CN112583315B - Three-vector model prediction torque control method for three-level permanent magnet synchronous motor - Google Patents
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Abstract
本发明公开了一种三电平永磁同步电动机三矢量模型预测转矩控制方法,采用矢量分区的方法选择电压矢量,通过将三电平逆变器备选矢量中的大矢量代入到价值函数中寻优,从而确定第一最优电压矢量,通过第一最优电压矢量的位置确定扇区,第二最优电压矢量从第一最优电压矢量所在扇区中的三个非零矢量代入价值函数中寻优得到,结合第一最优电压矢量、第二最优电压矢量和零矢量的作用时间控制三电平逆变器动作,这样第一最优电压矢量从原来的寻优27次降低到了6次,这样的寻优过程既考虑到了两个最优电压矢量的选择,又结合了其作用时间,保证所选的两个最优电压矢量能够保证中点电位平衡和较低的开关频率。
The invention discloses a three-level permanent magnet synchronous motor three-vector model prediction torque control method. The vector partition method is adopted to select the voltage vector, and the large vector in the three-level inverter candidate vector is substituted into the value function. The first optimal voltage vector is determined by searching for the optimal voltage vector, the sector is determined by the position of the first optimal voltage vector, and the second optimal voltage vector is substituted from the three non-zero vectors in the sector where the first optimal voltage vector is located. The value function is optimized, and the action time of the first optimal voltage vector, the second optimal voltage vector and the zero vector is combined to control the action of the three-level inverter, so that the first optimal voltage vector is optimized from the original 27 times. It is reduced to 6 times. This optimization process not only considers the selection of the two optimal voltage vectors, but also combines its action time to ensure that the selected two optimal voltage vectors can ensure the balance of the mid-point potential and lower switching. frequency.
Description
技术领域technical field
本发明涉及永磁同步电动机转矩控制,具体是涉及一种三电平永磁同步电动机三矢量模型预测转矩控制方法。The invention relates to torque control of permanent magnet synchronous motors, in particular to a three-level permanent magnet synchronous motor three-vector model predictive torque control method.
背景技术Background technique
由于永磁同步电机结构简单、体积小、功率密度高、效率高、运行性能优良等优点,近年来获得了广泛的应用,例如:交通领域、极爱单领域、车船的驱动领域,以及作为泵类、压缩机、高精度伺服系统等方面的转动机构。因此对永磁同步电机控制的研究也越来越多。Due to the advantages of simple structure, small size, high power density, high efficiency, and excellent operating performance, permanent magnet synchronous motors have been widely used in recent years, such as in the field of transportation, the field of love, the driving field of vehicles and ships, and as a pump Class, compressor, high-precision servo system and other aspects of the rotating mechanism. Therefore, there are more and more studies on the control of permanent magnet synchronous motors.
现有的永磁同步电机控制多用模型预测转矩控制,模型预测转矩控制是有限集预测算法中的一种经典控制方法,它非常适用于永磁同步电机控制系统,具有控制策略简单,动态性能好的优点,更适用于多标量、多约束条件、非线性系统。传统的模型预测转矩控制通过得到系统的预测模型,遍历可知数目的状态矢量,再根据预期控制目标设定合适的价值函数,通过价值函数来比较,即可得到功率器件未来需要执行的开关序列。Existing permanent magnet synchronous motor control uses model predictive torque control. Model predictive torque control is a classic control method in finite set prediction algorithms. It is very suitable for permanent magnet synchronous motor control systems. It has simple control strategies and dynamic The advantages of good performance are more suitable for multi-scalar, multi-constraint, and nonlinear systems. The traditional model predictive torque control obtains the predictive model of the system, traverses a known number of state vectors, and then sets an appropriate value function according to the expected control target. By comparing the value function, the switching sequence that the power device needs to execute in the future can be obtained. .
