CN113688499B - Modeling method of three-phase 12/8-pole switch reluctance motor based on dynamic and static test - Google Patents
Modeling method of three-phase 12/8-pole switch reluctance motor based on dynamic and static test Download PDFInfo
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Abstract
The invention discloses a three-phase 12/8-pole switch reluctance motor modeling method based on dynamic and static tests. Because of the nonlinearity and saturation of the switched reluctance motor, modeling of the switched reluctance motor requires the use of its flux linkage and torque characteristic data. And (3) performing static test by using a torque balance method to obtain four flux linkage curves, and performing dynamic test when the motor rotates to obtain the unsaturated inductance of the switched reluctance motor. And performing fitting calculation based on the curve obtained by the test to obtain flux linkage and torque characteristics of the switched reluctance motor at all positions and under current, and completing modeling. The modeling method can effectively improve the accuracy of a torque balancing method and reduce the complexity of a rotor position fixing method.
Description
Technical Field
The invention relates to a three-phase 12/8-pole switched reluctance motor modeling method based on dynamic and static testing, and belongs to the field of motor control.
Background
The switch reluctance motor has simple structure, the rotor has no permanent magnet and winding, and the torque is generated by the change of the air gap reluctance between the stator and the rotor. The speed regulation range is wide, the reliability is high, and the speed regulation device is suitable for severe environments and has wide application prospect. However, the doubly salient structure and the magnetic circuit saturation characteristics make it difficult to derive an accurate nonlinear mathematical model thereof from conventional electromagnetic and physical characteristics, and thus it is necessary to build a mathematical model thereof using the flux linkage characteristics of the switched reluctance motor. At present, two methods for testing the flux linkage characteristics of a switch reluctance motor exist: direct and indirect methods. The direct method is to directly measure the flux linkage characteristic by using a flux linkage sensor fixed on the motor, and the method has high cost and large error. The indirect method is to calculate flux linkage indirectly by measuring voltage and current, and the test method can be divided into two types: a rotor position fixing method and a torque balancing method. The rotor position fixing method needs a rotor fixing device, and the flux linkage characteristic of each position can be obtained by measuring the current and the voltage. The torque balancing method is to rotate the rotor to the opposite position by energizing the single phase, then to keep the same torque by using the symmetrical structure of the switch reluctance motor, and to apply different pulse voltages to each phase, so as to measure the flux linkage characteristic of the special position. In summary, both the rotor position fixing method and the torque balancing method have obvious disadvantages: the rotor position fixing method needs to design a measuring platform, has high measuring cost and long time consumption, and is difficult to operate; the torque balance method can obtain too few flux linkage characteristics and has large error of fitting results.
Disclosure of Invention
Aiming at the defects of high cost, complex operation and larger modeling error of a torque balance method in a rotor position fixing method, the invention provides a switch reluctance motor modeling method based on dynamic and static tests. The technical proposal is as follows:
step one: by using a torque balancing method, the characteristics that the torque of the switched reluctance motor is zero at the aligned position and the non-aligned position are utilized, and four special-position inductance characteristics of 0 degree, 7.5 degrees, 15 degrees and 22.5 degrees are obtained by supplying different pulse voltages to each phase.
Step two: when the switch reluctance motor runs at low speed, pulse voltage is injected into the non-conducting phase, and the current waveform of the phase winding is recorded. And calculating unsaturated inductances according to bus voltage, switching tube voltage drop, diode voltage drop and current slopes of all phases, solving the calculation of the unsaturated inductances by a formula (1), combining recorded corresponding position signals, and obtaining unsaturated inductance characteristics of the switched reluctance motor according to the symmetry of the inductances.
V in dc 、V D 、V T 、i ph Respectively representing direct current bus voltage, diode voltage drop, switching tube voltage drop and phase current.
