CN115913038A - Model prediction control method for double three-phase permanent magnet synchronous motor - Google Patents
Model prediction control method for double three-phase permanent magnet synchronous motor Download PDFInfo
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Abstract
The invention discloses a model predictive control method for a double three-phase permanent magnet synchronous motor, which fully utilizes voltage vectors on an alpha-beta plane and an x-y plane, respectively synthesizes large vectors and medium large vectors in the two planes into 12 virtual voltage vectors, synthesizes the medium large vectors and the small vectors into 12 virtual voltage vectors, and adds zero vectors, namely, the two planes respectively contain 25 virtual voltage vectors. The virtual voltage vector of the alpha-beta plane is used for electromechanical energy conversion to generate appropriate electromagnetic torque, and the virtual voltage vector of the x-y plane is used for inhibiting harmonic current to improve the system efficiency. The biplane prediction control method fully utilizes the voltage vectors of the two planes, improves the control precision, reduces the torque pulsation and greatly improves the control performance while ensuring the output power of the motor. The invention is also applicable to common multi-phase permanent magnet motors.
Description
Technical Field
The invention relates to a double three-phase permanent magnet synchronous motor, in particular to a model prediction control method of the double three-phase permanent magnet synchronous motor, and belongs to the technical field of motors.
Background
In recent years, with the rapid development of social productivity, in many industrial driving fields, the reliability of a transmission system is required to be higher and the requirements on the accuracy and rapidity of a control system are also stricter. Compared with the traditional three-phase motor, the double three-phase motor (also called as an asymmetric six-phase permanent magnet synchronous motor) has the advantages of large output power, small torque pulsation, high power density, strong fault-tolerant capability and the like, and is more and more widely applied to the industries of electric airplanes, automobiles, ship propulsion and the like.
Common control strategies for multi-phase motors are mainly vector control based on vector space decoupling, direct torque control and model predictive control. The vector control is similar to the vector control of a three-phase motor, the 12 maximum vectors at the outermost layer are used as basic voltage vectors in an alpha-beta plane, and the control method can obtain the maximum voltage utilization rate of the direct-current bus of the inverter. But the method ignores the harmonic plane of the multi-phase motor, leads to the fact that the stator current of the multi-phase motor contains a large amount of harmonic waves, reduces the operation efficiency of a motor system, has unique vector voltage in a period, and has the defects of large flux linkage and torque ripple fluctuation. The Control unit of Model Predictive Control (MPC) has the advantages of simple structure, fast response speed, easy processing of multivariable optimization Control, and the like, and is widely applied to multi-phase motors. However, the conventional MPC only performs optimized control on a fundamental plane participating in energy exchange, and does not fully consider harmonic loss caused by system nonlinearity, and only considers control voltage vectors on an alpha-beta plane, and because the impedance on a harmonic x-y sub-plane is low, harmonic voltages in phase voltages, particularly 5 th and 7 th harmonic voltages, generate large harmonic currents on the x-y sub-plane, the control effect is not ideal. If the dead zone effect of the inverter and the nonlinear factors of the system are considered, the voltage vector on the x-y harmonic sub-plane cannot be counteracted to be 0, so that larger current harmonics still exist during single-plane control, the harmonic loss is increased, and the system efficiency is reduced.
Disclosure of Invention
The invention aims to provide a model predictive control method for a double three-phase permanent magnet synchronous motor, which is used for solving the technical problems that a double three-phase permanent magnet motor under the traditional control method has a low-impedance harmonic plane, and a smaller harmonic voltage can generate a larger harmonic current, and a Model Predictive Control (MPC) method in the prior art only carries out optimized control on a fundamental plane participating in energy exchange, but does not fully consider harmonic loss caused by system nonlinear factors.
The purpose of the invention is realized by the following technical scheme:
a model prediction control method for a double three-phase permanent magnet synchronous motor comprises the following steps:
step 1: establishing a mathematical model of the double three-phase motor: clarke transformation is carried out on the double three-phase motor, and all variables of the motor are mapped to an alpha-beta sub-plane, an x-y sub-plane and an o sub-plane 1 -o 2 The three sub-planes are mutually orthogonal to obtain a Clarke-Park total transformation matrix of the double three-phase motor;
step 2: calculating space voltage vectors of an alpha-beta sub-plane and an x-y sub-plane;
and step 3: and (3) biplane virtual voltage vector synthesis is respectively carried out on an alpha-beta plane and an x-y plane: in order to improve the control accuracy, the switching state of the inverter is fully utilized, a large vector and a medium vector are combined into 12 virtual voltage vectors, the medium vector and a small vector are combined into 12 virtual voltage vectors, and 25 vectors are added with a zero vector, namely VV25; the large vector, the medium large vector and the small vector are divided according to the length of the vectors, the longest vector is the large vector, the shortest vector is the small vector, and the medium vector is the medium vector;
and 4, step 4: designing a cost function g of the predictive control of the biplane virtual voltage vector model;
step (ii) of5: respectively calculating reference voltage vectors of dq axes on an alpha-beta plane and an x-y plane, calculating the amplitude of the reference voltage according to the reference voltage value, calculating the phase angle theta of the reference voltage, determining the sector where the reference voltage is located according to the phase angle theta, and then selecting a synthetic virtual voltage vector vv of the alpha-beta plane and the x-y plane with the minimum cost function g i 、vv i+12 ；
And 6: resulting virtual voltage vector in the alpha-beta plane vv i 、vv i+12 Generating electromagnetic torque, driving the motor to run after PWM conversion, and generating a synthetic virtual voltage vector vv on an x-y plane i 、vv i+12 Harmonic currents are suppressed.
