阅读说明：本技术 基于矩阵变换器的永磁同步电机调制模型预测控制方法 (Permanent magnet synchronous motor modulation model prediction control method based on matrix converter ) 是由 程启明 叶培乐 谢怡群 周雅婷 傅文倩 程尹曼 于 2021-07-22 设计创作，主要内容包括：本发明涉及一种基于矩阵变换器的永磁同步电机调制模型预测控制方法,采集双级矩阵变换器的三相输入电压电流、滤波器输入电压和三相输出电流,以及永磁同步电机的转速和电角度；代入输入电流和输出电压预测模型；将整流级有效矢量代入整流级价值函数,求出整流级最小化价值函数所对应的占空比；利用输出电压和三角函数,求出输出电压所在扇区；通过逆变级价值函数,求出逆变级最小化价值函数所对应的占空比；将整流级和逆变级进行协调控制,运用开关序列,实现矩阵变换器-永磁同步电机的控制。本发明方法能够在保证PMSM运行在额定转速的前提下,提高系统的快速性和鲁棒性；减小系统计算负担,更好地改善波形质量,具有更低的电流纹波。(The invention relates to a matrix converter-based permanent magnet synchronous motor modulation model prediction control method, which comprises the steps of collecting three-phase input voltage current, filter input voltage and three-phase output current of a two-stage matrix converter, and the rotating speed and the electrical angle of a permanent magnet synchronous motor; substituting the input current and the output voltage prediction model; substituting the effective vector of the rectification stage into a rectification stage cost function to obtain a duty ratio corresponding to the minimum cost function of the rectification stage; calculating the sector of the output voltage by using the output voltage and a trigonometric function; calculating the duty ratio corresponding to the inverter minimum cost function through the inverter cost function; and carrying out coordination control on the rectification stage and the inversion stage, and realizing the control of the matrix converter-permanent magnet synchronous motor by using a switch sequence. The method can improve the rapidity and the robustness of the system on the premise of ensuring that the PMSM runs at the rated rotating speed; the system computing burden is reduced, the waveform quality is better improved, and the current ripple is lower.)

1. A permanent magnet synchronous motor modulation model predictive control method based on a matrix converter is characterized in that a three-phase voltage source drives a permanent magnet synchronous motor after sequentially passing through an LC filter, a rectification stage of the matrix converter and an inversion stage of the matrix converter;

the control method comprises the following steps:

three-phase voltage source voltage u_s(k) Current i_s(k) And a filter output voltage u_i(k) Substituting the input current prediction model to obtain the predicted power supply voltage u of the next period_s(k+1)、Current i_s(k +1), and then carrying out Park conversion to obtain a voltage u under an alpha beta coordinate system_sαβ(k +1), current i_sαβ(k +1), finally substituting into the value function of the rectification stage of the matrix converter to obtain the optimal adjacent current effective vector I corresponding to the minimum value function of the rectification stage_μAnd I_vDuty ratio d of_μAnd d_v；

Inverter stage of matrix converter outputs three-phase current i_o(k) Carrying out Clark conversion and Park conversion to obtain dq axis current i_odq(k) Then substituting the model into the output voltage prediction model to obtain the dq axis predicted output voltageThen, carrying out Park conversion to obtain the voltage under an alpha-beta coordinate systemAccording toSelecting voltage sector to obtain sector n of output voltage, and determining effective voltage vector U_m、U_n，U₀Is a zero vector and will finallySubstituting the value function into the inverter stage to obtain 3 effective voltage vectors U corresponding to the minimum value function of the inverter stage_m、U_nAnd U₀Duty ratio d of_m、d_nAnd d₀；

And finally, the duty ratios of the rectification stage and the inversion stage of the matrix converter are coordinated and matched to obtain a switching sequence, and the switching sequence is finally applied to the whole driving system.

