CN113783202A - Low-computation-quantity three-level four-bridge-arm active power filter FCS-MPC control method - Google Patents
Low-computation-quantity three-level four-bridge-arm active power filter FCS-MPC control method Download PDFInfo
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Abstract
本发明提出一种低运算量的三电平四桥臂有源电力滤波器FCS‑MPC控制方法,为降低三电平四桥臂有源电力滤波器FCS‑MPC控制系统的预测运算量,兼顾电压跳变限制及电流跟随控制性能,本发明通过对谐波参考电流等效转化,获得等效参考电压,根据参考电压γ坐标轴分量参考值,按照空间分层思想进行一次获取备选电压矢量相对应的开关序列集合,结合冗余矢量电流跟随性能等效原则与电压跳变限制原则对备选电压矢量相对应的开关序列集合进行二次筛选;以电压跟随性能最优原则,通过代价函数选取最优电压矢量,也即实现了电流跟随性最优控制,输出对应开关矢量,并在下一控制周期作用于有源电力滤波器,该方法极大地降低了预测运算量,可将运算量从81次降低到4‑18次。
The present invention proposes a low-computational three-level four-bridge active power filter FCS-MPC control method, in order to reduce the predicted calculation amount of the three-level four-bridge active power filter FCS-MPC control system, while taking into account Voltage jump limit and current follow control performance, the present invention obtains the equivalent reference voltage by equivalently transforming the harmonic reference current, and obtains the alternative voltage vector once according to the spatial layering idea according to the reference value of the γ coordinate axis component of the reference voltage The corresponding switching sequence set, combined with the redundant vector current following performance equivalent principle and the voltage jump limit principle, the secondary screening of the switching sequence set corresponding to the candidate voltage vector; based on the optimal voltage following performance principle, through the cost function The optimal voltage vector is selected, that is, the optimal control of current following is realized, the corresponding switching vector is output, and it acts on the active power filter in the next control cycle. This method greatly reduces the amount of prediction calculation, and can reduce the calculation amount from 81 was reduced to 4‑18.
Description
技术领域technical field
本发明涉及三电平四桥臂有源电力滤波器控制技术领域,具体是一种低运算量的三电平四桥臂有源电力滤波器FCS-MPC控制方法。The invention relates to the technical field of three-level four-bridge active power filter control, in particular to a low-computational three-level four-bridge active power filter FCS-MPC control method.
背景技术Background technique
科技的飞速发展,电力电子设备及非线性负载广泛应用于电力系统中,谐波污染问题日益严重。谐波治理和三相电流不平衡是低压配电网三相四线制系统中常见的两类问题,三电平四桥臂有源电力滤波器(Active Power Filters,APF)是一种可以综合解决以上两种电能质量问题的重要措施。有限集模型预测控制(Finite Control Set ModelPredictive Control,FCS-MPC)技术具有建模直观,控制简单,可实现多目标优化控制,且无PWM调制器及PI参数调节等优点,已成为多电平APF控制的主要研究方向。With the rapid development of science and technology, power electronic equipment and nonlinear loads are widely used in power systems, and the problem of harmonic pollution is becoming more and more serious. Harmonic control and three-phase current unbalance are two common problems in three-phase four-wire system of low-voltage distribution network. Three-level four-bridge active power filter (APF) is a kind of comprehensive Important measures to solve the above two power quality problems. Finite Control Set Model Predictive Control (FCS-MPC) technology has the advantages of intuitive modeling, simple control, multi-objective optimal control, and no PWM modulator and PI parameter adjustment. It has become a multi-level APF. The main research direction of control.
传统FCS-MPC直接应用于三电平四桥臂APF存在运算量大这一问题,且目前针对降低运算量方面的相关研究较少。因此,本发明提出一种低运算量的三电平四桥臂有源电力滤波器FCS-MPC控制方法。The direct application of the traditional FCS-MPC to the three-level four-arm APF has the problem of a large amount of computation, and there are few related studies on reducing the amount of computation at present. Therefore, the present invention proposes a low-computational three-level four-bridge active power filter FCS-MPC control method.
发明内容SUMMARY OF THE INVENTION
发明目的:为解决三电平四桥臂APF的FCS-MPC控制中存在的运算量大问题,实现兼顾冗余矢量电流跟随性能等效原则、电压跳变限制原则的三电平四桥臂APF的低运算量FCS-MPC控制。本发明提出了一种低运算量的三电平四桥臂有源电力滤波器FCS-MPC控制方法。Purpose of the invention: In order to solve the problem of large computational complexity in the FCS-MPC control of a three-level four-arm APF, a three-level four-arm APF that takes into account the equivalent principle of redundant vector current following performance and the principle of voltage jump limitation is realized. The low-computational FCS-MPC control. The invention proposes a low-computational three-level four-bridge arm active power filter FCS-MPC control method.