三电平逆变器相较于两电平逆变器来说有更小的开关频率和更广的矢量选择范围,然而在实际运用中需要考虑到中点电位平衡的问题。现有的模型预测控制策略中将中点电位平衡项引入到价值函数中,在寻优过程中考虑中点电位平衡问题,但也增加了控制策略的实行难度。Compared with the two-level inverter, the three-level inverter has a smaller switching frequency and a wider range of vector selection. However, in practical applications, the balance of the mid-point potential needs to be considered. In the existing model predictive control strategy, the midpoint potential balance term is introduced into the value function, and the midpoint potential balance problem is considered in the optimization process, but it also increases the difficulty of implementing the control strategy.
现有技术缺点:Disadvantages of the existing technology:
(1)已有的模型预测控制策略里在每个控制周期里有且只能得到一个大小固定,方向固定的电压矢量,但实际需要跟踪的参考电压矢量是不定的,因此输出的电压矢量不能有效的使得反馈转矩追踪参考转矩,直接导致永磁同步电机磁通脉动大,输出转矩脉动不平稳,电机稳态性能不佳。(1) In the existing model predictive control strategy, only one voltage vector with a fixed size and a fixed direction can be obtained in each control cycle, but the actual reference voltage vector to be tracked is uncertain, so the output voltage vector cannot be Effectively makes the feedback torque track the reference torque, which directly leads to the large magnetic flux pulsation of the permanent magnet synchronous motor, the unstable output torque pulsation, and the poor steady-state performance of the motor.
(2)三电平或更多电平拓扑结构的器件开关状态数目过多,计算成本过大,且存在复杂的冗余矢量,不易确定开关序列组合;(2) The number of switch states of devices with three-level or more-level topology is too large, the calculation cost is too large, and there are complex redundant vectors, so it is difficult to determine the switch sequence combination;
(3)价值函数中含有中点电位控制项,权重因子的整定变得更加的复杂,导致控制的精度不高,计算复杂;(3) The value function contains the mid-point potential control term, and the setting of the weight factor becomes more complicated, resulting in low control accuracy and complicated calculation;
(4)多矢量预测控制造成较高的开关频率,增加了开关损耗。(4) Multi-vector predictive control causes higher switching frequency and increases switching loss.
发明内容SUMMARY OF THE INVENTION
发明目的:针对以上缺点,本发明提供一种快速筛选矢量、降低开关损耗的三电平永磁同步电动机三矢量模型预测转矩控制方法。Purpose of the invention: In view of the above shortcomings, the present invention provides a three-vector model predictive torque control method for a three-level permanent magnet synchronous motor that can quickly screen vectors and reduce switching losses.
技术方案:为解决上述问题,本发明采用一种三电平永磁同步电动机三矢量模型预测转矩控制方法,包括以下步骤:Technical solution: In order to solve the above problems, the present invention adopts a three-level permanent magnet synchronous motor three-vector model predictive torque control method, which includes the following steps:
(1)根据永磁同步电动的状态空间模型,构建电流和磁通的状态方程,根据电流和磁通的状态方程得到转矩和磁通的预测模型,根据三电平逆变器直流侧电容电压模型得到第一电容电压预测模型;根据第一电容电压预测模型构建第一价值函数;(1) According to the state space model of permanent magnet synchronous motor, the state equations of current and magnetic flux are constructed, and the prediction model of torque and magnetic flux is obtained according to the state equations of current and magnetic flux. According to the DC side capacitance of the three-level inverter obtaining a first capacitor voltage prediction model from the voltage model; constructing a first value function according to the first capacitor voltage prediction model;
(2)采样得到k时刻的电流;(2) Sampling to obtain the current at time k;
(3)将采样取得的数据代入到转矩和磁通的预测模型中,得到下一时刻k+1时刻的转矩和磁链;(3) Substitute the data obtained by sampling into the prediction model of torque and magnetic flux, and obtain the torque and flux linkage at the next moment k+1;
