Method for reducing magnetic linkage pulsation
阅读说明：本技术 一种减小磁链脉动的方法 (Method for reducing magnetic linkage pulsation ) 是由 李耀华 赵承辉 秦玉贵 周逸凡 秦辉 苏锦仕 于 2019-07-29 设计创作，主要内容包括：一种减小磁链脉动的方法,对对磁链和转矩增减效果影响最大的电压矢量角度集合、对磁链和转矩增减效果影响最小的电压矢量角度集合、混合备选电压矢量角度集合以及含7个基本电压矢量的备选电压矢量集合分别进行仿真分析,得到混合备选电压矢量集合的稳态综合性能是最优的,该集合中每一个电压矢量角度值对应一个考虑磁链幅值约束的成本函数值,在所有的考虑磁链幅值约束的成本函数值中选择最小的成本函数值所对应的电压矢量角度,将该电压矢量施加给电机。本发明在混合备选电压矢量集合的基础上,利用考虑磁链幅值约束的成本函数,增强对磁链的有效约束,解决动态下转速阶跃出现较大磁链波动的问题。(A method for reducing flux linkage pulsation includes carrying out simulation analysis on a voltage vector angle set which has the largest influence on flux linkage and torque increase and decrease effects, a voltage vector angle set which has the smallest influence on flux linkage and torque increase and decrease effects, a mixed alternative voltage vector angle set and an alternative voltage vector set containing 7 basic voltage vectors respectively to obtain that the stable comprehensive performance of the mixed alternative voltage vector set is optimal, enabling each voltage vector angle value in the set to correspond to a cost function value considering flux linkage amplitude constraint, selecting a voltage vector angle corresponding to the smallest cost function value from all cost function values considering flux linkage amplitude constraint, and applying the voltage vector to a motor. According to the invention, on the basis of the mixed alternative voltage vector set, the cost function considering flux linkage amplitude constraint is utilized to enhance the effective constraint on flux linkages and solve the problem of large flux linkage fluctuation of the dynamic down-rotation step.)
1. A method of reducing flux linkage ripple, comprising the steps of:
the method comprises the following steps: respectively making a voltage vector angle set which has the greatest influence on flux linkage and torque increase and decrease effects, a voltage vector angle set which has the smallest influence on flux linkage and torque increase and decrease effects and a mixed candidate voltage vector angle set according to increase and decrease effects of voltage vectors on the flux linkage amplitude and the torque of the stator;
step two: through a surface permanent magnet synchronous motor model prediction direct torque control system, a voltage vector angle set with the largest influence on flux linkage and torque increase and decrease effects, a voltage vector angle set with the smallest influence on flux linkage and torque increase and decrease effects, a mixed candidate voltage vector angle set and a candidate voltage vector set containing 7 basic voltage vectors are subjected to simulation analysis respectively to obtain that the steady-state comprehensive performance of the mixed candidate voltage vector set is optimal, so that the mixed candidate voltage vector set is combined into a candidate voltage vector set for prediction control of a motor model;
step three: and each voltage vector angle value in the alternative voltage vector set subjected to motor model predictive control corresponds to a cost function value considering flux linkage amplitude constraint, the voltage vector angle corresponding to the minimum cost function value is selected from all the cost function values considering flux linkage amplitude constraint, and the voltage vector is applied to the motor.
2. The method for reducing the flux linkage pulsation according to claim 1, wherein in the first step, the effect of increasing and decreasing the amplitude of the stator flux linkage by the voltage vector is embodied by the relationship between the voltage vector and the amplitude of the stator flux linkage, and the relationship between the voltage vector and the amplitude of the stator flux linkage is as follows:
wherein, Delta psisIs the stator flux linkage amplitude variation, psis(k) Is the magnitude of the stator flux linkage at the current time K,vs is the magnitude of the voltage vector to be applied at the present time, Δ t is the acting time of the voltage vector application, α is the angle between the voltage vector and the stator flux linkage vector, and δ (K) is the torque angle at the present time K.
3. The method for reducing the flux linkage pulsation according to claim 1, wherein in the first step, the torque increase and decrease effect of the voltage vector is represented by a relationship between the voltage vector and the torque, and the relationship between the voltage vector and the torque is as follows:
where Δ Te is a torque variation amount, p is a pole pair number of the motor, ψfIs a permanent magnet flux linkage psis(k) Is the amplitude, L, of the stator flux linkage at the current K timedIs the d-axis stator inductance and,vs is the magnitude of the voltage vector to be applied at the present time, Δ t is the acting time of the voltage vector application, α is the angle between the voltage vector and the stator flux linkage vector, and δ (K) is the torque angle at the present time K.