采用分层优化的思想将三电平四桥臂APF的备选电压空间矢量按γ坐标轴高度分为13个平面,以两两相邻平面构建备选电压矢量集合。根据无差拍控制思想,将谐波参考电流代入系统电流预测模型转化为等效的电压预测模型,得到等效的参考电压矢量,根据参考电压矢量的γ分量实际位置,一次获取备选电压矢量相对应的备选开关序列集合,依据冗余矢量电流跟随性能等效原则与电压跳变限制原则对备选开关序列集合进行二次筛选,筛选出最终参与预测的备选电压矢量的开关序列集合;根据电压跟随代价函数,选取代价函数最小值对应的一组开关矢量作为系统的最优开关矢量,并在下一周期作用于有源电力滤波器,该方法极大地降低了预测运算量,可将运算量从81次降低到4-18次。Using the idea of hierarchical optimization, the candidate voltage space vector of the three-level four-arm APF is divided into 13 planes according to the height of the γ coordinate axis, and the candidate voltage vector set is constructed by two adjacent planes. According to the idea of deadbeat control, the harmonic reference current is substituted into the system current prediction model and transformed into an equivalent voltage prediction model, and the equivalent reference voltage vector is obtained. According to the actual position of the γ component of the reference voltage vector, the alternative voltage vector is obtained at one time For the corresponding set of candidate switching sequences, the secondary screening of the set of candidate switching sequences is carried out according to the principle of equivalent current following performance of redundant vectors and the principle of voltage jump limitation, and the set of switching sequences of candidate voltage vectors that will ultimately participate in the prediction is screened out. ; According to the voltage following cost function, a group of switching vectors corresponding to the minimum value of the cost function are selected as the optimal switching vectors of the system, and act on the active power filter in the next cycle. The amount of operations is reduced from 81 to 4-18.
技术方案:为实现本发明的目的,本发明所采用的技术方案是:一种低运算量的三电平四桥臂有源电力滤波器FCS-MPC控制方法,该方法包括如下步骤:Technical scheme: In order to realize the purpose of the present invention, the technical scheme adopted in the present invention is: a low computational complexity three-level four-bridge arm active power filter FCS-MPC control method, the method comprises the following steps:
(1)对tk时刻有源电力滤波器输出电流、谐波参考电流和电网电压进行采样,将上周期所选最优开关矢量作用于有源电力滤波器,进行控制延时补偿,根据预测模型计算出tk+1时刻的有源电力滤波器输出电流。(1) Sampling the output current, harmonic reference current and grid voltage of the active power filter at time tk, and applying the optimal switching vector selected in the previous cycle to the active power filter to compensate for the control delay, according to the prediction The model calculates the active power filter output current at time tk+1 .
(2)对tk时刻谐波参考电流进行延时补偿,得到tk+1时刻谐波参考电流。(2) Delay compensation for the harmonic reference current at time t k to obtain the harmonic reference current at time t k+1 .
(3)根据无差拍控制思想,将步骤(1)计算得到的tk+1时刻的有源电力滤波器输出电流和步骤(2)得到的谐波参考电流通过预测模型转化为等效参考电压。(3) According to the idea of deadbeat control, the output current of the active power filter at time t k+1 calculated in step (1) and the harmonic reference current obtained in step (2) are converted into equivalent reference through the prediction model Voltage.
(4)根据步骤(3)中获取的tk+1时刻等效参考电压矢量γ坐标轴参考值结合三电平四桥臂有源电力滤波器电压矢量空间分布,依据空间分层思想对三电平四桥臂有源电力滤波器的81个预测电压矢量进行一次选取。(4) According to the reference value of the γ coordinate axis of the equivalent reference voltage vector at time t k+1 obtained in step (3) Combined with the spatial distribution of the voltage vector of the three-level four-arm active power filter, the 81 predicted voltage vectors of the three-level four-arm active power filter are selected once according to the idea of space stratification.
(5)根据步骤(4)获取的备选电压矢量集合,结合冗余矢量电流跟随性能等效原则与电压跳变限制原则对备选电压矢量集合进行二次筛选。(5) According to the set of candidate voltage vectors obtained in step (4), the secondary screening of the set of candidate voltage vectors is carried out in combination with the equivalent principle of redundant vector current following performance and the principle of voltage jump limitation.
(6)在步骤(5)最终确定参与预测的电压矢量集合,根据代价函数选取具有最优电压跟随性的开关矢量作为最终优化开关矢量输出,并在下一控制周期作用于有源电力滤波器。(6) In step (5), the voltage vector set participating in the prediction is finally determined, and the switching vector with the optimal voltage followability is selected as the final optimized switching vector output according to the cost function, and acts on the active power filter in the next control cycle.
(7)下一控制周期重复上述过程。(7) The above process is repeated in the next control cycle.