2. The modulation model predictive control method for the PMSM based on the matrix converter as claimed in claim 1, wherein the rectification stage structure of the matrix converter comprises a, b, c three-phase bridge arms and a phaseThe bridge arm comprises a switch S which is sequentially connected from top to bottom_apAnd S_anThe b-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_bpAnd S_bnThe c-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_cpAnd S_cn；

The input current prediction model is as follows:

wherein the content of the first and second substances,

in the formula: t is_sIs the sampling time; k is a sampling interval; r_f、L_f、C_fThe LC filter comprises a resistor, an inductor and a capacitor; i.e. i_iInputting current for a rectifier stage; i is a unit vector;

cost function g of said rectifier stage_r＝d_μg_rμ+d_vg_rv，

In the formula: g_rμ、g_rvAre respectively I_μ、I_vA cost function of (a);

3. the matrix converter-based permanent magnet synchronous motor modulation model predictive control method of claim 2, wherein the inverter stage structure of the matrix converter comprises a three-phase bridge arm A, a three-phase bridge arm B and a three-phase bridge arm C, and the bridge arm A comprises switches S sequentially connected from top to bottom_ApAnd S_AnThe B-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_BpAnd S_BnThe C-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_CpAnd S_Cn；

The output voltage prediction model is as follows:

in the formula:predicting output voltages for d and q axes respectively; i.e. i_od、i_oqThe current components of d and q axes of the stator are respectively; l is_d、L_qD-axis and q-axis inductors respectively; r_s、ω_ePsi is stator resistance, electrical angular velocity, flux linkage, respectively;

the judgment mode of the sector where the output prediction voltage vector is located is as follows:

in the formula: theta^pPredicting the included angle corresponding to the sector where the voltage vector is located;output predicted voltage under an alpha coordinate system and a beta coordinate system;

predicted output voltage limit:

in the formula:predicting a reference voltage for the d-axis;predicting a reference voltage for the q-axis;predicting output voltage limit values for d and q axes;

a single inversion level cost function;

in the formula: u. of_oαref、u_oβrefAlpha and beta axis voltage components, respectively;predicting a reference voltage for an alpha axis;the reference voltage is predicted for the beta axis.

Technical Field

The invention relates to an electric transmission technology, in particular to a permanent magnet synchronous motor modulation model prediction control method based on a matrix converter.

Background

The Permanent Magnet Synchronous Motor (PMSM) has the advantages of simple structure, stable operation, small volume and high efficiency, and the PMSM is widely applied to the fields of civil manufacturing industry, aerospace and military along with the continuous improvement of material technology and control technology. The traditional power electronic driving device of the permanent magnet synchronous motor, such as a DC-AC inverter, an AC-DC-AC-DC-AC converter and the like, has the defects of low voltage transmission ratio, overlarge volume of an intermediate direct current capacitor, incapability of integration and the like.

An Indirect Matrix Converter (IMC) is a derivative topology of a Matrix Converter (MC) and has the following advantages compared to a conventional ac-dc-ac power Converter: input current and output current are sinusoidal, and harmonic content is small; the input power factor is adjustable, and generally, in order to reduce the reactive power of an input power grid, the power factor is set to be 1; the energy can flow in two directions, and the four-quadrant operation requirements of various complex transmission systems are met; and fourthly, no intermediate direct-current energy storage link exists, the size of the power converter is reduced, and the power density of the system is improved. Due to the advantages and characteristics of the IMC, the IMC is very suitable for forming an indirect matrix converter-motor speed regulating system by driving motors.

Permanent Magnet Synchronous Motor (PMSM) control systems mostly employ basic vector control and direct torque control methods. Vector control can decouple the alternating current and direct current components of stator current, decoupling control of a magnetic field and torque is achieved, the vector control is widely applied to motor control, a control mode mostly adopts double closed-loop control, namely an outer loop speed loop and an inner loop current loop, a controller of the vector control generally adopts a PID (proportion integration differentiation) regulator, but the PMSM is a nonlinear and strong-coupling system, and when external disturbance or motor parameters change, the control effect is greatly influenced.

Model Predictive Control (MPC) is a time domain Control method that solves the problem of constrained nonlinear system Control. The international automatic control union considers predictive control to be the most important control method after PID control, system identification, estimation and filtering in an investigation report issued in 2019 in 4 months, and is also considered to be the most influential control method in the future. While Finite Set model predictive Control (FCS-MPC) is widely used due to its intuitive concept, easy implementation, and simplified system constraints. The FCS-MPC uses a mathematical model of the system to predict the behavior at the next time and then selects the best switching vector by defining a predefined cost function based on the desired control objective. However, due to the lack of a modulation module, selecting and applying only a single switching vector to each switching state may cause the switching frequency of the MPC to change, thereby causing the system spectrum to expand and degrading the waveform quality of the system. Therefore, in order to fix the switching frequency, Modulation Model Predictive Control (MMPC) is introduced, the performance of MPC is improved by adding a space vector Modulation technique to the FCS-MPC algorithm, and the method is successfully applied to Direct matrix converters (Direct MC, DMC) and Indirect matrix converters (Indirect MC, IMC). Although the MMPC is successfully applied to the MC and the PMSM, the MMPC method has large calculation amount and high requirement on a hardware system, thereby limiting practical application.