The object of the invention can be further achieved by the following technical measures:
further, step 1, clarke-Park total transformation matrix T of double three-phase motor 6sr Comprises the following steps:
in the formula, theta is the rotor electrical angle; according to Clarke-Park total transformation matrix T 6sr The torque equation of the obtained double three-phase permanent magnet synchronous motor is shown as the formula (2):
T e ＝3p n (ψ d i q -ψ q i d ) (2)
in the formula i d 、i q Representing the components of the stator current in the d and q axes, Ψ d 、Ψ q Representing the components of the flux linkage in the d and q axes, p n The number of pole pairs of the motor is indicated.
Further, the α - β sub-plane and x-y sub-plane space voltage vector calculation formula in step 2 is as follows:
since six-phase inverters have 64 switch states, the voltage vectors that each switch state maps onto the α - β sub-plane and the x-y sub-plane are represented by equations (3) and (4) as follows:
in the formula v, v Z Representing the space voltage vectors, U, mapped onto the alpha-beta and x-y sub-planes, respectively dc The direct current bus voltage of the double three-phase motor driving inverter is represented; s. the a 、S b 、S c 、S d 、S e 、S f Respectively showing the switching states of the six bridge arms.
Further, in step 3:
large vector v in the alpha-beta sub-plane 4-6 And a large vector v 6-4 Small vector v 2-5 In phase, but with a large vector v in the x-y sub-plane 4-6 And a large vector v 6-4 Small vector v 2-5 But are in antiphase, so that in the x-y sub-plane, the medium-large vector v 4-6 The resulting flux linkage is also associated with a large vector v 6-4 Sum small vector v 2-5 The generated magnetic linkage is reversed; in order to inhibit the current harmonic on the x-y sub-plane, the large vector, the medium-large vector and the small vector are only needed to be offset to be 0 on the x-y sub-plane, and the harmonic current can be weakened; since the action time of each of the large vector, the medium vector and the small vector is different, in order to ensure that the offset on the x-y sub-plane is 0, the action time of the large vector, the medium vector and the small vector needs to be calculated;
calculating the action time of the large vector, the medium vector and the small vector according to the magnitude of each vector on the alpha-beta sub-plane, as shown in formulas (6) to (9):
vv i ＝t 1 v large +t 2 v medium-large (6)
t 1 v small +t 2 v medium-large ＝0 (7)
vv i+12 ＝t 3 v medium-large +t 4 v small (8)
t 3 v medium-large +t 4 v large ＝0 (9)
in the formula, vv i Is a virtual composite vector of the large vector and the medium large vector on the alpha-beta sub-plane; vv i+12 Is a virtual composite vector of the medium and small vectors on the alpha-beta sub-plane, t 1 、t 2 Is the resultant action time of large vector and medium-large vector, t 3 、t 4 Is the resultant action time of medium and small vectors, v large 、v medium-large 、v small The amplitudes of the large vector, the medium-large vector and the small vector are respectively; t is calculated from the expressions (6) to (9) 1 ＝0.73T s 、t 2 ＝0.27T s 、t 3 ＝0.58T s 、t 4 ＝0.42T s Wherein T is s Is the sampling period.
Further, in step 4, electromagnetic torque is controlled on an alpha-beta sub-plane, harmonic current is suppressed on an x-y sub-plane, and a cost function g of the double three-phase permanent magnet synchronous motor is represented by an equation (10):
g＝|i * α -i α (k+1)|+|i * β -i β (k+1)|+|i * x -i x (k+1)|+|i * y -i y (k+1)| (10)
in the formula i α 、i β 、i * α 、i * β Reference current and k +1 order prediction current, i, of the alpha-beta plane, respectively x 、i y 、i * x 、i * y Respectively, the reference current and the k +1 order prediction current for the x-y sub-plane.