进一步的,步骤(1)的方法具体如下:Further, the method of step (1) is as follows:
(1.1)对tk时刻有源电力滤波器输出电流[iα(tk),iβ(tk),iγ(tk)]、谐波参考电流和电网电压[eα(tk),eβ(tk),eγ(tk)]进行采样,下标α、β、γ指三相静止坐标系,iα(tk),iβ(tk),iγ(tk)为tk时刻有源电力滤波器输出电流在αβγ坐标系下实际值,为tk时刻谐波参考电流在αβγ坐标系下实际值,eα(tk),eβ(tk),eγ(tk)为tk时刻电网电压在αβγ坐标系下实际值;将上周期所选最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))作用于有源电力滤波器,下标A,B,C,N指有源电力滤波器四相桥臂,SA(tk),SB(tk),SC(tk),SN(tk)分别为tk时刻有源电力滤波器A相、B相、C相、N相桥臂作用的开关状态;(1.1) For the active power filter output current at time t k [i α (t k ), i β (t k ), i γ (t k )], harmonic reference current and the grid voltage [e α (t k ),e β (t k ),e γ (t k )] for sampling, the subscripts α, β, γ refer to the three-phase stationary coordinate system, i α (t k ),i β (t k ), i γ (t k ) is the actual value of the output current of the active power filter in the αβγ coordinate system at time t k , is the actual value of the harmonic reference current in the αβγ coordinate system at time t k , e α (t k ), e β (t k ), e γ (t k ) are the actual value of the grid voltage in the αβγ coordinate system at time t k ; The optimal switching vector S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) selected in the previous cycle is applied to the active power filter The subscripts A, B, C, and N refer to the four-phase bridge arm of the active power filter, S A (t k ), S B (t k ), S C (t k ), S N (t k ) respectively is the switching state of the active power filter A-phase, B -phase, C-phase, and N-phase bridge arms at time tk;
(1.2)进行控制延时补偿,根据预测模型计算出tk+1时刻的有源电力滤波器输出电流值为tk+1时刻有源电力滤波器输出电流α坐标轴实际值,为tk+1时刻有源电力滤波器输出电流β坐标轴实际值,为tk+1时刻有源电力滤波器输出电流γ坐标轴实际值。(1.2) Carry out control delay compensation, and calculate the output current value of the active power filter at the time of t k+1 according to the prediction model is the actual value of the output current α coordinate axis of the active power filter at time t k+1 , is the actual value of the output current β coordinate axis of the active power filter at time t k+1 , is the actual value of the output current γ coordinate axis of the active power filter at time t k+1 .
三电平四桥臂有源电力滤波器的电流预测模型为:The current prediction model of the three-level four-arm active power filter is:
vα(tk)为tk时刻有源电力滤波器输出电压矢量α坐标轴实际值,vβ(tk)为tk时刻有源电力滤波器输出电压矢量β坐标轴实际值,vγ(tk)为tk时刻有源电力滤波器输出电压矢量γ坐标轴实际值,tk时刻有源电力滤波器输出电压矢量vα(tk)、vβ(tk)、vγ(tk)与tk时刻作用开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))的关系如下:v α (t k ) is the actual value of the active power filter output voltage vector α coordinate axis at time t k , v β (t k ) is the actual value of the active power filter output voltage vector β coordinate axis at time t k , v γ (t k ) is the actual value of the active power filter output voltage vector γ coordinate axis at time t k , the active power filter output voltage vectors v α (t k ), v β ( t k ) , v γ ( The relationship between t k ) and the switching vector S(t k ) = (S A (t k ), S B (t k ), S C (t k ), S N (t k )) at time t k is as follows:
L为有源电力滤波器滤波电感,R为滤波电感等效电阻,Ts为系统的控制周期,Udc为三电平四桥臂有源电力滤波器直流侧单个电容电压。L is the filter inductor of the active power filter, R is the equivalent resistance of the filter inductor, Ts is the control period of the system, and U dc is the single capacitor voltage on the DC side of the three-level four-bridge active power filter.
进一步的,步骤(2)的方法具体如下:根据谐波参考电流的当前值和过去值,采用拉格朗日外推法,进行谐波参考电流未来值的估算,即谐波参考电流的延时补偿:Further, the method of step (2) is as follows: according to the current value and past value of the harmonic reference current, the Lagrangian extrapolation method is used to estimate the future value of the harmonic reference current, that is, the delay of the harmonic reference current. Time Compensation:
为tk时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk-1时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk-2时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk+1时刻谐波参考电流在αβγ坐标系下的参考值。 is the actual value of the harmonic reference current sampled at time t k in the αβγ coordinate system, is the actual value of the harmonic reference current sampled at time t k-1 in the αβγ coordinate system, is the actual value of the harmonic reference current sampled at time t k-2 in the αβγ coordinate system, is the reference value of the harmonic reference current in the αβγ coordinate system at time t k+1 .
