CN104316876A - Quick method for obtaining three-phase 12/8 pole SRM magnetic linkage characteristics with consideration on mutual inductance coupling - Google Patents

Abstract

The invention discloses a quick method for 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

A kind of fast method considering the acquisition three-phase 12/8 pole SRM flux linkage characteristic of Mutual Inductance Coupling

Technical field

The present invention relates to a kind of three-phase 12/8 pole switching reluctance motor flux linkage characteristic acquisition methods considering Mutual Inductance Coupling, without the need to rotor-position stationary installation, belong to electromechanical testing field.

Background technology

Switched reluctance machines (SRM) belongs to the one of variable reluctance motor, and its operation is followed " minimum reluctance principle ", and move by air-gap reluctance change generation between stator and rotor, rotor is without winding.Because structure is simple, firm, reliability is high, adds low-loss, the advantages such as speed-regulating range width, makes it have wide application prospect.But, due to double-salient-pole structure, and motor magnetic circuit localized design is comparatively saturated, electromagnetic property is made to present the non-linear of complexity, to such an extent as to accurate flux linkage model is difficult to obtain, and flux linkage characteristic is the fundamental characteristics of SRM, be related to the realization of the optimal design of motor, the raising of motor performance and more excellent control method.Therefore accurate flux linkage characteristic is obtained, significant to the further investigation of switched reluctance machines.

At present, the method obtaining flux linkage characteristic is mainly divided into computing method and the large class of mensuration two.Limited element analysis technique is general first-selected computing method.But due to finite element method modeling difficulty, resolving is complicated, and cycle computing time is long, and needs accurate motor size and material behavior, and the impact of motor end effect is difficult to be counted into, so mensuration is still the main method obtaining flux linkage characteristic at present.Mensuration is divided into again the direct method of measurement and the indirect method of measurement.The direct method of measurement needs that magnetic field sensor or inductive coil are loaded motor internal and measures, and not only operation is inconvenient but also cost is higher, therefore seldom adopts.The indirect method of measurement, based on SRM phase voltage balance equation, by measuring the electric current that motor winding terminal voltage and winding flow through, uses numerical integration indirectly to calculate magnetic linkage data.But the indirect method of measurement often needs high-precision position transducer and rotor-position stationary installation, adds the complexity of test macro, improves testing cost.Further, obtaining complete flux linkage characteristic by test is completely a not only consuming time but also complicated job.At present, there is a kind of flux linkage characteristic method of testing not needing rotor-position stationary installation and position transducer, by testing the magnetic linkage data of respective location, then having used Fourier series to obtain complete flux linkage characteristic, simple to operate, substantially increase testing efficiency.Although this method thinking is ingenious, when this method have ignored polyphase windings conducting, the impact of magnetic Field Coupling, increases measuring error, reduces the accuracy of measurement.

Summary of the invention

The present invention, in conjunction with mensuration and computing method, when considering Mutual Inductance Coupling, proposes a kind of fast method of the acquisition three-phase 12/8 pole SRM flux linkage characteristic without the need to rotor-position stationary installation.Adopt following technical scheme:

Step one, to motor A phase winding excitation, rotor can forward the aligned position of A phase to, recording voltage and current waveform, by calculating magnetic linkage during acquisition 22.5 ° of positions;

Step 2, removes excitation in step one, and to motor B, C two phase winding excitation, rotor-position keeps motionless, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 7.5 ° of positions;

Step 3, removes excitation in step 2, first gives motor B phase excitation, and rotor forwards B to and to align position, then gives B, C two-phase excitation, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 15 ° of positions;

Step 4, on the basis of step 3, to motor A, B, C phase excitation, rotor-position maintains static, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 0 ° of position;

Step 5, considers that magnetic Field Coupling is on the impact of data, revises data;

Step 6, regards magnetic linkage curve as piecewise function, sets up the mathematical model of flux linkage characteristic, utilizes the magnetic linkage data of above-mentioned 4 positions, solves mathematical model coefficient, obtain complete flux linkage characteristic.