(4)将三电平逆变器空间矢量图中的大矢量作为第一最优电压矢量的备选矢量代入到第一价值函数中,选出第一最优电压矢量;(4) Substitute the large vector in the three-level inverter space vector diagram into the first value function as the candidate vector of the first optimal voltage vector, and select the first optimal voltage vector;
(5)将第一最优电压矢量对应的扇区中的三个非零矢量作为第二最优电压矢量的备选矢量,零矢量作为第三电压矢量;(5) Three non-zero vectors in the sector corresponding to the first optimal voltage vector are used as candidate vectors for the second optimal voltage vector, and the zero vector is used as the third voltage vector;
(6)依次选取三个备选矢量作为第二最优电压矢量,计算第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间,并求出占空比,根据占空比调制出新电压矢量;(6) Select three candidate vectors in turn as the second optimal voltage vector, calculate the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector, and obtain the duty ratio. The empty ratio modulates a new voltage vector;
(7)根据第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间建立第二电容电压预测模型,并根据第二电容电压预测模型构建第二价值函数;(7) establishing a second capacitance voltage prediction model according to the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector, and building a second cost function according to the second capacitance voltage prediction model;
(8)将步骤6中,调制出的三个新电压矢量代入到第二价值函数中选出最优的第二最优电压矢量;(8) Substitute the three new voltage vectors modulated in step 6 into the second value function to select the optimal second optimal voltage vector;
(9)将所选的第一最优电压矢量、第二最优电压矢量和第三电压矢量对应的开关序列及对应的作用时间输入脉冲调制器控制三电平逆变器动作。(9) Input the switching sequence corresponding to the selected first optimal voltage vector, the second optimal voltage vector and the third voltage vector and the corresponding action time into the pulse modulator to control the action of the three-level inverter.
进一步的,所述步骤1中电流和磁通的状态方程为:Further, the state equations of the current and the magnetic flux in the
其中,iα、iβ分别表示定子电流矢量在α、β轴的分量;Ls表示定子电感;uα、uβ分别表示定子电压矢量在α、β轴下的分量;Rs表示定子电阻;ωr表示电动机的转子电角速度;ψα、ψβ分别表示电子磁链矢量在α、β轴下的分量。Among them, i α and i β represent the components of the stator current vector on the α and β axes respectively; L s represents the stator inductance; u α and u β represent the components of the stator voltage vector on the α and β axes respectively; R s represents the stator resistance ; ω r represents the rotor electrical angular velocity of the motor; ψ α , ψ β represent the components of the electron flux linkage vector under the α and β axes, respectively.
进一步的,所述步骤1中,转矩和磁通的预测模型为:Further, in the
ψs(k+1)=ψs(k)+Ts[us(k)-Rsis(k)]ψ s (k+1)=ψ s (k)+T s [u s (k)-R s i s (k)]
其中,Ts为采样周期;is(k+1)、ψs(k+1)、Te(k+1)分别为k+1时刻定子电流矢量、定子磁链和转矩矢量;is(k)、ψs(k)、us(k)、ωr(k)分别为k时刻定子电流矢量、定子磁链、定子电压矢量和转子的电角速度;j为虚数单位,p为极对数,为叉乘符号。Among them, T s is the sampling period; i s (k+1), ψ s (k+1), and Te (k+1) are the stator current vector, stator flux linkage and torque vector at time k+1, respectively; i s (k), ψ s (k), u s (k), and ω r (k) are the stator current vector, stator flux linkage, stator voltage vector and the electrical angular velocity of the rotor at time k, respectively; j is an imaginary unit, and p is Number of pole pairs, is the cross product symbol.
进一步的,所述步骤1中,电容电压预测模型为:Further, in the
其中,vc1(k)、vc2(k)为k时刻采样的电容电压;vc1(k+1)、vc2(k+1)为k+1时刻预测的电容电压;ic1(k)和ic2(k)是根据k时刻逆变器的开关状态和输出电流的定义值,C1、C2为直流侧两电容。Among them, v c1 (k) and v c2 (k) are the capacitor voltages sampled at time k; v c1 (k+1) and v c2 (k+1) are the predicted capacitor voltages at time k+1; i c1 (k ) and i c2 (k) are defined values according to the switching state and output current of the inverter at time k, C 1 and C 2 are the two capacitors on the DC side.
