CN112290858A - A fault-tolerant control method for phase-to-phase short circuit of five-phase permanent magnet synchronous motor based on multi-vector model prediction - Google Patents

A fault-tolerant control method for phase-to-phase short circuit of five-phase permanent magnet synchronous motor based on multi-vector model prediction Download PDF

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CN112290858A
CN112290858A CN202011166399.2A CN202011166399A CN112290858A CN 112290858 A CN112290858 A CN 112290858A CN 202011166399 A CN202011166399 A CN 202011166399A CN 112290858 A CN112290858 A CN 112290858A
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刘国海
王旭
陈前
赵文祥
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Jiangsu University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P29/00Arrangements for regulating or controlling electric motors, appropriate for both AC and DC motors
    • H02P29/02Providing protection against overload without automatic interruption of supply
    • H02P29/024Detecting a fault condition, e.g. short circuit, locked rotor, open circuit or loss of load
    • H02P29/028Detecting a fault condition, e.g. short circuit, locked rotor, open circuit or loss of load the motor continuing operation despite the fault condition, e.g. eliminating, compensating for or remedying the fault
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention discloses a five-phase permanent magnet synchronous motor interphase short circuit fault-tolerant control method based on multi-vector model prediction. The method comprises the following steps: detecting motor feedback rotation speed omegamBy a given rotational speed ω*Error of (2) to obtain iqrefSetting idrefIs 0; calculating the compensation voltage uα',uβ' and the compensating current iα',iβ'; sampling each phase current iA,iB,iC,iD,iEAnd short-circuit current, combined with compensation current iα',iβ' and transform the matrix to obtain the feedback d-q axis current id(k),iq(k) (ii) a Calculating reference voltage value by using dead-beat algorithm, and combining with compensation voltage uα',uβ' and back-emf compensation to obtain the reference value u of the alpha-beta axis voltageαref,uβref(ii) a Derivation baseA cost function of the voltage error; selecting an optimal voltage vector combination according to the shortest distance principle of the cost function; and selecting the optimal voltage vector combination and inputting the corresponding switching state of the optimal voltage vector combination into the PWM module, and inputting the obtained switching signal into the inverter to control the motor, thereby realizing the interphase short circuit fault-tolerant control of the five-phase permanent magnet synchronous motor.

Description

一种基于多矢量模型预测的五相永磁同步电机相间短路容错 控制方法A fault-tolerant control method for phase-to-phase short circuit of five-phase permanent magnet synchronous motor based on multi-vector model prediction

技术领域technical field

本发明涉及多相电机容错控制技术领域,通过注入补偿电压和电流实现五相永磁电机相间短路故障下容错控制,还涉及一种新颖的多矢量模型预测控制。适用于航空航天、电动汽车、舰船推进系统等对电机的可靠性有较高要求的场合。The invention relates to the technical field of fault-tolerant control of multi-phase motors, realizes fault-tolerant control under interphase short-circuit faults of five-phase permanent magnet motors by injecting compensation voltage and current, and also relates to a novel multi-vector model predictive control. It is suitable for occasions that have high requirements on the reliability of motors, such as aerospace, electric vehicles, and ship propulsion systems.

背景技术Background technique

永磁同步电机因为其高转矩密度、高效率以及高可靠性等特点,在电动汽车、航空航天以及海上巡航系统等领域应用越来越广泛。同时,对于飞行器、电动汽车等一些可靠性要求较高的场合,稳定可靠的电机驱动系统尤为重要。三相永磁同步电机在一些特殊的场合,存在着可靠性不足的缺点。而多相永磁电机凭借着其低转矩脉动和高容错性能,正是电机领域的研究热点。现有的容错方法主要集中在开路故障状态下,对短路故障的容错分析相对较少。与开路故障相比,由于永磁体的存在,五相永磁同步电机短路故障后,电机相电流短时间内急剧升高,电机转矩脉动提升,对系统危害性更大。现有短路容错主要关注电机的匝间短路和单相或对两相对中心短路,尚未有针对电机相间短路故障的容错控制。Permanent magnet synchronous motors are more and more widely used in electric vehicles, aerospace and marine cruise systems due to their high torque density, high efficiency and high reliability. At the same time, for some occasions with high reliability requirements such as aircraft and electric vehicles, a stable and reliable motor drive system is particularly important. The three-phase permanent magnet synchronous motor has the disadvantage of insufficient reliability in some special occasions. The multi-phase permanent magnet motor is a research hotspot in the field of motor because of its low torque ripple and high fault tolerance. The existing fault-tolerant methods mainly focus on the open-circuit fault state, and the fault-tolerant analysis of the short-circuit fault is relatively rare. Compared with the open-circuit fault, due to the existence of permanent magnets, after the short-circuit fault of the five-phase permanent magnet synchronous motor, the motor phase current increases sharply in a short time, and the motor torque ripple increases, which is more harmful to the system. The existing short-circuit fault tolerance mainly focuses on the inter-turn short circuit and the single-phase or two-phase center short-circuit of the motor, and there is no fault-tolerant control for the motor-phase short-circuit fault.

近年来,国内外学者对于模型预测控制进行了深入的研究,并取得了丰富的成果。模型预测控制(Model Predictive Control,MPC)具有动态响应快、控制简单灵活、便于处理非线性约束等特点,相比于直接转矩,MPC在矢量选择上更加准确有效,通过对电机状态进行预测,将预测值代入价值评价函数来选择最优电压矢量;与矢量控制相比,MPC无需电流环参数整定,可以获得更好的动态响特性。由于单个矢量的模型预测控制误差较大,会使电流中包含较多的谐波电流,多矢量的模型预测控制则成为研究热点。目前多矢量的模型预测控制主要集中在电机正常运行状态下,对电机容错状态下的研究较少。In recent years, scholars at home and abroad have carried out in-depth research on model predictive control, and have achieved rich results. Model Predictive Control (MPC) has the characteristics of fast dynamic response, simple and flexible control, and easy handling of nonlinear constraints. Compared with direct torque, MPC is more accurate and effective in vector selection. The optimal voltage vector is selected by substituting the predicted value into the value evaluation function; compared with vector control, MPC does not require current loop parameter tuning and can obtain better dynamic response characteristics. Due to the large error of the model predictive control of a single vector, the current will contain more harmonic currents, and the model predictive control of multiple vectors has become a research hotspot. At present, the multi-vector model predictive control mainly focuses on the normal running state of the motor, and there are few studies on the fault-tolerant state of the motor.

发明内容SUMMARY OF THE INVENTION

针对单矢量模型预测容错控制的精度不高以及使得电机在相间短路故障下能够容错运行,本发明提出了一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法。Aiming at the low accuracy of single-vector model prediction fault-tolerant control and the fault-tolerant operation of the motor under interphase short-circuit faults, the present invention proposes a phase-to-phase short-circuit fault-tolerant control method for a five-phase permanent magnet synchronous motor based on multi-vector model prediction.