Beneficial effect of the present invention: without the need to rotor-position stationary installation when 1. measuring, reduce experimental cost and experimental complexities; 2. consider the impact of SRM Mutual Inductance Coupling on flux linkage characteristic, improve the accuracy recording flux linkage characteristic; 3. the time obtaining complete flux linkage characteristic is shortened; 4. only need the data of measurement 4 positions, reduce request memory, be applicable to the product test of switched reluctance machines in enormous quantities.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of example test platform.

Fig. 2 is example SRM static torque family curve.

The electric current of A phase that Fig. 3 is θ when being 22.5 ° and voltage waveform.

The flux linkage characteristic curve of A phase that Fig. 4 is θ when being 22.5 °.

The electric current of B (or C) phase that Fig. 5 is θ when being 22.5 ° and voltage waveform.

The flux linkage characteristic curve of A phase that Fig. 6 is θ when being 7.5 °.

The voltage and current waveform of Fig. 7 is θ when being 22.5 ° B (or C) phase winding.

The flux linkage characteristic curve of A phase that Fig. 8 is θ when being 15 °.

The electric current of A phase that Fig. 9 is θ when being 0 ° and voltage waveform.

The flux linkage characteristic curve of A phase that Figure 10 is θ when being 0 °.

Figure 11 is that flux linkage characteristic that example is surveyed and conventional rotors position flux linkage characteristic that fixation is surveyed contrast.

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 finally adopts.

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 that Figure 17 case method and rotor-position fixation obtain contrasts.

Embodiment

Below in conjunction with accompanying drawing and instantiation, technical scheme of the present invention is described in detail.Example motor used is the switched reluctance machines of 1kW three-phase 12/8 pole.

The magnetic linkage ψ of switched reluctance machines is the function of phase current i and rotor position, can be obtained by the balance of voltage equation of motor.Balance of voltage equation is such as formula shown in (1):

v(t)＝Ri(t)+dψ(θ，i)/dt (1)

Wherein v (t) is phase voltage, and i (t) is phase current, and R is a phase resistance, and ψ (θ, i) is a phase magnetic linkage, and t is the time.Formula (1) can be write as following form:

$\mathrm{\ψ}(\mathrm{\θ},i)={\∫}_0^t[v\left(t\right)-\mathrm{Ri}\left(t\right)]\mathrm{dt}{|}_{\mathrm{\θ}=\mathrm{const}}---\left(2\right)$

Utilize computing machine to carry out numerical integration, formula (2) also can be expressed as further:

$\mathrm{\ψ}\left(n\right)=\underset{k=1}{\overset{n}{\mathrm{\Σ}}}[v\left(k\right)-\mathrm{Ri}\left(k\right)]T_s{|}_{\mathrm{\θ}=\mathrm{const}}---\left(3\right)$

Wherein n represents all sampled point numbers of calculating, k represent n before each sampled point, T _sfor the sampling period, ψ (n) is magnetic linkage, and v (k) is phase voltage, and i (k) is phase current.Because without permanent magnet in motor, so the initial value of magnetic linkage is 0Wb.

Fig. 1 is the schematic diagram of test platform, adopts asymmetrical half-bridge power converter.Asymmetrical half-bridge power converter is the power switch parts connecting direct supply and switched reluctance machines.

Wherein V ₁~ V ₆for switching tube (IGBT, MOSFET); D ₁~ D ₆for diode; CS ₁~ CS ₃for current sensor; VS ₁~ VS ₃for voltage sensor; PC is computer; DSP is digital signal processor; PC controls frequency and the dutycycle of phase voltage to DSP transfer instruction; DSP and gate drive circuit are to the V in power converter ₁~ V ₆switching signal is provided.Phase current and phase voltage are respectively by voltage sensor VS ₁~ VS ₃with current sensor CS ₁~ CS ₃measure and be stored in oscillograph so that subsequent treatment.Whole system no-rotor position stationary installation, so make motor resultant moment suffered by rotor when some position be zero, it is the core technology of this method that rotor-position maintains static.

