CN104316876B - Method for rapidly obtaining three-phase 12/8 pole SRM magnetic linkage characteristics with consideration on mutual inductance coupling - Google Patents
Method for rapidly obtaining three-phase 12/8 pole SRM magnetic linkage characteristics with consideration on mutual inductance coupling Download PDFInfo
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Abstract
The invention discloses a method for rapidly obtaining three-phase 12/8 pole SRM magnetic linkage characteristics with consideration on mutual inductance coupling; the method is free of a rotor position fixing device, simple in measuring operation, short in time consumption, considers the influence of mutual inductance coupling of a switch reluctance machine on the magnetic linkage characteristics, and improves accuracy for obtaining the magnetic linkage characteristics. The method comprises the steps of: introducing exciting current into a winding, respectively measuring characteristics of a magnetic linkage when the rotor is positioned at 0 degree, 7.5 degrees, 15 degrees and 22.5 degrees, correcting obtained data considering influence of mutual inductance coupling, then establishing a mathematical model for the magnetic linkage, solving coefficients of the mathematical model by the measured data, and finally obtaining the completed magnetic linkage characteristics. A testing platform is mainly composed of a three phase 12/8 pole switch reluctance machine, a controller, an asymmetric half-bridge power converter, voltage sensors VS1-VS3, current sensors CS1-CS3, a direct current power supply and an oscilloscope.
Description
Technical field
The present invention relates to a kind of 12/8 pole switching reluctance motor flux linkage characteristic of quick obtaining three-phase for considering Mutual Inductance Coupling
Method, without the need for rotor-position fixing device, belongs to electromechanical testing field.
Background technology
Switched reluctance machines (SRM) belong to one kind of variable reluctance motor, and its operation is followed " minimum reluctance principle ", move by
Between stator and rotor, air-gap reluctance change is produced, and rotor is without winding.Due to simple structure, firm, reliability height, low-loss is added, is adjusted
The advantages of fast wide ranges so as to have broad application prospects.However, due to double-salient-pole structure, and motor magnetic circuit localized design
More saturation so that electromagnetic property is presented complicated non-linear, so that accurate flux linkage model is hardly resulted in, and flux linkage characteristic
It is the fundamental characteristics of SRM again, is related to the optimization design of motor, the raising of motor performance and the realization of more excellent control method.
Therefore accurate flux linkage characteristic is obtained, the further investigation to switched reluctance machines is significant.
At present, the method for obtaining flux linkage characteristic is broadly divided into two big class of calculating method and measurement method.Limited element analysis technique is one
As first-selected computational methods.But as FInite Element modeling is difficult, resolving is complicated, and the calculating time cycle is long, Er Qiexu
Accurate motor size and material behavior is wanted, the impact of motor end effect is difficult to be counted into, so measurement method is still to obtain at present
Take the main method of flux linkage characteristic.Measurement method is divided into the direct method of measurement and the indirect method of measurement again.The direct method of measurement is needed magnetic field
Sensor or induction coil load motor internal measurement, and it is inconvenient but also relatively costly not only to operate, therefore seldom adopt.Measure indirectly
Method is based on SRM phase voltage equilibrium equations, by the electric current flow through on measurement motor winding terminal voltage and winding, with numerical integration
Calculate indirectly magnetic linkage data.But the indirect method of measurement generally requires high-precision position sensor and rotor-position fixes dress
Put, increased the complexity of test system, improve testing cost.Also, it is completely special by testing the complete magnetic linkage of acquisition
Property be one not only take but also the work of complexity.At present, there is one kind and do not needed rotor-position fixing device and position sensing
The flux linkage characteristic method of testing of device, by testing the magnetic linkage data of respective location, then obtains complete with Fourier space
Flux linkage characteristic, it is simple to operate, substantially increase testing efficiency.Although this method thinking is ingenious, this method have ignored many
When phase winding is turned on, the impact of magnetic coupling, increases measurement error, reduces the accuracy of measurement.
The content of the invention
The present invention combines measurement method and calculating method, in the case where Mutual Inductance Coupling is considered, it is proposed that one kind is without the need for rotor position
Put the fast method of the acquisition 12/8 pole SRM flux linkage characteristics of three-phase of fixing device.Adopt the following technical scheme that:
Step one, can go to the aligned position of A phases, recording voltage and current waveform to motor A phase winding excitations, rotor,
By calculating magnetic linkage when obtaining 22.5 ° of positions;
Step 2, removes excitation in step one, gives motor B, C two phase winding excitations, and rotor-position is remained stationary as, record electricity
Pressure and current waveform, by calculating the magnetic linkage for obtaining 7.5 ° of positions;
Step 3, removes excitation in step 2, first gives motor B phase excitations, and rotor goes to B and aligns position, then to B, C two
Phase excitation, recording voltage and current waveform, by calculating the magnetic linkage for obtaining 15 ° of positions;
Step 4, on the basis of step 3, maintains static to motor A, B, C phase excitation, rotor-position, recording voltage and
Current waveform, by calculating the magnetic linkage for obtaining 0 ° of position;
Data are modified by step 5, it is considered to impact of the magnetic coupling to data;
Step 6, regards magnetic linkage curve as piecewise function, sets up the mathematical model of flux linkage characteristic, using above-mentioned 4 positions
The magnetic linkage data put, solve mathematical model coefficient, obtain complete flux linkage characteristic.
