the magnetic-inductance L.sub.mc at any frequency can be obtained by the magnetic-inductance L.sub.mc at the reference frequency.

3. The measurement method for a B-H curve of magnetic material according to claim 1, wherein the magnetic-inductance L.sub.mc is equivalent to a lumped parameter representing the eddy current reaction in the iron core of the Epstein frame, the reluctance R.sub.mc is equivalent to a lumped parameter representing a nonlinear action of the iron core, and the vector model of the magnetic circuit of the iron core is {dot over (F)}=(R.sub.mc+jωL.sub.mc){dot over (Φ)}, wherein j represents an imaginary unit.

4. The measurement method for a B-H curve of magnetic material according to claim 3, wherein virtual magnetic power {dot over (S)}.sub.mc based on the vector model of the magnetic circuit is obtained by the MMF {dot over (F)} and the magnetic flux {dot over (Φ)}, as follows:
{dot over (S)}.sub.mc={dot over (Φ)}.Math.{dot over (F)}*={dot over (Φ)}.Math.[R.sub.mc.Math.{dot over (Φ)}*−jωL.sub.mc{dot over (Φ)}*]=R.sub.mc∥{dot over (Φ)}∥.sup.2−jωL.sub.mc∥{dot over (Φ)}∥.sup.2.

5. The measurement method for a B-H curve of magnetic material according to claim 4, wherein the virtual magnetic power {dot over (S)}.sub.mc and electric power {dot over (S)}.sub.e are in a convertible relationship of {dot over (S)}.sub.e=jω{dot over (S)}.sub.mc=ω.sup.2L.sub.mc∥{dot over (Φ)}∥.sup.2+jωR.sub.mc∥{dot over (Φ)}∥.sup.2, wherein the real part is the active power input by using the excitation coil, and the imaginary part is reactive power input by using the excitation coil.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 is a schematic diagram of a measurement platform of a B-H curve of magnetic material of the present invention.

[0019] FIG. 2 is a flowchart of a measurement of a B-H curve of magnetic material of the present invention.

[0020] FIG. 3 is a reference B-H curve which excludes the eddy current effect and is measured by applying the present invention.

[0021] FIG. 4 is a comparison diagram of a 200 Hz B-H curve derived by applying the present invention and an actually measured curve.

[0022] FIG. 5 is a comparison diagram of an 800 Hz B-H curve derived by applying the present invention and an actually measured curve.

DETAILED DESCRIPTION

[0023] Technical solutions of the present invention are further described in detail below with reference to accompanying drawings.

[0024] The present invention provides a measurement method for a B-H curve of magnetic material. A measurement apparatus includes an Epstein frame, an alternating power supply, a power analyzer, and an oscilloscope. The core content of the present invention is to perform electromagnetic coupling modeling on an Epstein frame based on a vector model of a magnetic circuit. An iron core of the Epstein frame is formed by laminating a silicon steel sheet to be measured, and an excitation coil and a detection coil with the same turns number are wound around the iron core.

[0025] The vector model of the magnetic circuit includes three “magnetic components”: an MMF {dot over (F)}, a reluctance R.sub.mc, and a magnetic-inductance L.sub.mc. Interaction of the three magnetic components may represent a magnetic flux Φ that flows in a magnetic circuit, where the MMF and the magnetic flux are vectors, a specific relationship is {dot over (F)}={dot over (Φ)}.Math.(R.sub.mc+jωL.sub.mc), and an angle between the MMF and the magnetic flux is

[00002]$\theta =\arctan \left(\frac{\omega L_{mc}}{R_{mc}}\right).$

[0026] Virtual magnetic power {dot over (S)}.sub.mc in the magnetic circuit may be calculated by using the MMF and the magnetic flux, which is expressed as {dot over (S)}.sub.mc={dot over (Φ)}.Math.{dot over (F)}*={dot over (Φ)}.Math.[R.sub.mc.Math.{dot over (Φ)}*−jωL.sub.mc{dot over (Φ)}*]=R.sub.mc∥{dot over (Φ)}∥.sup.2−jωL.sub.mc∥{dot over (Φ)}∥.sup.2. According to the law of conservation of energy and the electromagnetic energy conversion relationship, the virtual magnetic power {dot over (S)}.sub.mc in the magnetic circuit is obtained by converting electric power {dot over (S)}.sub.e input by the excitation coil. Two forms of power satisfy a relationship {dot over (S)}.sub.e=jω{dot over (S)}.sub.mc=ω.sup.2L.sub.mc∥{dot over (Φ)}∥.sup.2+jωR.sub.mc∥{dot over (Φ)}∥.sup.2, where the real part represents the active power in an electric circuit represented by parameters of the magnetic circuit, and the imaginary part represents the reactive power in the electric circuit represented by the parameters of the magnetic circuit.

[0027] The magnetic-inductance L.sub.mc in the vector model of the magnetic circuit of the Epstein frame represents a reaction of the eddy current of an iron core. The magnetic-inductance is related to the resistance R of the iron core and the frequency f of the magnetic flux, but unrelated to the magnitude of the magnetic flux.