为达到技术目的,本发明采用如下技术方案:For achieving technical purpose, the present invention adopts following technical scheme:

一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,包括如下步骤:A fault-tolerant control method for phase-to-phase short circuit of a five-phase permanent magnet synchronous motor based on multi-vector model prediction, comprising the following steps:

步骤1,将检测到的五相永磁同步电机的反馈转速ωm与将给定转速ω*相比较,得到电机的转速误差,采用PI控制器根据转速误差计算得到五相永磁同步电机的q轴电流参考值iqref;id为d轴电流,由于采用id=0控制,五相永磁同步电机的d轴电流参考值idref设为0;Step 1, compare the detected feedback speed ωm of the five-phase permanent magnet synchronous motor with the given speed ω* to obtain the speed error of the motor, and use the PI controller to calculate the five-phase permanent magnet synchronous motor according to the speed error. q-axis current reference value i qref ; id is the d -axis current, since id =0 control is adopted, the d -axis current reference value idref of the five-phase permanent magnet synchronous motor is set to 0;

步骤2,当五相永磁同步电机发生相间短路故障时,可根据磁动势不变和中性点为0的约束条件,在对应相发生开路故障的基础上加入补偿电压uα',uβ'和补偿电流iα',iβ'来消除相间短路电流的影响;Step 2, when the phase-to-phase short-circuit fault occurs in the five-phase permanent magnet synchronous motor, the compensation voltage u α ', u can be added on the basis of the open-circuit fault of the corresponding phase according to the constraint that the magnetomotive force is constant and the neutral point is 0. β ' and compensation current i α ', i β ' to eliminate the influence of interphase short-circuit current;

步骤3,利用电流传感器采样五相永磁电机的A、B、C、D、E相电流iA,iB,iC,iD,iE和相间短路故障时的短路电流isc,根据采样电流确定短路故障对应相缺失时的降阶矩阵,利用所选取的降阶矩阵,对采样得到的五相永磁电机的相电流进行矩阵变换,并加入之前计算得到的补偿电流iα',iβ',可得到故障时五相永磁同步电机反馈的d-q轴电流id(k),iq(k);Step 3, use the current sensor to sample the A, B, C, D, E phase currents i A , i B , i C , i D , i E of the five-phase permanent magnet motor and the short-circuit current i sc during the interphase short-circuit fault, according to The sampling current determines the reduced-order matrix when the short-circuit fault corresponds to the missing phase, and the selected reduced-order matrix is used to perform matrix transformation on the phase current of the five-phase permanent magnet motor obtained by sampling, and add the previously calculated compensation current i α ', i β ', the dq -axis currents id (k) and i q (k) fed back by the five-phase permanent magnet synchronous motor during fault can be obtained;

步骤4,根据五相电机反馈的d-q轴电流以及电流参考值,利用无差拍电流预测算法可预测出α-β轴电压参考值,并加入之前计算得到的补偿电压uα',uβ'以及反电势补偿可得到短路补偿之后的α-β轴电压参考值uαref,uβrefStep 4, according to the dq-axis current and the current reference value fed back by the five-phase motor, use the deadbeat current prediction algorithm to predict the α-β axis voltage reference value, and add the previously calculated compensation voltages u α ', u β ' And back EMF compensation can obtain the α-β axis voltage reference values u αref , u βref after short-circuit compensation;

步骤5,结合基本的五相电机离散预测模型以及从静止坐标系到旋转坐标系的变换矩阵,在容错备选电压矢量的基础上可构建基于电压误差的价值函数;Step 5, combining the basic five-phase motor discrete prediction model and the transformation matrix from the stationary coordinate system to the rotating coordinate system, on the basis of the fault-tolerant candidate voltage vector, a value function based on the voltage error can be constructed;

步骤6,根据之前得到的α-β轴电压参考值uαref,uβref,在扇区内通过最短距离的原则进行备选矢量的电压误差判断,可选取出最优的电压矢量组合以及相应作用时间分配;Step 6: According to the previously obtained α-β axis voltage reference values u αref , u βref , the voltage error judgment of the candidate vector is carried out in the sector through the principle of the shortest distance, and the optimal voltage vector combination and corresponding effect can be selected. time management;

步骤7,选取最优电压矢量组合其对应的的开关状态输入到PWM模块,可得到各相的开关信号,将得到的开关信号输入到逆变器中控制电机,实现五相永磁同步电机的相间短路容错控制。Step 7, select the optimal voltage vector combination and input its corresponding switch state to the PWM module, and obtain the switch signal of each phase, and input the obtained switch signal into the inverter to control the motor to realize the five-phase permanent magnet synchronous motor. Phase-to-phase short-circuit fault tolerance control.

进一步,步骤2中所述的补偿电压和电流的推导方法为:在相间短路故障情况下,需要在其余健康相产生补偿电流来抵消相间短路电流的影响,而相间短路故障又可分为相邻相和不相邻相间短路故障,需分别对其分析,具体步骤如下:Further, the derivation method of the compensation voltage and current described in step 2 is: in the case of an interphase short circuit fault, it is necessary to generate a compensation current in the remaining healthy phases to offset the influence of the interphase short circuit current, and the interphase short circuit fault can be divided into adjacent The short-circuit faults between phases and non-adjacent phases need to be analyzed separately. The specific steps are as follows:

步骤2.1,假设相邻相相间短路故障发生在C、D两相,根据故障前后磁动势保持不变的原则可得到:Step 2.1, assuming that the short-circuit fault between adjacent phases occurs in the C and D phases, according to the principle that the magnetomotive force remains unchanged before and after the fault, it can be obtained:

NiA+γNiB2Nisc3Nisc4iE=0Ni A +γNi B2 Ni sc3 Ni sc4 i E =0

其中,N为电机绕组匝数,γ=2/5π;Among them, N is the number of turns of the motor winding, γ=2/5π;

当C、D两相发生故障时,在其余健康相A、B、E相补偿的电流需满足中性点电流之和为0:When two phases C and D fail, the current compensated in the remaining healthy phases A, B, and E must meet the neutral point current sum of 0:

iA+iB+iE=0i A + i B + i E = 0

假设不相邻相相间短路故障发生在B、E两相,根据故障前后磁动势保持不变和中性点电流之和为0的原则可得到:Assuming that the non-adjacent phase-to-phase short-circuit fault occurs in the B and E phases, according to the principle that the magnetomotive force remains unchanged before and after the fault and the sum of the neutral point current is 0, it can be obtained:

NiA+γNisc2NiC3NiD4isc=0Ni A +γNi sc2 Ni C3 Ni D4 i sc =0

iA+iC+iD=0i A +i C +i D =0

步骤2.2,根据约束条件可得到C、D相发生相间短路故障时其余相基于短路电流isc的补偿电流为:Step 2.2, according to the constraints, the compensation currents of the remaining phases based on the short-circuit current i sc when the phase-to-phase short-circuit fault occurs in the C and D phases can be obtained as:

Figure BDA0002745940700000031
Figure BDA0002745940700000031

再通过Clarke变换矩阵,可将补偿电流变换到α-β轴上得到iα',iβ':Then through the Clarke transformation matrix, the compensation current can be transformed to the α-β axis to obtain i α ', i β ':

Figure BDA0002745940700000032
Figure BDA0002745940700000032

Figure BDA0002745940700000033
Figure BDA0002745940700000033

其中,

Figure BDA0002745940700000034
为C、D相缺失下的Clarke变换矩阵;in,
Figure BDA0002745940700000034
is the Clarke transformation matrix under the absence of C and D phases;

相似地,B、E相发生相间短路故障时,基于短路电流的补偿电流以及变换到α-β轴上的电流可计算为:Similarly, when phase-to-phase short-circuit faults occur in phases B and E, the compensation current based on the short-circuit current and the current transformed to the α-β axis can be calculated as:

Figure BDA0002745940700000035
Figure BDA0002745940700000035

Figure BDA0002745940700000036
Figure BDA0002745940700000036

Figure BDA0002745940700000037
Figure BDA0002745940700000037

其中,

Figure BDA0002745940700000038
为B、E相缺失下的Clarke变换矩阵;in,
Figure BDA0002745940700000038
is the Clarke transformation matrix under the absence of B and E phases;

步骤2.3,为了生成其余健康相的补偿电流,需要在前馈电压上产生补偿电压,当C、D相发生相间短路故障时,确定电机的数学模型;Step 2.3, in order to generate the compensation current of the remaining healthy phases, the compensation voltage needs to be generated on the feedforward voltage. When the phase-to-phase short-circuit fault occurs in the C and D phases, the mathematical model of the motor is determined;

根据基尔霍夫电压定律可分别得到每一相绕组的电压方程,而C、D相发生故障需将两相绕组当成一个回路来求解:According to Kirchhoff's voltage law, the voltage equation of each phase winding can be obtained separately, and when the C and D phases fail, the two-phase winding must be regarded as a loop to solve:

Figure BDA0002745940700000041
Figure BDA0002745940700000041

其中,Uxe(x=A,B,C,D,E)为每相绕组电阻和电感的电压降;Ux(x=A,B,C,D,E)为每相相电压;ex(x=A,B,C,D,E)为每相的反电势;Rs为每相绕组的电阻;L为每相绕组的电感;Among them, U xe (x=A, B, C, D, E) is the voltage drop of the winding resistance and inductance of each phase; U x (x=A, B, C, D, E) is the phase voltage of each phase; e x (x=A, B, C, D, E) is the back EMF of each phase; R s is the resistance of each phase winding; L is the inductance of each phase winding;

结合健康相的补偿电流和变换矩阵,可以得到α-β轴上的补偿电压uα',uβ':Combining the compensation current and transformation matrix of the healthy phase, the compensation voltage u α ', u β ' on the α-β axis can be obtained:

Figure BDA0002745940700000042
Figure BDA0002745940700000042

相似地,确定B、E相发生短路故障时的电机数学模型,其补偿电压如下所示:Similarly, determine the mathematical model of the motor when the B and E phases have a short-circuit fault, and the compensation voltage is as follows:

Figure BDA0002745940700000043
Figure BDA0002745940700000043

Figure BDA0002745940700000044
Figure BDA0002745940700000044

进一步,步骤3中所述反馈的d-q轴电流的计算如下所示:Further, the calculation of the feedback d-q axis current in step 3 is as follows:

由于反馈电流用来生成电压参考值,而这个过程是在五相电机开路容错控制的基础上,因此,利用电流传感器采集到的电流需去除短路电流的组成部分,将采集到的各相电流iA,iB,iC,iD,iE经过Clarke矩阵变换到α-β轴上,然后减去补偿电流iα',iβ'来消除短路电流的组成,再经过Park矩阵变换到d-q轴上得到电流id(k),iq(k),

Figure BDA0002745940700000045
为C、D相缺失的Park变换矩阵,
Figure BDA0002745940700000046
为C、D相缺失下的Clarke变换矩阵,假如为相邻相相间短路故障:Since the feedback current is used to generate the voltage reference value, and this process is based on the open-circuit fault-tolerant control of the five-phase motor, therefore, the current collected by the current sensor needs to remove the short-circuit current component, and the collected current i of each phase needs to be removed. A , i B , i C , i D , i E are transformed to the α-β axis through Clarke matrix, and then the compensation current i α ', i β ' is subtracted to eliminate the composition of short-circuit current, and then transformed to dq through Park matrix The currents id (k), i q ( k) are obtained on the axis,
Figure BDA0002745940700000045
is the Park transformation matrix with missing phases C and D,
Figure BDA0002745940700000046
is the Clarke transformation matrix under the absence of C and D phases, if it is a short-circuit fault between adjacent phases:

Figure BDA0002745940700000047
Figure BDA0002745940700000047

进一步,步骤4中α-β轴电压参考值uαref,uβref的计算如下所示:Further, the calculation of the α-β axis voltage reference values u αref and u βref in step 4 is as follows:

步骤4.1,根据无差拍电流预测的方法,将反馈的电流和电流参考值代入预测方程可得到dq轴电压参考值:Step 4.1, according to the deadbeat current prediction method, substitute the feedback current and current reference value into the prediction equation to obtain the dq axis voltage reference value:

Figure BDA0002745940700000051
Figure BDA0002745940700000051

其中,udref,uqref为d-q轴参考电压,idref,iqref为d-q轴参考电流,Ld,Lq为d-q轴电感,Ts为采样时间,ωe为电角频率,ed(k),eq(k)为容错状态下k时刻的d-q轴反电势,id(k),iq(k)为k时刻的电流;Among them, u dref , u qref are the dq-axis reference voltage, idref , i qref are the dq-axis reference current, L d , L q are the dq-axis inductance, T s is the sampling time, ω e is the electrical angle frequency, ed ( k), e q (k) is the dq -axis back-EMF at time k in the fault-tolerant state, id (k), i q (k) are the current at time k;

步骤4.2,根据Park逆矩阵可将dq轴电压参考值变换到α-β轴上,此时都是在开路容错的基础身上进行预测,因此,需要将补偿电压uα',uβ'添加进去得到α-β轴电压参考值uαref,uβref,假如为相邻相相间短路故障,则:Step 4.2, according to the Park inverse matrix, the dq axis voltage reference value can be transformed to the α-β axis. At this time, the prediction is made on the basis of open circuit fault tolerance. Therefore, it is necessary to add the compensation voltage u α ', u β ' into it Obtain the α-β axis voltage reference values u αref , u βref , if it is a short-circuit fault between adjacent phases, then:

Figure BDA0002745940700000052
Figure BDA0002745940700000052

步骤4.3,根据步骤2.3可知得到的α-β轴电压参考值uαref,uβref包含健康相反电势的组成部分,以相邻相相间短路故障为例,最终的α-β轴电压参考值uαref *,uβref *可计算为:Step 4.3, according to step 2.3, the obtained α-β axis voltage reference value u αref , u βref contains the components of the healthy opposite potential. Taking the short-circuit fault between adjacent phases as an example, the final α-β axis voltage reference value u αref * , u βref * can be calculated as:

Figure BDA0002745940700000053
Figure BDA0002745940700000053

进一步,步骤5中基于电压误差的价值函数的推导如下所示:Further, the derivation of the value function based on the voltage error in step 5 is as follows:

步骤5.1,基本的模型预测控制思想是将备选电压矢量依次代入价值函数中滚动优化,根据备选电压矢量产生的电流与电流参考值的误差来筛选出最优电压矢量,其过程可以表示为:Step 5.1, the basic model predictive control idea is to sequentially substitute the candidate voltage vectors into the value function for rolling optimization, and screen out the optimal voltage vector according to the error between the current generated by the candidate voltage vector and the current reference value, and the process can be expressed as :

Figure BDA0002745940700000054
Figure BDA0002745940700000054

g=|idref-id(k+1)|2+|iqref-iq(k+1)|2 g=|i dref -i d (k+1)| 2 +|i qref -i q (k+1)| 2

其中,ud(k),uq(k)为k时刻备选电压矢量的d-q轴电压,id(k+1),iq(k+1)为k+1时刻的电流;Among them, u d (k), u q (k) are the dq-axis voltage of the candidate voltage vector at time k, and id (k+1), i q (k+1) are the current at time k+1;

步骤5.2,结合步骤4.1的无差拍预测过程,基于电流误差的价值函数可以转化为基于电压误差的价值函数:In step 5.2, combined with the deadbeat prediction process in step 4.1, the value function based on current error can be transformed into a value function based on voltage error:

Figure BDA0002745940700000061
Figure BDA0002745940700000061

步骤5.3,五相永磁同步电机的dq轴电感如果偏差不大,d轴电压误差和q轴电压误差的权重因子即可忽略,再将基于电压误差的价值函数通过Park矩阵变换到α-β轴上,即可得到最终的价值函数:Step 5.3, if the deviation of the dq-axis inductance of the five-phase permanent magnet synchronous motor is not large, the weighting factors of the d-axis voltage error and the q-axis voltage error can be ignored, and then the value function based on the voltage error is transformed into α-β through the Park matrix On the axis, the final value function can be obtained:

g=|uαref-uα(k)|2+|uβref-uβ(k)|2g=|u αref −u α (k)| 2 +|u βref −u β (k)| 2 .