4. The method for reducing flux linkage pulsation according to claim 1, wherein in the first step, the set of voltage vector angles that most affect flux linkage and torque increase and decrease effects is:
∠Vs∈{0°,90°-δ,180°,270°-δ} (6)
wherein, delta is an included angle between a voltage vector and a rotor flux linkage vector.
5. The method of claim 1, wherein in the first step, the set of voltage vector angles that has minimal impact on flux linkage and torque increase and decrease effects is:
∠Vs∈{90°,-δ,270°,180°-δ} (7)
wherein, delta is an included angle between a voltage vector and a rotor flux linkage vector.
6. The method of claim 1, wherein in step one, the set of mixed candidate voltage vector angles is:
∠Vs∈{0°,90°-δ,180°,270°-δ,90°,-δ,270°,180°-δ} (8)。
7. the method according to claim 1, wherein in the second step, the set of candidate voltage vectors comprising 7 basic voltage vectors is: angle VsE {0 °,60 °,120 °,180 °,240 °,320 °, zero voltage vector }.
8. The method of claim 1, wherein in step three, the cost function is constrained by considering flux linkage amplitude as:
wherein, gfIs a flux linkage amplitude constraint.
Technical Field
The invention relates to a method for reducing flux linkage pulsation.
Background
The direct torque control technology is based on a stator flux linkage coordinate system and directly takes the torque as a control object, so that a large amount of calculation and dependency on motor parameters during rotation coordinate transformation are avoided, the dynamic performance is good, and the torque response time is short.
Under the rotation speed fluctuation, even when the applied voltage vector is reduced to the maximum extent, although the effect on the flux linkage is reduced, the influence of the reduction of the flux linkage on the cost function is ignored, the system is more biased to the torque control, the alternative voltage vector selected by the direct torque control system based on the model prediction control only controls the torque, the flux linkage is sacrificed, and therefore, the large flux linkage fluctuation occurs at the rotation speed step, and the control performance is influenced.
Disclosure of Invention
The invention aims to overcome the defects and provide a method for reducing flux linkage pulsation so as to improve the performance of a direct torque control system of a permanent magnet synchronous motor.
In order to achieve the above object, the present invention comprises the steps of:
a method of reducing flux linkage ripple, comprising the steps of:
the method comprises the following steps: respectively making a voltage vector angle set which has the greatest influence on flux linkage and torque increase and decrease effects, a voltage vector angle set which has the smallest influence on flux linkage and torque increase and decrease effects and a mixed candidate voltage vector angle set according to increase and decrease effects of voltage vectors on the flux linkage amplitude and the torque of the stator;
step two: through a surface permanent magnet synchronous motor model prediction direct torque control system, a voltage vector angle set with the largest influence on flux linkage and torque increase and decrease effects, a voltage vector angle set with the smallest influence on flux linkage and torque increase and decrease effects, a mixed candidate voltage vector angle set and a candidate voltage vector set containing 7 basic voltage vectors are subjected to simulation analysis respectively to obtain that the steady-state comprehensive performance of the mixed candidate voltage vector set is optimal, so that the mixed candidate voltage vector set is combined into a candidate voltage vector set for motor model prediction control;
step three: and each voltage vector angle value in the alternative voltage vector set subjected to motor model predictive control corresponds to a cost function value considering flux linkage amplitude constraint, the voltage vector angle corresponding to the minimum cost function value is selected from all the cost function values considering flux linkage amplitude constraint, and the voltage vector is applied to the motor.
The further improvement of the invention is that in the step one, the effect of increasing and decreasing the stator flux linkage amplitude by the voltage vector is reflected by the relation between the voltage vector and the stator flux linkage amplitude, and the relation between the voltage vector and the stator flux linkage amplitude is as follows:
wherein, Delta psisIs the stator flux linkage amplitude variation, psis(k) Is the magnitude of the stator flux linkage at the current time K,vs is the magnitude of the voltage vector to be applied at the present time, Δ t is the acting time of the voltage vector application, α is the angle between the voltage vector and the stator flux linkage vector, and δ (K) is the torque angle at the present time K.