进一步的,所述步骤4中,第一价值函数为:Further, in the
其中,为转矩给定值,为定子磁通给定值,λ1、λ2、λ3为权重系数,Fsw为一个控制周期内开关管发生开通和关断的动作变换次数。in, is the torque given value, is the given value of the stator magnetic flux, λ 1 , λ 2 , λ 3 are the weight coefficients, and F sw is the switching times of switching on and off in a control cycle.
进一步的,所述步骤6中,第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间分别为t1、t2和t0:Further, in the step 6, the action times of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector are respectively t 1 , t 2 and t 0 :
t0=Ts-t1-t2 t 0 =T s -t 1 -t 2
其中,S为一个量,且 为转矩和磁通在第一最优电压矢量作用下的变化率; 为转矩和磁通在第二最优电压矢量作用下的变化率;为转矩和磁通在零矢量作用下的变化率。in, S is a quantity, and is the rate of change of torque and magnetic flux under the action of the first optimal voltage vector; is the rate of change of torque and magnetic flux under the action of the second optimal voltage vector; is the rate of change of torque and flux under the action of zero vector.
进一步的,t1、t2、t0在0~Ts范围内,且为保证t1、t2、t0在0~Ts范围内,需作如下处理:Further, t 1 , t 2 , and t 0 are in the range of 0 to T s , and to ensure that t 1 , t 2 , and t 0 are in the range of 0 to T s , the following processing is required:
(6.1)当作用时间t1、t2和t0中任意两个作用时间小于0,且另一个作用时间大于Ts,则令小于0的作用时间等于0,大于Ts的作用时间等于Ts;(6.1) When any two of the action times t 1 , t 2 and t 0 are less than 0, and the other action time is greater than T s , then the action time less than 0 is equal to 0, and the action time greater than T s is equal to T s ;
(6.2)当作用时间t1+t2≤Ts,则各矢量的作用时间不变;(6.2) When the action time t 1 +t 2 ≤T s , the action time of each vector remains unchanged;
(6.3)当作用时间t1+t2≥Ts,则需要将三个矢量的作用时间代入如下公式进行修正:(6.3) When the action time t 1 +t 2 ≥T s , the action time of the three vectors needs to be substituted into the following formula for correction:
其中:t1'、t'2和t'0分别表示修正后的第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间。Wherein: t 1 ', t' 2 and t' 0 respectively represent the action time of the corrected first optimal voltage vector, the second optimal voltage vector and the third voltage vector.
进一步的,所述步骤6中,新电压矢量的调制公式:Further, in the step 6, the modulation formula of the new voltage vector is:
其中,uα2、uβ2为新电压矢量的α、β轴分量,uopt1_α、uopt1_β为第一最优电压矢量的α、β轴分量,uopt2_n_α、uopt2_n_β为第二最优电压矢量集合中第n个电压矢量的α、β轴分量,第一最优电压矢量uopt1、第二最优电压矢量uopt2_n与零矢量u0的占空比分别ηopt1、ηopt2_n、η0。Among them, u α2 and u β2 are the α and β axis components of the new voltage vector, u opt1_α and u opt1_β are the α and β axis components of the first optimal voltage vector, and u opt2_n_α and u opt2_n_β are the second optimal voltage vector set In the α and β axis components of the nth voltage vector, the duty ratios of the first optimal voltage vector u opt1 , the second optimal voltage vector u opt2_n and the zero vector u 0 are η opt1 , η opt2_n , and η 0 , respectively.
进一步的,所述步骤7中第二电容电压预测模型为:Further, the second capacitor voltage prediction model in the
其中,v'c1(k+1)、v'c2(k+1)为第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间下k+1时刻的直流侧两电容电压,v'c1(k)、v'c2(k)为第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间下k时刻两电容电压,ic11(k)、ic21(k)、ic31(k)、ic12(k)、ic22(k)、ic32(k)分别为第一最优电压矢量、第二最优电压矢量和第三电压矢量作用时的输出电流值。Among them, v' c1 (k+1), v' c2 (k+1) are the two voltages on the DC side at time k+1 under the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector Capacitor voltage, v' c1 (k), v' c2 (k) are the two capacitor voltages at time k under the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector, i c11 (k) , ic21 (k), ic31 (k), ic12 (k), ic22 (k), ic32 (k) are the first optimal voltage vector, the second optimal voltage vector and the third voltage vector respectively Output current value when active.