Step three: by passing throughAnd (2) calculating a special angle of the switched reluctance motor, and dividing the inductance characteristic into three stages. Wherein θ is 1 Represents the rotor position when the front edge of the stator and the rear edge of the rotor of the switch reluctance motor are overlapped, theta 2 Represents the rotor position, theta, when the front edge of the stator of the switch reluctance motor coincides with the front edge of the rotor a Representing rotor position, θ, of a switched reluctance motor when the stator is aligned with the rotor center hr For rotor position, beta, where the rotor front coincides with the stator centre line r Is the rotor pole arc beta s Is the stator pole arc, N r Is the rotor pole pair number.
Step four: theta < theta at 0 deg. < theta 1 The phase inductance is considered equal to the unsaturated inductance.
Step five: at theta 1 ＜θ＜θ hr The unsaturated inductance and the phase inductance are considered to be linear in position, and a linear function can be used to fit the unsaturated inductance and the phase inductance, as shown in formula (3). Obtaining theta based on unsaturated inductance 1 To theta hr Position phase inductance.
L(θ)＝k(i)L un (θ,i)+L 0 (i) (3)
Step six: at theta hr ＜θ＜θ a The location, the unsaturated inductance and the phase inductance are considered to be quadratic, and a quadratic function can be used to fit the unsaturated inductance and the phase inductance, as shown in equation (4). After the unsaturated inductor and the phase inductor are fitted, the phase inductance data is reversely solved based on the unsaturated inductance data and a quadratic function root-finding formula to obtain theta hr To theta 2 Position phase inductance.
L un (θ)＝a(i)L(θ,i) 2 +b(i)L(θ,i)+c(i) (4)
Step seven: the steps are integrated to obtain [0, theta ] a ]The complete inductance characteristic can be obtained according to the symmetry of the inductance characteristic of the switch reluctance motor, the flux linkage characteristic is calculated by the formula (5), and the torque characteristic is calculated by the formula (6).
ψ k (θ,i k )＝L k (θ,i k )i k (5)
Wherein i is k ，T k ，ψ k Respectively representing the k-th phase winding current, torque and flux linkage.
Step eight: and D, based on the flux linkage and the torque characteristics of the switched reluctance motor obtained in the step seven, completing the establishment of a mathematical model of the switched reluctance motor.
The invention has the beneficial effects that: (1) the defect of overlarge precision error of a torque balance method is overcome, and the flux linkage and the torque characteristic of the switch reluctance motor can be obtained more accurately; (2) the measuring process is simple to operate, short in time consumption and low in cost, and modeling of the switched reluctance motor can be achieved.
Drawings
Fig. 1 is a graph showing four flux linkage characteristics obtained by a torque balance method.
Fig. 2 is an unsaturated inductance diagram.
Fig. 3 is a graph of unsaturated inductance versus phase inductance.
FIG. 4 is a graph comparing calculated flux linkage with experimental tests.
Fig. 5 is a graph comparing calculated torque with experimental test.
Fig. 6 is a graph showing the relative current in the electric state of the rotation speed 1560rpm, the switching angle 5 DEG, guan Duanjiao deg.
FIG. 7 is a graph showing the relative current in the power generation state of 1000rpm, 30℃on-off angle, guan Duanjiao ℃.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and specific examples. The example motor used was a 1kW three-phase 12/8 pole switched reluctance motor.
Step one: the torque balance method is used, the characteristics that the torque of the switched reluctance motor is zero at the aligned position and the non-aligned position are utilized, and the inductance characteristics at the positions of 0 degree, 7.5 degrees, 15 degrees and 22.5 degrees are obtained by supplying different pulse voltages to each phase of the motor, as shown in figure 1; the phase inductance calculation formula is shown as formula (7).
Wherein U is phase voltage, i is phase resistance, and R is winding resistance.
Step two: when the switch reluctance motor runs at low speed, pulse voltage is injected into the non-conductive phase, and the current waveform and the corresponding position signal of the phase winding are recorded. And calculating unsaturated inductances according to bus voltage, switching tube voltage drop, diode voltage drop and current slopes of all phases, solving the calculation of the unsaturated inductances by a formula (1), combining recorded corresponding position signals, and obtaining unsaturated inductance characteristics of the switched reluctance motor according to the symmetry of the inductances. As shown in fig. 2.