In a further improvement of the present invention, in the first step, the torque increasing and decreasing effect of the voltage vector is expressed by a relationship between the voltage vector and the torque, and the relationship between the voltage vector and the torque is as follows:
where Δ Te is a torque variation amount, p is a pole pair number of the motor, ψfIs a permanent magnet flux linkage psis(k) Is the amplitude, L, of the stator flux linkage at the current K timedIs the d-axis stator inductance and,vs is the magnitude of the voltage vector to be applied at the present time, Δ t is the acting time of the voltage vector application, α is the angle between the voltage vector and the stator flux linkage vector, and δ (K) is the torque angle at the present time K.
The further improvement of the invention is that in the step one, the set of voltage vector angles which have the greatest influence on flux linkage and torque increase and decrease effects is as follows:
∠Vs∈{0°,90°-δ,180°,270°-δ} (6)
wherein, delta is an included angle between a voltage vector and a rotor flux linkage vector.
The invention further improves the method that in the step one, the set of voltage vector angles which have the smallest influence on flux linkage and torque increase and decrease effects is as follows:
∠Vs∈{90°,-δ,270°,180°-δ} (7)
wherein, delta is an included angle between a voltage vector and a rotor flux linkage vector.
The further improvement of the invention is that in the step one, the vector angle set of the mixed alternative voltage is as follows:
∠Vs∈{0°,90°-δ,180°,270°-δ,90°,-δ,270°,180°-δ} (8)。
the further improvement of the invention is that in the step two, the candidate voltage vector set containing 7 basic voltage vectors is as follows: angle VsE {0 °,60 °,120 °,180 °,240 °,320 °, zero voltage vector }.
The further improvement of the invention is that in the third step, the cost function of the flux linkage amplitude constraint is considered as follows:
wherein, gfIs a flux linkage amplitude constraint.
Compared with the prior art, the invention has the following beneficial effects: because the angle set of each candidate voltage vector is different, the voltage vector selected by each candidate voltage vector applied to the motor is also different, thereby bringing different performance influences. According to the invention, on the basis of the mixed alternative voltage vector set, the cost function considering flux linkage amplitude constraint is utilized to enhance the effective constraint on flux linkages and solve the problem of large flux linkage fluctuation of the dynamic down-rotation step. The method is completely consistent with the method without magnetic linkage constraint in a steady state, and the method does not generate large fluctuation of magnetic linkage due to the magnetic linkage constraint in a dynamic state, thereby verifying the effectiveness of the method.
Further, in steady state, consider flux linkage amplitude constraint gfThe flux linkage amplitude constraint g is considered as a static flux linkage constraint term, and the flux linkage amplitude constraint g is considered as a static flux linkage constraint termfAnd does not actually work. Constraining g by considering flux linkage amplitudefThe addition of the term enhances the constraint on the flux linkage amplitude.
Drawings
Fig. 1 is a graph of the change of the flux linkage motion of the stator after applying a non-zero voltage vector, neglecting the rotor rotation motion and the resistance voltage drop of the stator.
Fig. 2 is a diagram of the actual rotational speed of the motor for the set of candidate voltage vector angles at which flux linkage and torque changes are greatest.
FIG. 3 is a diagram of motor torque for a set of candidate voltage vector angles that maximize flux linkage and torque variation.
FIG. 4 is a motor torque error plot for the set of candidate voltage vector angles for which flux linkage and torque variation are greatest.
Fig. 5 is a stator flux linkage amplitude plot for the set of candidate voltage vector angles at which flux linkage and torque changes are greatest.
Fig. 6 is a stator flux linkage error plot for the set of candidate voltage vector angles at which flux linkage and torque changes are greatest.
Fig. 7 is a stator flux linkage trajectory plot for the set of candidate voltage vector angles at which flux linkage and torque changes are greatest.
Fig. 8 is a stator current diagram for the a-phase of the motor for the set of candidate voltage vector angles at which flux linkage and torque changes are greatest.
FIG. 9 is a graph of a cost function for a set of candidate voltage vector angles for which flux linkage and torque changes are greatest.
Fig. 10 is a plot of the actual motor speed for a set of candidate voltage vector angles that minimize flux linkage and torque variation.
FIG. 11 is a motor torque diagram for a set of candidate voltage vector angles that minimize flux linkage and torque variation.
