CN110165961B - Memory motor magnetic regulation current prediction method based on Fourier fitting - Google Patents
Memory motor magnetic regulation current prediction method based on Fourier fitting Download PDFInfo
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- CN110165961B CN110165961B CN201910421799.4A CN201910421799A CN110165961B CN 110165961 B CN110165961 B CN 110165961B CN 201910421799 A CN201910421799 A CN 201910421799A CN 110165961 B CN110165961 B CN 110165961B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/22—Current control, e.g. using a current control loop
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Abstract
The invention discloses a memory motor magnetic regulation current prediction method based on Fourier fitting, which comprises the following steps: (1) an experimental device is adopted to obtain the air gap flux density B when different currents I are applied to the permanent magnetg(ii) a (2) According to current I and air gap flux density BgIn relation to (2)Data, calculating the magnetic density B of the permanent magnet by adopting the flux continuous principlemCalculating the magnetic field intensity H of the permanent magnet by adopting the ampere loop theoremm(ii) a (3) According to B of permanent magnetsmAnd HmFitting a return line and a hysteresis loop of a permanent magnet of the memory motor to obtain a Fourier fitting hysteresis model; (4) predicting the initial magnetization state B of the permanent magnet of the memory motor based on the Fourier fitting hysteresis modelg1To the target magnetization state Bg2Required current I for magnetic regulation*. The method is simple in calculation and high in accuracy, and can be applied to accurate prediction of the online magnetic current regulation of the memory motor.
Description
Technical Field
The invention relates to the technical field of motors, in particular to a memory motor magnetic regulation current prediction method based on Fourier fitting.
Background
The memory motor is used as a novel permanent magnet synchronous motor, has two advantages of high efficiency and high torque density, is easy to realize high efficiency under all working conditions, and has wide application prospect. The development of memory motors benefits from the significant breakthrough in the field of rare earth permanent magnet materials in recent years. Unlike conventional permanent magnets, many new rare earth permanent magnet materials have low coercivity and highly nonlinear hysteresis loops, which allow the magnetization state of such permanent magnets to be changed by applying current pulses. When the memory motor is operated, the process of applying current pulses to the non-linear permanent magnets in the motor to change their magnetization state is called online magnetic tuning. The pulse current required to go from the current magnetization state to the target magnetization state needs to be predicted, which is made difficult by the high non-linearity of the hysteresis loop.
The prediction of the pulse current needs to use a hysteresis model, and the commonly used hysteresis model comprises a parallelogram model and a Preisach model. The parallelogram model has poor prediction precision, and the Preisach model has high prediction time cost and does not meet the engineering prediction requirements.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a memory motor magnetic regulation current prediction method based on Fourier fitting, aiming at the problems in the prior art.
The technical scheme is as follows: the memory motor magnetic regulation current prediction method based on Fourier fitting comprises the following steps:
(1) an experimental device is adopted to obtain the air gap flux density B when different currents I are applied to the permanent magnetg；
(2) According to current I and air gap flux density BgThe magnetic flux density B of the permanent magnet is calculated by adopting the magnetic flux continuous principlemCalculating the magnetic field intensity H of the permanent magnet by adopting the ampere loop theoremm；
(3) According to B of permanent magnetsmAnd HmFitting a return line and a hysteresis loop of a permanent magnet of the memory motor to obtain a Fourier fitting hysteresis model;
(4) predicting the initial magnetization state B of the permanent magnet of the memory motor based on the Fourier fitting hysteresis modelg1To the target magnetization state Bg2The required current I needed for the required magnetic regulation.
Further, the step (1) specifically comprises:
(1.1) constructing a closed magnetic circuit consisting of silicon steel, a permanent magnet and an air gap as an experimental device;
(1.2) applying different currents I to the experimental device, changing the working point of the permanent magnet, and measuring the air gap flux density B by using a gauss metergThe change of the applied current I is measured by using a current clamp and an oscilloscope.
Further, the step (2) specifically comprises:
(2.1) air gap flux density B based on flux continuity principlegMagnetic density with permanent magnet BmThe magnetic flux density B of the permanent magnet is calculated according to the following formulam：
In the formula, SgDenotes the air gap area, SmRepresents the permanent magnet area;
(2.2) magnetic density B of air gap according to current IgUsing ampere-loop theorem to calculate the magnetic field strength H of the permanent magnet according to the following formulam：
Wherein N is the number of turns of the coil, lgThickness of the magnetization direction of the air gap, /)lIs the thickness of the silicon steel in the magnetization directionmThickness in the direction of magnetization of the permanent magnet, mugIs the air gap relative permeability, μlIs the relative permeability of silicon steel, SlThe area of the silicon steel is shown.
Further, when the return line of the permanent magnet of the memory motor is fitted in the step (3), the fitting formula is as follows:
B＝kr·H+Bri，i＝1,2,3,...
wherein B is magnetic density, H is magnetic field intensity, krTo restore the line slope, BriThe intercept of the ith recovery line on the B axis is shown.