进一步,步骤6中最优电压矢量组合选取的具体步骤如下所示:Further, the specific steps for selecting the optimal voltage vector combination in step 6 are as follows:

假如相邻相相间短路故障:In case of short-circuit fault between adjacent phases:

步骤6.1,根据两相缺失后的Clarke变换矩阵和开关状态,可得到容错之后的矢量分布图,根据六个非零矢量将矢量分布分图分为六个扇区;Step 6.1, according to the Clarke transformation matrix and switching state after the two-phase missing, the vector distribution map after fault tolerance can be obtained, and the vector distribution map is divided into six sectors according to six non-zero vectors;

步骤6.2,由步骤4.3得到的α-β轴电压参考值可确定参考电压矢量的幅值和相位,进而确定参考矢量位于的扇区,假设参考矢量位于第一扇区,根据步骤5.3确定的价值函数可将矢量选择简化为一个数学问题,在扇区内寻找电压误差最小的合成矢量,即最寻找最靠近参考矢量的点,可由参考电压矢量的顶点分别向三条边作垂线,最短距离将在三条垂线中产生;In step 6.2, the α-β axis voltage reference value obtained in step 4.3 can determine the amplitude and phase of the reference voltage vector, and then determine the sector where the reference vector is located. Assuming that the reference vector is located in the first sector, according to the value determined in step 5.3 The function can simplify the vector selection into a mathematical problem. Find the composite vector with the smallest voltage error in the sector, that is, find the point closest to the reference vector. The vertex of the reference voltage vector can draw vertical lines to the three sides, and the shortest distance will be Produced in three perpendicular lines;

步骤6.3,矢量组合可分为两种情况,非零矢量和零矢量的组合以及两个非零矢量的组合,组合1分别包含U0,U4和U0,U6的矢量合成;Step 6.3, the vector combination can be divided into two cases, the combination of a non-zero vector and a zero vector and the combination of two non-zero vectors, the combination 1 contains the vector synthesis of U 0 , U 4 and U 0 , U 6 respectively;

其中r1和r2分别是非零矢量U4,U6的作用时间,可以计算得到:where r 1 and r 2 are the action times of the non-zero vectors U 4 and U 6 respectively, which can be calculated as:

Figure BDA0002745940700000062
Figure BDA0002745940700000062

其中,Usref=uαref+juβref为参考电压,θs=arctan(uβref/uαref);Wherein, U sref =u αref +ju βref is the reference voltage, θ s =arctan(u βref /u αref );

组合2则是非零矢量U4,U6的矢量合成,其合成矢量顶点的范围就是三角形的第三条边;Combination 2 is the vector composition of non-zero vectors U 4 and U 6 , and the range of the composite vector vertices is the third side of the triangle;

其中r3和r4分别是非零矢量U4,U6的作用时间,矢量合成将遵循平行四边形法则,可以计算得到:where r 3 and r 4 are the action times of the non-zero vectors U 4 and U 6 respectively. The vector synthesis will follow the parallelogram law, which can be calculated as:

Figure BDA0002745940700000071
Figure BDA0002745940700000071

其中d1,d2可以表示为:where d 1 , d 2 can be expressed as:

Figure BDA0002745940700000072
Figure BDA0002745940700000072

θ1为d1和U4夹角,最优矢量组合将在以上组合中产生,即g=min{g1,g2,g3}:θ 1 is the angle between d 1 and U 4 , and the optimal vector combination will be generated in the above combination, that is, g=min{g 1 ,g 2 ,g 3 }:

g1=|Usref-r1U4|2 g 1 =|U sref -r 1 U 4 | 2

g2=|Usref-r2U6|2 g 2 =|U sref -r 2 U 6 | 2

g3=|Usref-(r3U6+r4U4)|2 g 3 =|U sref -(r 3 U 6 +r 4 U 4 )| 2

其中g1,g2,g3为三种情况下价值函数的表达。Among them g 1 , g 2 , g 3 are the expressions of the value function in three cases.

本发明具有以下有益效果:The present invention has the following beneficial effects:

1、本发明将相间短路故障的影响分为开路故障和相间短路电流的影响,在开路容错控制的算法上加入补偿电压和电流来消除相间短路电流的影响,从而实现了五相永磁同步电机相间短路故障的容错控制,提高了电机的容错性能,使其能适用于电动汽车等需要高可靠性和宽调速范围的应用领域,方法简单易于实现。1. The present invention divides the influence of interphase short-circuit fault into the influence of open-circuit fault and interphase short-circuit current, and adds compensation voltage and current to the algorithm of open-circuit fault-tolerant control to eliminate the influence of interphase short-circuit current, thereby realizing a five-phase permanent magnet synchronous motor. The fault-tolerant control of phase-to-phase short-circuit fault improves the fault-tolerant performance of the motor, making it suitable for electric vehicles and other application fields that require high reliability and wide speed regulation range, and the method is simple and easy to implement.

2、本发明采用的多矢量模型预测控制可以在容错矢量分布图的不对称形状扇区内通过最短距离的原则选择出最优矢量组合,相比于传统的多矢量控制方法极大减小的计算负担,简单易于实现。并且针对不对称形状扇区的分析方法可以利用在各种状态下的扇区,而不仅局限于在正常状态下的对称形状扇区,适用性更广。2. The multi-vector model predictive control adopted by the present invention can select the optimal vector combination through the principle of the shortest distance in the asymmetric shape sector of the fault-tolerant vector distribution map, which greatly reduces the amount of Computational burden, simple and easy to implement. And the analysis method for the asymmetric shape sector can use the sector in various states, not only limited to the symmetrical shape sector in the normal state, and has wider applicability.

3、本发明采用的无差拍控制方法计算出参考电压,相比于PI调节器具有更快的动态响应,并且对交流信号的跟踪性能更好。3. The deadbeat control method adopted in the present invention calculates the reference voltage, has faster dynamic response than the PI regulator, and has better tracking performance for the AC signal.

附图说明Description of drawings

图1:相邻相相间短路电机数学模型(以C、D相为例);Figure 1: Mathematical model of adjacent phase-to-phase short-circuit motor (taking C and D phases as examples);

图2:不相邻相相间短路电机数学模型(以B、E相为例);Figure 2: Mathematical model of non-adjacent phase-to-phase short-circuit motor (taking B and E phases as examples);

图3:相邻相相间短路矢量分布图;Figure 3: Vector distribution diagram of short-circuit between adjacent phases;

图4:相邻相相间短路扇区分布图;Figure 4: Distribution of short-circuit sectors between adjacent phases;

图5:最优矢量组合选取原则;Figure 5: Selection principle of optimal vector combination;

图6:U0和U4矢量合成;Figure 6: U 0 and U 4 vector synthesis;

图7:U0和U6矢量合成;Figure 7: U 0 and U 6 vector synthesis;

图8:U4和U6矢量合成;(a)为方式1、(b)为方式2;Figure 8: U 4 and U 6 vector synthesis; (a) is mode 1, (b) is mode 2;

图9:基于多矢量模型预测的五相永磁同步电机相间短路容错控制框图;(a)相邻相相间短路容错控制图;(b)不相邻相相间短路容错控制图;Figure 9: Fault-tolerant control block diagram of five-phase permanent magnet synchronous motor based on multi-vector model prediction; (a) fault-tolerant control diagram for short-circuit between adjacent phases; (b) fault-tolerant control diagram for short-circuit between non-adjacent phases;

图10:五相永磁同步电机从故障到容错的电流及转矩波形;(a)相邻相相间短路容错;(b)不相邻相相间短路容错;Figure 10: Current and torque waveforms of five-phase permanent magnet synchronous motor from fault to fault tolerance; (a) fault tolerance for short-circuit between adjacent phases; (b) fault tolerance for short-circuit between non-adjacent phases;

图11:五相永磁同步电机短路容错控制时的负载突变电流及转矩波形;(a)相邻相相间短路容错(给定转速100r/min,负载由1-2-1Nm);(b)不相邻相相间短路容错(给定转速100r/min,负载由0-1-0Nm);Figure 11: Load mutation current and torque waveform during short-circuit fault-tolerant control of five-phase permanent magnet synchronous motor; (a) short-circuit fault tolerance between adjacent phases (given speed 100r/min, load from 1-2-1Nm); (b) ) fault tolerance of non-adjacent phase-to-phase short circuit (the given speed is 100r/min, and the load is 0-1-0Nm);

图12:五相永磁同步电机短路容错控制时的转速突变电流及转矩波形;(a)相邻相相间短路容错(给定负载2Nm,转速由50-100-50r/min);(b)不相邻相相间短路容错(给定负载1Nm,转速由50-100-50r/min)。Figure 12: Speed mutation current and torque waveform during short-circuit fault-tolerant control of five-phase permanent magnet synchronous motor; (a) short-circuit fault tolerance between adjacent phases (given load 2Nm, speed from 50-100-50r/min); (b) ) Short-circuit fault tolerance between non-adjacent phases (for a given load of 1Nm, the rotational speed is 50-100-50r/min).