进一步的,所述步骤7中第二价值函数gn为:Further, in the
其中,gn为第二价值函数。Among them, g n is the second value function.
有益效果:本发明相对于现有技术,其显著优点是通过第一最优电压矢量的位置确定扇区从而选出第二最优电压矢量,降低了寻优次数,并结合两个最优矢量和零矢量的作用时间,保证了中点电位平衡和较低的开关频率;使用三矢量模型预测控制,合成的矢量不仅在方向可以变化,还可以改变其大小,使其达到的控制效果最优。Beneficial effect: Compared with the prior art, the present invention has the significant advantage that the sector is determined by the position of the first optimal voltage vector to select the second optimal voltage vector, which reduces the number of optimizations, and combines the two optimal voltage vectors and the action time of the zero vector to ensure the neutral point potential balance and lower switching frequency; using the three-vector model predictive control, the synthesized vector can not only change in direction, but also change its size to achieve the best control effect. .
附图说明Description of drawings
图1是本发明NPC三电平逆变器拓扑图;1 is a topology diagram of an NPC three-level inverter of the present invention;
图2是本发明提供的矢量分区的三电平基本空间矢量分布图;Fig. 2 is the three-level basic space vector distribution diagram of the vector partition provided by the present invention;
图3是本发明三电平逆变器驱动永磁同步电机三矢量模型预测控制的框图;Fig. 3 is the block diagram of the three-vector model predictive control of the three-level inverter-driven permanent magnet synchronous motor of the present invention;
图4是本发明矢量选择的流程图。Figure 4 is a flow chart of the vector selection of the present invention.
具体实施方式Detailed ways
本实施例中一种三电平永磁同步电动机三矢量模型预测转矩控制方法,其中In this embodiment, a three-level permanent magnet synchronous motor three-vector model predicted torque control method, wherein
根据永磁同步电动的状态空间模型,构建电流和磁通的状态方程为:According to the state space model of permanent magnet synchronous electromotive force, the state equations of current and magnetic flux are constructed as:
其中,iα、iβ分别表示定子电流矢量在α、β轴的分量;Ls表示定子电感;uα、uβ分别表示定子电压矢量在α、β轴下的分量;Rs表示定子电阻;ωr表示电动机的转子电角速度;ψα、ψβ分别表示电子磁链矢量在α、β轴下的分量。Among them, i α and i β represent the components of the stator current vector on the α and β axes respectively; L s represents the stator inductance; u α and u β represent the components of the stator voltage vector on the α and β axes respectively; R s represents the stator resistance ; ω r represents the rotor electrical angular velocity of the motor; ψ α , ψ β represent the components of the electron flux linkage vector under the α and β axes, respectively.