进一步的,步骤(3)的方法具体如下:根据无差拍控制思想,将步骤(2)得到的tk+1时刻谐波参考电流和步骤(1)通过控制延时补偿得到的tk+1时刻有源电力滤波器输出电流值通过预测模型等效转化为tk+1时刻的参考电压矢量 Further, the method of step (3) is as follows: according to the deadbeat control idea, the harmonic reference current at time t k+1 obtained in step (2) is and the output current value of the active power filter at time t k+1 obtained by controlling the delay compensation in step (1) Equivalently transformed into the reference voltage vector at time t k+1 through the prediction model
进一步的,步骤(4)的方法具体如下:将三电平四桥臂有源电力滤波器tk+1时刻能够输出的81个预测电压矢量在三相静止坐标系αβγ下进行表示,81个预测电压矢量以原点中心对称的规律分布在αβγ坐标系中,tk+1时刻三电平四桥臂有源电力滤波器能够输出的81个预测电压矢量终点的γ坐标轴分量分布于上,共计十三个平面;其中预测电压矢量的最大幅值为三电平四桥臂有源电力滤波器直流侧两个电容电压之和2Udc,tk+1时刻每个预测电压矢量均有tk+1时刻的一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))相对应,tk+1时刻三电平四桥臂有源电力滤波器作用一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))产生相应的一个预测电压矢量表示如下:Further, the method of step (4) is as follows: the 81 predicted voltage vectors that can be output by the three-level four-arm active power filter at time t k+1 are represented in the three-phase static coordinate system αβγ, and the 81 The predicted voltage vector is distributed in the αβγ coordinate system according to the law of center symmetry of the origin, and the γ coordinate axis components of the end points of the 81 predicted voltage vectors that can be output by the three-level four-arm active power filter at time tk+1 are distributed in There are thirteen planes in total; the maximum magnitude of the predicted voltage vector is the sum of the two capacitor voltages on the DC side of the three-level four-bridge active power filter 2U dc , and each predicted voltage vector at time t k+1 A set of switching vectors S(t k +1 )=(S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N (t k+1 )) correspondingly, the three-level four-arm active power filter acts on a set of switching vectors S(t k+1 )=(S A (t k+1 ) , S at time t k+1 B (t k+1 ), S C (t k+1 ), S N (t k+1 )) generate a corresponding predicted voltage vector It is expressed as follows:
以p表示开关状态为1,o表示开关状态为0,n表示开关状态为-1,p、o、n构成的一组开关序列表示tk+1时刻作用于三电平四桥臂有源电力滤波器A相、B相、C相、N相桥臂的开关状态;将tk+1时刻三电平四桥臂有源电力滤波器能够输出的81个电压矢量的终点所在的十三个平面两两相邻的平面定义为一层,总计十二层,每一层中所有的电压矢量构成一组备选电压矢量集合,所有电压矢量对应的开关矢量构成备选开关序列集合。空间分层思想即根据步骤(3)中tk+1时刻参考电压矢量实际位置,将其相邻两平面上所有电压矢量纳入备选电压矢量集合,排除其余十一个平面上的电压矢量,即备选电压矢量的一次获取,各层对应的以p、o、n表示的备选开关序列集合如下:P means the switch state is 1, o means the switch state is 0, n means the switch state is -1, and a group of switch sequences formed by p, o, and n means that the active state of the three-level four-bridge arm acts at t k+1 . The switching states of the A-phase, B-phase, C-phase, and N-phase bridge arms of the power filter; the thirteenth point where the end points of the 81 voltage vectors that can be output by the three-level four-arm active power filter at time tk+1 Two adjacent planes are defined as one layer, twelve layers in total, all voltage vectors in each layer constitute a set of candidate voltage vectors, and switching vectors corresponding to all voltage vectors constitute a set of candidate switching sequences. The idea of space stratification is based on the reference voltage vector at time t k+1 in step (3) In the actual position, all the voltage vectors on the adjacent two planes are included in the set of candidate voltage vectors, and the voltage vectors on the remaining eleven planes are excluded, that is, the candidate voltage vector is obtained at one time, and each layer corresponds to p, o, n. The set of alternative switch sequences represented are as follows:
进一步的,步骤(5)的方法具体如下:三电平四桥臂有源电力滤波器能够输出的81个预测电压矢量中,含有两个预测电压矢量空间位置完全重叠的为冗余矢量,冗余矢量电流跟随性能等效原则,即上周期作用最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应的电压矢量属于冗余矢量时,对步骤(4)得到的备选开关序列集合进行二次筛选,保留其中冗余矢量对应开关序列与S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应开关序列相同的一组开关序列,排除冗余矢量对应开关序列中与S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应开关序列不同的开关序列;电压跳变限制原则即:三电平四桥臂有源电力滤波器上周期tk时刻作用的最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))与下周期tk+1时刻作用的开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))必须满足约束条件:Further, the method of step (5) is as follows: among the 81 predicted voltage vectors that can be output by the three-level four-bridge active power filter, the one that contains two predicted voltage vectors whose spatial positions completely overlap is a redundant vector, and the redundant vector is a redundant vector. The equivalent principle of residual vector current following performance, that is, the optimal switching vector S(t k ) = (S A (t k ), S B (t k ), S C (t k ), S N (t k ))) when the corresponding voltage vector belongs to the redundant vector, perform secondary screening on the set of candidate switch sequences obtained in step (4), and keep the switch sequence corresponding to the redundant vector and S(t k )=(S A (t k ) ), S B (t k ), S C (t k ), S N (t k )) correspond to a group of switch sequences with the same switch sequence, excluding the redundant vector corresponding to the switch sequence with S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) correspond to different switching sequences of switching sequences; the voltage jump limitation principle is: three-level four-bridge active The optimal switching vector S(t k ) acting at the time of cycle t k on the power filter = (S A (t k ), S B (t k ), S C (t k ), S N (t k )) and The switching vector S(t k+1 ) acting at the next cycle t k+1 time = (S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N ( t k+1 )) must satisfy the constraints:
对步骤(4)得到的备选开关序列集合依据冗余矢量电流跟随性能等效原则和电压跳变限制原则,筛选出最终参与预测的备选电压矢量的开关序列集合。For the set of candidate switching sequences obtained in step (4), according to the principle of equivalent current following performance of redundant vectors and the principle of voltage jump limitation, the set of switching sequences of candidate voltage vectors that ultimately participate in the prediction is selected.