具体实施方式Detailed ways

下面将结合附图,仔细说明该实施例的具体实施方式和实施效果。The specific implementation manner and implementation effect of this embodiment will be described in detail below with reference to the accompanying drawings.

由附图1和2的电机等效数学模型可以看出相邻相间短路和不相邻相间短路故障发生时,短路故障的影响可以分为开路故障的影响和短路电流的影响,因此本发明将在开路容错控制的基础上入补偿电压uα',uβ'和补偿电流iα',iβ'来实现短路容错控制。It can be seen from the equivalent mathematical models of the motor in Figures 1 and 2 that when adjacent-phase short-circuit and non-adjacent-phase short-circuit faults occur, the influence of short-circuit faults can be divided into the influence of open-circuit faults and the influence of short-circuit current. Therefore, the present invention will On the basis of the open-circuit fault-tolerant control, the compensation voltage u α ', u β ' and the compensation current i α ', i β ' are input to realize the short-circuit fault-tolerant control.

以C、D相为例,相邻相相间短路Clarke和Park变换矩阵为:Taking phases C and D as examples, the Clarke and Park transformation matrices of short-circuit between adjacent phases are:

Figure BDA0002745940700000081
Figure BDA0002745940700000081

Figure BDA0002745940700000082
Figure BDA0002745940700000082

根据故障前后磁动势保持不变的原则可得到:According to the principle that the magnetomotive force remains unchanged before and after the fault, it can be obtained:

NiA+γNiB2Nisc3Nisc4iE=0Ni A +γNi B2 Ni sc3 Ni sc4 i E =0

在其余健康相A、B、E相补偿的电流需满足中性点电流之和为0:The current compensated in the remaining healthy phases A, B, and E must meet the neutral point current sum of 0:

iA+iB+iE=0i A + i B + i E = 0

假设不相邻相相间短路故障发生在B、E两相,根据故障前后磁动势保持不变和中性点电流之和为0的原则可得到:Assuming that the non-adjacent phase-to-phase short-circuit fault occurs in the B and E phases, according to the principle that the magnetomotive force remains unchanged before and after the fault and the sum of the neutral point current is 0, it can be obtained:

NiA+γNisc2NiC3NiD4isc=0Ni A +γNi sc2 Ni C3 Ni D4 i sc =0

iA+iC+iD=0i A +i C +i D =0

根据约束条件可得到C、D相发生相间短路故障时其余相基于短路电流isc的补偿电流为:According to the constraints, the compensation currents of the remaining phases based on the short-circuit current i sc when the phase-to-phase short-circuit fault occurs in the C and D phases can be obtained as:

Figure BDA0002745940700000091
Figure BDA0002745940700000091

再通过C、D相缺失下的Clarke变换矩阵,可将补偿电流变换到α-β轴上得到iα',iβ':Then through the Clarke transformation matrix under the absence of C and D phases, the compensation current can be transformed to the α-β axis to obtain i α ', i β ':

Figure BDA0002745940700000092
Figure BDA0002745940700000092

Figure BDA0002745940700000093
Figure BDA0002745940700000093

为了生成其余健康相的补偿电流,需要在前馈电压上产生补偿电压。根据基尔霍夫电压定律可分别得到每一相绕组的电压方程,而C、D相发生故障需将两相绕组当成一个回路来求解:In order to generate the compensation current for the remaining healthy phases, a compensation voltage needs to be generated on the feedforward voltage. According to Kirchhoff's voltage law, the voltage equation of each phase winding can be obtained separately, and when the C and D phases fail, the two-phase winding must be regarded as a loop to solve:

Figure BDA0002745940700000094
Figure BDA0002745940700000094

结合健康相的补偿电流和变换矩阵,可以得到α-β轴上的补偿电压uα',uβ':Combining the compensation current and transformation matrix of the healthy phase, the compensation voltage u α ', u β ' on the α-β axis can be obtained:

Figure BDA0002745940700000095
Figure BDA0002745940700000095

以B、E相为例,不相邻相相间短路Clarke和Park变换矩阵为:Taking phases B and E as an example, the Clarke and Park transformation matrices of short-circuit between non-adjacent phases are:

Figure BDA0002745940700000101
Figure BDA0002745940700000101

Figure BDA0002745940700000102
Figure BDA0002745940700000102

相似地,B、E相发生相间短路故障时,基于短路电流的补偿电流以及变换到α-β轴上的电流可计算为:Similarly, when phase-to-phase short-circuit faults occur in phases B and E, the compensation current based on the short-circuit current and the current transformed to the α-β axis can be calculated as:

Figure BDA0002745940700000103
Figure BDA0002745940700000103

Figure BDA0002745940700000104
Figure BDA0002745940700000104

Figure BDA0002745940700000105
Figure BDA0002745940700000105

其补偿电压如下所示:Its compensation voltage is as follows:

Figure BDA0002745940700000106
Figure BDA0002745940700000106

Figure BDA0002745940700000107
Figure BDA0002745940700000107

Clarke变换矩阵的最后一行是零序分量,满足中性点之和为0的原则,在计算中通常是被忽略的。The last row of the Clarke transformation matrix is the zero-sequence component, which satisfies the principle that the sum of the neutral points is 0, which is usually ignored in the calculation.

由附图3和4可以看出C、D相相间短路故障时,非零矢量将矢量分布图划分了六个扇区,当参考电压矢量求解出后可以根据参考电压矢量的相位角判断出坐落的扇区。It can be seen from Figures 3 and 4 that when the phase-to-phase short-circuit fault occurs between phases C and D, the non-zero vector divides the vector distribution diagram into six sectors. When the reference voltage vector is solved, the location can be determined according to the phase angle of the reference voltage vector. sector.

Figure BDA0002745940700000108
Figure BDA0002745940700000108

由于每个扇区的情况都很相似,因此以参考电压矢量坐落于第一扇区为例。Since the situation of each sector is very similar, it is taken as an example that the reference voltage vector is located in the first sector.

