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 PDF

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CN113783202A
CN113783202A CN202111006049.4A CN202111006049A CN113783202A CN 113783202 A CN113783202 A CN 113783202A CN 202111006049 A CN202111006049 A CN 202111006049A CN 113783202 A CN113783202 A CN 113783202A
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郭金星
王贵峰
武泽文
高煦杰
吴玮
李沛儒
祝莘莘
马一鸣
王生壮
黄英豪
曹传攻
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Jiangsu Kelu Electric Co ltd
Jiangsu Normal University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for AC mains or AC distribution networks
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H02J3/1835—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control
    • H02J3/1842—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control wherein at least one reactive element is actively controlled by a bridge converter, e.g. active filters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E40/20—Active power filtering [APF]

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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。

Figure 202111006049

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.

Figure 202111006049

Description

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A low-computation three-level four-bridge active power filter FCS-MPC control method

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

Figure BDA0003237236410000021
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)
Figure BDA0003237236410000021
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

Figure BDA0003237236410000022
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，
Figure BDA0003237236410000023
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
Figure BDA0003237236410000022
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 ,
Figure BDA0003237236410000023
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

Figure BDA0003237236410000024
为tk+1时刻有源电力滤波器输出电流α坐标轴实际值，
Figure BDA0003237236410000025
为tk+1时刻有源电力滤波器输出电流β坐标轴实际值，
Figure BDA0003237236410000031
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
Figure BDA0003237236410000024
is the actual value of the output current α coordinate axis of the active power filter at time t k+1 ,
Figure BDA0003237236410000025
is the actual value of the output current β coordinate axis of the active power filter at time t k+1 ,
Figure BDA0003237236410000031
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:

Figure BDA0003237236410000032
Figure BDA0003237236410000032

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:

Figure BDA0003237236410000033
Figure BDA0003237236410000033

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:

Figure BDA0003237236410000034
Figure BDA0003237236410000034

Figure BDA0003237236410000035
为tk时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000036
为tk-1时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000037
为tk-2时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000038
为tk+1时刻谐波参考电流在αβγ坐标系下的参考值。
Figure BDA0003237236410000035
is the actual value of the harmonic reference current sampled at time t k in the αβγ coordinate system,
Figure BDA0003237236410000036
is the actual value of the harmonic reference current sampled at time t k-1 in the αβγ coordinate system,
Figure BDA0003237236410000037
is the actual value of the harmonic reference current sampled at time t k-2 in the αβγ coordinate system,
Figure BDA0003237236410000038
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

Figure BDA0003237236410000039
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
Figure BDA0003237236410000041
通过预测模型等效转化为tk+1时刻的参考电压矢量
Figure BDA0003237236410000042
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
Figure BDA0003237236410000039
and the output current value of the active power filter at time t k+1 obtained by controlling the delay compensation in step (1)
Figure BDA0003237236410000041
Equivalently transformed into the reference voltage vector at time t k+1 through the prediction model
Figure BDA0003237236410000042

Figure BDA0003237236410000043
Figure BDA0003237236410000043

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

Figure BDA0003237236410000044
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
Figure BDA0003237236410000045
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
Figure BDA0003237236410000046
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
Figure BDA0003237236410000044
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
Figure BDA0003237236410000045
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
Figure BDA0003237236410000046
It is expressed as follows:

Figure BDA0003237236410000047
Figure BDA0003237236410000047

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

Figure BDA0003237236410000048
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)
Figure BDA0003237236410000048
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:

Figure BDA0003237236410000051
Figure BDA0003237236410000051

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:

Figure BDA0003237236410000052
Figure BDA0003237236410000052

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:

Figure BDA0003237236410000061
Figure BDA0003237236410000061

式中，

Figure BDA0003237236410000062
为tk+1时刻参考电压矢量αβγ坐标系下参考值，
Figure BDA0003237236410000063
为tk+1时刻预测电压矢量αβγ坐标系下预测值。
Figure BDA0003237236410000064
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,
Figure BDA0003237236410000062
is the reference value in the reference voltage vector αβγ coordinate system at time t k+1 ,
Figure BDA0003237236410000063
is the predicted value of the predicted voltage vector αβγ coordinate system at time t k+1 .
Figure BDA0003237236410000064
The relationship with the switching vector S(t k +1 ) acting on the system at time t k+1 is as follows:

Figure BDA0003237236410000065
Figure BDA0003237236410000065

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

Figure BDA0003237236410000066
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，
Figure BDA0003237236410000071
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
Figure BDA0003237236410000066
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 ,
Figure BDA0003237236410000071
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