[0028] Furthermore, the magnetic-inductance L.sub.mc may change the magnitude and the phase of the magnetic flux. The magnitude of the effect of the magnetic-inductance on the change of the magnetic flux may be represented by a magnetic reactance {dot over (X)}.sub.mc, {dot over (X)}.sub.mc=jωL.sub.mc.

[0029] The reluctance R.sub.mc in the vector model of the magnetic circuit of the Epstein frame represents nonlinearity of the iron core, which is related to a saturation degree of the magnetic flux. The reluctance R.sub.mc may change the magnitude of the magnetic flux, but does not change the phase thereof.

[0030] Furthermore, the magnetic flux in the Epstein frame is determined jointly by the magnetic-inductance L.sub.mc and the reluctance R.sub.mc, that is, determined jointly by the reaction of the eddy current of the iron core and the nonlinearity of the iron core. The combined effect of the magnetic-inductance L.sub.mc and the reluctance R.sub.mc is referred to as the magnetic impedance which is represented as Ż.sub.mc. The magnetic impedance is a vector, the magnitude of the magnetic impedance is ∥Ż.sub.mc∥=√{square root over (R.sub.mc.sup.2+(ωL.sub.mc).sup.2)}, and a relationship among the magnetic impedance, the MMF, and the magnetic flux is {dot over (F)}=Ż.sub.mc.Math.{dot over (Φ)}.

[0031] Furthermore, a relationship between the virtual magnetic power {dot over (S)}.sub.mc and the electric power {dot over (S)}.sub.e may be explained as follows: Power consumed by the magnetic-inductance in the magnetic circuit is obtained by dividing the active power input by the excitation coil by ω, and power consumed by the reluctance in the magnetic circuit is obtained by dividing the reactive power input by the excitation coil by ω; and the power consumed by the magnetic-inductance in the magnetic circuit is power consumed by the eddy current of the iron core, and the power consumed by the reluctance is power stored by the iron core.

[0032] Based on the vector model of the magnetic circuit, the specific process of measuring the B-H curve is as follows:

[0033] A voltage {dot over (U)}.sub.E with a reference frequency f is applied to the excitation coil to generate an exciting current İ.sub.E and generate an induced voltage {dot over (U)}.sub.D on the detection coil. The magnetic flux {dot over (Φ)} in the iron core of the Epstein frame may be represented as {dot over (Φ)}={dot over (U)}.sub.D/(2πfN.sub.2), where N.sub.2 is the turns number of the detection coil. Active power fed to an excitation coil is measured by using a power analyzer (with copper loss of the excitation coil being removed), and a magnetic-inductance L.sub.mc is obtained according to a relationship P=ω.sup.2L.sub.mc∥{dot over (Φ)}∥.sup.2 between the active power and the magnetic-inductance. A maximum value of the exciting current İ.sub.E corresponding to each induced voltage {dot over (U)}.sub.D is observed by using an oscilloscope to obtain the MMF F and the magnetic flux {dot over (Φ)} of the magnetic circuit in the iron core of the Epstein frame and then a magnetic impedance Ż.sub.mc of the whole iron core is obtained. The reluctance R.sub.mc of the iron core under the action of the exciting current İ.sub.E is obtained based on ∥Ż.sub.mc∥=√{square root over (R.sub.mc.sup.2+(ωL.sub.mc).sup.2)} of the magnetic impedance and the known magnetic-inductance L.sub.mc. The magnetic flux density {dot over (B)} of the iron core is obtained by dividing the known magnetic flux {dot over (Φ)} by a cross-sectional area S of the iron core. A magnetic permeability μ of the iron core is obtained by a formula R.sub.mc=l/(μS) of the reluctance R.sub.mc, and then a magnetic field strength {dot over (H)} corresponding to the magnetic flux density {dot over (B)} is obtained, where l is an average length of the magnetic circuit of the iron core. An exciting voltage {dot over (U)}.sub.E is adjusted and the measurement process is repeated to obtain a reference B-H curve, where the reference B-H curve is a B-H curve only considering a nonlinear reluctance of the iron core.

[0034] A B-H curve, considering the eddy current effect in a magnetic field at any frequency, may be derived from the reference B-H curve. A specific process is as follows: The reluctance R.sub.mc may be obtained on the reference B-H curve in a case that any magnetic flux density value ∥{dot over (B)}∥ is known, and the magnetic impedance Ż.sub.mc of the magnetic circuit may be obtained in a case that the magnetic-inductance L.sub.mc corresponding to the eddy current reaction at the frequency is known, then an MMF {dot over (F)} is obtained in this case by using {dot over (F)}=Ż.sub.mc.Math.{dot over (Φ)}, then a magnetic field strength {dot over (H)} is obtained, {dot over (H)}={dot over (F)}/l, and the B-H curve considering the eddy current effect is obtained.

[0035] The magnetic-inductance L.sub.mc is related to the resistance R of the iron core. Because of the skin effect, the resistance changes with a frequency of a magnetic field, and the magnetic-inductance also changes accordingly.