由附图5结合推导的基于电压的价值函数可以看出,矢量选择被简化为一个数学问题,在扇区内寻找电压误差最小的合成矢量,即最寻找最靠近参考矢量的点,可由参考电压矢量的顶点分别向三条边作垂线,最短距离将在三条垂线中产生。附图6和7分别是一个非零电压矢量和零矢量的组合,其中r1和r2分别是非零矢量U4,U6的作用时间,可以计算得到:It can be seen from the voltage-based cost function derived in conjunction with Fig. 5 that the vector selection is simplified as a mathematical problem, searching for the synthetic vector with the smallest voltage error in the sector, that is, the point closest to the reference vector, which can be determined by the reference voltage. The vertices of the vector are perpendicular to the three sides, and the shortest distance will be generated in the three perpendiculars. Figures 6 and 7 are a combination of a non-zero voltage vector and a zero vector respectively, wherein r 1 and r 2 are the action time of the non-zero vectors U 4 and U 6 respectively, which can be calculated as:

Figure BDA0002745940700000111
Figure BDA0002745940700000111

附图8是两个非零电压矢量的组合,其中r3和r4分别是非零矢量U4,U6的作用时间,矢量合成将遵循平行四边形法则,可以计算得到:Figure 8 is a combination of two non-zero voltage vectors, where r 3 and r 4 are the action times of the non-zero vectors U 4 and U 6 respectively. The vector synthesis will follow the parallelogram law, which can be calculated as:

Figure BDA0002745940700000112
Figure BDA0002745940700000112

最优矢量组合将在以上组合中产生,即g=min{g1,g2,g3}:The optimal vector combination will result in the above combination, i.e. g=min{g 1 ,g 2 ,g 3 }:

g1=|Usref-r1U4|2 g 1 =|U sref -r 1 U 4 | 2

g2=|Usref-r2U6|2 g 2 =|U sref -r 2 U 6 | 2

g3=|Usref-(r3U6+r4U4)|2 g 3 =|U sref -(r 3 U 6 +r 4 U 4 )| 2

附图9则是基于多矢量模型预测的五相永磁同步电机相间短路容错控制框图。附图10是五相永磁同步电机从相间短路故障到容错控制的切换,不论是相邻相还是不相邻相间短路,本发明提出的短路容错控制都可减小故障引起的转矩脉动,同时恢复健康相电流的正弦度,具有很好的容错性能。附图11和附图12则分别验证了本发明提出容错控制的动态性能,面对负载突变和转速突变都能具有很快的响应,电机可以在不同条件在保持很好的运行性能。FIG. 9 is a block diagram of fault tolerance control of five-phase permanent magnet synchronous motor phase-to-phase short-circuit based on multi-vector model prediction. Figure 10 shows the switching of five-phase permanent magnet synchronous motor from interphase short-circuit fault to fault-tolerant control. Whether it is adjacent phase or non-adjacent phase-to-phase short circuit, the short-circuit fault-tolerant control proposed by the present invention can reduce the torque ripple caused by the fault, At the same time, the sine of the healthy phase current is restored, and it has good fault tolerance. Figures 11 and 12 respectively verify the dynamic performance of the fault-tolerant control proposed by the present invention, which can respond quickly to sudden changes in load and speed, and the motor can maintain good operating performance under different conditions.

在本说明书的描述中,参考术语“一个实施例”、“一些实施例”、“示意性实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不一定指的是相同的实施例或示例。而且,描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, reference to the terms "one embodiment," "some embodiments," "exemplary embodiment," "example," "specific example," or "some examples", etc., is meant to incorporate the embodiments A particular feature, structure, material, or characteristic described by an example or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

尽管已经示出和描述了本发明的实施例,本领域的普通技术人员可以理解:在不脱离本发明的原理和宗旨的情况下可以对这些实施例进行多种变化、修改、替换和变型,本发明的范围由权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, The scope of the invention is defined by the claims and their equivalents.

Claims (6)