Further, when the hysteresis loop of the permanent magnet of the memory motor is fitted in the step (3), the coordinate system is firstly turned over and then fitted, and the adopted fitting formula is as follows:
wherein B is magnetic density, H is magnetic field intensity, a0、ak、bkIs a third order Fourier series expansion coefficient.
Further, when the hysteresis loops of the permanent magnet of the memory motor are fitted in step (3), the left half hysteresis loop H ═ f (B) is obtained by fitting, and then the right half hysteresis loop H ═ f (-B) is directly obtained according to the left half hysteresis loop through the central symmetry principle.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
1. the invention describes the magnetic hysteresis loop through the engineering model based on the engineering experiment, can simultaneously meet two targets of small calculated amount and high precision, has lower time cost for predicting the magnetic regulating current and more accurate prediction result, and is more suitable for engineering calculation.
2. When the hysteresis loop is fitted, the complexity of describing the hysteresis loop is skillfully simplified in a mode of turning over a coordinate system, so that the hysteresis loop can be described by an elementary function, the fitting precision of a third-order Fourier series to the hysteresis loop is very high, and the prediction precision is further improved.
Drawings
FIG. 1 is a schematic flow diagram of one embodiment of the present invention;
FIG. 2 is a graph of a nonlinear permanent magnet Fourier fit hysteresis model.
Detailed Description
The embodiment provides a memory motor magnetic regulation current prediction method based on Fourier fitting, as shown in FIG. 1, comprising the following steps:
(1) an experimental device is adopted to obtain the air gap flux density B when different currents I are applied to the permanent magnetg。
The experimental device is a closed magnetic circuit formed by silicon steel, a permanent magnet and an air gap, the width of the air gap is proper and not too small, so that a gauss meter can be placed conveniently to measure the air gap flux density; it should not be too large to prevent the air gap magnetic density from changing insignificantly when current is applied due to too large air magnetic resistance. For the circuit, a coil with proper turns needs to be selected to provide magnetomotive force for the magnetizing device. Meanwhile, the coil should have proper thickness, and should not be too thin, so as to prevent the coil from being unable to bear the magnetizing and demagnetizing current; it should not be too thick to prevent the slots inside the magnetiser from not accommodating enough turns. And (5) building an experiment platform for measuring and taking experiment data. The control module is composed of FPGA (field programmable array circuit) for controlling H bridge, and the measurement module is composed of current clamp, oscilloscope and gaussmeter. Applying different currents I to the experimental device, changing the working point of the permanent magnet, and measuring the air gap flux density B by using a gauss metergVariations of (2)The variation of the applied current I is measured by using a current clamp and an oscilloscope.
(2) According to current I and air gap flux density BgThe magnetic flux density B of the permanent magnet is calculated by adopting the magnetic flux continuous principlemCalculating the magnetic field intensity H of the permanent magnet by adopting the ampere loop theoremm。
Wherein, the air gap flux density B is based on the flux continuity principlegMagnetic density with permanent magnet BmThe magnetic flux density B of the permanent magnet is calculated according to the following formulam：
In the formula, SgDenotes the air gap area, SmRepresents the permanent magnet area;
and according to the current I and the air gap flux density BgUsing ampere-loop theorem to calculate the magnetic field strength H of the permanent magnet according to the following formulam：
Wherein N is the number of turns of the coil, lgThickness of the magnetization direction of the air gap, /)lIs the thickness of the silicon steel in the magnetization directionmThickness in the direction of magnetization of the permanent magnet, mugIs the air gap relative permeability, μlIs the relative permeability of silicon steel, SlThe area of the silicon steel is shown.
(3) According to B of permanent magnetsmAnd HmAnd data fitting is carried out on the return line and the hysteresis loop of the permanent magnet of the memory motor to obtain a Fourier fitting hysteresis model.
Wherein according to B of the permanent magnetmAnd HmThe data can be plotted as a scatter plot of the hysteresis loop and the return line, as shown in fig. 2. The reply lines may be expressed as straight lines, and all of the reply lines have the same slope. In order to reduce error, at least scattered points on three recovery lines are measured, and after fitting, under the condition that the slope difference of the three recovery lines is not largeAnd averaging the slope of the obtained product to obtain the final slope of the recovery line, wherein the adopted fitting formula is as follows:
B＝kr·H+Bri，i＝1,2,3,...
wherein B is magnetic density, H is magnetic field intensity, krTo restore the line slope, BriThe intercept of the ith recovery line on the B axis is shown.
According to P shown in FIG. 21Q1，P2Q2，P3Q3Fitting the Fourier with three regression lines of the hysteresis model, where R1，R2，R3Respectively, the intersection points of the three return lines and the vacuum load line. When a tiny continuous current is applied, the working point of the permanent magnet starts to move on the return line, and when the current is removed, the working point of the permanent magnet falls to the intersection point of the return line and the vacuum load line.