Further, step 5 first performs reference voltage vector calculation:
deducing a discretization model of the double three-phase permanent magnet synchronous motor by adopting a forward Euler formula, calculating the k-order voltage of a dq axis on an alpha-beta plane, and using v d (k) And v q (k) The calculation method is shown as formula (11):
in the formula R S Denotes the stator resistance, L d 、L q Representing the components of the inductance in the d and q axes, i d (k)、i d (k+1)、i q (k)、i q (k + 1) predicted currents of k order and k +1 order of dq axis, respectively, e d 、e q Are dq-axis back electromotive forces, respectively; in the formula, the k +1 order predicted current is calculated by formula (12):
ω e for the rotor electrical angular velocity, the voltage of the k-th order of the dq axis in the alpha-beta plane is respectively v d (k) And v q (k) Represents;
to compensate the control delay, the dq axis k +2 order predicted current value is further calculated according to the Euler discrete formula, as shown in formula (13):
reference current i according to dq axis d ref And i d ref And k +2 order predicted current value, and calculating to obtain a reference voltage value v of dq axis d ref And v q ref As shown in formula (14):
then, according to the reference voltage v d ref And v q ref Calculating the amplitude of a reference voltage, and calculating the phase angle of the reference voltage on an alpha-beta plane of a stationary coordinate system, wherein the amplitude of the reference voltage is v d ref And v q ref Is open root, the phase angle tan theta = v of the reference voltage d ref /v q ref (ii) a After the phase angle theta of the reference voltage is obtained, the sector where the voltage vector is located is determined according to the phase angle theta, and the sector where the cost function is minimum and the voltage vector is located is selectedDetermining the position of the region, determining the resultant alpha-beta plane virtual voltage vector vv i 、vv i+12 。
Calculating a reference voltage value d of dq axis on x-y plane d ref And d q ref ：
e dxy 、e qxy Respectively are d-axis counter electromotive force and q-axis counter electromotive force on an x-y plane;
then, according to the reference voltage value d d ref And d q ref Calculating the amplitude of the reference voltage and calculating the phase angle of the reference voltage on the x-y plane of the stationary coordinate system, the amplitude of the reference voltage being d d ref And d q ref Root of square sum, phase angle tan θ = d of reference voltage d ref /d q ref (ii) a After a reference voltage phase angle theta is solved, determining the sector according to the phase angle theta, selecting the sector position where the cost function is minimum and the synthetic voltage vector is located, and determining the virtual voltage vector vv on the synthetic x-y plane i 、vv i+12 。
Compared with the prior art, the invention has the beneficial effects that: the invention provides an MPC control method based on biplane virtual voltage vectors, which fully utilizes voltage vectors on two planes of alpha-beta and x-y, respectively synthesizes large vectors and medium-large vectors in the two planes into 12 virtual voltage vectors, synthesizes the medium-large vectors and small vectors into 12 virtual voltage vectors, and adds zero vectors, namely, the two planes respectively contain 25 virtual voltage vectors. The virtual voltage vector of the alpha-beta plane is used for electromechanical energy conversion to generate appropriate electromagnetic torque, and the virtual voltage vector of the x-y plane is used for inhibiting harmonic current to improve the system efficiency. The biplane prediction control method fully utilizes the voltage vectors of the two planes, improves the control precision, reduces the torque pulsation and greatly improves the control performance while ensuring the output power of the motor. The invention is also applicable to common multi-phase permanent magnet motors.
Drawings
FIG. 1 is a dual three-phase motor drive topology;
FIG. 2 is a vector diagram of the alpha-beta sub-plane and x-y sub-plane spatial voltages;
FIG. 3 is an alpha-beta plane synthetic virtual voltage vector diagram;
FIG. 4 is an x-y plane synthetic virtual voltage vector diagram;
FIG. 5 is a block diagram of model predictive control based on vectors of biplane virtual voltages;
FIG. 6 (a) is a steady-state simulation waveform diagram of VV13, FIG. 6 (b) is a dynamic simulation waveform diagram of VV13, FIG. 6 (c) is a steady-state waveform diagram of VV25-Bi, and FIG. 6 (d) is a dynamic waveform diagram of VV 25-Bi;
FIG. 7 is a waveform diagram of motor experiment at a rotation speed of 350 r/min;
fig. 8 is a waveform diagram of motor experiment when increasing and decreasing load.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
The double three-phase permanent magnet synchronous motor is also called as an asymmetric six-phase permanent magnet synchronous motor, and the phase belt angle of the motor is 30 degrees, which is the same as that of a symmetric twelve-phase motor. Each phase of stator winding of the double three-phase motor is respectively connected with six bridge arms of the inverter, and a driving topological diagram of the double three-phase motor is shown in figure 1.