[0036] Furthermore, values of the magnetic-inductance L.sub.mc at different frequencies f.sub.1 and f.sub.2 satisfy a relationship

[00003]$\frac{L_{\mathrm{mc}\_1}}{L_{\mathrm{mc}\_2}}=\sqrt{\frac{f_2}{f_1}},$

hence, the value of the magnetic-inductance at any frequency may be obtained by the magnetic-inductance L.sub.mc at the reference frequency. A B-H curve, considering an eddy current effect at any frequency, may be derived from the B-H curve considering the eddy current effect at the reference frequency.

[0037] A measurement platform of a B-H curve of magnetic material shown in FIG. 1 mainly includes a programmable alternating power supply, an Epstein frame, a power analyzer, and an oscilloscope. A B-H curve with a 400 Hz reference frequency is measured based on the platform. A B-H curve with a 200 Hz frequency and a B-H curve with an 800 Hz frequency are derived on this basis. A flowchart thereof is shown in FIG. 2.

[0038] First, a 400 Hz exciting voltage {dot over (U)}.sub.E is applied to the excitation coil by using the alternating power supply. The exciting voltage U.sub.E is adjusted to control a magnetic field strength. A peak U.sub.E_peak of the exciting voltage and a peak I.sub.E_peak of the exciting current are observed by using the oscilloscope. Active power P input to an electric circuit (copper loss of the excitation coil is removed) is observed by using the power analyzer.

[0039] The value of the magnetic flux ∥{dot over (Φ)}∥ the magnetic circuit of the iron core is derived by using the peak U.sub.E_peak of the exciting voltage. The value ∥{dot over (F)}∥ of the MMF obtained by using the peak of the exciting current.

[0040] By using a relationship P=ω.sup.2L.sub.mc∥{dot over (Φ)}∥.sup.2 between the active power P of the electric circuit and the magnetic flux ∥{dot over (Φ)}∥, the value L.sub.mc of the magnetic-inductance of the eddy current of the iron core at a 400 Hz frequency is obtained.

[0041] By using a relationship {dot over (F)}=Ż.sub.mc.Math.{dot over (Φ)} between the MMF and a magnetic flux, the value of the magnetic impedance ∥Ż.sub.mc∥ of the magnetic circuit is obtained, and then the value of the reluctance R.sub.mc of the magnetic circuit is obtained according to ∥Ż.sub.mc∥=√{square root over (R.sub.mc.sup.2+(ωL.sub.mc).sup.2)}.

[0042] Magnetic permeabilities of the iron core at different magnetic fluxes may be obtained by a R.sub.mc=l/(μs). The magnetic field strengths H at different magnetic flux density values B may be obtained according to a relationship B=μH.

[0043] The exciting voltage {dot over (U)}.sub.E is adjusted and the foregoing steps are repeated to obtain a plurality of groups of (B, H) data, and draw out a reference B-H curve excluding the eddy current effect at a 400 Hz reference frequency, as shown in FIG. 3.

[0044] Since the values of the magnetic-inductance at different frequencies satisfy the relationship

[00004]$\frac{L_{\mathrm{mc}\_1}}{L_{\mathrm{mc}\_2}}=\sqrt{\frac{f_2}{f_1}},$

the values of the magnetic-inductance at 200 Hz and 800 Hz may be obtained by using the value L.sub.mc_400 of the magnetic-inductance at 400 Hz, and are respectively written as L.sub.mc_200 and L.sub.mc_800 By using the reference B-H curve, a corresponding value of the reluctance R.sub.mc at a certain magnetic flux density B is obtained. By using the reluctance and the magnetic-inductance, values of the magnetic impedance at the frequencies 200 Hz and 800 Hz are obtained by using ∥Ż.sub.mc∥=√{square root over (R.sub.mc.sup.2+(ωL.sub.mc).sup.2)}, then values ∥{dot over (F)}∥ of the MMF generating the magnetic flux density at the frequencies 200 Hz and 800 Hz may be obtained, magnetic field strengths H may be further obtained by using {dot over (H)}={dot over (F)}/l, and finally B-H curves at the frequencies 200 Hz and 800 Hz may be obtained. FIG. 4 and FIG. 5 compare the B-H curves derived at the frequencies 200 Hz and 800 Hz and the actually measured B-H curve respectively.

[0045] In general, the present invention provides a measurement method for a B-H curve based on a vector model of a magnetic circuit. If there is a need to obtain a B-H curve at a certain high frequency, a specific high-frequency power supply is not necessary any more. Therefore, difficulty of measuring the high-frequency B-H curve may be reduced, and a new idea is provided for characteristic simulation of the silicon steel sheet considering the eddy current reaction.

[0046] The foregoing descriptions are only exemplary implementations of the present invention. The protection scope of the present invention is not limited to the foregoing implementations. Any equivalent modification or variation made according to the disclosure of the present invention by a person of ordinary skill in the art all should fall within the protection scope of the claims.