进一步的,步骤(6)的方法具体如下:步骤(6)的方法具体如下:将步骤(5)得到的最终参与预测的备选开关序列集合,根据电压跟随代价函数g,选取代价函数最小值对应的一组开关矢量作为系统的最优开关矢量,即电压跟随误差最小的一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1)),作用于下一控制周期:Further, the method of step (6) is as follows: the method of step (6) is as follows: the set of candidate switching sequences that are finally involved in prediction obtained in step (5) is selected according to the voltage following the cost function g, and the minimum value of the cost function is selected. The corresponding set of switching vectors is used as the optimal switching vector of the system, that is, a set of switching vectors with the smallest voltage following error S(t k+1 )=(S A (t k+1 ), S B (t k+1 ) ,S C (t k+1 ),S N (t k+1 )), acting on the next control cycle:
式中,为tk+1时刻参考电压矢量αβγ坐标系下参考值,为tk+1时刻预测电压矢量αβγ坐标系下预测值。与tk+1时刻作用于系统的开关矢量S(tk+1)关系如下:In the formula, is the reference value in the reference voltage vector αβγ coordinate system at time t k+1 , is the predicted value of the predicted voltage vector αβγ coordinate system at time t k+1 . The relationship with the switching vector S(t k +1 ) acting on the system at time t k+1 is as follows:
有益效果:与现有技术相比,本发明的技术方案具有如下有益效果:Beneficial effects: Compared with the prior art, the technical scheme of the present invention has the following beneficial effects:
针对三电平四桥臂有源电力滤波器的电压矢量分布,按照空间分层思想有效的降低了预测运算量,同时结合冗余矢量电流跟随性能等效原则与电压跳变限制原则,进一步降低了预测运算量,预测运算量从81次缩减到4-18次的同时,兼顾电流最优跟踪性能。Aiming at the voltage vector distribution of the three-level four-arm active power filter, according to the space layering idea, the amount of prediction calculation is effectively reduced, and at the same time, the equivalent principle of redundant vector current following performance and the principle of voltage jump limitation are combined to further reduce the In order to reduce the number of prediction operations, the number of prediction operations is reduced from 81 times to 4-18 times, while taking into account the optimal current tracking performance.
附图说明Description of drawings
图1三电平四桥臂APF的电压矢量空间分布图;Figure 1. The voltage vector space distribution diagram of the three-level four-arm APF;
图2一种低运算量的三电平四桥臂APF的FCS-MPC控制方法流程图;Fig. 2 is a kind of flow chart of the FCS-MPC control method of the three-level four-bridge arm APF of low computational complexity;
图3一种低运算量的三电平四桥臂APF的FCS-MPC控制方法谐波电流补偿前后电网三相电流;(a)补偿前电网三相电流波形图,(b)补偿后电网三相电流波形图;Fig. 3 FCS-MPC control method of a three-level four-arm APF with low computational complexity Phase current waveform diagram;
图4一种低运算量的三电平四桥臂APF的FCS-MPC控制方法谐波电流补偿前后电网A相电流谐波分析。(a)补偿前电网A相电流谐波分析图,(b)补偿后电网A相电流谐波分析图。Fig. 4 A FCS-MPC control method of a low-computation three-level four-bridge APF control method before and after the harmonic current compensation of the grid phase A current harmonic analysis. (a) The current harmonic analysis diagram of phase A of the grid before compensation, (b) the current harmonic analysis diagram of phase A of the grid after compensation.