Because the phase belt angle of the double three-phase motor is 30 degrees, 5-order and 7-order harmonic magnetic potential can be automatically eliminated in the motor, so that 6-order torque pulsation is eliminated, the minimum number of the torque pulsation is increased to 12, the double three-phase motor can effectively inhibit the torque pulsation, and the double three-phase motor is widely applied to industrial production.
The six-phase inverter can be regarded as a three-phase inverter with two neutral points isolated from each other, and the inverter comprises 6 bridge arms in total, and each bridge arm comprises 2 power switching devices. The output state of the six-phase inverter bridge arm can be represented by a vector S]Is represented by [ S ]]＝{S a ,S b ,S c ,S d ,S e ,S f In which S is a 、S b 、S c 、S d 、S e 、S f Respectively showing six bridge armsThe on-off state of (1) is set when the upper arm is on and the lower arm is off, and otherwise is set to 0. Thus, the six-phase inverter has 2 in common 6 =64 switch states.
Similar to a three-phase motor, a vector decoupling method is usually adopted when a mathematical model of the double three-phase motor is analyzed, the Clarke transformation is carried out on the double three-phase motor, and all variables of the motor are mapped to an alpha-beta sub-plane, an x-y sub-plane and an o sub-plane 1 -o 2 Sub-planes, and the three sub-planes are mutually orthogonal. Due to the x-y sub-planes and o 1 -o 2 The sub-planes are orthogonal to the plane of rotation of the air gap flux of the machine, hence x-y, o 1 -o 2 The current components on the sub-planes do not generate rotating magnetic potential, and the current components on the two planes do not participate in the electromechanical energy conversion process. If two three-phase inverters connected in parallel are isolated from each other in the drive system of a double three-phase machine, the three-phase inverter is at o 1 -o 2 The zero sequence current component on the sub-plane is 0, so that the vector sum of the zero sequence current components on the x-y sub-plane is ensured to be 0 by controlling the zero sequence current components on the x-y sub-plane.
Because only the current component on the alpha-beta sub-plane participates in electromechanical energy conversion, only the variable on the alpha-beta sub-plane needs to be subjected to rotating coordinate transformation, and the Clarke-Park total transformation matrix T of the double three-phase motor can be obtained 6sr As shown in formula (1).
In the formula, θ represents the rotor electrical angle. According to Clarke-Park total transformation matrix T 6sr The torque equation of the double three-phase permanent magnet synchronous motor can be obtained as shown in the formula (2).
T e ＝3p n (ψ d i q -ψ q i d ) (2)
In the formula i d 、i q 、Ψ d 、Ψ q Representing the components of stator current and flux linkage in d and q axes, respectively, p n The number of pole pairs of the motor is indicated.
Since six-phase inverters have 64 switch states, the voltage vector that each switch state maps onto the α - β sub-plane and the x-y sub-plane can be represented by equations (3) and (4):
wherein v, v Z Representing the space voltage vector, U, mapped onto the alpha-beta and x-y sub-planes, respectively dc Representing the dc bus voltage of the inverter. The voltage vector diagrams of 64 switch states of the six-phase inverter on the alpha-beta sub-plane and the x-y sub-plane can be drawn by the equations (3) and (4), as shown in fig. 2.
Each plane contains 48 valid vectors, corresponding to 60 switch states, respectively, and 4 zero vectors, corresponding to switch states "0-0, 0-7, 7-0, 7-7". According to the grouping of the voltage vectors, the 48 effective voltage vectors can be divided into 4 regular dodecagons, which are respectively composed of 12 large vectors, 12 medium vectors and 12 small vectors. Substituting equations (3) and (4) according to the conduction states of six bridge arms of the six-phase inverter can obtain 48 effective voltage vectors and 4 zero vectors. And dividing the voltage into a large vector, a medium vector and a small vector according to the magnitude of the effective voltage amplitude.
Because the impedance on the x-y sub-plane is very small, very small harmonic voltage vectors can also generate very large harmonic current on the x-y sub-plane, so the idea of biplane prediction can be introduced, 25 virtual voltage vectors are synthesized on the alpha-beta sub-plane for generating required magnetic flux and torque, and 25 virtual voltage vectors are synthesized on the x-y sub-plane for inhibiting the harmonic current, thereby improving the accuracy and stability of motor control and achieving good control effect.