Beneficial effects of the present invention:Without the need for rotor-position fixing device when 1. measuring, reduce experimental cost and experiment is multiple
Polygamy;2. impact of the SRM Mutual Inductance Couplings to flux linkage characteristic is considered, the accuracy for measuring flux linkage characteristic is improve;3. shorten
Obtain the time of complete flux linkage characteristic;4. only need to measure the data of 4 positions, reduce request memory, it is adaptable to high-volume
The product test of switched reluctance machines.
Description of the drawings
Fig. 1 is the schematic diagram of example test platform.
Fig. 2 is example SRM static torque characteristic curves.
Fig. 3 is the electric current and voltage waveform of θ A phases when being 22.5 °.
Fig. 4 is the flux linkage characteristic curve of θ A phases when being 22.5 °.
Fig. 5 be θ be 22.5 ° when B (or C) phase electric current and voltage waveform.
Fig. 6 is the flux linkage characteristic curve of θ A phases when being 7.5 °.
Fig. 7 be θ be 22.5 ° when B (or C) phase winding voltage and current waveform.
Fig. 8 is the flux linkage characteristic curve of θ A phases when being 15 °.
Fig. 9 is the electric current and voltage waveform of θ A phases when being 0 °.
Figure 10 is the flux linkage characteristic curve of θ A phases when being 0 °.
Figure 11 is the surveyed flux linkage characteristic of example and the surveyed flux linkage characteristic contrast of conventional rotors position fixation.
Figure 12 is the distribution of motor-field under two kinds of different excitation modes.
Figure 13 is the contrast of flux linkage characteristic under two kinds of different excitation modes.
Figure 14 is the magnetic linkage curve of four positions that example is finally adopted.
Figure 15 is the relation of magnetic linkage and rotor-position.
Figure 16 is the relation between each coefficient and phase current.
The complete flux linkage characteristic contrast that Figure 17 case methods are obtained with rotor-position fixation.
Specific embodiment
Below in conjunction with accompanying drawing and instantiation, technical scheme is described in detail.Used by example, motor is
The switched reluctance machines of one 12/8 pole of 1kW three-phases.
The magnetic linkage ψ of switched reluctance machines is the function of phase current i and rotor position, can be by the voltage equation of motor
Obtain.Shown in voltage equation such as formula (1):
V (t)=Ri (t)+d ψ (θ, i)/dt (1)
Wherein v (t) is phase voltage, and i (t) is phase current, and R is a phase resistance, and (θ, is i) a phase magnetic linkage to ψ, and t is the time.Formula
(1) form can be written as:
Numerical integration is carried out using computer, formula (2) can also be further represented as:
Wherein n represent all sampled point numbers of calculating, k represent n before each sampled point, TSFor sampling period, ψ
N () is magnetic linkage, v (k) is phase voltage, and i (k) is phase current.Because without permanent magnet in motor, the initial value of magnetic linkage is 0Wb.
Schematic diagrams of the Fig. 1 for test platform, using asymmetrical half-bridge power inverter.Asymmetrical half-bridge power inverter is
The power switch part of connection DC source and switched reluctance machines.
Wherein V1~V6For switching tube (IGBT, MOSFET);D1~D6For diode;CS1~CS3For current sense
Device;VS1~VS3For voltage sensor;PC is computer;DSP is digital signal processor;PC gives DSP transmission instruction control phase voltages
Frequency and dutycycle;DSP and gate drive circuit are to the V in power inverter1~V6Switching signal is provided.Phase current and phase
Voltage passes through voltage sensor VS respectively1~VS3With current sensor CS1~CS3Measure and be stored in oscillograph so as to follow-up
Process.Whole system no-rotor position fixing device, so, make motor resultant moment suffered by rotor at some positions be zero, turn
It is the core technology of this method that sub- position maintains static.
The expression formula of one phase torque is as follows:
(θ, is i) magnetic coenergy to wherein W ', Tph(θ i) is a phase torque.