FIG. 12 is a motor torque error plot for a set of candidate voltage vector angles that minimize flux linkage and torque variation.
Fig. 13 is a stator flux linkage amplitude plot for the set of candidate voltage vector angles that minimize flux linkage and torque variation.
Fig. 14 is a stator flux linkage error plot for the set of candidate voltage vector angles that minimize flux linkage and torque variation.
Fig. 15 is a stator flux linkage trajectory plot for a set of candidate voltage vector angles that minimize flux linkage and torque variation.
Fig. 16 is a diagram of motor a-phase stator currents for a set of candidate voltage vector angles that minimize flux linkage and torque variation.
FIG. 17 is a cost function plot for the set of candidate voltage vector angles that minimize flux linkage and torque variation.
Fig. 18 is a graph of the actual rotation speed of the permanent magnet synchronous motor under the mixed candidate voltage vector angle set.
Fig. 19 is a diagram of the permanent magnet synchronous motor torque under the mixed candidate voltage vector angle set.
Fig. 20 is a diagram of a permanent magnet synchronous motor torque error under a hybrid candidate voltage vector angle set.
Fig. 21 is a permanent magnet synchronous motor stator flux linkage amplitude diagram under a mixed candidate voltage vector angle set.
Fig. 22 is a permanent magnet synchronous motor stator flux linkage error diagram under a mixed candidate voltage vector angle set.
Fig. 23 is a permanent magnet synchronous motor stator flux linkage track diagram under a mixed candidate voltage vector angle set.
Fig. 24 is a stator current diagram of a-phase of a permanent magnet synchronous motor under a mixed alternative voltage vector angle set.
FIG. 25 is a graph of a cost function for a set of hybrid candidate voltage vector angles.
Fig. 26 is a diagram of the actual rotational speed of the permanent magnet synchronous motor of the present invention.
Fig. 27 is a torque diagram of a permanent magnet synchronous motor of the present invention.
Fig. 28 is a torque error diagram of a permanent magnet synchronous motor of the present invention.
Fig. 29 is a stator flux linkage amplitude diagram of the permanent magnet synchronous motor of the present invention.
Fig. 30 is a stator flux linkage error diagram of a permanent magnet synchronous motor of the present invention.
Fig. 31 is a stator flux linkage diagram of a permanent magnet synchronous motor according to the present invention.
Fig. 32 is a diagram of a-phase stator current of the permanent magnet synchronous motor of the present invention.
FIG. 33 is a cost function diagram of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The idea of the method is to combine the mixed alternative voltage vector set with a new cost function considering flux linkage amplitude constraint to realize effective constraint on flux linkages, firstly to verify the superiority of the mixed alternative voltage vector set, and then to combine a new cost function to effectively constrain flux linkages. The method comprises the following specific steps:
the method comprises the following steps: in the stator flux linkage coordinate system, if the amplitude of the voltage vector is fixed, the increasing and decreasing effects of the voltage vector on the amplitude of the stator flux linkage are only related to the included angle between the voltage vector and the stator flux linkage vector, and the increasing and decreasing effects of the voltage vector on the torque are only related to the included angle between the voltage vector and the rotor flux linkage vector, namely, if the amplitude of the voltage vector is fixed, the increasing and decreasing effects of the voltage vector on the amplitude of the stator flux linkage and the torque are only related to the angle of the voltage vector. Therefore, based on the increase and decrease effects of the voltage vector on the stator flux linkage amplitude and the torque, a voltage vector angle set having the largest influence on the flux linkage and the torque increase and decrease effects, a voltage vector angle set having the smallest influence on the flux linkage and the torque increase and decrease effects, and a mixed candidate voltage vector angle set are respectively determined. The specific process is as follows:
referring to fig. 1, the stator flux linkage amplitude and the torque at the next time after the voltage vector is applied to the inverter are shown in equations (1) and (2).
Wherein the content of the first and second substances,is the magnitude of the stator flux linkage at the current time K,is the stator flux linkage amplitude at time k +1,is the magnitude of the voltage vector to be applied currently, Δ t is the action time of the voltage vector application, and α is the angle between the voltage vector and the stator flux linkage vector. T ise(k +1) is the motor torque at the time k +1, p is the pole pair number of the motor, ψfIs a magnetic flux linkage of a permanent magnet,is the amplitude, L, of the stator flux linkage at the current K timedFor d-axis stator inductance, α is the angle between the voltage vector and the stator flux vector, and δ (K) is the torque angle at the current time K.