Figure BDA0003237236410000072
为tk+1时刻有源电力滤波器输出电流α坐标轴实际值，
Figure BDA0003237236410000073
为tk+1时刻有源电力滤波器输出电流β坐标轴实际值，
Figure BDA0003237236410000074
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
Figure BDA0003237236410000072
is the actual value of the output current α coordinate axis of the active power filter at time t k+1 ,
Figure BDA0003237236410000073
is the actual value of the output current β coordinate axis of the active power filter at time t k+1 ,
Figure BDA0003237236410000074
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:

Figure BDA0003237236410000075
Figure BDA0003237236410000075

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:

Figure BDA0003237236410000076
Figure BDA0003237236410000076

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:

Figure BDA0003237236410000081
Figure BDA0003237236410000081

Figure BDA0003237236410000082
为tk时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000083
为tk-1时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000084
为tk-2时刻采样的谐波参考电流在αβγ坐标系下的实际值，
Figure BDA0003237236410000085
为tk+1时刻谐波参考电流在αβγ坐标系下的参考值。
Figure BDA0003237236410000082
is the actual value of the harmonic reference current sampled at time t k in the αβγ coordinate system,
Figure BDA0003237236410000083
is the actual value of the harmonic reference current sampled at time t k-1 in the αβγ coordinate system,
Figure BDA0003237236410000084
is the actual value of the harmonic reference current sampled at time t k-2 in the αβγ coordinate system,
Figure BDA0003237236410000085
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

Figure BDA0003237236410000086
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
Figure BDA0003237236410000087
代入预测模型等效转化得到tk+1时刻的参考电压矢量
Figure BDA0003237236410000088
4) According to the idea of deadbeat control, the harmonic reference current at time t k+1 obtained in step 3) is
Figure BDA0003237236410000086
and step 2) the output current value of the active power filter at time t k+1 obtained by controlling the delay compensation
Figure BDA0003237236410000087
Substitute into the prediction model for equivalent transformation to obtain the reference voltage vector at time t k+1
Figure BDA0003237236410000088

Figure BDA0003237236410000089
Figure BDA0003237236410000089

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

Figure BDA00032372364100000810
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
Figure BDA00032372364100000811
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
Figure BDA00032372364100000812
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
Figure BDA00032372364100000810
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
Figure BDA00032372364100000811
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
Figure BDA00032372364100000812
It is expressed as follows:

Figure BDA0003237236410000091
Figure BDA0003237236410000091

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

Figure BDA0003237236410000092
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).
Figure BDA0003237236410000092
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:

Figure BDA0003237236410000093
Figure BDA0003237236410000093

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:

Figure BDA0003237236410000101
Figure BDA0003237236410000101

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:

Figure BDA0003237236410000102
Figure BDA0003237236410000102

式中，

Figure BDA0003237236410000103
为tk+1时刻参考电压矢量αβγ坐标系下参考值，
Figure BDA0003237236410000104
为tk+1时刻预测电压矢量αβγ坐标系下预测值。
Figure BDA0003237236410000105
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,
Figure BDA0003237236410000103
is the reference value in the reference voltage vector αβγ coordinate system at time t k+1 ,
Figure BDA0003237236410000104
is the predicted value of the predicted voltage vector αβγ coordinate system at time t k+1 .
Figure BDA0003237236410000105
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:

Figure BDA0003237236410000106
Figure BDA0003237236410000106

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.

Claims (7)