For the 12/8 pole switching reluctance motor of 1kW three-phases in example, static torque characteristic curve is as shown in Figure 2.Each phase
Curve differs 15 °, can be obtained by translation.Between each phase, the relation of static torque is represented by:
Wherein TA(θ)、TB(θ) and TC(θ) static torque of A, B, C three-phase is respectively, θ is the absolute mechanical angle of rotor.It is fixed
The absolute mechanical angle of adopted A phases non-aligned position is 0 °.
Step one:Add excitation voltage, rotor go to the aligned position of A phases, i.e. θ for 22.5 ° to A phase windings.Then give A
Phase winding two ends add DC pulse voltage, and the electric current and voltage waveform for now recording A phase windings is as shown in Figure 3.By formula
(3) magnetic linkage of the position is calculated as shown in figure 4, flux linkage characteristic curve when i.e. θ is 22.5 °.
Step 2:Remove the excitation to A phases, and while add identical DC pulse voltage to B, C phase around two ends, now
Rotor stills remain in θ for 22.5 ° of positions, and reason is as follows:
Known by formula (5),
T is known by above formulaB(22.5 °) and TC's (22.5 °) is 0Nm with joint efforts, so rotor can keep in situ.
Now B, C biphase magnetic linkage can be obtained by formula (3), and the magnetic linkage relation between A, B, C three-phase is represented by formula (7)
Wherein, ψA(θ)、ψB(θ)、ψC(θ) it is A, B, C three-phase magnetic linkage respectively.Therefore,
ψ is known by formula (8)A(7.5 °)=ψB(22.5 °)=ψC(22.5 °), so, A phases are special in the magnetic linkage that θ is 7.5 ° of positions
Property can be by being calculated.If Fig. 5 is the voltage and current waveform of B (or C) phase winding, Fig. 6 is calculated ψA
The waveform of (7.5 °).
Step 3:Go to the aligned position of B phases to B phase independent excitations, rotor.Then to two phase winding two ends of B, C simultaneously
In addition identical DC pulse voltage, now rotor can be parked in the non-aligned position of A phases, i.e. θ for 0 °, known by formula (5),
So, it is 0Nm with joint efforts that B, C are biphase, and it is that 0 ° of position is motionless that rotor maintains θ.In the same manner, B, C biphase magnetic linkage can be by
Formula (3) draws, known by formula (7),
So ψA(15 °)=ψB(0 °)=ψC(0 °), A phases can be by being calculated in the flux linkage characteristic that θ is 15 ° of positions.
If Fig. 7 is the voltage and current waveform of B (or C) phase winding, Fig. 8 is calculated ψAThe waveform of (15 °).
Step 4:From the figure 3, it may be seen that when θ is 0 °, TA(0 °)=0Nm, therefore, in an ideal case, add to A phase windings
Upper excitation voltage, rotor still will not be rotated.But, in practical situation, as motor is unlikely to be complete in machining
Symmetrical, θ is unstable when being 0 °, and rotor can align position rotation to A, so in instances, biphase plus constant straight to B, C
While stream voltage, add DC pulse voltage to A phase windings two ends, now rotor remains motionless.A phase windings are recorded now
Electric current and voltage waveform it is as shown in Figure 9.By formula (3), ψ can be obtainedAThe waveform such as Figure 10 of (0 °).
Step 5:By more than, four steps can obtain magnetic linkage spies of the SRM on 0 °, 7.5 °, 15 ° and 22.5 ° position
Linearity curve.Curve obtained is contrasted with traditional rotor-position fixation curve obtained, as shown in figure 11.Understand, when turn
Sub- position at 0 °, 7.5 ° and 22.5 °, two curves preferably, and position when being 15 ° the goodness of fit it is poor.This is due to measurement
It is biphase while excitation, the impact of magnetic coupling during 15 ° of positions.When 0 ° and 7.5 ° of positions is measured, although more than to a phase excitation,
But as the air permeability 0 ° and 7.5 ° position is little, magnetic field is difficult to saturation, so magnetic coupling is negligible.
For the motor in example, there are two kinds of different excitation modes, as shown in figure 13, the excitation mode of Form1 is
The excitation mode of NNNSSSNNNSSS, Form2 is NSNSNSNSNSNS.So that B, C are biphase as an example, for Form1, the biphase product of B, C
Raw magnetic field direction in stator yoke is identical, and this can promote the magnetic field saturation of stator yoke, shown in such as Figure 12 (a).For Form2,
The magnetic direction of the biphase generation of B, C is conversely, the magnetic field of stator yoke can be weakened, such as Figure 12 (b) is shown.Two ways is to flux linkage characteristic
Impact it is as shown in figure 13.Therefore, the excitation mode from Form2 can make result more accurate.Four measured positions
Flux linkage characteristic is as shown in figure 14.
