阅读说明：本技术 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 (Low-computation-quantity three-level four-bridge-arm active power filter FCS-MPC control method ) 是由 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 于 2021-08-30 设计创作，主要内容包括：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 invention provides a low-computation-quantity three-level four-bridge-arm active power filter FCS-MPC control method, which aims to reduce the prediction computation quantity of a three-level four-bridge-arm active power filter FCS-MPC control system and give consideration to voltage jump limitation and current following control performance; according to the method, the optimal voltage vector is selected through the cost function according to the principle of optimal voltage following performance, optimal control of current following performance is achieved, the corresponding switch vector is output and acts on the active power filter in the next control period, the prediction calculation amount is greatly reduced, and the calculation amount can be reduced from 81 times to 4-18 times.)

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 t_kSampling 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 model_k+1The current output by the active power filter at the moment;

(2) for t_kTime delay compensation is carried out on the time harmonic reference current to obtain t_k+1A time harmonic reference current;

(3) according to the dead beat control idea, the t obtained by the calculation in the step (1) is used_k+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 axisCombining 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 t_kTime active power filter output current [ i ]_α(t_k),i_β(t_k),i_γ(t_k)]Harmonic reference currentAnd the grid voltage [ e ]_α(t_k),e_β(t_k),e_γ(t_k)]Sampling is carried out, subscripts alpha, beta and gamma refer to a three-phase static coordinate system, i_α(t_k),i_β(t_k),i_γ(t_k) Is t_kThe actual value of the output current of the active power filter under the alpha beta gamma coordinate system at the moment,is t_kActual value of time harmonic reference current in alpha beta gamma coordinate system, e_α(t_k),e_β(t_k),e_γ(t_k) Is t_kThe 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 period_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Acting on the active power filter, subscripts a, B, C, N referring to the four-phase arm of the active power filter, S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Are each t_kSwitching 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 filter_k+1Output current value of active power filter at time Is t_k+1Time active power filter outputThe current alpha is measured as the actual value of the axis,is t_k+1The active power filter outputs the actual value of the current beta coordinate axis at the moment,is t_k+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:

wherein v is_α(t_k) Is t_kThe output voltage vector alpha coordinate axis actual value v of the moment active power filter_β(t_k) Is t_kThe output voltage vector beta coordinate axis actual value v of the moment active power filter_γ(t_k) Is t_kThe output voltage vector gamma coordinate axis actual value of the active power filter at the moment, t_kOutput voltage vector v of time active power filter_α(t_k)、v_β(t_k)、v_γ(t_k) And t_kMoment-action switching vector S (t)_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) The relationship of) is as follows:

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, U_dcThe 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:

wherein the content of the first and second substances,is t_kThe actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-1The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-2The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k+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 used_k+1Time harmonic reference currentAnd step (1) t obtained by controlling delay compensation_k+1Time-of-day active power filteringOutput current value of the deviceSubstituting into a prediction model to obtain t_k+1Reference voltage vector of time of day

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 t_k+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 t_k+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 inThirteen 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 filter_dc，t_k+1Each predicted voltage vector at a timeAll have t_k+1A set of switching vectors S (t) of time instants_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Correspond to t_k+1One group of switching vectors S (t) acted by three-level four-bridge-arm active power filter at moment_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Generate a corresponding one of the predicted voltage vectors)Is represented as follows:

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 t_k+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 t_k+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 vectorIn 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:

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 performance_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 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 reserved_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) A group of switching sequences corresponding to the same switching sequence, excluding the redundancy vector corresponding to S (t) in the switching sequence_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) 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 t_kOptimum switching vector S (t) acting at a time_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) ) with the lower period t_k+1Switching vector S (t) acting at a time_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) The constraint must be satisfied:

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)＝(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:

in the formula (I), the compound is shown in the specification,is t_k+1The reference voltage vector alpha beta gamma coordinate system at the moment,is t_k+1Predicting value under the coordinate system of the time prediction voltage vector alpha beta gamma,and t_k+1Switching vector S (t) acting on the system at a time_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) The relationship is as follows:

Technical Field

The invention relates to the technical field of control of three-level four-bridge arm active power filters, in particular to a low-computation-quantity FCS-MPC control method of a three-level four-bridge arm active power filter.

Background

With the rapid development of science and technology, power electronic equipment and nonlinear loads are widely applied to power systems, and the problem of harmonic pollution is increasingly serious. Harmonic control and three-phase current imbalance are two common problems in a three-phase four-wire system of a low-voltage distribution network, and an Active Power Filter (APF) with three levels and four bridge arms is an important measure which can comprehensively solve the two Power quality problems. The FCS-MPC (Finite Control Set Model Predictive Control) technology has the advantages of intuitive modeling, simple Control, realization of multi-target optimization Control, no PWM (pulse width modulation) modulator and PI (proportional integral) parameter adjustment and the like, and has become the main research direction of multi-level APF Control.