1.一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,包括如下步骤:1. a five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction, is characterized in that, comprises the steps: 步骤1,将检测到的五相永磁同步电机的反馈转速ωm与将给定转速ω*相比较,得到电机的转速误差,采用PI控制器根据转速误差计算得到五相永磁同步电机的q轴电流参考值iqref;id为d轴电流,由于采用id=0控制,五相永磁同步电机的d轴电流参考值idref设为0;Step 1, compare the detected feedback speed ωm of the five-phase permanent magnet synchronous motor with the given speed ω* to obtain the speed error of the motor, and use the PI controller to calculate the five-phase permanent magnet synchronous motor according to the speed error. q-axis current reference value i qref ; id is the d -axis current, since id =0 control is adopted, the d -axis current reference value idref of the five-phase permanent magnet synchronous motor is set to 0; 步骤2,当五相永磁同步电机发生相间短路故障时,可根据磁动势不变和中性点为0的约束条件,在对应相发生开路故障的基础上加入补偿电压uα',uβ'和补偿电流iα',iβ'来消除相间短路电流的影响;Step 2, when the phase-to-phase short-circuit fault occurs in the five-phase permanent magnet synchronous motor, the compensation voltage u α ', u can be added on the basis of the open-circuit fault of the corresponding phase according to the constraint that the magnetomotive force is constant and the neutral point is 0. β ' and compensation current i α ', i β ' to eliminate the influence of interphase short-circuit current; 步骤3,利用电流传感器采样五相永磁电机的A、B、C、D、E相电流iA,iB,iC,iD,iE和相间短路故障时的短路电流isc,根据采样电流确定短路故障对应相缺失时的降阶矩阵,利用所选取的降阶矩阵,对采样得到的五相永磁电机的相电流进行矩阵变换,并加入之前计算得到的补偿电流iα',iβ',可得到故障时五相永磁同步电机反馈的d-q轴电流id(k),iq(k);Step 3, use the current sensor to sample the A, B, C, D, E phase currents i A , i B , i C , i D , i E of the five-phase permanent magnet motor and the short-circuit current i sc during the interphase short-circuit fault, according to The sampling current determines the reduced-order matrix when the short-circuit fault corresponds to the missing phase. Using the selected reduced-order matrix, the phase current of the five-phase permanent magnet motor obtained by sampling is converted into a matrix, and the compensation current i α ' obtained before is added. i β ', the dq -axis currents id (k) and i q (k) fed back by the five-phase permanent magnet synchronous motor during fault can be obtained; 步骤4,根据五相电机反馈的d-q轴电流以及电流参考值,利用无差拍电流预测算法可预测出α-β轴电压参考值,并加入之前计算得到的补偿电压uα',uβ'以及反电势补偿可得到短路补偿之后的α-β轴电压参考值uαref,uβrefStep 4, according to the dq-axis current and the current reference value fed back by the five-phase motor, use the deadbeat current prediction algorithm to predict the α-β axis voltage reference value, and add the previously calculated compensation voltage u α ', u β ' And back EMF compensation can obtain the α-β axis voltage reference values u αref , u βref after short-circuit compensation; 步骤5,结合基本的五相电机离散预测模型以及从静止坐标系到旋转坐标系的变换矩阵,在容错备选电压矢量的基础上可构建基于电压误差的价值函数;Step 5, combining the basic five-phase motor discrete prediction model and the transformation matrix from the stationary coordinate system to the rotating coordinate system, on the basis of the fault-tolerant candidate voltage vector, a value function based on the voltage error can be constructed; 步骤6,根据之前得到的α-β轴电压参考值uαref,uβref,在扇区内通过最短距离的原则进行备选矢量的电压误差判断,可选取出最优的电压矢量组合以及相应作用时间分配;Step 6: According to the previously obtained α-β axis voltage reference values u αref , u βref , the voltage error judgment of the candidate vector is carried out in the sector through the principle of the shortest distance, and the optimal voltage vector combination and corresponding effect can be selected. time management; 步骤7,选取最优电压矢量组合其对应的的开关状态输入到PWM模块,可得到各相的开关信号,将得到的开关信号输入到逆变器中控制电机,实现五相永磁同步电机的相间短路容错控制。Step 7, select the optimal voltage vector combination and input its corresponding switch state to the PWM module, and obtain the switch signal of each phase, and input the obtained switch signal into the inverter to control the motor to realize the five-phase permanent magnet synchronous motor. Phase-to-phase short-circuit fault tolerance control. 2.根据权利要求1所述的一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,步骤2中所述的补偿电压和电流的推导方法为:在相间短路故障情况下,需要在其余健康相产生补偿电流来抵消相间短路电流的影响,而相间短路故障又可分为相邻相和不相邻相间短路故障,需分别对其分析,具体步骤如下:2. a kind of five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction according to claim 1, is characterized in that, the derivation method of the compensation voltage and current described in step 2 is: In the case of short-circuit fault, compensation current needs to be generated in the remaining healthy phases to offset the influence of inter-phase short-circuit current, and inter-phase short-circuit fault can be divided into adjacent phase and non-adjacent phase-to-phase short-circuit faults, which need to be analyzed separately. The specific steps are as follows: 步骤2.1,假设相邻相相间短路故障发生在C、D两相,根据故障前后磁动势保持不变的原则可得到:Step 2.1, assuming that the short-circuit fault between adjacent phases occurs in the C and D phases, according to the principle that the magnetomotive force remains unchanged before and after the fault, it can be obtained: NiA+γNiB2Nisc3Nisc4iE=0Ni A +γNi B2 Ni sc3 Ni sc4 i E =0 其中,N为电机绕组匝数,γ=2/5π;Among them, N is the number of turns of the motor winding, γ=2/5π; 当C、D两相发生故障时,在其余健康相A、B、E相补偿的电流需满足中性点电流之和为0:When two phases C and D fail, the current compensated in the remaining healthy phases A, B, and E must meet the neutral point current sum of 0: iA+iB+iE=0i A + i B + i E = 0 假设不相邻相相间短路故障发生在B、E两相,根据故障前后磁动势保持不变和中性点电流之和为0的原则可得到:Assuming that the non-adjacent phase-to-phase short-circuit fault occurs in the B and E phases, according to the principle that the magnetomotive force remains unchanged before and after the fault and the sum of the neutral point current is 0, it can be obtained: NiA+γNisc2NiC3NiD4isc=0Ni A +γNi sc2 Ni C3 Ni D4 i sc =0 iA+iC+iD=0i A +i C +i D =0 步骤2.2,根据约束条件可得到C、D相发生相间短路故障时其余相基于短路电流isc的补偿电流为:Step 2.2, according to the constraints, the compensation currents of the remaining phases based on the short-circuit current i sc when the phase-to-phase short-circuit fault occurs in the C and D phases can be obtained as:
Figure FDA0002745940690000021
Figure FDA0002745940690000021
再通过Clarke变换矩阵,可将补偿电流变换到α-β轴上得到iα',iβ':Then through the Clarke transformation matrix, the compensation current can be transformed to the α-β axis to obtain i α ', i β ':
Figure FDA0002745940690000022
Figure FDA0002745940690000022
Figure FDA0002745940690000023
Figure FDA0002745940690000023
其中,
Figure FDA0002745940690000024
为C、D相缺失下的Clarke变换矩阵;
in,
Figure FDA0002745940690000024
is the Clarke transformation matrix under the absence of C and D phases;
相似地,B、E相发生相间短路故障时,基于短路电流的补偿电流以及变换到α-β轴上的电流可计算为:Similarly, when phase-to-phase short-circuit faults occur in phases B and E, the compensation current based on the short-circuit current and the current transformed to the α-β axis can be calculated as:
Figure FDA0002745940690000025
Figure FDA0002745940690000025
Figure FDA0002745940690000026
Figure FDA0002745940690000026
Figure FDA0002745940690000027
Figure FDA0002745940690000027
其中,
Figure FDA0002745940690000028
为B、E相缺失下的Clarke变换矩阵;
in,
Figure FDA0002745940690000028
is the Clarke transformation matrix under the absence of B and E phases;
步骤2.3,为了生成其余健康相的补偿电流,需要在前馈电压上产生补偿电压,当C、D相发生相间短路故障时,确定电机的数学模型;Step 2.3, in order to generate the compensation current of the remaining healthy phases, the compensation voltage needs to be generated on the feedforward voltage. When the phase-to-phase short-circuit fault occurs in the C and D phases, the mathematical model of the motor is determined; 根据基尔霍夫电压定律可分别得到每一相绕组的电压方程,而C、D相发生故障需将两相绕组当成一个回路来求解:According to Kirchhoff's voltage law, the voltage equation of each phase winding can be obtained separately, and when the C and D phases fail, the two-phase winding must be regarded as a loop to solve:
Figure FDA0002745940690000031
Figure FDA0002745940690000031
其中,Uxe(x=A,B,C,D,E)为每相绕组电阻和电感的电压降;Ux(x=A,B,C,D,E)为每相相电压;ex(x=A,B,C,D,E)为每相的反电势;Rs为每相绕组的电阻;L为每相绕组的电感;Among them, U xe (x=A, B, C, D, E) is the voltage drop of the winding resistance and inductance of each phase; U x (x=A, B, C, D, E) is the phase voltage of each phase; e x (x=A, B, C, D, E) is the back EMF of each phase; R s is the resistance of each phase winding; L is the inductance of each phase winding; 结合健康相的补偿电流和变换矩阵,可以得到α-β轴上的补偿电压uα',uβ':Combining the compensation current and transformation matrix of the healthy phase, the compensation voltage u α ', u β ' on the α-β axis can be obtained:
Figure FDA0002745940690000032
Figure FDA0002745940690000032
相似地,确定B、E相发生短路故障时的电机数学模型,其补偿电压如下所示:Similarly, determine the mathematical model of the motor when the B and E phases have a short-circuit fault, and the compensation voltage is as follows:
Figure FDA0002745940690000033
Figure FDA0002745940690000033
Figure FDA0002745940690000034
Figure FDA0002745940690000034