Disclosure of Invention

In order to further improve the driving efficiency of the permanent magnet synchronous motor, a matrix converter-based permanent magnet synchronous motor modulation model prediction control method is provided, an MMPC method is improved, and the MMPC method is combined with MC and PMSM, so that the system calculation amount and the execution time are effectively reduced, and the waveform quality is improved.

The technical scheme of the invention is as follows: a permanent magnet synchronous motor modulation model predictive control method based on a matrix converter,

the three-phase voltage source drives the permanent magnet synchronous motor after sequentially passing through the LC filter, the rectification stage of the matrix converter and the inversion stage of the matrix converter;

the control method comprises the following steps:

three-phase voltage source voltage u_s(k) Current i_s(k) And a filter output voltage u_i(k) Substituting the input current prediction model to obtain the predicted power supply voltage u of the next period_s(k +1), current i_s(k +1), and then carrying out Park conversion to obtain a voltage u under an alpha beta coordinate system_sαβ(k +1), current i_sαβ(k +1), finally substituting into the value function of the rectification stage of the matrix converter to obtain the optimal adjacent current effective vector I corresponding to the minimum value function of the rectification stage_μAnd I_vDuty ratio d of_μAnd d_v；

Inverter stage of matrix converter outputs three-phase current i_o(k) Carrying out Clark conversion and Park conversion to obtain dq axis current i_odq(k) Then substituting the model into the output voltage prediction model to obtain the dq axis predicted output voltageThen, carrying out Park conversion to obtain the voltage under an alpha-beta coordinate systemAccording toSelecting voltage sector to obtain sector n of output voltage, and determining effective voltage vector U_m、U_n，U₀Is a zero vector and will finallySubstituting into the value function of the inverter stage to calculate the minimum value of the inverter stage3 voltage effective vectors U corresponding to the cost function_m、U_nAnd U₀Duty ratio d of_m、d_nAnd d₀；

And finally, the duty ratios of the rectification stage and the inversion stage of the matrix converter are coordinated and matched to obtain a switching sequence, and the switching sequence is finally applied to the whole driving system.

Further, the rectification stage structure of the matrix converter comprises a three-phase bridge arm a, a three-phase bridge arm b and a three-phase bridge arm c, wherein the a-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_apAnd S_anThe b-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_bpAnd S_bnThe c-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_cpAnd S_cn；

The input current prediction model is as follows:

wherein the content of the first and second substances,

in the formula: t is_sIs the sampling time; k is a sampling interval; r_f、L_f、C_fThe LC filter comprises a resistor, an inductor and a capacitor; i.e. i_iInputting current for a rectifier stage; i is a unit vector;

cost function g of said rectifier stage_r＝d_μg_rμ+d_vg_rv，

In the formula:g_rμ、g_rvare respectively I_μ、I_vA cost function of (a);

furthermore, the inverter stage structure of the matrix converter comprises three-phase bridge arms A, B and C, wherein the bridge arm A comprises a switch S which is sequentially connected from top to bottom_ApAnd S_AnThe B-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_BpAnd S_BnThe C-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_CpAnd S_Cn；

The output voltage prediction model is as follows:

in the formula:predicting output voltages for d and q axes respectively; i.e. i_od、i_oqThe current components of d and q axes of the stator are respectively; l is_d、L_qD-axis and q-axis inductors respectively; r_s、ω_ePsi is stator resistance, electrical angular velocity, flux linkage, respectively;

the judgment mode of the sector where the output prediction voltage vector is located is as follows:

in the formula: theta^pPredicting the included angle corresponding to the sector where the voltage vector is located;output predicted voltage under an alpha coordinate system and a beta coordinate system;

predicted output voltage limit:

in the formula:predicting a reference voltage for the d-axis;predicting a reference voltage for the q-axis;predicting output voltage limit values for d and q axes;

a single inversion level cost function;

in the formula: u. of_oαref、u_oβrefAlpha and beta axis voltage components, respectively;predicting a reference voltage for an alpha axis;the reference voltage is predicted for the beta axis.