The traditional FCS-MPC is directly applied to the three-level four-bridge-arm APF, so that the problem of large operation amount exists, and related researches aiming at reducing the operation amount are few at present. Therefore, the invention provides a low-computation-quantity three-level four-leg active power filter FCS-MPC control method.

Disclosure of Invention

The purpose of the invention is as follows: the method aims to solve the problem of large operation amount in FCS-MPC control of the three-level four-bridge arm APF, and realizes low operation amount FCS-MPC control of the three-level four-bridge arm APF which gives consideration to the equivalent principle of redundant vector current following performance and the voltage jump limiting principle. The invention provides a low-computation-quantity three-level four-bridge-arm active power filter FCS-MPC control method.

And dividing the candidate voltage space vector of the three-level four-bridge arm APF into 13 planes according to the height of a gamma coordinate axis by adopting a layered optimization idea, and constructing a candidate voltage vector set by using two adjacent planes. According to the dead beat control idea, substituting harmonic reference current into a system current prediction model to convert the harmonic reference current into an equivalent voltage prediction model to obtain an equivalent reference voltage vector, acquiring an alternative switch sequence set corresponding to the alternative voltage vector for the first time according to the actual position of a gamma component of the reference voltage vector, carrying out secondary screening on the alternative switch sequence set according to a redundant vector current following performance equivalence principle and a voltage jump limiting principle, and screening out a switch sequence set of the alternative voltage vector which finally participates in prediction; according to the voltage following cost function, a group of switch vectors corresponding to the minimum value of the cost function is selected as the optimal switch vector of the system and acts on the active power filter in the next period, and the method greatly reduces the prediction calculation amount and can reduce the calculation amount from 81 times to 4-18 times.

The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a low-computation-quantity three-level four-leg active power filter FCS-MPC control method comprises the following steps:

(1) for t_kSampling 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 model_k+1The active power filter outputs current at a time.

(2) For t_kTime delay compensation is carried out on the time harmonic reference current to obtain t_k+1The time harmonic reference current.

(3) According to the dead beat control idea, the t obtained by the calculation in the step (1) is used_k+1And (3) converting the output current of the active power filter at the moment and the harmonic reference current obtained in the step (2) into equivalent reference voltage through a prediction model.

(4) According to t acquired in the step (3)_k+1Reference value of time equivalent reference voltage vector gamma coordinate axisAnd (4) selecting 81 predicted voltage vectors of the three-level four-bridge arm active power filter once according to a space layering idea by combining the space distribution of the voltage vectors of the three-level four-bridge arm active power filter.

(5) And (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) And (5) finally determining a voltage vector set participating in prediction, 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.

Further, the method of the step (1) is specifically as follows:

(1.1) to t_kTime active power filter output current [ i ]_α(t_k),i_β(t_k),i_γ(t_k)]Harmonic reference currentAnd the grid voltage [ e ]_α(t_k),e_β(t_k),e_γ(t_k)]Sampling is carried out, subscripts alpha, beta and gamma refer to a three-phase static coordinate system, i_α(t_k),i_β(t_k),i_γ(t_k) Is t_kConstantly active electric filterThe actual value of the output current of the wave filter under an alpha beta gamma coordinate system,is t_kActual value of time harmonic reference current in alpha beta gamma coordinate system, e_α(t_k),e_β(t_k),e_γ(t_k) Is t_kThe 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 period_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Acting on the active power filter, subscripts a, B, C, N referring to the four-phase arm of the active power filter, S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Are each t_kSwitching 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 prediction model_k+1Output current value of active power filter at timeIs t_k+1The active power filter outputs the actual value of the current alpha coordinate axis at the moment,is t_k+1The active power filter outputs the actual value of the current beta coordinate axis at the moment,is t_k+1And the active power filter outputs the actual value of the current gamma coordinate axis at the moment.

The current prediction model of the three-level four-bridge arm active power filter is as follows:

v_α(t_k) Is t_kThe output voltage vector alpha coordinate axis actual value v of the moment active power filter_β(t_k) Is t_kThe output voltage vector beta coordinate axis actual value v of the moment active power filter_γ(t_k) Is t_kThe output voltage vector gamma coordinate axis actual value of the active power filter at the moment, t_kOutput voltage vector v of time active power filter_α(t_k)、v_β(t_k)、v_γ(t_k) And t_kMoment-action switching vector S (t)_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) The relationship of) is as follows:

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, and U_dcThe voltage of a single capacitor at the direct current side of the three-level four-bridge arm active power filter is obtained.