It is found from fig. 2 that the medium vector v is in the alpha-beta sub-plane 4-6 And a large vector v 6-4 Small vector v 2-5 In phase, but with a large vector v in the x-y sub-plane 4-6 And largeVector v 6-4 Small vector v 2-5 But are in antiphase, so that on the x-y sub-plane, the medium-large vector v 4-6 The resulting flux linkage is also associated with a large vector v 6-4 Sum small vector v 2-5 The resulting flux linkage is reversed. Therefore, in order to suppress the current harmonics on the x-y sub-plane, the large vector, the medium-large vector and the small vector are only needed to be offset to 0 on the x-y sub-plane, so that the harmonic current can be weakened. Since the action times of the large, medium and small vectors are different each, in order to ensure that the cancellation is 0 on the x-y sub-plane, the action times of the large, medium and small vectors need to be calculated. According to the magnitude of each vector on the alpha-beta sub-plane, the action time of the large vector, the medium vector and the small vector can be calculated, as shown in formulas (6) to (9).
vv i ＝t 1 v large +t 2 v medium-large (6)
t 1 v small +t 2 v medium-large ＝0 (7)
vv i+12 ＝t 3 v medium-large +t 4 v small (8)
t 3 v medium-large +t 4 v large ＝0 (9)
In the formula, vv i Is a virtual composite vector of the large vector and the medium large vector on the alpha-beta sub-plane; vv i+12 Is a virtual composite vector of the medium and small vectors on the alpha-beta sub-plane, t 1 、t 2 Is the resultant action time of large vector and medium-large vector, t 3 、t 4 Is the combined action time of a medium-large vector and a small vector, v large 、v medium-large 、v small The amplitudes of the large vector, the medium-large vector and the small vector are respectively; t is calculated from the expressions (6) to (9) 1 ＝0.73T s 、t 2 ＝0.27T s 、t 3 ＝0.58T s 、t 4 ＝0.42T s Wherein T is s Is the sampling period. The alpha-beta plane synthetic virtual voltage vector diagram is shown in figure 3.
Similarly, the large vector and the medium vector are combined into 12 virtual voltage vectors on the x-y sub-plane, the medium vector and the small vector are combined into 12 virtual voltage vectors, the components of the virtual voltage vectors on the alpha-beta sub-plane are 0, the acting time of each vector is calculated, and the x-y plane combined virtual voltage vector diagram is shown in fig. 4.
Model predictive control based on biplane virtual voltage vectors is as follows:
1. and (3) calculating a cost function:
the cost function g of the DTP-PMSM is expressed by equation (10) in view of controlling the electromagnetic torque on the α - β sub-plane and suppressing the harmonic current on the x-y sub-plane.
g＝|i * α -i α (k+1)|+|i * β -i β (k+1)|+|i * x -i x (k+1)|+|i * y -i y (k+1)| (10)
2. Reference voltage vector calculation:
the discretization model of the double three-phase permanent magnet synchronous motor is deduced by adopting a forward Euler formula, so that the k-order voltage of a dq axis on an alpha-beta plane can be calculated by using v d (k) And v q (k) The calculation method is shown as formula (11).
In the formula i d (k)、i d (k+1)、i q (k)、i q (k + 1) predicted currents of order k and order k +1 of dq axis, e d 、e q Respectively dq-axis back emf. In the formula, the predicted current of the k +1 order is calculated by formula (12):
in order to reduce the calculation workload, improve the control rapidity and compensate the control delay, the dq axis k +2 order predicted current value can be further calculated according to an Euler discrete formula, as shown in formula (13).
Reference current i according to dq axis d ref And i d ref And k +2 order predicted current value, and reference voltage value v of dq axis can be calculated d ref And v q ref As shown in equation (14).
Then, according to the reference voltage v d ref And v q ref Calculating the amplitude of a reference voltage, and calculating the phase angle of the reference voltage on an alpha-beta plane of a stationary coordinate system, wherein the amplitude of the reference voltage is v d ref And v q ref Root of square sum, phase angle tan θ = v of reference voltage d ref /v q ref (ii) a After a reference voltage phase angle theta is obtained, determining a sector where the reference voltage phase angle theta is located according to the phase angle theta, selecting the sector where the cost function is minimum and the synthetic voltage vector is located, and determining a synthetic alpha-beta plane virtual voltage vector vv i 、vv i+12 。
Similarly, on the x-y plane, the k-order voltage of the dq axis can be calculated according to the discretization model of the motor, and d is used d (k) And d q (k) The calculation method is shown in formula (15).
In the formula i dxy (k)、i dxy (k+1)、i qxy (k)、i qxy (k + 1) predicted currents of order k and k +1 of dq axis on the x-y plane, e dxy 、e qxy Respectively, dq-axis back emf in the x-y plane. The predicted current of the k +1 order in the equation can be calculated by equation (16).
And further calculating the dq axis k +2 order predicted current value according to an Euler discrete formula, as shown in formula (17).