根据永磁同步电动机电流和磁通的状态方程,对其中的微分项进行离散化处理,计算得到永磁同步电动机转矩和磁通的预测模型为:According to the state equation of the permanent magnet synchronous motor current and magnetic flux, the differential term is discretized, and the prediction model of the permanent magnet synchronous motor torque and magnetic flux is calculated as follows:
ψs(k+1)=ψs(k)+Ts[us(k)-Rsis(k)]ψ s (k+1)=ψ s (k)+T s [u s (k)-R s i s (k)]
其中,Ts为采样周期;is(k+1)、ψs(k+1)、Te(k+1)分别为k+1时刻定子电流矢量、定子磁链和转矩矢量;is(k)、ψs(k)、us(k)、ωr(k)分别为k时刻定子电流矢量、定子磁链、定子电压矢量和转子的电角速度;j为虚数单位,p为极对数,为叉乘符号。Among them, T s is the sampling period; i s (k+1), ψ s (k+1), and Te (k+1) are the stator current vector, stator flux linkage and torque vector at
如图1所示,三电平逆变器有三个桥臂,为A、B、C三相,每一相上有四个开关管。在正常工作时,每相有三种开关状态,对于A相,“P”状态对应的是Sa1和Sa2导通,Sa3和Sa4截止;“O”状态对应Sa2和Sa3导通,Sa1和Sa4截止;“N”状态对应Sa3和Sa4导通,Sa1和Sa2截止。因此三相桥臂有27种开关状态,有19种不同的电压矢量。不同的电压矢量对于中点电位的影响是不同的,因此在控制系统中需要设置中点电位平衡控制。根据三电平逆变器直流侧电容电压模型得到第一电容电压预测模型为:As shown in Figure 1, the three-level inverter has three bridge arms, which are three-phase A, B, and C, and each phase has four switching tubes. During normal operation, each phase has three switching states. For phase A, the "P" state corresponds to the conduction of Sa1 and Sa2, and the conduction of Sa3 and Sa4; the state of "O" corresponds to the conduction of Sa2 and Sa3, and the conduction of Sa1 and Sa4; The "N" state corresponds to that Sa3 and Sa4 are turned on, and Sa1 and Sa2 are turned off. Therefore, the three-phase bridge arm has 27 switching states and 19 different voltage vectors. Different voltage vectors have different effects on the midpoint potential, so it is necessary to set the midpoint potential balance control in the control system. According to the DC side capacitor voltage model of the three-level inverter, the first capacitor voltage prediction model is obtained as:
其中,vc1(k)、vc2(k)为k时刻采样的电容电压;vc1(k+1)、vc2(k+1)为k+1时刻预测的电容电压;ic1(k)和ic2(k)是根据k时刻逆变器的开关状态和输出电流的定义值,C1、C2为直流侧两电容,ia(k)、ib(k)、ic(k)为三相定子电流,idc(k)为直流母线电流,H1a、H1b、H1c、H2a、H2b、H2c为三相状态值,对A相来说,“P”状态时H1a为1,其余为0;“O”状态时H1b为1,其余为0;“N”状态时H1c为1,其余为0。Among them, v c1 (k) and v c2 (k) are the capacitor voltages sampled at time k; v c1 (k+1) and v c2 (k+1) are the predicted capacitor voltages at
以永磁同步电动机的电磁转矩和磁通预测值与参考值之差的绝对值与逆变器直流侧电容电压之差绝对值及开关频率限制构建目标第一价值函数g:The target first value function g is constructed by the absolute value of the difference between the electromagnetic torque and magnetic flux predicted value of the permanent magnet synchronous motor and the reference value, the absolute value of the difference between the DC side capacitor voltage of the inverter and the switching frequency limit:
其中,为转矩给定值,为定子磁通给定值,λ1、λ2、λ3为权重系数,Fsw为一个控制周期内开关管发生开通和关断的动作变换次数,具体计算如下:in, is the torque given value, is the given value of the stator magnetic flux, λ 1 , λ 2 , and λ 3 are the weight coefficients, and F sw is the switching times of switching on and off in a control cycle. The specific calculation is as follows:
Fsw=|Sa(k)-Sa(k-1)|+|Sb(k)-Sb(k-1)|+|Sc(k)-Sc(k-1)|F sw =|S a (k)-S a (k-1)|+|S b (k)-S b (k-1)|+|S c (k)-S c (k-1)|
其中Sa(k)、Sb(k)、Sc(k)为k时刻逆变器三相的开关状态;Sa(k-1)、Sb(k-1)、Sc(k-1)为上一时刻k-1时刻逆变器三相的开关状态。Among them, S a (k), S b (k), S c (k) are the switching states of the three-phase inverter at time k; S a (k-1), S b (k-1), S c (k -1) is the switching state of the three-phase inverter at the last moment k-1.