In order to realize mathematical simplification of the hysteresis loop, the Fourier fitting hysteresis model adopts a mode of inverting a coordinate system, and the hysteresis loop is regarded as an H-B relation. There are three important considerations for fitting function selection: the fitting accuracy is as high as possible, the fitting function monotonicity conforms to the actual monotonicity of the hysteresis loop, and the expression of the fitting function is as concise as possible. Through comprehensive consideration, the three requirements can be well met by the third-order Fourier series, and the fitting formula is as follows:
a0、ak、bkis a third order Fourier series expansion coefficient.
Due to the central symmetry of the hysteresis loop, only half of the hysteresis loop needs to be fitted. The left half hysteresis loop H-f (-B) is obtained by fitting, and the right half hysteresis loop H-f (-B) is directly obtained according to the left half hysteresis loop by the central symmetry principle.
As shown in FIG. 2A1B1C1A2Is the left half of the hysteresis loop, A1B2C2A2Is the right half of the hysteresis loop. When no current is applied, the working point of the permanent magnet is located on the load line (e.g., R)1) (ii) a When the continuous current is applied, the working point of the permanent magnet starts from the intersection point of the load line and the return line and moves along the return line; when the current is high to a certain degree, the working point of the permanent magnet reaches the intersection point (such as Q) of the return line and the hysteresis loop1Or P1) And begins to move along the hysteresis loop.
(4) Predicting the initial magnetization state B of the permanent magnet of the memory motor based on the Fourier fitting hysteresis modelg1To the target magnetization state Bg2The required current I needed for the required magnetic regulation.
Specifically, during prediction, firstly, simulation initialization is carried out, a Fourier fitting hysteresis model is led into finite element simulation software to serve as a nonlinear permanent magnet hysteresis model, and the initial magnetization state B is usedg1As the initial state of simulation, the current direction is determined, and B is comparedg1And Bg2Size. If B isg1<Bg2A magnetizing current pulse needs to be applied. If B isg1>Bg2A demagnetization current pulse needs to be applied. In the simulation, a plurality of current pulses with the amplitude gradually increased in steps are applied to the nonlinear permanent magnet. Air gap flux density B obtained after current pulse is applied for a certain timeg1And Bg2If the error is less than 1%, the amplitude of the current pulse is the required current I for magnetic regulation.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (1)
1. A memory motor magnetic regulation current prediction method based on Fourier fitting is characterized by comprising the following steps:
(1) an experimental device is adopted to obtain the air gap flux density B when different currents I are applied to the permanent magnetg(ii) a The method specifically comprises the following steps:
(1.1) constructing a closed magnetic circuit consisting of silicon steel, a permanent magnet and an air gap as an experimental device;
(1.2) applying to the Experimental apparatusChanging the working point of the permanent magnet at different currents I, and measuring the air gap flux density B by using a gaussmetergMeasuring the change of the applied current I by using a current clamp and an oscilloscope;
(2) according to current I and air gap flux density BgThe magnetic flux density B of the permanent magnet is calculated by adopting the magnetic flux continuous principlemCalculating the magnetic field intensity H of the permanent magnet by adopting the ampere loop theoremm(ii) a The method specifically comprises the following steps:
(2.1) air gap flux density B based on the principle of flux continuitygMagnetic density with permanent magnet BmThe magnetic flux density B of the permanent magnet is calculated according to the following formulam：
In the formula, SgDenotes the air gap area, SmRepresents the permanent magnet area;
(2.2) magnetic density B of air gap according to current IgUsing ampere-loop theorem to calculate the magnetic field strength H of the permanent magnet according to the following formulam：
Wherein N is the number of turns of the coil, lgThickness of the magnetization direction of the air gap, /)lIs the thickness of the silicon steel in the magnetization directionmThickness in the direction of magnetization of the permanent magnet, mugIs the air gap relative permeability, μlIs the relative permeability of silicon steel, SlThe area of the silicon steel is shown;
(3) according to B of permanent magnetsmAnd HmFitting a return line and a hysteresis loop of a permanent magnet of the memory motor to obtain a Fourier fitting hysteresis model; when the hysteresis loop of the permanent magnet of the memory motor is fitted in the step (3), the coordinate system is firstly overturned and then the fitting is carried out, and the fitting formula is as follows:
wherein B is magnetic density, H is magnetic field intensity, a0、ak、bkThe coefficient is a third-order Fourier series expansion coefficient;
when the return line of the permanent magnet of the memory motor is fitted, the fitting formula is as follows:
B＝kr·H+Bri，i＝1,2,3,...
wherein B is magnetic density, H is magnetic field intensity, krTo restore the line slope, BriThe intercept of the ith recovery line on the B axis;
when the hysteresis loops of the permanent magnet of the memory motor are fitted, the left half hysteresis loop H-f (B) is obtained by fitting, and the right half hysteresis loop H-f (-B) is directly obtained according to the left half hysteresis loop through the central symmetry principle;
(4) predicting the initial magnetization state B of the permanent magnet of the memory motor based on the Fourier fitting hysteresis modelg1To the target magnetization state Bg2The required current I needed for the required magnetic regulation.
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