Step 6:The flux linkage characteristic of 4 positions obtained based on five steps of the above, the present invention are proposed one kind and have been obtained
The fast method of whole flux linkage characteristic curve.
In the case where phase current is certain, magnetic linkage is as shown in figure 15 with the relation of rotor-position.Flux linkage characteristic curve in figure
Three parts are divided into, respectively [0 °, 7.5 °), [7.5 °, 15 °) and [15 °, 22.5 °].In each several part, magnetic linkage can be with table
It is shown as:
A in formula1, a2, b1, b2, k, m, n are coefficients undetermined, and θ is rotor-position, and ψ (θ) is motors Based on Flux Linkage, ψ7.5It is 7.5 °
Magnetic linkage during position.
As flux linkage characteristic is smooth and continuous, so listing below equation:
ψ in formula0Magnetic linkage when being 0 ° of position, ψ15Magnetic linkage when being 15 ° of positions, ψ22.5Magnetic linkage when being 22.5 ° of positions.
Solve obtaining for above-mentioned equation:
Known by formula (13), the coefficient in formula (11) can be with 0 ° for measuring, 7.5 °, and 15 °, 22.5 ° of magnetic linkage is represented.
As seen from the above analysis, when one timing of electric current, coefficient can be determined by formula (13), and then, just can be obtained by formula (11)
To rotor other positions magnetic linkage.As long as now changing size of current, repeat to determine coefficient, be just obtained not by formula (11)
With the magnetic linkage under size of current, so as to obtain complete flux linkage characteristic curve.Figure 16 is the pass between size of current and each coefficient
System.The flux linkage characteristic contrast that this example method therefor and traditional rotor-position fixation are obtained is as shown in figure 17.Empirical tests,
The data of two methods are coincide preferably, demonstrate feasibility and the accuracy of proposition method.
Claims (1)
1. it is a kind of consider Mutual Inductance Coupling 12/8 pole SRM flux linkage characteristics of quick obtaining three-phase method, it is characterised in that:Consider
Impact of the Mutual Inductance Coupling to flux linkage characteristic, tests without the need for rotor-position fixing device, and the method realizes that step is as follows:
Step one:The aligned position of A phases, recording voltage and current waveform can be gone to, passed through to motor A phase winding excitations, rotor
Calculate magnetic linkage when obtaining 22.5 ° of positions;
Step 2:Remove excitation in step one, give motor B, C two phase winding excitations, rotor-position is remained stationary as, recording voltage and
Current waveform, by calculating the magnetic linkage for obtaining 7.5 ° of positions;
Step 3:Excitation in step 2 is removed, motor B phase excitations are first given, rotor goes to B and aligns position, then encourages to B, C are biphase
Magnetic, recording voltage and current waveform, by calculating the magnetic linkage for obtaining 15 ° of positions;
Step 4:On the basis of step 3, maintain static to motor A, B, C phase excitation, rotor-position, recording voltage and electric current
Waveform, by calculating the magnetic linkage for obtaining 0 ° of position;
Step 5:Consider impact of the magnetic coupling to surveyed data, data measured is modified;
Step 6:Magnetic linkage curve is represented with piecewise function:
A in formula1, a2, b1, b2, k, m, n are coefficients undetermined, and θ is rotor-position, ψ7.5Magnetic linkage when being 7.5 ° of positions, using institute
The 4 magnetic linkage data surveyed solve undetermined coefficient, obtain the relation of these undetermined coefficients and surveyed data:
ψ in formula0Magnetic linkage when being 0 ° of position, ψ15Magnetic linkage when being 15 ° of positions, ψ22.5Magnetic linkage when being 22.5 ° of positions, now only
Size of current to be changed, repeats to determine that coefficient is obtained complete flux linkage characteristic by formula (2).
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CN106772155B (en) * | 2016-12-20 | 2019-11-05 | 江苏大学 | A kind of method for rapidly judging of switched reluctance machines pole polarity |
CN108429505A (en) * | 2018-03-01 | 2018-08-21 | 西北工业大学 | A kind of switched reluctance machines instantaneous torque on-line identification method |
CN108429504B (en) * | 2018-03-01 | 2020-11-20 | 西北工业大学 | Switched reluctance motor torque control method based on low-cost position sensor |
CN110661467B (en) * | 2018-06-29 | 2021-09-14 | 北京自动化控制设备研究所 | Switched reluctance motor position estimation method based on flux linkage characteristic coordinate transformation |
CN111190128B (en) * | 2018-11-15 | 2022-10-18 | 北京自动化控制设备研究所 | Detection algorithm for BH characteristics of ferromagnetic material of reluctance motor |
CN113688499B (en) * | 2021-07-09 | 2024-02-27 | 西北工业大学 | Modeling method of three-phase 12/8-pole switch reluctance motor based on dynamic and static test |
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