具体实施方式Detailed ways
下面结合附图,以三电平四桥臂有源电力滤波器的三相四线制低压供电系统对本发明作进一步说明,该发明的具体实施步骤如:Below in conjunction with the accompanying drawings, the present invention will be further described with a three-phase four-wire low-voltage power supply system of a three-level four-bridge arm active power filter. The specific implementation steps of the present invention are as follows:
1)对tk时刻有源电力滤波器输出电流[iα(tk),iβ(tk),iγ(tk)]、谐波参考电流和电网电压[eα(tk),eβ(tk),eγ(tk)]进行采样,下标α、β、γ指三相静止坐标系,iα(tk),iβ(tk),iγ(tk)为tk时刻有源电力滤波器输出电流在αβγ坐标系下实际值,为tk时刻谐波参考电流在αβγ坐标系下实际值,eα(tk),eβ(tk),eγ(tk)为tk时刻电网电压在αβγ坐标系下实际值;将上周期所选最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))作用于有源电力滤波器,下标A,B,C,N指有源电力滤波器四相桥臂,SA(tk),SB(tk),SC(tk),SN(tk)分别为tk时刻有源电力滤波器A相、B相、C相、N相桥臂作用的开关状态;1) For the active power filter output current at time t k [i α (t k ), i β (t k ), i γ (t k )], harmonic reference current and the grid voltage [e α (t k ),e β (t k ),e γ (t k )] for sampling, the subscripts α, β, γ refer to the three-phase stationary coordinate system, i α (t k ),i β (t k ), i γ (t k ) is the actual value of the output current of the active power filter in the αβγ coordinate system at time t k , is the actual value of the harmonic reference current in the αβγ coordinate system at time t k , e α (t k ), e β (t k ), e γ (t k ) are the actual value of the grid voltage in the αβγ coordinate system at time t k ; The optimal switching vector S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) selected in the previous cycle is applied to the active power filter The subscripts A, B, C, and N refer to the four-phase bridge arm of the active power filter, S A (t k ), S B (t k ), S C (t k ), S N (t k ) respectively is the switching state of the active power filter A-phase, B -phase, C-phase, and N-phase bridge arms at time tk;
2)进行控制延时补偿,根据预测模型计算出tk+1时刻的有源电力滤波器输出电流值为tk+1时刻有源电力滤波器输出电流α坐标轴实际值,为tk+1时刻有源电力滤波器输出电流β坐标轴实际值,为tk+1时刻有源电力滤波器输出电流γ坐标轴实际值。2) Carry out control delay compensation, and calculate the output current value of the active power filter at the time of t k+1 according to the prediction model is the actual value of the output current α coordinate axis of the active power filter at time t k+1 , is the actual value of the output current β coordinate axis of the active power filter at time t k+1 , is the actual value of the output current γ coordinate axis of the active power filter at time t k+1 .
三电平四桥臂有源电力滤波器的电流预测模型为:The current prediction model of the three-level four-arm active power filter is:
vα(tk)为tk时刻有源电力滤波器输出电压矢量α坐标轴实际值,vβ(tk)为tk时刻有源电力滤波器输出电压矢量β坐标轴实际值,vγ(tk)为tk时刻有源电力滤波器输出电压矢量γ坐标轴实际值,tk时刻有源电力滤波器输出电压矢量vα(tk)、vβ(tk)、vγ(tk)与tk时刻作用开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))的关系如下:v α (t k ) is the actual value of the active power filter output voltage vector α coordinate axis at time t k , v β (t k ) is the actual value of the active power filter output voltage vector β coordinate axis at time t k , v γ (t k ) is the actual value of the active power filter output voltage vector γ coordinate axis at time t k , the active power filter output voltage vectors v α (t k ), v β ( t k ) , v γ ( The relationship between t k ) and the switching vector S(t k ) = (S A (t k ), S B (t k ), S C (t k ), S N (t k )) at time t k is as follows:
L为有源电力滤波器滤波电感,R为滤波电感等效电阻,Ts为系统的控制周期,Udc为三电平四桥臂有源电力滤波器直流侧单个电容电压。L is the filter inductor of the active power filter, R is the equivalent resistance of the filter inductor, Ts is the control period of the system, and U dc is the single capacitor voltage on the DC side of the three-level four-bridge active power filter.
3)根据谐波参考电流的当前值和过去值,采用拉格朗日外推法,进行谐波参考电流未来值的估算,即谐波参考电流的延时补偿:3) According to the current value and past value of the harmonic reference current, the Lagrangian extrapolation method is used to estimate the future value of the harmonic reference current, that is, the delay compensation of the harmonic reference current:
为tk时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk-1时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk-2时刻采样的谐波参考电流在αβγ坐标系下的实际值,为tk+1时刻谐波参考电流在αβγ坐标系下的参考值。 is the actual value of the harmonic reference current sampled at time t k in the αβγ coordinate system, is the actual value of the harmonic reference current sampled at time t k-1 in the αβγ coordinate system, is the actual value of the harmonic reference current sampled at time t k-2 in the αβγ coordinate system, is the reference value of the harmonic reference current in the αβγ coordinate system at time t k+1 .