Further, the method of the step (2) is specifically 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:

is t_kThe actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-1The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-2The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k+1And (3) reference values of the harmonic reference current at the moment in an alpha beta gamma coordinate system.

Further, the method of the step (3) is specifically as follows: according to the dead beat control idea, the t obtained in the step (2) is used_k+1Time harmonic reference currentAnd step (1) t obtained by controlling delay compensation_k+1Output current value of time active power filterEquivalent transformation into t by predictive model_k+1Reference voltage vector of time of day

Further, the method of the step (4) is specifically as follows: three-level four-bridge arm active power filter t_k+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 t_k+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 inThirteen 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 filter_dc，t_k+1Each predicted voltage vector at a timeAll have t_k+1A set of switching vectors S (t) of time instants_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Correspond to t_k+1One group of switching vectors S (t) acted by three-level four-bridge-arm active power filter at moment_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Generate a corresponding predicted voltage vectorIs represented as follows:

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 t_k+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 t_k+1Thirteen 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, are defined as one layer, twelve layers are counted, all the voltage vectors in each layer form a group of alternative voltage vector sets, and the switch vectors corresponding to all the voltage vectors form an alternative switch sequence set. The idea of spatial layering is according to t in step (3)_k+1Time reference voltage vectorIn 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:

further, the method of the step (5) is specifically as follows: the three-level four-bridge arm active power filter can output 81 predicted voltage vectors, two vectors with completely overlapped space positions of the predicted voltage vectors are redundant vectors, and the redundant vectors follow the performance equivalence principle, namely the optimal switch vector S (t) acted by the upper period_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 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 reserved_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) A group of switching sequences corresponding to the same switching sequence, excluding the redundancy vector corresponding to S (t) in the switching sequence_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) 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 t_kOptimum switching vector S (t) acting at a time_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) ) with the lower period t_k+1Switching vector S (t) acting at a time_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) The constraint must be satisfied:

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.

Further, the method of step (6) is specifically as follows: the method of the step (6) is concretely 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)＝(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:

in the formula (I), the compound is shown in the specification,is t_k+1The reference voltage vector alpha beta gamma coordinate system at the moment,is t_k+1And predicting the value under the coordinate system of the time prediction voltage vector alpha beta gamma.And t_k+1Switching vector S (t) acting on the system at a time_k+1) The relationship is as follows:

has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial effects:

aiming at the voltage vector distribution of the three-level four-bridge arm active power filter, the prediction operand is effectively reduced according to a space layering idea, and meanwhile, the prediction operand is further reduced by combining a redundant vector current following performance equivalent principle and a voltage jump limiting principle, and the current optimal tracking performance is considered while the prediction operand is reduced from 81 times to 4-18 times.

Drawings

FIG. 1 is a voltage vector space distribution diagram of a three-level four-leg APF;

FIG. 2 is a flow chart of an FCS-MPC control method of a low-operand three-level four-leg APF;

FIG. 3 shows three-phase currents of a power grid before and after harmonic current compensation in a low-computation-amount FCS-MPC control method for three-level four-bridge-arm APF; (a) the power grid three-phase current oscillogram before compensation, (b) the power grid three-phase current oscillogram after compensation;

FIG. 4 shows a low-computation-quantity FCS-MPC control method for three-level four-leg APF, and power grid A-phase current harmonic analysis before and after harmonic current compensation. (a) A harmonic analysis diagram of the A-phase current of the power grid before compensation, and (b) a harmonic analysis diagram of the A-phase current of the power grid after compensation.

Detailed Description

The invention is further explained by a three-phase four-wire low-voltage power supply system of a three-level four-leg active power filter with reference to the attached drawings, and the specific implementation steps of the invention are as follows:

1) for t_kTime active power filter output current [ i ]_α(t_k),i_β(t_k),i_γ(t_k)]Harmonic reference currentAnd the grid voltage [ e ]_α(t_k),e_β(t_k),e_γ(t_k)]Sampling is carried out, subscripts alpha, beta and gamma refer to a three-phase static coordinate system, i_α(t_k),i_β(t_k),i_γ(t_k) Is t_kThe actual value of the output current of the active power filter under the alpha beta gamma coordinate system at the moment,is t_kActual value of time harmonic reference current in alpha beta gamma coordinate system, e_α(t_k),e_β(t_k),e_γ(t_k) Is t_kThe 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 period_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Acting on the active power filter, subscripts a, B, C, N referring to the four-phase arm of the active power filter, S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) Are each t_kSwitching 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;

2) performing control delay compensation, and calculating t according to the prediction model_k+1Output current value of active power filter at timeIs t_k+1The active power filter outputs the actual value of the current alpha coordinate axis at the moment,is t_k+1The active power filter outputs the actual value of the current beta coordinate axis at the moment,is t_k+1And the active power filter outputs the actual value of the current gamma coordinate axis at the moment.