Because of the need to suppress torque ripple in the x-y plane, the dq-axis reference current i in the x-y plane dxy ref And i dxy ref Should be 0, the reference voltage value d of the dq axis on the x-y plane can be calculated according to equation (18) d ref And d q ref 。
Then, according to the reference voltage value d d ref And d q ref Calculating the amplitude of the reference voltage and calculating the phase angle of the reference voltage on the x-y plane of the stationary coordinate system, the amplitude of the reference voltage being d d ref And d q ref Root of square sum, phase angle tan θ = d of reference voltage d ref /d q ref (ii) a After a reference voltage phase angle theta is solved, determining the sector according to the phase angle theta, selecting the sector position where the cost function is minimum and the synthetic voltage vector is located, and determining the virtual voltage vector vv on the synthetic x-y plane i 、vv i+12 。
The double three-phase permanent magnet synchronous motor is subjected to Clarke-Park conversion, k +2 order prediction currents are respectively calculated on an alpha-beta plane and an x-y plane, reference voltage vectors on the two planes are obtained after the prediction currents are compared with the reference currents, the optimal synthetic voltage vectors are respectively selected on the two planes through a cost function, and the virtual voltage vector vv on the alpha-beta plane i 、vv i+12 Generating electromagnetic torque, driving the motor to run after PWM conversion, and generating virtual voltage vector vv in the x-y plane i 、vv i+12 Harmonic currents are suppressed. Vector based on biplane virtual voltagesThe model predictive control block diagram is shown in fig. 5.
In order to prove the correctness of the method, simulation is carried out in an MATLAB/Simulink environment, a double three-phase permanent magnet synchronous motor is used as a control object in the simulation, the sampling frequency is set to be 10KHz, and table 1 shows simulation parameters of the double three-phase permanent magnet synchronous motor. The simulation results are shown in fig. 6, in which (a) is a VV13 steady-state waveform diagram in which 13 predicted voltage vectors are synthesized only in the α - β plane; graph (b) is a VV13 dynamic waveform diagram; FIG. (c) is a diagram of VV25-Bi steady state waveforms for 25 predicted voltage vectors synthesized in the alpha-beta and x-y biplanes, respectively; FIG. d is a diagram showing the VV25-Bi dynamic waveform. In the figure, n (r/min) represents the rotation speed, uabcdef (V) represents the 6-phase voltage, and Te (n.m) represents the electromagnetic torque.
TABLE 1 simulation parameters of dual three-phase PMSM
Firstly, the steady-state performance of the motor under the conditions of 400r/min and 15N 9632m of torque is researched in a simulation mode, and the fact that the phase current waveform distortion is seriously changed in the VV13 method compared with the VV25-Bi control method can be found from the graph, which shows that the VV13 method only inhibits the harmonic current of an x-y plane to a certain extent, but the inhibition effect is obviously poorer than the two latter methods. Compared with the VV13 method, the phase current waveform of the VV25-Bi is closer to a sine wave, and the fact that the harmonic waves in the phase current of the motor can be effectively restrained by adopting the biplane synthesized virtual voltage vector is shown, and the system efficiency is improved.
Secondly, the dynamic performance of the motor under the condition of increasing load torque is researched by simulation. It can be found from the figure that by adopting the VV25-Bi method, the response of the motor rotating speed is faster, the overshoot is smaller, the set torque can be quickly reached, and the motor rotating speed drop is smaller when a load is suddenly applied. When the VV13 method is adopted, the rotating speed response of the motor is slow, the overshoot is large, and the rotating speed drop of the motor is maximum when a load is suddenly added, because the VV13 method only uses a large vector and a medium large vector to synthesize a predicted voltage vector on a single plane, and does not fully utilize all voltage vectors of double planes, the anti-interference capability of the motor is weaker, and the dynamic response characteristic is poorer.
In order to verify the steady-state performance of the motor, the steady-state performance of the motor is verified by using an experimental platform, and at the rotating speed of 350r/min, an experimental waveform diagram of the motor is shown in fig. 7, wherein fig. 7 (a) is a waveform diagram under a VV13 method, fig. 7 (b) is a waveform diagram under a VV25-Bi method, n (350 r/min/div) expresses the rotating speed, te (20N.m/div) expresses the electromagnetic torque, ia expresses a-phase current, and id expresses d-phase current. In the figure, the rotating speed n, the electromagnetic torque Te and the phase current i are respectively shown from top to bottom a 、i d And (6) wave-form. From the figure, it is found that when the motor works at 350r/min, the phase current waveform distortion of the method adopting the VV13 is more serious, which shows that the phase current of the motor contains more harmonic current, and besides, the pulsation of the motor speed and torque is also more serious than that of the method adopting the VV25-Bi, because the method adopting the VV13 only uses a large vector and a medium vector to synthesize a prediction vector on a single plane, and the voltage vector of the motor is not fully utilized to suppress the harmonic current on an x-y plane, so that the larger harmonic current and the larger torque pulsation are formed. Under the VV25-Bi method, the phase current waveform is smoother and more approaches to a sine wave, the motor rotating speed and torque pulsation are smaller, and the harmonic content in the phase current is less, so that good stability is represented.