4)根据无差拍控制思想,将步骤3)得到的tk+1时刻谐波参考电流和步骤2)通过控制延时补偿得到的tk+1时刻有源电力滤波器输出电流值代入预测模型等效转化得到tk+1时刻的参考电压矢量 4) According to the idea of deadbeat control, the harmonic reference current at time t k+1 obtained in step 3) is and step 2) the output current value of the active power filter at time t k+1 obtained by controlling the delay compensation Substitute into the prediction model for equivalent transformation to obtain the reference voltage vector at time t k+1
5)将三电平四桥臂有源电力滤波器tk+1时刻能够输出的81个预测电压矢量在三相静止坐标系αβγ下进行表示,81个预测电压矢量以原点中心对称的规律分布在αβγ坐标系中,tk+1时刻三电平四桥臂有源电力滤波器能够输出的81个预测电压矢量终点的γ坐标轴分量分布于上,共计十三个平面;其中预测电压矢量的最大幅值为三电平四桥臂有源电力滤波器直流侧两个电容电压之和2Udc,tk+1时刻每个预测电压矢量均有tk+1时刻的一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))相对应,tk+1时刻三电平四桥臂有源电力滤波器作用一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))产生相应的一个预测电压矢量表示如下:5) The 81 predicted voltage vectors that can be output by the three-level four-arm active power filter at time t k+1 are represented in the three-phase static coordinate system αβγ, and the 81 predicted voltage vectors are distributed regularly with the center of the origin symmetrical In the αβγ coordinate system, the γ coordinate axis components of the end points of the 81 predicted voltage vectors that can be output by the three-level four-arm active power filter at time t k+1 are distributed in There are thirteen planes in total; the maximum magnitude of the predicted voltage vector is the sum of the two capacitor voltages on the DC side of the three-level four-bridge active power filter 2U dc , and each predicted voltage vector at time t k+1 A set of switching vectors S(t k +1 )=(S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N (t k+1 )) correspondingly, the three-level four-arm active power filter acts on a set of switching vectors S(t k+1 )=(S A (t k+1 ) , S at time t k+1 B (t k+1 ), S C (t k+1 ), S N (t k+1 )) generate a corresponding predicted voltage vector It is expressed as follows:
以p表示开关状态为1,o表示开关状态为0,n表示开关状态为-1,p、o、n构成的一组开关序列表示tk+1时刻作用于三电平四桥臂有源电力滤波器A相、B相、C相、N相桥臂的开关状态;将tk+1时刻三电平四桥臂有源电力滤波器能够输出的81个电压矢量的终点所在的十三个平面两两相邻的平面定义为一层,总计十二层,每一层中所有的电压矢量构成一组备选电压矢量集合,其中所有电压矢量对应的开关矢量构成备选开关序列集合。空间分层思想即根据步骤4)中tk+1时刻参考电压矢量实际位置,将其相邻两平面上所有电压矢量纳入备选电压矢量集合,排除其余十一个平面上的电压矢量,即备选电压矢量的一次获取,各层对应的以p、o、n表示的备选开关序列集合如下:P means the switch state is 1, o means the switch state is 0, n means the switch state is -1, and a group of switch sequences formed by p, o, and n means that the active state of the three-level four-bridge arm acts at t k+1 . The switching states of the A-phase, B-phase, C-phase, and N-phase bridge arms of the power filter; the thirteenth point where the end points of the 81 voltage vectors that can be output by the three-level four-arm active power filter at time tk+1 Two adjacent planes of two planes are defined as one layer, a total of twelve layers, all voltage vectors in each layer constitute a set of candidate voltage vectors, and switch vectors corresponding to all voltage vectors constitute a set of candidate switch sequences. The idea of spatial layering is based on the reference voltage vector at time t k+1 in step 4). In the actual position, all the voltage vectors on the adjacent two planes are included in the set of candidate voltage vectors, and the voltage vectors on the remaining eleven planes are excluded, that is, the candidate voltage vector is obtained at one time, and each layer corresponds to p, o, n. The set of alternative switch sequences represented are as follows:
6)三电平四桥臂有源电力滤波器能够输出的81个预测电压矢量中,含有两个预测电压矢量空间位置完全重叠的为冗余矢量,冗余矢量电流跟随性能等效原则,即上周期作用最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应的电压矢量属于冗余矢量时,对步骤5)得到的备选开关序列集合进行二次筛选,保留其中冗余矢量对应开关序列与S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应开关序列相同的一组开关序列,排除冗余矢量对应开关序列中与S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))对应开关序列不同的开关序列;电压跳变限制原则即:三电平四桥臂有源电力滤波器上周期tk时刻作用的最优开关矢量S(tk)=(SA(tk),SB(tk),SC(tk),SN(tk))与下周期tk+1时刻作用的开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))必须满足约束条件:6) Among the 81 predicted voltage vectors that can be output by the three-level four-arm active power filter, the redundant vector that contains two predicted voltage vectors whose spatial positions completely overlap, and the redundant vector current follows the equivalent principle of performance, that is, The voltage vector corresponding to the optimal switching vector S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) belongs to the redundant vector , perform secondary screening on the set of candidate switch sequences obtained in step 5), and keep the switch sequence corresponding to the redundant vector and S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) corresponds to a group of switching sequences with the same switching sequence, excluding redundant vectors corresponding to the switching sequence in the same sequence as S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) correspond to different switching sequences of switching sequences; the principle of voltage jump limitation is: the maximum effect of the three-level four-bridge active power filter at the time of cycle t k The optimal switching vector S(t k )=(S A (t k ), S B (t k ), S C (t k ), S N (t k )) and the switching vector acting at the moment of t k+1 in the next cycle S(t k+1 )=(S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N (t k+1 )) must satisfy the constraints:
对步骤5)得到的备选开关序列集合依据冗余矢量电流跟随性能等效原则和电压跳变限制原则,筛选出最终参与预测的备选电压矢量的开关序列集合。For the set of candidate switching sequences obtained in step 5), according to the principle of equivalent current following performance of redundant vectors and the principle of voltage jump limitation, the set of switching sequences of candidate voltage vectors that ultimately participate in the prediction is selected.