The invention has the beneficial effects that: compared with a matrix converter-permanent magnet synchronous motor control system, the permanent magnet synchronous motor modulation model prediction control method based on the matrix converter improves dynamic response and shortens transient time; the invention introduces a modulation model predictive control method, reduces the complexity of the system and is simple to realize; the invention combines the matrix converter and the modulation model predictive control method of the PMSM, and can improve the rapidity and the robustness of the system on the premise of ensuring that the PMSM runs at the rated rotating speed; the invention adopts an improved model predictive control method for the two-stage matrix converter, better improves the waveform quality by reducing the calculation burden of the system, and has lower current ripple.

Drawings

FIG. 1 is a topological structure diagram of an indirect matrix converter-permanent magnet synchronous machine (IMC-PMSM) of the present invention;

FIG. 2 is a block diagram of a conventional finite set model predictive control (FCS-MPC) applied to an IMC-PMSM control;

FIG. 3 is a control block diagram of a conventional MMPC applied to an IMC-PMSM;

FIG. 4 is a switch sequence diagram;

FIG. 5 is a control block diagram of the improved MMPC applied to the IMC-PMSM;

FIG. 6 is an output voltage vector diagram;

FIG. 7 is an exploded view of a predicted voltage vector;

FIG. 8a is a diagram of the rotation speed of an FCS-MPC based motor according to an embodiment;

FIG. 8b is a graph of motor speed based on a conventional MMPC;

FIG. 8c is the motor speed based on the modified MMPC;

FIG. 9a is a graph of output A-phase current based on FCS-MPC;

FIG. 9b is a graph of the output A-phase current based on a conventional MMPC;

FIG. 9c shows the output A-phase current based on the modified MMPC;

FIG. 10a is a graph of output A-phase current THD based on FCS-MPC;

FIG. 10b is a graph of the output A-phase current THD based on a conventional MMPC;

FIG. 10c shows the output A-phase current THD based on the modified MMPC;

FIG. 11a shows the rotation speed of a motor based on FCS-MPC when the load is constant and the rotation speed is changed;

FIG. 11b shows the motor speed based on a conventional MMPC with constant load and varying speed;

FIG. 11c shows the motor speed based on the modified MMPC with constant load and varying speed;

FIG. 12a is a graph showing the output A-phase current of the FCS-MPC with constant load and varying speed;

FIG. 12b is the output A-phase current of a conventional MMPC with constant load and varying speed;

FIG. 12c is the output A-phase current of the modified MMPC at constant load and varying speed;

FIG. 13a is a graph of the dq axis current of an FCS-MPC with constant load and varying speed;

FIG. 13b is the dq axis current of a conventional MMPC with constant load and varying speed;

FIG. 13c is the dq axis current for the modified MMPC at constant load and varying speed;

FIG. 14a shows the motor speed of the FCS-MPC with constant speed and varying load torque;

FIG. 14b shows the motor speed of a conventional MMPC with constant speed and varying load torque;

FIG. 14c shows the motor speed for the modified MMPC with constant speed and varying load torque;

FIG. 15a is the output current of FCS-MPC with constant rotation speed and varying load torque;

FIG. 15b is the output current of a conventional MMPC with constant speed and varying load torque;

fig. 15c shows the output current of the modified MMPC with constant rotational speed and varying load torque.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.

Fig. 1 is a topology structure diagram of an indirect matrix converter-permanent magnet synchronous motor IMC-PMSM according to the present invention, and the topology includes a three-phase voltage source, an LC filter, an IMC rectification stage, an IMC inversion stage, and a Permanent Magnet Synchronous Motor (PMSM) in this order.

Switching variable S of rectification stage and inversion stage of IMC_ijIs defined as:

in the formula: i belongs to { a, B, C, A, B, C }, and ABC and ABC are three phases of a rectification input stage and an inversion output stage of the IMC respectively; j belongs to { n, p }, and p and n are an upper bridge arm and a lower bridge arm of the IMC respectively.

In the mathematical model of IMC rectification stage, the DC side voltage u_dcRectifying stage switching variables and input voltage u for IMC_iIs the function of:

u_dc＝[S_ap-S_an S_bp-S_bn S_cp-S_cn]u_i (2)

input current i_iAnd a direct side current i_dcThe relationship is as follows:

in the inverter stage, the DC side current i_dcSwitching variables and output currents i for inverter stages_oI.e.:

i_dc＝[S_Ap-S_An S_Bp-S_Bn S_Cp-S_Cn]i_o (4)

output voltage u_oAnd a DC side voltage u_dcThe relationship is as follows:

in order to ensure safe operation of IMC, the following 3 constraints need to be satisfied: firstly, any two phases at the input side cannot be short-circuited; each phase at the output side can not be opened; ③ the voltage on the direct current side must be positive.