The expression formula of one phase torque is as follows:

$T_{\mathrm{ph}}(\mathrm{\θ},i)=\frac{\∂W^{\′}(\mathrm{\θ},i)}{\∂\mathrm{\θ}}{|}_{i=\mathrm{const}}=\frac{\∂\left({\∫}_0^i\mathrm{\ψ}(\mathrm{\θ},i)\mathrm{di}\right)}{\∂\mathrm{\θ}}{|}_{i=\mathrm{const}}---\left(4\right)$

Wherein W ' (θ, i) is magnetic coenergy, T _ph(θ, i) is a phase torque.

For the 1kW three-phase 12/8 pole switching reluctance motor in example, static torque family curve as shown in Figure 2.Each phase curve differs 15 °, obtains by translation.Between each phase, the relation of static torque can be expressed as:

Wherein T _a(θ), T _b(θ) and T _c(θ) be respectively the static torque of A, B, C three-phase, θ is the absolute mechanical angle of rotor.The absolute mechanical angle of definition A phase non-aligned position is 0 °.

Step one: add field voltage to A phase winding, rotor can forward the aligned position of A phase to, and namely θ is 22.5 °.Add DC pulse voltage then to A phase winding two ends, now record the electric current of A phase winding and voltage waveform as shown in Figure 3.The magnetic linkage of this position is calculated as shown in Figure 4, flux linkage characteristic curve when namely θ is 22.5 ° by formula (3).

Step 2: remove the excitation to A phase, and around two ends, identical DC pulse voltage is added to B, C phase simultaneously, now rotor still remains on θ is 22.5 ° of positions, and reason is as follows:

Known by formula (5),

T is known by above formula _b(22.5 °) and T _cmaking a concerted effort of (22.5 °) is 0Nm, so rotor can remain on origin-location.

Now the magnetic linkage of B, C two-phase can be obtained by formula (3), and the magnetic linkage relation between A, B, C three-phase can be expressed as formula (7)

Wherein, ψ _a(θ), ψ _b(θ), ψ _c(θ) be A, B, C three-phase magnetic linkage respectively.Therefore,

ψ is known by formula (8) _a(7.5 °)=ψ _b(22.5 °)=ψ _c(22.5 °), so A phase can by calculating at the flux linkage characteristic that θ is 7.5 ° of positions.As the voltage and current waveform that Fig. 5 is B (or C) phase winding, Fig. 6 is the ψ calculated _athe waveform of (7.5 °).

Step 3: to B phase independent excitation, rotor forwards the aligned position of B phase to.Then give the DC pulse voltage that B, C two phase winding two ends are simultaneously in addition identical, now rotor can be parked in the non-aligned position of A phase, and namely θ is 0 °, is known by formula (5),

So B, C two-phase is made a concerted effort for 0Nm, and it is that 0 ° of position is motionless that rotor maintains θ.In like manner, the magnetic linkage of B, C two-phase can be drawn by formula (3), is known by formula (7),

So ψ _a(15 °)=ψ _b(0 °)=ψ _c(0 °), A phase can by calculating at the flux linkage characteristic that θ is 15 ° of positions.As the voltage and current waveform that Fig. 7 is B (or C) phase winding, Fig. 8 is the ψ calculated _athe waveform of (15 °).

Step 4: as shown in Figure 3, when θ is 0 °, T _a(0 °)=0Nm, therefore, ideally, add field voltage to A phase winding, rotor still can not rotate.But, in actual conditions, because motor can not be full symmetric when machining, instability when θ is 0 °, rotor can to A align position rotate, so in instances, while adding constant DC voltage to B, C two-phase, add DC pulse voltage to A phase winding two ends, now rotor remains motionless.Now record the electric current of A phase winding and voltage waveform as shown in Figure 9.By formula (3), ψ can be obtained _athe waveform of (0 °) is as Figure 10.