The increase and decrease effect of the voltage vector on the stator flux linkage amplitude is related to the included angle between the voltage vector and the stator flux linkage vector and the voltage vector amplitude, as shown in formula (3).
Wherein, Delta psisIs the stator flux linkage amplitude variation, psis(k) Is the magnitude of the stator flux linkage at the current time K,where Vs is the magnitude of the voltage vector to be currently applied, Δ t is the action time for which the voltage vector is applied, and α isAnd the included angle between the voltage vector and the stator flux linkage vector.
As can be seen from equation (3), the increasing and decreasing effect of the voltage vector on the stator flux linkage amplitude is proportional to the voltage vector amplitude, and forms a cosine curve approximately with the included angle between the voltage vector and the stator flux linkage vector, that is, α is 0, the stator flux linkage amplitude is increased maximally, α is 180, the stator flux linkage amplitude is decreased maximally, α is 90 or 270, and the stator flux linkage amplitude is changed minimally.
The increase and decrease effect of the voltage vector on the torque is related to the included angle between the voltage vector and the rotor flux linkage vector and the amplitude of the voltage vector, as shown in formula (4).
Where Δ Te is a torque variation amount, p is a pole pair number of the motor, ψfIs a permanent magnet flux linkage psis(k) Is the amplitude, L, of the stator flux linkage at the current K timedIs the d-axis stator inductance and,wherein Vs is the magnitude of the voltage vector to be applied at present, Δ t is the acting time of the voltage vector application, α is the angle between the voltage vector and the stator flux vector, δ is the torque angle, and δ (K) is the torque angle at the moment K at present.
As can be seen from equation (4), the torque increase and decrease effect of the voltage vector is proportional to the voltage vector amplitude, and the angle between the voltage vector and the rotor flux linkage vector is approximately sinusoidal, that is, α + δ is 90, the torque increase is maximum, α + δ is 270, the torque decrease is maximum, α + δ is 0 or α + δ is 180, and the torque change is minimum.
If the voltage vector amplitude is fixed, the increasing and decreasing effects of the voltage vector on the stator flux linkage amplitude are only related to the included angle between the voltage vector and the stator flux linkage vector, and the increasing and decreasing effects of the voltage vector on the torque are only related to the included angle between the voltage vector and the rotor flux linkage vector, namely, if the voltage vector amplitude is fixed, the increasing and decreasing effects of the voltage vector on the stator flux linkage amplitude and the torque are only related to the angle of the voltage vector. Therefore, the voltage vector magnitude is fixed as shown in equation (5).
Wherein the content of the first and second substances,for fixed voltage vector magnitude, UdcIs the dc bus voltage.
As is known from the above reasoning, α is 0, the stator flux linkage amplitude is increased maximally, α is 180, the stator flux linkage amplitude is decreased maximally, α is 90 or 270, and the stator flux linkage amplitude is changed minimally, so α is 0, α is 180, and α is a voltage vector angle that has the greatest influence on the flux linkage change, and α is 90 or 270, and has the smallest influence on the flux linkage change. When the α + δ is 90, the torque is increased maximally, the α + δ is 270, the torque is decreased maximally, the α + δ is 0 or the α + δ is 180, and the torque variation is minimized, so that α -90 ° - δ (k) and 270 ° - δ (k) are voltage vector angles that most affect the torque variation, and α - δ (k) and 180 ° - δ (k) are voltage vector angles that least affect the torque variation.
And combining the voltage vector angle alpha which has the greatest influence on flux linkage change with 0 and alpha with 180 and the voltage vector angle alpha which has the greatest influence on torque change with 90-delta (k) and 270-delta (k), and making a candidate voltage vector angle set which has the greatest influence on flux linkage and torque under a stator flux linkage coordinate system, wherein the candidate voltage vector angle set is shown as a formula (6).
∠Vs∈{0°,90°-δ,180°,270°-δ} (6)
And combining the voltage vector angle alpha with the minimum influence on flux linkage change with the voltage vector angle alpha with the minimum influence on torque change with the voltage vector angle, and working out a candidate voltage vector angle set with the minimum.
∠Vs∈{90°,-δ,270°,180°-δ} (7)
And combining the two sets to prepare a mixed alternative voltage vector angle set as shown in a formula (8).