From these constraints, it can be seen that only 3 valid vectors of the rectifier stage satisfy the condition in each sampling period.

The input filter side mathematical model is:

in the formula: l is_f、C_fRespectively a filter inductor and a filter capacitor; u. of_s、i_sAre respectively power supplyVoltage and current.

Because the Model Predictive Control (MPC) is a control algorithm based on a discrete mathematical model, the forward euler method is adopted to discretize the formula (6) to obtain:

wherein the content of the first and second substances,

in the formula: t is_sIs the sampling time; k is a sampling interval; i is a unit vector.

The mathematical model of a Permanent Magnet Synchronous Motor (PMSM) in a dq coordinate system is as follows:

in the formula: u. of_od、u_oqThe d-axis voltage component and the q-axis voltage component of the stator are respectively; i.e. i_od、i_oqThe current components of d and q axes of the stator are respectively; l is_d、L_qD-axis and q-axis inductors respectively; r_s、ω_eAnd psi are stator resistance, electrical angular velocity, flux linkage, respectively.

By applying the forward euler method, the discrete mathematical model of the PMSM in the dq coordinate system is as follows:

wherein the content of the first and second substances,

FIG. 2 is a block diagram of a conventional FCS-MPC applied to an IMC-PMSM control. FCS-MPC substitutes IMC rectification stage effective vector into input filter mathematical model (formula (7)) to obtain power supply voltage u_s(k) Current i_s(k) And a filter voltage u_i(k) Substituting the predicted reactive power into an input reactive power prediction model to obtain the predicted reactive power q of the next period_in(k + 1). Substituting the effective vector of the inversion stage into a discrete mathematical model (formula (9)) of the PMSM in the dq coordinate system to obtain an output predicted current value i_o(k) Then, Clark conversion and Park conversion are continued to obtain dq axis current i_odq(k) Substituting the dq axis current into the output current prediction model to obtain the predicted dq axis current i of the next period_odq(k +1), finally combining the IMC rectification stage and the IMC inversion stage by combining the weight factors to obtain a value function of the whole system, and finally applying the value function to the whole system.

The Clark transformation is to convert abc coordinates into stationary alpha and beta coordinates, and the specific formula is as follows:

the cost function of the IMC rectification stage is:

g_r＝|0-(u_sα(k+1)i_sβ(k+1)-u_sβ(k+1)i_sα(k+1))| (11)

in the formula: u. of_sα、u_sβRespectively, the power supply voltage alpha and beta axis voltage components; i.e. i_sα、i_sβRespectively are power supply current alpha and beta axis current components;

because the power supply voltage is a given value of the system, the following can be obtained:

u_s(k+1)＝u_s(k) (12)

the cost function of the IMC inversion stage is:

in the formula:is a d-axis reference current;is a q-axis reference current. Because the motor adopts vector control, the d-axis reference currentq-axis reference currentCan be obtained by a velocity loop.

The value function of the whole indirect matrix converter-permanent magnet synchronous motor system is as follows:

g＝g_i+λg_r (14)

in the formula: λ is a weighting factor.

FIG. 3 is a control block diagram of a conventional MMPC applied to an IMC-PMSM. MMPC requires selection of optimal adjacent effective vector I at rectification stage of IMC_μAnd I_vCorresponding duty cycle, I_iFor current effective vector I of rectifier stage₁～I₆One of them, the subscripts μ, v, represents the best two adjacent ones of the 6 significant vectors. The supply voltage u_s(k) Current i_s(k) And a filter voltage u_i(k) The input current prediction model is brought in to obtain the predicted power of the next periodSource voltage u_s(k +1) and a current i_s(k +1), and carrying out Park conversion to obtain the power supply voltage u under the alpha beta coordinate system_sαβ(k +1) and a current i_sαβ(k +1), and finally substituting the value function into the rectification stage to obtain the optimal adjacent effective vector I_μAnd I_vCorresponding duty cycle d_μAnd d_v. MMPC requires 3 effective vectors U in IMC inversion stage_m、U_nAnd U₀The corresponding duty cycle. Wherein U is_mAnd U_nAre respectively the effective vectors U in FIG. 6₁～U₆，U₀Is a zero vector. Will output three-phase current i_o(k) Carrying out Clark conversion and Park conversion to obtain dq axis current i_odq(k) Then substituting the predicted model of the output current to obtain the predicted current i of the dq axis in the next period_odq(k +1), and finally substituting the value function into the inversion stage to obtain the duty ratio d_m、d_nAnd d₀. And finally, the duty ratios of the rectification stage and the inversion stage are coordinated and matched to obtain a switching sequence, and the switching sequence is finally applied to the whole system. The MMPC rectification stage cost function is defined as:

g_r＝d_μg_rμ+d_vg_rv (15)

in the formula: d_μ、d_vAre respectively adjacent vectors I_μ、I_vDuty cycle of (d); g_rμ、g_rvAre respectively I_μ、I_vA cost function of (2).