1. A low-computation-quantity three-level four-leg active power filter FCS-MPC control method is characterized by comprising the following steps of:
(1) for tkSampling the output current, harmonic reference current and power grid voltage of the active power filter at the moment, acting the optimal switch vector selected in the previous period on the active power filter to control delay compensation, and calculating t according to a prediction modelk+1The current output by the active power filter at the moment;
(2) for tkTime delay compensation is carried out on the time harmonic reference current to obtain tk+1A time harmonic reference current;
(3) according to the dead beat control idea, the t obtained by the calculation in the step (1) is usedk+1Converting the output current of the active power filter and the harmonic reference current obtained in the step (2) into equivalent reference voltage through a prediction model at the moment;
(4) according to t obtained in (3)k+1Reference value of time equivalent reference voltage vector gamma coordinate axis
Figure FDA0003237236400000011
Combining the spatial distribution of voltage vectors of the three-level four-bridge arm active power filter, and selecting 81 predicted voltage vectors of the three-level four-bridge arm active power filter once according to a spatial layering idea;
(5) performing secondary screening on the alternative voltage vector set according to the alternative voltage vector set obtained in the step (4) by combining a redundant vector current following performance equivalent principle and a voltage jump limiting principle;
(6) finally determining a voltage vector set participating in prediction in the step (5), selecting a switching vector with optimal voltage following performance as a final optimized switching vector output according to the cost function, and acting on the active power filter in the next control period;
(7) the process is repeated for the next control cycle.
2. The FCS-MPC control method for the three-level four-leg active power filter with low computation amount as recited in claim 1, wherein the method in the step (1) is as follows:
(11) to tkTime active power filter output current [ i ]α(tk),iβ(tk),iγ(tk)]Harmonic reference current
Figure FDA0003237236400000012
And the grid voltage [ e ]α(tk),eβ(tk),eγ(tk)]Sampling is carried out, subscripts alpha, beta and gamma refer to a three-phase static coordinate system, iα(tk),iβ(tk),iγ(tk) Is tkThe actual value of the output current of the active power filter under the alpha beta gamma coordinate system at the moment,
Figure FDA0003237236400000013
is tkActual value of time harmonic reference current in alpha beta gamma coordinate system, eα(tk),eβ(tk),eγ(tk) Is tkThe actual value of the voltage of the power grid under an alpha beta gamma coordinate system at the moment; selecting the optimal switching vector S (t) of the last periodk)＝(SA(tk),SB(tk),SC(tk),SN(tk) Acting on the active power filter, subscripts a, B, C, N referring to the four-phase arm of the active power filter, SA(tk),SB(tk),SC(tk),SN(tk) Are each tkSwitching states of bridge arm actions of A phase, B phase, C phase and N phase of the active power filter are kept at the moment;
(1.2) performing control delay compensation, and calculating t according to a current prediction model of the three-level four-bridge-arm active power filterk+1Output current value of active power filter at time
Figure FDA0003237236400000014
Figure FDA0003237236400000015
Is tk+1Time active power filter outputThe current alpha is measured as the actual value of the axis,
Figure FDA0003237236400000021
is tk+1The active power filter outputs the actual value of the current beta coordinate axis at the moment,
Figure FDA0003237236400000022
is tk+1Outputting an actual value of a current gamma coordinate axis by the active power filter at the moment;
the current prediction model of the three-level four-bridge arm active power filter is as follows:
Figure FDA0003237236400000023
wherein v isα(tk) Is tkThe output voltage vector alpha coordinate axis actual value v of the moment active power filterβ(tk) Is tkThe output voltage vector beta coordinate axis actual value v of the moment active power filterγ(tk) Is tkThe output voltage vector gamma coordinate axis actual value of the active power filter at the moment, tkOutput voltage vector v of time active power filterα(tk)、vβ(tk)、vγ(tk) And tkMoment-action switching vector S (t)k)＝(SA(tk),SB(tk),SC(tk),SN(tk) The relationship of) is as follows:
Figure FDA0003237236400000024
wherein, L is the filter inductance of the active power filter, R is the equivalent resistance of the filter inductance, Ts is the control period of the system, UdcThe voltage of a single capacitor at the direct current side of the three-level four-bridge arm active power filter is obtained.
3. The FCS-MPC control method for the three-level four-leg active power filter with low computation amount as recited in claim 2, wherein the method in the step (2) is as follows: according to the current value and the past value of the harmonic reference current, estimating the future value of the harmonic reference current by adopting a Lagrange extrapolation method, namely, the delay compensation of the harmonic reference current:
Figure FDA0003237236400000025
wherein,
Figure FDA0003237236400000026
is tkThe actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,
Figure FDA0003237236400000027
is tk-1The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,
Figure FDA0003237236400000028
is tk-2The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,
Figure FDA0003237236400000029
is tk+1And (3) reference values of the harmonic reference current at the moment in an alpha beta gamma coordinate system.
4. The FCS-MPC control method for the three-level four-leg active power filter with low computation amount as recited in claim 3, wherein the method in the step (3) is as follows: according to the dead beat control idea, the t obtained in the step (2) is usedk+1Time harmonic reference current
Figure FDA00032372364000000210
And step (1) t obtained by controlling delay compensationk+1Time-of-day active power filteringOutput current value of the device
Figure FDA0003237236400000031
Substituting into a prediction model to obtain tk+1Reference voltage vector of time of day