The current prediction model of the three-level four-bridge arm active power filter is as follows:

v_α(t_k) Is t_kThe output voltage vector alpha coordinate axis actual value v of the moment active power filter_β(t_k) Is t_kThe output voltage vector beta coordinate axis actual value v of the moment active power filter_γ(t_k) Is t_kThe output voltage vector gamma coordinate axis actual value of the active power filter at the moment, t_kActive power at any momentFilter output voltage vector v_α(t_k)、v_β(t_k)、v_γ(t_k) And t_kMoment-action switching vector S (t)_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) The relationship of) is as follows:

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, and U_dcThe voltage of a single capacitor at the direct current side of the three-level four-bridge arm active power filter is obtained.

3) 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:

is t_kThe actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-1The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k-2The actual value of the harmonic reference current sampled at the moment in the alpha beta gamma coordinate system,is t_k+1And (3) reference values of the harmonic reference current at the moment in an alpha beta gamma coordinate system.

4) According to the dead beat control idea, t obtained in the step 3) is used_k+1Time harmonic reference currentAnd step 2) t obtained by controlling delay compensation_k+1Output current value of time active power filterSubstituting into a prediction model to obtain t_k+1Reference voltage vector of time of day

5) Three-level four-bridge arm active power filter t_k+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 t_k+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 inThirteen 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 filter_dc，t_k+1Each predicted voltage vector at a timeAll have t_k+1A set of switching vectors S (t) of time instants_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Correspond to t_k+1One group of switching vectors S (t) acted by three-level four-bridge-arm active power filter at moment_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) Generate a corresponding predicted voltage vectorIs represented as follows:

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 t_k+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 t_k+1Thirteen planes, in which the end points of 81 voltage vectors capable of being output by the three-level four-leg active power filter are located, are defined as one layer, twelve layers are counted, all the voltage vectors in each layer form a group of alternative voltage vector sets, and the switch vectors corresponding to all the voltage vectors form an alternative switch sequence set. Spatial layering idea i.e. according to t in step 4)_k+1Time reference voltage vectorIn 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:

6) the three-level four-bridge arm active power filter can output 81 predicted voltage vectors, two vectors with completely overlapped space positions of the predicted voltage vectors are redundant vectors, and the redundant vectors follow the performance equivalence principle, namely the optimal switch vector of the upper period actionS(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, the alternative switch sequence set obtained in the step 5) is subjected to secondary screening, and the switch sequence corresponding to the redundant vector and S (t) are reserved_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) A group of switching sequences corresponding to the same switching sequence, excluding the redundancy vector corresponding to S (t) in the switching sequence_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) 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 t_kOptimum switching vector S (t) acting at a time_k)＝(S_A(t_k),S_B(t_k),S_C(t_k),S_N(t_k) ) with the lower period t_k+1Switching vector S (t) acting at a time_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) The constraint must be satisfied:

screening out the switching sequence set of the candidate voltage vectors which finally participate in prediction for the candidate switching sequence set obtained in the step 5) according to the redundant vector current following performance equivalence principle and the voltage jump limiting principle.

7) Selecting a group of switching vectors corresponding to the minimum value of the cost function as the optimal switching vector of the system, namely a group of switching vectors S (t) with the minimum voltage following error according to the voltage following cost function g of the candidate switching sequence set finally participating in prediction obtained in the step 6)_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)And (3) period:

in the formula (I), the compound is shown in the specification,is t_k+1The reference voltage vector alpha beta gamma coordinate system at the moment,is t_k+1And predicting the value under the coordinate system of the time prediction voltage vector alpha beta gamma.And t_k+1Switching vector S (t) acting on the system at a time_k+1)＝(S_A(t_k+1),S_B(t_k+1),S_C(t_k+1),S_N(t_k+1) The relationship is as follows:

8) and repeating the steps in the next control period.

Fig. 1 is a voltage vector space distribution diagram of a three-level four-leg APF, and fig. 2 is a flow chart of an FCS-MPC control method of a low-operand three-level four-leg APF. Fig. 3 shows three-phase currents of a power grid before and after harmonic current compensation in a three-level four-leg APF low-voltage power distribution system by using the low-computation FCS-MPC control method, and fig. 4 shows a harmonic analysis of a phase current of the power grid before and after harmonic current compensation, which can be shown in fig. 3 and 4.