Assuming that the duty cycle is inversely related to the cost function, it is defined as follows:

in the formula: k is a proportionality coefficient.

Combining formula (15) and formula (16), eliminating K, d_μAnd d_vThe following can be obtained:

thereby obtaining a minimum cost function g_rminAnd g_rminDuty ratio d of corresponding adjacent vector_μAnd d_v。

The MMPC inverse stage cost function is defined as:

g_i＝d_mg_im+d_ng_in+d₀g_i0 (18)

in the formula: d_m、d_n、d₀Are respectively U_m、U_n、U₀Duty cycle of (d); g_im、g_in、g_i0Are respectively U_m、U_n、 U₀A cost function of (2).

Similar to the IMC rectification stage principle, we can deduce d_m、d_n、d₀Respectively as follows:

thereby obtaining a minimum cost function g_iminAnd g_iminCorresponding duty cycle d_m、d_n、d₀。

Fig. 4 is a switch sequence diagram. The rectification stage and the inversion stage of the IMC cooperate with each other during a sampling period. And when the switch of the rectification stage is switched every time, the inverter stage is in a zero vector state, so that the loss caused by current conversion can be reduced.

In FIG. 4, the duty ratio d₁、d₂、d₃And d₄Is formed by the duty cycle d of the rectifier stage_μ、d_vAnd inverter stage duty cycle d_m、d_nPermutation and combination, which is defined as:

FIG. 5 is a control block diagram of the improved MMPC of the present invention applied to an IMC-PMSM. MMPC requires selection of optimal adjacent effective vector I at rectification stage of IMC_μAnd I_vCorresponding duty cycle of wherein_μAnd I_vRepresenting 6 current effective vectors I of the rectifier stage₁～I₆The most optimal two neighboring active vectors. The supply voltage u_s(k) Current i_s(k) And a filter output voltage u_i(k) Substituting the input current prediction model to obtain the predicted power supply voltage u of the next period_s(k +1), current i_s(k +1), and then carrying out Park conversion to obtain a voltage u under an alpha beta coordinate system_sαβ(k +1), current i_sαβ(k +1), finally substituting into the value function of the rectifier stage to obtain the duty ratio d corresponding to the minimum value function of the rectifier stage_μAnd d_v. MMPC requires 3 effective vectors U in IMC inversion stage_m、U_nAnd U₀The corresponding duty cycle. Wherein U is_m、U_nAnd U₀Is the active vector in fig. 6. U shape_iRespectively a current effective vector U of a rectifier stage₁～U₆Wherein i is m or n. Will invert the stage to output three-phase current i_oCarrying out Clark conversion and Park conversion to obtain dq axis current i_odqThen substituting the model into the output voltage prediction model to obtain the dq axis predicted output voltageThen, carrying out Park conversion to obtain the voltage under an alpha-beta coordinate systemAccording toThe voltage sector selection is performed to obtain the sector n where the output voltage is located, and as can be seen from fig. 6, the obtained sector n can determine the effective vector U of the output voltage_m、U_nAnd finally willSubstituting the value function into the inverter stage to calculate the duty ratio d corresponding to the minimum value function of the inverter stage_m、d_nAnd d₀. Final rectification stageAnd the switching sequence is obtained by coordination and coordination with the duty ratio of the inverter stage and is finally applied to the whole driving system.

The working principle of the IMC-PMSM modulation model predictive control system is as follows:

(1) as shown in FIG. 5, the three-phase input voltage and current (u) of the two-stage matrix converter are collected_i、i_i) Filter input voltage (u)_s) And three-phase output current i of two-stage matrix converter_oAnd of a permanent magnet synchronous machineSpeed of rotation omegaAnd an electrical angle θ;

(2) substituting the input current and the output voltage prediction model;

(3) substituting the effective vector of the rectification stage into a rectification stage cost function to obtain a duty ratio corresponding to the minimum cost function of the rectification stage;

(4) calculating the sector of the output voltage by using the output voltage and a trigonometric function;

(5) calculating the duty ratio corresponding to the inverter minimum cost function through the inverter cost function;

(6) and carrying out coordination control on the rectification stage and the inversion stage, and realizing the control of the matrix converter-permanent magnet synchronous motor by using a switch sequence.