In order to verify the dynamic performance of the motor, an experiment of the influence of sudden increase and sudden decrease of the load on the rotating speed, the electromagnetic torque and the phase current of the motor is carried out, and the experimental waveform is shown in fig. 8. In the case of the VV13 method, FIG. 8 (a) is a waveform diagram, and in the case of the VV25-Bi method, FIG. 8 (b) is a waveform diagram, where n (350 r/min/div) represents the rotation speed, te (20N.m/div) represents the electromagnetic torque, and ia represents the a-phase current. In the figure, the rotation speed n, the electromagnetic torque Te and the phase current i are shown from top to bottom a 、i d And (6) wave-form. From the graph, it can be found that when the load suddenly increases or suddenly decreases, the VV25-Bi method has the advantages of faster motor speed and torque response, smaller overshoot and better power quality. And the motor torque rising slope of VV13 is smaller, the response speed is slower, and the overshoot amount is also larger. This is because the VV13 does not fully utilize the voltage vectors of the two planes to control the motor.
In conclusion, compared with the VV13 method, the method has the advantages that the motor harmonic content of VV25-Bi is less, the dynamic response speed of the motor is higher, the overshoot is smaller, the good control characteristic is shown, and the method can better inhibit the harmonic current of an x-y plane.
In addition to the above embodiments, the present invention may have other embodiments, and all technical solutions formed by equivalent substitutions or equivalent transformations fall within the scope of the present invention.
Claims (6)
1. A model prediction control method for a double three-phase permanent magnet synchronous motor is characterized by comprising the following steps:
step 1: establishing a mathematical model of the double three-phase motor: clarke transformation is carried out on the double three-phase motor, and each variable of the motor is mapped to an alpha-beta sub-plane, an x-y sub-plane and an o 1 -o 2 The three sub-planes are mutually orthogonal to obtain a Clarke-Park total transformation matrix of the double three-phase motor;
step 2: calculating space voltage vectors of the alpha-beta sub-plane and the x-y sub-plane;
and step 3: and (3) biplane virtual voltage vector synthesis is respectively carried out on an alpha-beta plane and an x-y plane: in order to improve the control accuracy, the switching state of the inverter is fully utilized, the large vector and the medium vector are combined into 12 virtual voltage vectors, the medium vector and the small vector are combined into 12 virtual voltage vectors, and the sum of the 12 virtual voltage vectors and the zero vector is 25 vectors which are called as VV25; the large vector, the medium vector and the small vector are divided according to the length of the vectors, the longest vector is the large vector, the shortest vector is the small vector, and the medium vector is the medium vector;
and 4, step 4: designing a cost function g of the predictive control of the biplane virtual voltage vector model;
and 5: respectively calculating reference voltage vectors of dq axes on an alpha-beta plane and an x-y plane, calculating the amplitude of the reference voltage according to the reference voltage value, calculating the phase angle theta of the reference voltage, determining the sector where the reference voltage is located according to the phase angle theta, and then selecting a synthetic virtual voltage vector vv of the alpha-beta plane and the x-y plane with the minimum cost function g i 、vv i+12 ；
Step 6: resulting virtual voltage vector in the alpha-beta plane vv i 、vv i+12 Generating electromagnetic torque, driving the motor to run after PWM conversion, and generating a synthetic virtual voltage vector vv on an x-y plane i 、vv i+12 Harmonic currents are suppressed.
2. The model predictive control method for a double three-phase permanent magnet synchronous motor according to claim 1, wherein step 1 is performed by using Clarke-Park total transformation matrix T of the double three-phase motor 6sr Comprises the following steps:
in the formula, theta is the rotor electrical angle; according to Clarke-Park total transformation matrix T 6sr The torque equation of the obtained double three-phase permanent magnet synchronous motor is shown as the formula (2):
T e ＝3p n (ψ d i q -ψ q i d ) (2)
in the formula i d 、i q Representing the components of the stator current in the d and q axes, Ψ d 、Ψ q Representing the components of the flux linkage in the d and q axes, p n The number of pole pairs of the motor is indicated.