如图2所示,三电平逆变器的空间矢量分别为3个零矢量,12个正负冗余小矢量,6个中矢量和6个大矢量,其中大矢量对中点电位无影响,因此以大矢量为中心将空间矢量图分为六个扇区。As shown in Figure 2, the space vectors of the three-level inverter are 3 zero vectors, 12 positive and negative redundant small vectors, 6 medium vectors and 6 large vectors, of which the large vectors have no effect on the midpoint potential , so the space vector is divided into six sectors centered on the large vector.
将三电平逆变器空间矢量图中的大矢量作为第一最优电压矢量的备选矢量代入到第一价值函数g中,选取使结果最小的电压矢量作为第一最优电压矢量uopt1;将与第一最优电压矢量uopt1在同一扇区的非零矢量纳入第二最优电压矢量备选集合中,每个扇区中有三个备选电压矢量;并将与第一最优电压矢量uopt1在同一扇区的零矢量作为第三电压矢量。Substitute the large vector in the three-level inverter space vector diagram as the candidate vector of the first optimal voltage vector into the first value function g, and select the voltage vector that minimizes the result as the first optimal voltage vector u opt1 ; Include the non-zero vectors in the same sector as the first optimal voltage vector u opt1 into the second optimal voltage vector candidate set, and there are three candidate voltage vectors in each sector; The zero vector of the voltage vector u opt1 in the same sector is used as the third voltage vector.
依次选取三个备选电压矢量作为第二最优电压矢量,计算第一最优电压矢量uopt1、第二最优电压矢量uopt2和第三电压矢量(零矢量)u0的作用时间,根据转矩和磁链无差拍控制原则,在一个采样周期结束后,转矩和磁链预测值等于给定值,即:Select three candidate voltage vectors in turn as the second optimal voltage vector, calculate the action time of the first optimal voltage vector u opt1 , the second optimal voltage vector u opt2 and the third voltage vector (zero vector) u 0 , according to According to the deadbeat control principle of torque and flux linkage, after a sampling period ends, the predicted value of torque and flux linkage is equal to the given value, namely:
其中为转矩和磁通在第一最优电压矢量作用下的变化率;为转矩和磁通在第二最优电压矢量作用下的变化率; 为转矩和磁通在零矢量作用下的变化率;为第一最优电压矢量uopt1作用下的转矩和磁链的预测值;Te(k+1)opt2_n、|ψs(k+1)opt2_n|为第二最优电压矢量集合中第n个电压矢量uopt2_n作用下的转矩和磁链的预测值;Te(k+1)_0、|ψS(k+1)_0|为第三电压矢量(零矢量)作用下转矩和磁链的预测值。in is the rate of change of torque and magnetic flux under the action of the first optimal voltage vector; is the rate of change of torque and magnetic flux under the action of the second optimal voltage vector; is the rate of change of torque and magnetic flux under the action of zero vector; are the predicted values of torque and flux linkage under the action of the first optimal voltage vector u opt1 ; T e (k+1) opt2_n , |ψ s (k+1) opt2_n | Predicted values of torque and flux linkage under the action of n voltage vectors u opt2_n ; Te (k+1) _0 , |ψ S (k+1) _0 | are the torque under the action of the third voltage vector (zero vector) and the predicted value of the flux linkage.
第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间分别为t1、t2和t0:The action times of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector are respectively t 1 , t 2 and t 0 :
t0=Ts-t1-t2 t 0 =T s -t 1 -t 2
其中,S为一个量,且in, S is a quantity, and
计算出t1、t2、t0后,为保证t1、t2、t0在0~Ts范围内,需作如下处理:After calculating t 1 , t 2 , and t 0 , in order to ensure that t 1 , t 2 , and t 0 are within the range of 0 to T s , the following processing is required:
(6.1)当作用时间t1、t2和t0中任意两个作用时间小于0,且另一个作用时间大于Ts,则令小于0的作用时间等于0,大于Ts的作用时间等于Ts;(6.1) When any two of the action times t 1 , t 2 and t 0 are less than 0, and the other action time is greater than T s , then the action time less than 0 is equal to 0, and the action time greater than T s is equal to T s ;
(6.2)当作用时间t1+t2≤Ts,则各矢量的作用时间不变;(6.2) When the action time t 1 +t 2 ≤T s , the action time of each vector remains unchanged;
(6.3)当作用时间t1+t2≥Ts,则需要将三个矢量的作用时间代入如下公式进行修正:(6.3) When the action time t 1 +t 2 ≥T s , the action time of the three vectors needs to be substituted into the following formula for correction:
其中:t1'、t'2和t'0分别表示修正后的第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间。Wherein: t 1 ', t' 2 and t' 0 respectively represent the action time of the corrected first optimal voltage vector, the second optimal voltage vector and the third voltage vector.