Step 5: the flux linkage characteristic curve of SRM on 0 °, 7.5 °, 15 ° and 22.5 ° of positions can be obtained by above four steps.Curve obtained and traditional rotor-position fixation curve obtained are contrasted, as shown in figure 11.Known, when rotor-position is 0 °, 7.5 ° and 22.5 °, two curves are better, and when position is 15 °, the goodness of fit is poor.Two-phase excitation simultaneously when this is owing to measuring 15 ° of positions, the impact of magnetic Field Coupling.When measurement 0 ° and 7.5 ° of positions, although more than to a phase excitation, due to little at the air permeability of 0 ° and 7.5 ° position, magnetic field is difficult to saturated, so magnetic Field 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.For B, C two-phase, the direction in stator yoke, magnetic field produced for Form1, B, C two-phase is identical, and this can promote that the magnetic field of stator yoke is saturated, as shown in Figure 12 (a).The magnetic direction produced for Form2, B, C two-phase is contrary, can weaken the magnetic field of stator yoke, as shown in Figure 12 (b).Two kinds of modes on the impact of flux linkage characteristic as shown in figure 13.Therefore, select the excitation mode of Form2 that result can be made more accurate.The flux linkage characteristic of four measured positions as shown in figure 14.

Step 6: based on the flux linkage characteristic of 4 positions that above five steps obtains, the present invention proposes a kind of fast method obtaining complete flux linkage characteristic curve.

When phase current is certain, the relation of magnetic linkage and rotor-position as shown in figure 15.In figure, flux linkage characteristic curve has been divided into three parts, be respectively [0 °, 7.5 °), [7.5 °, 15 °) and [15 °, 22.5 °].In each several part, magnetic linkage can be expressed as:

A in formula ₁, a ₂, b ₁, b ₁, k, m, n are coefficients undetermined, and θ is rotor-position, and ψ (θ) is motors Based on Flux Linkage, ψ _7.5it is magnetic linkage during 7.5 ° of positions.

Because flux linkage characteristic is smooth and continuous print, so list following equation:

$\left\{\begin{array}{c}{b}_1={\mathrm{\ψ}}_0\\ {7.5}^m{a}_1+b_1={\mathrm{\ψ}}_{7.5}\\ {\mathrm{\ψ}}_{7.5}+7.5k={\mathrm{\ψ}}_{15}\\ {7.5}^n{a}_2+b_2={\mathrm{\ψ}}_{15}\\ b_2={\mathrm{\ψ}}_{22.5}\\ {7.5}^{(m-1)}{\mathrm{ma}}_1=k\\ {-7.5}^{n-1}{\mathrm{na}}_2=k\end{array}\right.---\left(15\right)$

ψ in formula ₀magnetic linkage during 0 ° of position, ψ ₁₅magnetic linkage during 15 ° of positions, ψ _22.5it is magnetic linkage during 22.5 ° of positions.

Solve obtaining of above-mentioned equation:

$\left\{\begin{array}{c}{b}_1={\mathrm{\ψ}}_0\\ b_2={\mathrm{\ψ}}_{22.5}\\ k=({\mathrm{\ψ}}_{15}-{\mathrm{\ψ}}_{7.5})/7.5\\ m=7.5k/({\mathrm{\ψ}}_{7.5}-{\mathrm{\ψ}}_0)\\ n=7.5k/({\mathrm{\ψ}}_{22.5}-{\mathrm{\ψ}}_{15})\\ a_1=({\mathrm{\ψ}}_{7.5}-{\mathrm{\ψ}}_0)/{7.5}^m\\ a_2=({\mathrm{\ψ}}_{15}-{\mathrm{\ψ}}_{22.5})/{7.5}^n\end{array}\right.---\left(13\right)$

Known by formula (13), the coefficient in formula (11) can with 0 ° of measuring, 7.5 °, and 15 °, the magnetic linkage of 22.5 ° represents.

As seen from the above analysis, when electric current one timing, coefficient all can be determined by formula (13), and then through type (11) just can obtain the magnetic linkage of rotor in other positions.As long as now change size of current, repeat to determine coefficient, through type (11) just can obtain the magnetic linkage under different size of current, thus obtains complete flux linkage characteristic curve.Figure 16 is the relation between size of current and each coefficient.The flux linkage characteristic contrast this example method therefor and traditional rotor-position fixation obtained as shown in figure 17.Empirical tests, the data of two kinds of methods are coincide better, demonstrate feasibility and the accuracy of put forward the methods.