Figure FDA0003237236400000032
Figure FDA0003237236400000033
5. The FCS-MPC control method for the three-level four-leg active power filter with low computation amount as recited in claim 4, wherein the method in the step (4) is as follows: three-level four-bridge arm active power filter tk+181 predicted voltage vectors capable of being output at the moment are expressed under a three-phase static coordinate system alpha beta gamma, the 81 predicted voltage vectors are distributed in the alpha beta gamma coordinate system according to a rule that the origin centers are symmetrical, and tk+1The gamma coordinate axis components of 81 predicted voltage vector end points which can be output by the time three-level four-bridge arm active power filter are distributed in
Figure FDA0003237236400000034
Thirteen planes in total; the maximum amplitude of the predicted voltage vector is 2U of the sum of two capacitor voltages at the direct current side of the three-level four-bridge-arm active power filterdc，tk+1Each predicted voltage vector at a time
Figure FDA0003237236400000035
All have tk+1A set of switching vectors S (t) of time instantsk+1)＝(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1) Correspond to tk+1One group of switching vectors S (t) acted by three-level four-bridge-arm active power filter at momentk+1)＝(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1) Generate a corresponding one of the predicted voltage vectors)
Figure FDA0003237236400000036
Is represented as follows:
Figure FDA0003237236400000037
p represents the switch state as 1, o represents the switch state as 0, n represents the switch state as-1, and a group of switch sequences consisting of p, o and n represents tk+1The method comprises the steps of constantly acting on the switching states of A-phase, B-phase, C-phase and N-phase bridge arms of a three-level four-bridge arm active power filter; will tk+1Defining thirteen planes adjacent to each other, in which the endpoints of 81 voltage vectors capable of being output by the three-level four-leg active power filter are located, as one layer, totaling twelve layers, forming a group of alternative voltage vector sets by all the voltage vectors in each layer, forming an alternative switch sequence set by the switch vectors corresponding to all the voltage vectors, and adopting a space layering idea that the switch vectors corresponding to the voltage vectors in the step (3) are arranged according to the t in the step (3)k+1Time reference voltage vector
Figure FDA0003237236400000038
In the actual position, all voltage vectors on two adjacent planes are included in the alternative voltage vector set, voltage vectors on the remaining eleven planes are excluded, that is, the alternative voltage vectors are obtained once, and the alternative switching sequence sets represented by p, o and n corresponding to each layer are as follows:
Figure FDA0003237236400000041
6. the FCS-MPC control method of the three-level four-leg active power filter with low computation amount as recited in claim 1, wherein the method of step (5) is as follows:
the three-level four-bridge arm active power filter comprises 81 predicted voltage vectors which can be output by the three-level four-bridge arm active power filter, wherein the two predicted voltage vectors are completely overlapped in space position and are redundant vectors, and the optimal switch vector S (t) is acted on the upper cycle according to the equivalent principle of redundant vector current following performancek)＝(SA(tk),SB(tk),SC(tk),SN(tk) When the corresponding voltage vector belongs to the redundancy vector, the alternative switch sequence set obtained in the step (4) is subjected to secondary screening, and the switch sequence corresponding to the redundancy vector and S (t) are reservedk)＝(SA(tk),SB(tk),SC(tk),SN(tk) A group of switching sequences corresponding to the same switching sequence, excluding the redundancy vector corresponding to S (t) in the switching sequencek)＝(SA(tk),SB(tk),SC(tk),SN(tk) A switching sequence that differs for the corresponding switching sequence;
the voltage jump limiting principle is as follows: three-level four-bridge arm active power filter upper period tkOptimum switching vector S (t) acting at a timek)＝(SA(tk),SB(tk),SC(tk),SN(tk) ) with the lower period tk+1Switching vector S (t) acting at a timek+1)＝(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1) The constraint must be satisfied:
Figure FDA0003237236400000042
and (4) screening out the switch sequence set of the alternative voltage vectors which finally participate in prediction according to the redundant vector current following performance equivalence principle and the voltage jump limiting principle.
7. The method of claim 1A low-computation-quantity three-level four-leg active power filter FCS-MPC control method is characterized in that the method in the step (6) is as follows: selecting a group of switching vectors corresponding to the minimum value of the cost function as the optimal switching vector of the system according to the voltage following cost function g, namely selecting a group of switching vectors S (t) with the minimum voltage following error from the candidate switching sequence set finally participating in prediction obtained in the step (5)k+1)＝(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1) Act on the next control cycle:
Figure FDA0003237236400000051
in the formula,
Figure FDA0003237236400000052
is tk+1The reference voltage vector alpha beta gamma coordinate system at the moment,
Figure FDA0003237236400000053
is tk+1Predicting value under the coordinate system of the time prediction voltage vector alpha beta gamma,
Figure FDA0003237236400000054
and tk+1Switching vector S (t) acting on the system at a timek+1)＝(SA(tk+1),SB(tk+1),SC(tk+1),SN(tk+1) The relationship is as follows:
Figure FDA0003237236400000055
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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
CN117833248A (en) * 2024-03-06 2024-04-05 电子科技大学 Model-free predictive control method for T-shaped three-level parallel active power filter

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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
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