∠Vs∈{0°,90°-δ,180°,270°-δ,90°,-δ,270°,180°-δ} (8)
Step two: and (3) respectively carrying out simulation analysis on the three different alternative voltage vector sets and four schemes of a traditional alternative voltage vector set containing 7 basic voltage vectors based on the surface permanent magnet synchronous motor model prediction direct torque control system, and verifying that the steady-state comprehensive performance of the scheme of the mixed alternative voltage vector set is optimal, so that the mixed alternative voltage vector set is selected to be used as the alternative voltage vector set for the motor model prediction control.
In the second step, the traditional alternative voltage vector set containing 7 basic voltage vectors is less than VsThe method is characterized in that the method belongs to {0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 320 degrees and zero voltage vectors }, the 4 alternative voltage vector angle set schemes are respectively subjected to simulation analysis in a surface permanent magnet synchronous motor model prediction direct torque control system, and the comparison simulation uses a traditional cost function g as shown in a formula (9).
Wherein the content of the first and second substances,is the true torque at the current time k, Te(k +1) is the motor torque at time k +1,is the stator flux linkage amplitude at the current time k,is the stator flux linkage amplitude at time k + 1.
Subtracting each angle in the alternative voltage vector angle set under 4 different schemes from the stator flux linkage vector angle to obtain an included angle alpha between the voltage vector and the stator flux linkage vector, as shown in formulas (10) and (11), respectively substituting alpha corresponding to each angle into formulas (10) and (11) for calculation to obtain different k +1 time constantsAmplitude of the sub flux linkageValue and motor torque T at time k +1e(k +1) value, and then will be differentValue sum TeThe value of (k +1) and the reference flux linkage and the reference torque are substituted into equation (9) to calculate the cost function value.
And finally, selecting the voltage vector corresponding to the minimum cost function value from all the cost function values in the set to apply to the motor so as to ensure that the motor can operate correctly and smoothly. Each alternative voltage vector angle set is different, and the voltage vector selected by the alternative voltage vector angle set and applied to the motor is also different, so that different performance influences are brought.
A surface permanent magnet synchronous motor model prediction direct torque control simulation model is established based on MATLAB/Simulink. The simulation model is a discrete model with a sampling period of 5 × 10-5And s. The dc bus voltage is 312V. The parameters of the rotating speed PI regulator are as follows: kp＝5，KI10, the PI regulator output has upper and lower limits of [ -35, 35 [ ]]. The reference speed was 60rpm, stepped to 30rpm at 1 s. The load torque was initially 10n.m, stepped to 30n.m at 0.5 s. The reference stator flux linkage amplitude is 0.3 Wb. The total simulation duration is 1.5 s. The parameters of the surface permanent magnet synchronous motor for simulation are shown in table 1.
TABLE 1 simulation surface-mounted PMSM parameters
Parameters of the electric machine
Numerical value
Stator resistor
0.2Ω
d-axis inductor
0.0085H
q-axis inductor
0.0085H
Rotor flux linkage
0.175Wb
Number of pole pairs
4
Moment of inertia
0.089kg.m2
Viscous damping
0.005N.m.s
The comparison between the different properties was evaluated using the following criteria: the steady state evaluation index of the surface permanent magnet synchronous motor model prediction direct torque control system adopts the torque ripple root mean square error Trip_RMSEMagnetic flux ripple root mean square error psirip_RMSEAnd the mean value m of the evaluation functionaveRespectively expressed by the formulas (12) to (15), wherein n is the number of samples.
The evaluation function is defined as shown in equation (14).
The average value of the evaluation function is shown in equation (15).
And under the system dynamic state (reference rotating speed step), the time required by the actual torque to reach 35N.m from 0N.m is used as the dynamic evaluation index of the surface permanent magnet synchronous motor model prediction direct torque control system.
Under different alternative voltage vector sets, the actual rotating speed, the motor torque, the torque error, the stator flux linkage amplitude, the stator flux linkage error, the stator flux linkage track, the a-phase stator current and the evaluation function of the permanent magnet synchronous motor are shown in fig. 2-25, and the simulation evaluation results are shown in table 2.
TABLE 2 simulation Performance
The comparison of the analysis results of the simulation performance shows that:
1. compared with the steady-state comprehensive performance, the mixing effect is optimal.