Step three: the specific angle of the switched reluctance motor is calculated and the inductance characteristic is divided into three stages as shown in fig. 3. The calculation formula of the special angle is shown as formula (2).
Step four: theta < theta at 0 deg. < theta 1 The phase inductance is equal to the unsaturated inductance.
Step five: at theta 1 ＜θ＜θ hr The linear function relation between the phase inductance and the unsaturated inductance is established according to the formula (3).
Will L (θ) hr ，i)、L(θ 1 ，i)、L un (θ hr ，i)、L un (θ 1 I) taking a linear function solution to obtain k (i) and L 0 (i) Wherein L is un (θ 1 I) and L (θ) 1 I) can be calculated from the linear region of the unsaturated inductance, L (θ) hr I) approximately 15 ° position phase inductance. The specific calculation formula is shown as formula (8).
Step six: at theta hr ＜θ＜θ a The position establishes a quadratic function relation between the phase inductance and the unsaturated inductance as formula(4) As shown. Will L (θ) hr ，i)、L(θ a ，i)、L un (θ hr )、L un (θ a ) And k (i) is carried into a quadratic function as shown in a formula (9), and a (i), b (i) and c (i) are obtained by solving according to a formula (10). Wherein L (θ) a I) 22.5 ° position phase inductance. After the quadratic function relation between the unsaturated inductance and the phase inductance is obtained, the value of the phase inductance is reversely solved by using a quadratic function root-finding formula according to the value of the unsaturated inductance, and a larger positive value is taken from the two values. The specific calculation formula is shown as formula (11).
Step seven: the complete inductance characteristics obtained by the steps are used for calculating the flux linkage characteristics and the torque characteristics, and the curves are shown in fig. 4 and 5.
Step eight: and D, based on the flux linkage and the torque characteristics of the switched reluctance motor obtained in the step seven, completing the establishment of a mathematical model of the switched reluctance motor.
The switched reluctance motor obtained by the invention is compared with simulation and experimental results for verification. Fig. 6 shows the comparison of the phase currents of the switched reluctance motor in the electric state of the rotation speed 1560rpm and the switching angle of 5 degrees and Guan Duanjiao degrees, the solid line is an experimental result, and the dotted line is a characteristic simulation result calculated based on the invention. Fig. 7 shows the comparison of the relative currents of the switched reluctance motor in the power generation state with the rotation speed of 1000rpm and the switching angle of 30 degrees and Guan Duanjiao degrees, the solid line is the experimental result, and the dotted line is the characteristic simulation result calculated based on the invention. The above comparative verification demonstrates the accuracy of the present invention.
Although embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives, and variations may be made in the above embodiments by those skilled in the art without departing from the spirit and principles of the invention.
Claims (4)
1. A modeling method of a three-phase 12/8-pole switch reluctance motor based on dynamic and static tests is characterized by comprising the following steps: the method comprises the following steps of performing static test by using a torque balance method to obtain four flux linkage curves, performing dynamic test when the motor rotates to obtain unsaturated inductance of the switched reluctance motor, performing fitting calculation on the curves obtained by the test to obtain flux linkage and torque characteristics of the switched reluctance motor at all positions and under current, and completing modeling, wherein the modeling method can effectively improve the accuracy of the torque balance method and reduce the complexity of a rotor position fixing method, and the method comprises the following implementation steps:
step one: by using a torque balance method and utilizing the characteristic that the torque of the switched reluctance motor is zero at the aligned position and the non-aligned position, four special-position inductance characteristics of 0 DEG, 7.5 DEG, 15 DEG and 22.5 DEG are obtained by supplying different pulse voltages to each phase,
step two: when the switch reluctance motor runs at low speed, pulse voltage is injected into a non-conductive phase, current waveforms of phase windings are recorded, unsaturated inductances are calculated according to bus voltage, switching tube voltage drop, diode voltage drop and current slopes of each phase, the calculation of the unsaturated inductances is solved by a formula (1), the recorded corresponding position signals are combined, the unsaturated inductance characteristics of the switch reluctance motor are obtained according to the symmetry of the inductances,