The structure of the rectifier circuit in the step (2) is as follows:

the rectification stage structure of the matrix converter comprises a three-phase bridge arm a, a three-phase bridge arm b and a three-phase bridge arm c, wherein the a-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_apAnd S_anThe b-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_bpAnd S_bnThe c-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_cpAnd S_cn；

The inverter stage circuit structure in the step (2) is specifically as follows:

the inverter structure of the matrix converter comprises three-phase bridge arms A, B and C, wherein the bridge arm A comprises a switch S which is sequentially connected from top to bottom_ApAnd S_AnThe B-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_BpAnd S_BnThe C-phase bridge arm comprises a switch S which is sequentially connected from top to bottom_CpAnd S_Cn；

The step (2) is specifically as follows:

(21) collecting three-phase input voltage and current of a matrix converter, filter input voltage and three-phase output current, and substituting the three-phase input voltage and the three-phase output current into an input current prediction model;

wherein the content of the first and second substances,

in the formula: t is_sIs the sampling time; k is a sampling interval; r_f、L_f、C_fRespectively a filter resistor, an inductor and a capacitor; u. of_s、i_s、u_i、i_iThe power supply voltage, the power supply current, the IMC rectification stage input voltage and the IMC rectification stage current are respectively.

(22) Collecting IMC three-phase output current, substituting into a PMSM output voltage prediction model:

in the formula (I), the compound is shown in the specification,predicting output voltages for d and q axes respectively; i.e. i_od、i_oqThe current components of d and q axes of the stator are respectively; l is_d、L_qD-axis and q-axis inductors respectively; r_s、ω_ePsi are respectivelyStator resistance, electrical angular velocity, flux linkage.

(23) And solving the corresponding voltage and current according to a formula.

The step (3) is specifically as follows:

(31) establishing a single rectification grade value function;

in the formula: i.e. i_od、i_oqThe current components of d and q axes of the stator are respectively;is a d-axis reference current;is a q-axis reference current.

(32) Knowing the relationship between the input current, the direct current and the output current of the IMC;

input current i_iAnd a direct side current i_dcThe relationship is as follows:

direct side current i_dcAnd an output current i_oThe relationship of (1) is:

i_dc＝[S_Ap-S_An S_Bp-S_Bn S_Cp-S_Cn]i_o

(33) establishing a whole rectification grade value function;

g_r＝d_μg_rμ+d_vg_rv

in the formula: i is_μAnd I_vOptimizing adjacent current effective vectors for the rectifier stage; d_μ、d_vRespectively corresponding to the optimal adjacent current vector I_μ、I_vDuty cycle of (d); g_rμ、g_rvAre respectively I_μ、I_vValue letter ofAnd (4) counting.

(34) And solving the duty ratio of the effective vector according to the duty ratio cost function.

The step (4) is specifically as follows:

outputting a predicted voltage vectorThe judging mode of the located sector is as follows:

in the formula: theta^pPredicting the included angle corresponding to the sector where the voltage vector is located;the predicted voltage is output under an alpha coordinate system and a beta coordinate system.

And (5) the improved modulation model predictive control derivation is as follows:

(51) relationship between output voltage, DC voltage and output voltage

DC side voltage u_dcRectifying stage switching variables and input voltage u for IMC_iIs the function of:

u_dc＝[S_ap-S_an S_bp-S_bn S_cp-S_cn]u_i

output voltage u_oAnd a DC side voltage u_dcThe relationship is as follows:

(52) predicted output voltage limit:

in the formula:predicting a reference voltage for the d-axis;predicting a reference voltage for the q-axis;the output voltage limit values are predicted for the d and q axes.

(53) Establishing a single inversion level value function;

in the formula: u. of_oαref、u_oβrefAlpha and beta axis voltage components, respectively;predicting a reference voltage for an alpha axis;the reference voltage is predicted for the beta axis.

Fig. 6 is an inverter stage output voltage vector diagram. Wherein U is₁～U₆As a valid vector, U₀And U₇Is a zero vector.