第一最优电压矢量uopt1、第二最优电压矢量uopt2_n与零矢量u0的占空比分别ηopt1、ηopt2_n、η0,根据占空比调制出新电压矢量:The duty cycles of the first optimal voltage vector u opt1 , the second optimal voltage vector u opt2_n and the zero vector u 0 are η opt1 , η opt2_n , and η 0 respectively, and a new voltage vector is modulated according to the duty cycle:
其中,uα2、uβ2为新电压矢量的α、β轴分量,uopt1_α、uopt1_β为第一最优电压矢量的α、β轴分量,uopt2_n_α、uopt2_n_β为第二最优电压矢量集合中第n个电压矢量的α、β轴分量。Among them, u α2 and u β2 are the α and β axis components of the new voltage vector, u opt1_α and u opt1_β are the α and β axis components of the first optimal voltage vector, and u opt2_n_α and u opt2_n_β are the second optimal voltage vector set The α and β axis components of the nth voltage vector in .
在三电平逆变器中,第一最优电压矢量、第二最优电压矢量和第三电压矢量对中点电位有不同的影响,因此根据三个电压矢量的作用时间重新建立直流侧两电容的预测电压,第二电容电压预测模型为:In a three-level inverter, the first optimal voltage vector, the second optimal voltage vector and the third voltage vector have different effects on the midpoint potential, so the two voltages on the DC side are re-established according to the action time of the three voltage vectors. The predicted voltage of the capacitor, the second capacitor voltage prediction model is:
其中,v'c1(k+1)、v'c2(k+1)为第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间下k+1时刻的直流侧两电容电压,v'c1(k)、v'c2(k)为第一最优电压矢量、第二最优电压矢量和第三电压矢量的作用时间下k时刻两电容电压,ic11(k)、ic21(k)、ic31(k)、ic12(k)、ic22(k)、ic32(k)分别为第一最优电压矢量、第二最优电压矢量和第三电压矢量作用时的输出电流值。Among them, v' c1 (k+1), v' c2 (k+1) are the two voltages on the DC side at time k+1 under the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector Capacitor voltage, v' c1 (k), v' c2 (k) are the two capacitor voltages at time k under the action time of the first optimal voltage vector, the second optimal voltage vector and the third voltage vector, i c11 (k) , ic21 (k), ic31 (k), ic12 (k), ic22 (k), ic32 (k) are the first optimal voltage vector, the second optimal voltage vector and the third voltage vector respectively Output current value when active.
根据第二电容电压预测模型构建第二价值函数gn为:The second value function g n constructed according to the second capacitor voltage prediction model is:
将依次选取三个备选电压矢量作为第二最优电压矢量调制出的三个新电压矢量代入第二价值函数gn中,选取使结果最小的电压矢量作为第二最优电压矢量,最后将选择的第一最优电压矢量、第二最优电压矢量和第三电压矢量(零矢量)对应的开关序列及其作用时间输入脉冲调制器来控制三电平逆变器动作。The three new voltage vectors modulated by sequentially selecting three candidate voltage vectors as the second optimal voltage vector are substituted into the second value function g n , and the voltage vector with the smallest result is selected as the second optimal voltage vector, and finally the The selected switching sequences corresponding to the first optimal voltage vector, the second optimal voltage vector and the third voltage vector (zero vector) and their action time are input to the pulse modulator to control the action of the three-level inverter.
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