3. The model predictive control method of a double three-phase permanent magnet synchronous motor according to claim 1, characterized in that the space voltage vector calculation formulas of the α - β sub-plane and the x-y sub-plane in step 2 are as follows:
since six-phase inverters have 64 switch states, the voltage vectors that each switch state maps onto the α - β sub-plane and the x-y sub-plane are represented by equations (3) and (4) as follows:
in the formula v, v Z Representing the space voltage vector, U, mapped onto the alpha-beta and x-y sub-planes, respectively dc Representing the direct current bus voltage of the double three-phase motor driving inverter; s. the a 、S b 、S c 、S d 、S e 、S f Respectively showing the switching states of the six bridge arms.
4. The model predictive control method of a double three-phase permanent magnet synchronous motor according to claim 1, characterized in that in step 3: calculating the action time of the large vector, the medium vector and the small vector according to the magnitude of each vector on the alpha-beta sub-plane, as shown in formulas (6) to (9):
vv i ＝t 1 v large +t 2 v medium-large (6)
t 1 v small +t 2 v medium-large ＝0 (7)
vv i+12 ＝t 3 v medium-large +t 4 v small (8)
t 3 v medium-large +t 4 v large ＝0 (9)
in the formula, vv i Is a virtual composite vector of the large vector and the medium large vector on the alpha-beta sub-plane; vv i+12 Is a virtual composite vector of the medium and small vectors on the alpha-beta sub-plane, t 1 、t 2 Is the resultant action time of large vector and medium-large vector, t 3 、t 4 Is the combined action time of a medium-large vector and a small vector, v large 、v medium-large 、v small The amplitudes of the large vector, the medium-large vector and the small vector are respectively; t is calculated from the expressions (6) to (9) 1 ＝0.73T s 、t 2 ＝0.27T s 、t 3 ＝0.58T s 、t 4 ＝0.42T s Wherein T is s Is the sampling period.
5. The model predictive control method for a dual three-phase permanent magnet synchronous motor according to claim 1, wherein the cost function g in step 4 is:
g＝|i * α -i α (k+1)|+|i * β -i β (k+1)|+|i * x -i x (k+1)|+|i * y -i y (k+1)| (10)
in the formula i α 、i β 、i * α 、i * β Reference current and predicted current of k +1 level, i, of the alpha-beta plane, respectively x 、i y 、i * x 、i * y Respectively, the reference current and the k +1 order prediction current for the x-y sub-plane.
6. The model predictive control method for the double three-phase permanent magnet synchronous motor according to claim 1, wherein the reference voltage vector calculation method in step 5 is as follows: deducing a discretization model of the double three-phase permanent magnet synchronous motor by adopting a forward Euler formula, calculating the k-order voltage of a dq axis on an alpha-beta plane, and using v d (k) And v q (k) The calculation method is shown as formula (11):
in the formula R S Denotes the stator resistance, L d 、L q Representing the components of the inductance in the d and q axes, i d (k)、i d (k+1)、i q (k)、i q (k + 1) predicted currents of order k and order k +1 of dq axis, e d 、e q Dq-axis back electromotive force respectively; in the formula, the predicted current of the k +1 order is calculated by formula (12):
ω e for the rotor electrical angular velocity, the voltage of the k-th order of the dq axis in the alpha-beta plane is respectively v d (k) And v q (k) Representing;
in order to compensate the control delay, a dq axis k +2 order predicted current value is further calculated according to an Euler discrete formula, as shown in formula (13):
reference current i according to dq axis d ref And i d ref And k +2 order predicted current value, and calculating to obtain the reference voltage value v of dq axis d ref And v q ref As shown in formula (14):
then, according to the reference voltage v d ref And v q ref Calculating the amplitude of the reference voltage and calculating the phase angle of the reference voltage on the alpha-beta plane of the stationary coordinate system, wherein the amplitude of the reference voltage is v d ref And v q ref Is open root, the phase angle tan theta = v of the reference voltage d ref /v q ref (ii) a After a reference voltage phase angle theta is obtained, determining a sector where the reference voltage phase angle theta is located according to the phase angle theta, selecting the sector where the cost function is minimum and the synthetic voltage vector is located, and determining a synthetic alpha-beta plane virtual voltage vector vv i 、vv i+12 ；
Calculating a reference voltage value d of dq axis on x-y plane d ref And d q ref ：
e dxy 、e qxy Respectively are d-axis counter electromotive force and q-axis counter electromotive force on an x-y plane;
then, according to the reference voltage value d d ref And d q ref Is calculated to the reference voltage amplitude and is at restCalculating the phase angle of a reference voltage on the x-y plane of the coordinate system, wherein the amplitude of the reference voltage is d d ref And d q ref Is open root, the phase angle tan theta = d of the reference voltage d ref /d q ref (ii) a After a reference voltage phase angle theta is solved, determining the sector according to the phase angle theta, selecting the sector position where the cost function is minimum and the synthetic voltage vector is located, and determining the virtual voltage vector vv on the synthetic x-y plane i 、vv i+12 。
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