FIG. 7 is a vector exploded view of the predicted output voltage.To predict the output voltage u_oαm、u_oβmAre respectively U_mThe alpha and beta axes of (1) correspond to the vector u_oαn、u_oβnAre respectively U_nThe α and β axes of (1) correspond to vectors.

(54) The expected space vector of the output phase voltage is placed in the alpha beta coordinate system, and the principle of volt-second balance is knownEffective vector u_omAnd u_onAnd zero vector u_o0The action time is specifically as follows:

in the formula: u. of_oαm、u_oβmAre respectively U_mThe corresponding components of the α and β axes of (1); u. of_oαn、u_oβnAre respectively U_nThe corresponding components of the α and β axes of (1); u. of_oα0、u_oβ0Are respectively U₀The corresponding components of the α and β axes of (1); t is_m、T_nAnd T₀Respectively representing effective voltage vectors U_m、U_nAnd zero vector U₀The time of action; t is_sIs the sampling time.

(55) The duty cycle is obtained from steps (53) and (54):

wherein the content of the first and second substances,

the step (6) is specifically as follows:

the inverter-level zero vector is distributed at each vector switching moment of the rectifier-level to ensure zero current conversion, and the duty ratio of the matched switching tube is as follows:

to verify the performance of the improved MMPC proposed herein for IMC-PMSM systems, the method was compared to conventional FSC-MPC, conventional MMPC methods, with simulation parameters as shown in Table 1, and sampling frequency T_sIs 50 kHz.

TABLE 1

(1) Constant speed control situation

The motor load is set to 4 N.m, and the set rotation speed is 1000 r/min. FIGS. 8a 8c are comparative graphs of constant rotation speed of the motor under 3 control methods. As can be seen from the figure, 3 control methods can reach constant rotating speed in a short time and accord with the characteristic of fast dynamic response of model predictive control; FCS-MPC has the defects of unfixed switching frequency and the like, so a large amount of ripples are generated; although the traditional MMPC control method fixes the switching frequency and improves the waveform quality, the system has heavier calculation load and the waveform still has fluctuation; the improved MMPC method reduces system calculation amount on the basis of the traditional MMPC, better improves waveform quality and enables the waveform to be smooth.

Fig. 9a to 9c are comparative graphs of output a-phase current under 3 control methods. As can be seen from the figure, the FSC-MPC causes the output current to have a large amount of ripples and high harmonic content; the harmonic content of the traditional MMPC control is reduced compared with that of FSC-MPC; the improved MMPC can better improve the waveform quality and enable the waveform to be smoother.

Fig. 10a to 10c are comparative graphs of the output a-phase current THD under 3 control methods. As can be seen, the THD values of the 3 control methods are 40.10%, 27.58% and 3.62%, respectively, and further verify that the modified MMPC has lower current harmonic content and better waveform quality than the conventional MMPC and FCS-MPC.

(2) Variable speed control situation

In order to verify the system rotation speed regulation capacity, the load 4N m is kept, the rotation speed of the motor is reduced from 1000r/min to 800r/min at 0.2s, and the system simulation is shown in FIGS. 11a to 11 c. As can be seen, the 3 control methods all respond quickly and stabilize to a given speed.

Fig. 12a to 12c are output a-phase current contrasts under 3 control methods. As can be seen from the figure, at 0.2s, the rotating speed changes, and the output A-phase current fluctuates; after 0.003s, the currents of the 3 control methods can be stabilized, and the waveform quality of the improved MMPC method is better than that of the FCS-MPC and the traditional MMPC.

FIGS. 13 a-13 c are dq-axis current comparisons under 3 controls. As can be seen, the improved MMPC method has the least dq-axis current ripple compared to the other two methods, further verifying that the improved MMPC method can better improve waveform quality.

(3) Variable load torque control scenario

In order to verify the load torque regulation capacity of the system, the rotating speed of the motor is 1000r/min under 3 control methods; at 0.2s, the load torque was from 1N · m to 4N · m, and system simulations are shown in fig. 15 and 16, comparing 3 control methods.

FIGS. 14a to 14c are comparisons of the motor rotation speeds under 3 controls. As can be seen, the 3 control methods all respond quickly and stabilize to a given speed.

Fig. 15a to 15c are output three-phase current comparisons under 3 controls. As can be seen, the improved MMPC method has a smaller output current ripple than the FCS-MPC and the conventional MMPC method, and it is fully verified that the performance of the improved MMPC is much higher than the conventional FCS-MPC and the conventional MMPC method.

The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.