3.根据权利要求1所述的一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,步骤3中所述反馈的d-q轴电流的计算如下所示:3. a kind of five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction according to claim 1, is characterized in that, the calculation of the d-q axis current of feedback described in step 3 is as follows: 由于反馈电流用来生成电压参考值,而这个过程是在五相电机开路容错控制的基础上,因此,利用电流传感器采集到的电流需去除短路电流的组成部分,将采集到的各相电流iA,iB,iC,iD,iE经过Clarke矩阵变换到α-β轴上,然后减去补偿电流iα',iβ'来消除短路电流的组成,再经过Park矩阵变换到d-q轴上得到电流id(k),iq(k),
Figure FDA0002745940690000041
为C、D相缺失的Park变换矩阵,
Figure FDA0002745940690000042
为C、D相缺失下的Clarke变换矩阵,假如为相邻相相间短路故障:
Since the feedback current is used to generate the voltage reference value, and this process is based on the open-circuit fault-tolerant control of the five-phase motor, the current collected by the current sensor needs to remove the components of the short-circuit current, and the collected current i of each phase needs to be removed. A , i B , i C , i D , i E are transformed to the α-β axis through Clarke matrix, and then the compensation current i α ', i β ' is subtracted to eliminate the composition of short-circuit current, and then transformed to dq through Park matrix The currents id (k), i q ( k) are obtained on the axis,
Figure FDA0002745940690000041
is the Park transformation matrix with missing phases C and D,
Figure FDA0002745940690000042
is the Clarke transformation matrix under the absence of C and D phases, if it is a short-circuit fault between adjacent phases:
Figure FDA0002745940690000043
Figure FDA0002745940690000043
4.根据权利要求1所述的一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,步骤4中α-β轴电压参考值uαref,uβref的计算如下所示:4. a kind of five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction according to claim 1, is characterized in that, in step 4, the calculation of α-β axis voltage reference value u αref , u βref As follows: 步骤4.1,根据无差拍电流预测的方法,将反馈的电流和电流参考值代入预测方程可得到dq轴电压参考值:Step 4.1, according to the deadbeat current prediction method, substitute the feedback current and current reference value into the prediction equation to obtain the dq axis voltage reference value:
Figure FDA0002745940690000044
Figure FDA0002745940690000044
其中,udref,uqref为d-q轴参考电压,idref,iqref为d-q轴参考电流,Ld,Lq为d-q轴电感,Ts为采样时间,ωe为电角频率,ed(k),eq(k)为容错状态下k时刻的d-q轴反电势,id(k),iq(k)为k时刻的电流;Among them, u dref , u qref are the dq-axis reference voltage, idref , i qref are the dq-axis reference current, L d , L q are the dq-axis inductance, T s is the sampling time, ω e is the electrical angle frequency, ed ( k), e q (k) is the dq -axis back-EMF at time k in the fault-tolerant state, id (k), i q (k) are the current at time k; 步骤4.2,根据Park逆矩阵可将dq轴电压参考值变换到α-β轴上,此时都是在开路容错的基础身上进行预测,因此,需要将补偿电压uα',uβ'添加进去得到α-β轴电压参考值uαref,uβref,假如为相邻相相间短路故障,则:Step 4.2, according to the Park inverse matrix, the dq axis voltage reference value can be transformed to the α-β axis. At this time, the prediction is made on the basis of open circuit fault tolerance. Therefore, it is necessary to add the compensation voltage u α ', u β ' into it Obtain the α-β axis voltage reference values u αref , u βref , if it is a short-circuit fault between adjacent phases, then:
Figure FDA0002745940690000045
Figure FDA0002745940690000045
步骤4.3,根据步骤2.3可知得到的α-β轴电压参考值uαref,uβref包含健康相反电势的组成部分,以相邻相相间短路故障为例,最终的α-β轴电压参考值uαref *,uβref *可计算为:Step 4.3, according to step 2.3, the obtained α-β axis voltage reference value u αref , u βref contains the components of the healthy opposite potential. Taking the short-circuit fault between adjacent phases as an example, the final α-β axis voltage reference value u αref * , u βref * can be calculated as:
Figure FDA0002745940690000046
Figure FDA0002745940690000046
5.根据权利要求1所述的一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,步骤5中基于电压误差的价值函数的推导如下所示:5. a kind of five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction according to claim 1, is characterized in that, in step 5, the derivation based on the value function of voltage error is as follows: 步骤5.1,基本的模型预测控制思想是将备选电压矢量依次代入价值函数中滚动优化,根据备选电压矢量产生的电流与电流参考值的误差来筛选出最优电压矢量,其过程可以表示为:Step 5.1, the basic model predictive control idea is to sequentially substitute the candidate voltage vectors into the value function for rolling optimization, and screen out the optimal voltage vector according to the error between the current generated by the candidate voltage vector and the current reference value, and the process can be expressed as :
Figure FDA0002745940690000051
Figure FDA0002745940690000051
g=|idref-id(k+1)|2+|iqref-iq(k+1)|2 g=|i dref -i d (k+1)| 2 +|i qref -i q (k+1)| 2 其中,ud(k),uq(k)为k时刻备选电压矢量的d-q轴电压,id(k+1),iq(k+1)为k+1时刻的电流;Among them, u d (k), u q (k) are the dq-axis voltages of the candidate voltage vector at time k, and id (k+1), i q (k+1) are the currents at time k+1; 步骤5.2,结合步骤4.1的无差拍预测过程,基于电流误差的价值函数可以转化为基于电压误差的价值函数:In step 5.2, combined with the deadbeat prediction process in step 4.1, the value function based on current error can be transformed into a value function based on voltage error:
Figure FDA0002745940690000052
Figure FDA0002745940690000052
步骤5.3,五相永磁同步电机的dq轴电感如果偏差不大,d轴电压误差和q轴电压误差的权重因子即可忽略,再将基于电压误差的价值函数通过Park矩阵变换到α-β轴上,即可得到最终的价值函数:Step 5.3, if the deviation of the dq-axis inductance of the five-phase permanent magnet synchronous motor is not large, the weighting factors of the d-axis voltage error and the q-axis voltage error can be ignored, and then the value function based on the voltage error is transformed into α-β through the Park matrix On the axis, the final value function can be obtained: g=|uαref-uα(k)|2+|uβref-uβ(k)|2g=|u αref −u α (k)| 2 +|u βref −u β (k)| 2 .
6.根据权利要求1所述的一种基于多矢量模型预测的五相永磁同步电机相间短路容错控制方法,其特征在于,步骤6中最优电压矢量组合选取的具体步骤如下所示:6. a kind of five-phase permanent magnet synchronous motor phase-to-phase short-circuit fault-tolerant control method based on multi-vector model prediction according to claim 1, is characterized in that, in step 6, the concrete steps that optimal voltage vector combination is selected are as follows: 假如相邻相相间短路故障:In case of short-circuit fault between adjacent phases: 步骤6.1,根据两相缺失后的Clarke变换矩阵和开关状态,可得到容错之后的矢量分布图,根据六个非零矢量将矢量分布分图分为六个扇区;Step 6.1, according to the Clarke transformation matrix and switching state after the two-phase missing, the vector distribution map after fault tolerance can be obtained, and the vector distribution map is divided into six sectors according to six non-zero vectors; 步骤6.2,由步骤4.3得到的α-β轴电压参考值可确定参考电压矢量的幅值和相位,进而确定参考矢量位于的扇区,假设参考矢量位于第一扇区,根据步骤5.3确定的价值函数可将矢量选择简化为一个数学问题,在扇区内寻找电压误差最小的合成矢量,即最寻找最靠近参考矢量的点,可由参考电压矢量的顶点分别向三条边作垂线,最短距离将在三条垂线中产生;In step 6.2, the α-β axis voltage reference value obtained in step 4.3 can determine the amplitude and phase of the reference voltage vector, and then determine the sector where the reference vector is located. Assuming that the reference vector is located in the first sector, according to the value determined in step 5.3 The function can simplify the vector selection into a mathematical problem. Find the composite vector with the smallest voltage error in the sector, that is, find the point closest to the reference vector. The vertex of the reference voltage vector can draw vertical lines to the three sides, and the shortest distance will be Produced in three perpendicular lines; 步骤6.3,矢量组合可分为两种情况,非零矢量和零矢量的组合以及两个非零矢量的组合,组合1分别包含U0,U4和U0,U6的矢量合成;Step 6.3, the vector combination can be divided into two cases, the combination of a non-zero vector and a zero vector and the combination of two non-zero vectors, the combination 1 contains the vector synthesis of U 0 , U 4 and U 0 , U 6 respectively; 其中r1和r2分别是非零矢量U4,U6的作用时间,可以计算得到:where r 1 and r 2 are the action times of the non-zero vectors U 4 and U 6 respectively, which can be calculated as:
Figure FDA0002745940690000061
Figure FDA0002745940690000061
其中,Usref=uαref+juβref为参考电压,θs=arctan(uβref/uαref);Wherein, U sref =u αref +ju βref is the reference voltage, θ s =arctan(u βref /u αref ); 组合2则是非零矢量U4,U6的矢量合成,其合成矢量顶点的范围就是三角形的第三条边;Combination 2 is the vector composition of non-zero vectors U 4 and U 6 , and the range of the composite vector vertices is the third side of the triangle; 其中r3和r4分别是非零矢量U4,U6的作用时间,矢量合成将遵循平行四边形法则,可以计算得到:where r 3 and r 4 are the action times of the non-zero vectors U 4 and U 6 respectively. The vector synthesis will follow the parallelogram law, which can be calculated as:
Figure FDA0002745940690000062
Figure FDA0002745940690000062
其中d1,d2可以表示为:where d 1 , d 2 can be expressed as:
Figure FDA0002745940690000063
Figure FDA0002745940690000063
θ1为d1和U4夹角,最优矢量组合将在以上组合中产生,即g=min{g1,g2,g3}:θ 1 is the angle between d 1 and U 4 , and the optimal vector combination will be generated in the above combination, that is, g=min{g 1 ,g 2 ,g 3 }: g1=|Usref-r1U4|2 g 1 =|U sref -r 1 U 4 | 2 g2=|Usref-r2U6|2 g 2 =|U sref -r 2 U 6 | 2 g3=|Usref-(r3U6+r4U4)|2 g 3 =|U sref -(r 3 U 6 +r 4 U 4 )| 2 其中g1,g2,g3为三种情况下价值函数的表达。Among them g 1 , g 2 , g 3 are the expressions of the value function in three cases.
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