Claims (4)

1. consider the fast method of the acquisition three-phase 12/8 pole SRM flux linkage characteristic of Mutual Inductance Coupling for one kind, it is characterized in that: consider the impact of Mutual Inductance Coupling on flux linkage characteristic, test is without the need to rotor-position stationary installation, and the acquisition flux linkage characteristic method performing step that the present invention announces is as follows:

Step one: to motor A phase winding excitation, rotor can forward the aligned position of A phase to, recording voltage and current waveform, by calculating magnetic linkage during acquisition 22.5 ° of positions;

Step 2: remove excitation in step one, to motor B, C two phase winding excitation, rotor-position keeps motionless, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 7.5 ° of positions;

Step 3: remove excitation in step 2, first gives motor B phase excitation, and rotor forwards B to and to align position, then gives B, C two-phase excitation, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 15 ° of positions;

Step 4: on the basis of step 3, to motor A, B, C phase excitation, rotor-position maintains static, recording voltage and current waveform, by calculating the magnetic linkage of acquisition 0 ° of position;

Step 5: consider that magnetic Field Coupling is on the impact of surveyed data, revises data measured;

Step 6: represented by magnetic linkage curve piecewise function, set up the mathematical model of flux linkage characteristic, utilizes the magnetic linkage data of above-mentioned 4 positions, solves mathematical model coefficient, obtain complete flux linkage characteristic.

2. a kind of fast method considering the acquisition three-phase 12/8 pole SRM flux linkage characteristic of Mutual Inductance Coupling according to claim 1, it is characterized in that: only need measure rotor at 0 °, 7.5 °, 15 °, the magnetic linkage data of 22.5 ° of these four positions, and according to step one to step 4 operation, without the need to rotor-position stationary installation.

3. a kind of fast method considering the acquisition three-phase 12/8 pole SRM flux linkage characteristic of Mutual Inductance Coupling according to claim 1, it is characterized in that: consider the impact of switched reluctance machines Mutual Inductance Coupling on flux linkage characteristic, have chosen the excitation mode that the saturated impact in a kind of magnetic field is little, improve the accuracy of result.

4. a kind of fast method considering the acquisition three-phase 12/8 pole SRM flux linkage characteristic of Mutual Inductance Coupling according to claim 1, is characterized in that: for the foundation of magnetic linkage mathematical model, magnetic linkage curve is expressed as piecewise function:

A in formula ₁, a ₂, b ₁, b ₁, k, m, n are coefficients undetermined, and θ is rotor-position, and ψ (θ) is motors Based on Flux Linkage, ψ _7.5be magnetic linkage during 7.5 ° of positions, utilize 4 magnetic linkage data surveying to solve undetermined coefficient, obtain these undetermined coefficients with survey the relation of data:

$\left\{\begin{array}{c}{b}_1={\mathrm{\ψ}}_0\\ b_2={\mathrm{\ψ}}_{22.5}\\ k=({\mathrm{\ψ}}_{15}-{\mathrm{\ψ}}_{7.5})/7.5\\ m=7.5k/({\mathrm{\ψ}}_{7.5}-{\mathrm{\ψ}}_0)\\ n=7.5k/({\mathrm{\ψ}}_{22.5}-{\mathrm{\ψ}}_{15})\\ a_1=({\mathrm{\ψ}}_{7.5}-{\mathrm{\ψ}}_0)/{7.5}^m\\ a_2=({\mathrm{\ψ}}_{15}-{\mathrm{\ψ}}_{22.5})/{7.5}^n\end{array}\right.---\left(2\right)$

ψ in formula ₀magnetic linkage during 0 ° of position, ψ ₁₅magnetic linkage during 15 ° of positions, ψ _22.5it is magnetic linkage during 22.5 ° of positions.As long as now change size of current, repeat to determine that coefficient can obtain complete flux linkage characteristic by formula (2).