7)将步骤6)得到的最终参与预测的备选开关序列集合,根据电压跟随代价函数g,选取代价函数最小值对应的一组开关矢量作为系统的最优开关矢量,即电压跟随误差最小的一组开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1)),作用于下一控制周期:7) Using the set of candidate switching sequences obtained in step 6) to finally participate in the prediction, according to the voltage following cost function g, select a group of switching vectors corresponding to the minimum value of the cost function as the optimal switching vector of the system, that is, the one with the smallest voltage following error. A set of switching vectors S(t k+1 )=(S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N (t k+1 )), Act on the next control cycle:
式中,为tk+1时刻参考电压矢量αβγ坐标系下参考值,为tk+1时刻预测电压矢量αβγ坐标系下预测值。与tk+1时刻作用于系统的开关矢量S(tk+1)=(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1))关系如下:In the formula, is the reference value in the reference voltage vector αβγ coordinate system at time t k+1 , is the predicted value of the predicted voltage vector αβγ coordinate system at time t k+1 . The switching vector S(t k +1 )=(S A (t k+1 ), S B (t k+1 ), S C (t k+1 ), S N (t k+1 )) relation is as follows:
8)下一控制周期重复上述步骤。8) Repeat the above steps in the next control cycle.
图1为三电平四桥臂APF的电压矢量空间分布图,图2为低运算量三电平四桥臂APF的FCS-MPC控制方法流程图。图3为低运算量FCS-MPC控制方法在三电平四桥臂APF低压配电系统中谐波电流补偿前后电网三相电流,图4为谐波电流补偿前后电网A相电流谐波分析,由图3和图4可以表明,本发明所提出的低运算量三电平四桥臂有源电力滤波器FCS-MPC控制方法,在有效降低三电平四桥臂APF模型预测计算量(缩减至4-18次)的同时,兼顾高性能的电流跟踪性能。FIG. 1 is a voltage vector space distribution diagram of a three-level four-arm APF, and FIG. 2 is a flowchart of an FCS-MPC control method for a three-level four-arm APF with low computational complexity. Figure 3 shows the three-phase current of the power grid before and after harmonic current compensation in the three-level four-arm APF low-voltage power distribution system with the low computational complexity FCS-MPC control method, and Figure 4 shows the harmonic analysis of the power grid phase A current before and after the harmonic current compensation. It can be shown from Fig. 3 and Fig. 4 that the FCS-MPC control method of the low-computational three-level four-arm active power filter proposed by the present invention can effectively reduce the predicted computation amount of the three-level four-arm APF model (reduced). to 4-18 times) while taking into account the high-performance current tracking performance.
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CN114336660A (en) * | 2021-12-27 | 2022-04-12 | 江苏师范大学 | A UPQC Direct Current Predictive Control Method Based on Power Angle |
CN117492371A (en) * | 2023-12-29 | 2024-02-02 | 中国科学院合肥物质科学研究院 | Optimization method, system and equipment for active power filter model predictive control |
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CN114336660A (en) * | 2021-12-27 | 2022-04-12 | 江苏师范大学 | A UPQC Direct Current Predictive Control Method Based on Power Angle |
CN114336660B (en) * | 2021-12-27 | 2024-04-12 | 江苏师范大学 | UPQC direct current prediction control method based on power angle |
CN117492371A (en) * | 2023-12-29 | 2024-02-02 | 中国科学院合肥物质科学研究院 | Optimization method, system and equipment for active power filter model predictive control |
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