v in dc 、V D 、V T 、i ph Respectively represents direct current bus voltage, diode voltage drop, switching tube voltage drop and phase current,
step three: calculating a special angle of the switched reluctance motor through the method (2), and dividing the inductance characteristic into three stages, wherein theta 1 Represents the rotor position when the front edge of the stator and the rear edge of the rotor of the switch reluctance motor are overlapped, theta 2 Represents the rotor position, theta, when the front edge of the stator of the switch reluctance motor coincides with the front edge of the rotor a Representing rotor position, θ, of a switched reluctance motor when the stator is aligned with the rotor center hr For rotor position, beta, where the rotor front coincides with the stator centre line r Is the rotor pole arc beta s Is the stator pole arc, N r As the pole pair number of the rotor,
step four: theta < theta at 0 deg. < theta 1 The position, the phase inductance is considered to be equal to the unsaturated inductance,
step five: at theta 1 ＜θ＜θ hr The position is considered that the unsaturated inductance and the phase inductance are in a linear relation, and a linear function can be used for fitting the unsaturated inductance and the phase inductance, as shown in formula (3), and theta is obtained based on the unsaturated inductance 1 To theta hr The inductance of the phase of the position,
L(θ)＝k(i)L un (θ,i)+L 0 (i) (3)
step six: at theta hr ＜θ＜θ a The position is considered that the unsaturated inductance and the phase inductance are in a quadratic relation, the unsaturated inductance and the phase inductance can be fitted by using a quadratic function, as shown in formula (4), after the unsaturated inductance and the phase inductance are fitted, the phase inductance data is reversely solved based on the unsaturated inductance data and a quadratic function root-finding formula, and theta is obtained hr To theta 2 The inductance of the phase of the position,
L un (θ)＝a(i)L(θ,i) 2 +b(i)L(θ,i)+c(i) (4)
step seven: the inductance characteristics of [0, thetaa ] are obtained by integrating the steps, the complete inductance characteristics can be obtained according to the symmetry of the inductance characteristics of the switch reluctance motor, the flux linkage characteristics are obtained by calculating in the formula (5), the torque characteristics are obtained by calculating in the formula (6),
ψ k (θ,i k )＝L k (θ,i k )i k (5)
wherein, k i，T k ，ψ k respectively represent the kth phase winding current, torque and flux linkage,
step eight: and D, based on the flux linkage and the torque characteristics of the switched reluctance motor obtained in the step seven, completing the establishment of a mathematical model of the switched reluctance motor.
2. The modeling method for the three-phase 12/8-pole switched reluctance motor based on dynamic and static testing according to claim 1, wherein the modeling method is characterized by comprising the following steps: in the first step, the phase inductances of four special positions of the switch reluctance motor are obtained through a torque balance method.
3. The modeling method for the three-phase 12/8-pole switched reluctance motor based on dynamic and static testing according to claim 1, wherein the modeling method is characterized by comprising the following steps: in step five at θ 1 <θ<θ hr Position, phase inductance and unsaturated inductance are linear, using a linear function L (θ) =k (i) L un (θ,i)+L 0 (i) And fitting the unsaturated inductor and the phase inductor, and solving to obtain the phase inductor.
4. The modeling method for the three-phase 12/8-pole switched reluctance motor based on dynamic and static testing according to claim 1, wherein the modeling method is characterized by comprising the following steps: in step six, at θ hr <θ<θ a The position of the unsaturated inductor and the phase inductance are in a quadratic function relation, and a quadratic function L is used un (θ)＝a(i)L(θ,i) 2 And (3) fitting the unsaturated inductor and the phase inductor by +b (i) L (theta, i) +c (i), and solving the phase inductor reversely by using a quadratic function root-finding formula.
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| US5107195A (en) * | 1991-02-11 | 1992-04-21 | General Electric Company | Rotor position estimator for a switched reluctance machine using a lumped parameter flux/current model |
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| US10637386B2 (en) * | 2018-07-26 | 2020-04-28 | Enedym Inc. | Torque ripple reduction in switched reluctance machine |
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