2. Under the dynamic condition, the torque flux linkage is maximum, the alternative voltage vectors containing 7 basic voltage vectors are mixed, and the flux linkage has large fluctuation under the step of the rotating speed; the torque flux linkage is the minimum candidate voltage vector, and the dynamic response is slow.
The reason that flux linkage fluctuation occurs in the rotation speed step is that under the rotation speed fluctuation, the system is more biased to control the torque, and the alternative voltage vector selected by the system only controls the torque, so that flux linkage is sacrificed.
The system performance before and after the speed step is shown in table 3.
TABLE 3 System Performance (11 th sampling point corresponding to 1s speed step time)
As can be seen from table 3, the applied voltage vector at this time reduces the torque to the maximum extent, and the effect on the flux linkage is also reduced, but the effect of the reduction on the flux linkage on the cost function is ignored, and thus flux linkage pulsation is caused.
The simulation result can verify that the steady-state comprehensive performance of the scheme of the mixed candidate voltage vector set is optimal, so that the mixed candidate voltage vector set is selected to serve as the candidate voltage vector set for predictive control of the motor model.
Step three: on the basis of the mixed alternative voltage vector set, a new cost function considering flux linkage amplitude constraint is used, effective constraint on flux linkages is enhanced, the problem that large flux linkage fluctuation occurs in a dynamic down-rotation step is solved, simulation analysis is carried out, and the effectiveness of the method is verified. The specific process is as follows:
in order to solve the problem of large flux linkage pulsation during the dynamic step change of the rotating speed, the invention provides a cost function g considering flux linkage amplitude constraint on the basis of using a mixed alternative voltage vector angle set (8 alternative voltage vectors), as shown in a formula (16), wherein the flux linkage amplitude constraint g is consideredfAs shown in equation (17).
In steady state, consider flux linkage amplitude constraint gfTo zero, the cost function still takes the torque and magnetism into accountAnd (3) link control, in a dynamic state, when a flux linkage error is larger, constraint is added to the flux linkage, so that the control to the flux linkage is enhanced, larger flux linkage pulsation is avoided, and a flux linkage amplitude constraint g is considered in a static flux linkage constraint itemfAnd does not actually work. Constraining g by considering flux linkage amplitudefThe addition of the term enhances the constraint on the flux linkage amplitude.
The set of candidate voltage vectors is shown as a formula (18), the cost function is shown as a formula (9), and the optimal voltage vector is selected from the set of candidate voltage vectors by using the cost function of the invention and is applied to the motor.
∠Vs∈{0°,90°-δ,180°,270°-δ,90°,-δ,270°,180°-δ} (18)
Actual rotating speed, motor torque, torque error, stator flux amplitude, stator flux error, stator flux trajectory, a-phase stator current and evaluation functions of the permanent magnet synchronous motor are shown in fig. 26-33, and simulation evaluation results are shown in table 4.
Table 4 simulation evaluation results
Steady state torque RMSE/N.m (0-1s)
1.0378
Steady state magnetic linkage RMSE/Wb (0-1s)
0.0082
Mean value of steady-state evaluation function (0-1s)
0.0327
Dynamic torque response time/s
2.00E-3
The system performance before and after the speed step is shown in table 5.
TABLE 5 System Performance (11 th sample corresponds to 1s speed step time)
Sampling point
Applied voltage vector angle
Torque moment
Magnetic linkage
1
270
30.63375
0.300301
2
214.4844
31.45472
0.308947
3
180
30.76016
0.308819
4
90
29.56393
0.301236
5
37.52582
28.60902
0.291981
6
0
29.21193
0.291781
7
-55.046
30.26434
0.298914
8
180
31.0807
0.307565
9
180
31.01975
0.312538
10
126.6914
30.04858
0.303313
11
216.7982
29.08611
0.294008
12
215.485
29.0075
0.288415
13
270
27.82373
0.280768
14
0
26.6385
0.273286
15
0
25.90241
0.273319
16
270
26.69381
0.282023
17
220.1031
27.47134
0.290778
18
221.9873
26.69197
0.290699
19
270
25.50411
0.283729
20
-45.3077
24.31767
0.276911
Simulation results show that the magnetic linkage constraint is completely consistent with that of the magnetic linkage constraint in a steady state, and the magnetic linkage constraint does not cause large fluctuation in a dynamic state, so that the effectiveness of the invention is verified.