CN104993485A - Parallel hybrid active filtering system and control method therefor - Google Patents

Abstract

The invention discloses a parallel hybrid active filtering system, and the system comprises three groups of reactive filters which are respectively connected to three phase lines of an AC power grid. The three groups of reactive filters are respectively connected to an active filter, and three phase lines of the AC power grid are also connected with a nonlinear load. Each reactive filter comprises a capacitor and an inductor, which are sequentially connected to the three phase lines of the AC power grid in a series manner. The invention also discloses a control method for the system, and the method comprises the steps: firstly building a mathematic model for the system; secondly building a linear active-disturbance-rejection control mathematic model, and building a repeated control compensation linear active-disturbance-rejection control model according to the internal model principle; and finally carrying out the control of the system through combining the repeated control compensation linear active-disturbance-rejection control model and the linear active-disturbance-rejection control mathematic model. According to the invention, a problem that the control precision of active filters in the prior art is poor is solved.

Description

A kind of parallel connection mixed type active filter system and control method thereof

Technical field

The invention belongs to active filter technical field, be specifically related to a kind of parallel connection mixed type active filter system, the invention still further relates to the control method of parallel connection mixed type active filter system.

Background technology

Along with the fast development of power electronic technology, in modern electric network, non-linear power electronic equipment is widely used.The use of power electronic equipment makes line voltage and electric current that serious distortion occur, and have impact on the quality of electric energy, therefore becomes topmost harmonic source in modern industry.Shunt Hybrid Active Power Filter is formed in parallel by active filter and passive filter, combine the advantage of passive filter and active filter, can either effectively compensate harmonic wave, be compared to simple APF, cost can be made again to reduce, start to show extremely strong competitiveness.Nowadays, Active Power Filter-APF compares control and Current Hysteresis Comparison Control from the most frequently used triangular carrier, and to more complicated control method as space voltage vector control, track with zero error, adaptive control etc., they have respective pluses and minuses.

Triangular wave control method is simple with its control method, switching frequency is fixedly widely used, but its shortcoming is that robustness is poor.When Active Power Filter-APF be applied to widely nonlinear load situation time, just must consider stability problem.Parameter uncertainties on nonlinear load and circuit or Unmarried pregnancy all likely make system unstability, and this will seriously limit widely using of active filter.So, seek a kind of can be good at ensureing the stability of a system and robustness control method and to be applied to active power filter system be very necessary.Auto Disturbances Rejection Control Technique (Auto Disturbance RejectionController, ADRC) is a kind of nonlinear control techniques proposed in recent years, and this controller does not rely on the concrete Mathematical Modeling of controlled device.While its core advantage is to observe the state variable of system by extended state observer, and observe the comprehensive disturbance of system, obtain generalized state error and feedforward compensation, counteracting are carried out to disturbance term, therefore making control system all increase significantly in stability and robustness.But Active Disturbance Rejection Control brings larger difficulty to theory analysis and engineering design, control design case parameter too much (about 10) simultaneously, and gamma controller is difficult to carry out frequency-domain analysis conventional in engineering to determine boundary of stability.So for above problem, all controllers and ESO are realized obtaining linear active disturbance rejection controller (Linear active disturbance rejectioncontrol all in linear form, LADRC), controling parameters is dropped to 4 by LADRC, and have clearer and more definite physical significance, be extremely convenient to engineer applied.But linear active disturbance rejection controller can only the part of bucking-out system non-linear, still there is certain uncertainty in system, cannot realize good control precision.

Summary of the invention

The object of this invention is to provide a kind of parallel connection mixed type active filter system, solve the problem of the control precision difference of the active filter existed in prior art.

Another object of the present invention is to provide a kind of control method of parallel connection mixed type active filter system.

First technical scheme of the present invention is, a kind of parallel connection mixed type active filter system, comprise three components and be not connected to passive filter in AC network triple line, three groups of passive filters are all connected to active filter again, and AC network triple line is also connected with nonlinear load.

The feature of the present invention first technical scheme is also,

Passive filter comprises the electric capacity and inductance that are sequentially connected in series in AC network triple line.

Second technical scheme of the present invention is, a kind of control method of parallel connection mixed type active filter system, based on parallel connection mixed type active filter system, is specifically implemented according to following steps:

Step 1, set up the Mathematical Modeling of parallel connection mixed type active filter system:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[s_A-\frac{1}{3}(s_A+s_B+s_C)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[s_B-\frac{1}{3}(s_A+s_B+s_C)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[s_C-\frac{1}{3}(s_A+s_B+s_C)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(1\right)$

In formula (1): ω is the angular frequency of circuital current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, i _a, i _b, i _cbe respectively three-phase current on line side value, u _dcfor DC voltage value, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence value, s _a, s _b, s _crepresent on off state, s _j(j=A, B, C) value is as follows:

S _jthe switch function of (j=A, B, C), under symmetric regular-sampled SPWM controls, is separately expressed as:

In formula (3): t represents the sampling time, T _cfor PWM switch periods, d is duty ratio, and m represents sampled point, m=1,2,3 ... ..,

Formula (3) is obtained by Fourier expansion:

$s_j=d_j+{\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(-1)}^n\frac{2}{n\mathrm{\π}}sin\left({\mathrm{nd}}_j\mathrm{\π}\right)cos\left(\frac{2n\mathrm{\π}t}{T_c}\right),j=A,B,C---\left(4\right)$

In formula (4), d _jrepresent duty ratio, T _cfor PWM switch periods,

Under high switching frequency f, ignore s _jthe high-frequency harmonic composition of (j=A, B, C) switch function, obtaining low frequency model by Fourier expansion expression formula is:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[d_A-\frac{1}{3}(d_A+d_B+d_C)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[d_B-\frac{1}{3}(d_A+d_B+d_C)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[d_C-\frac{1}{3}(d_A+d_B+d_C)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(5\right)$

In formula (5), r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter (1) capacitance, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, s _a, s _b, s _crepresent on off state, d _j(j=A, B, C) represents duty ratio,

Adopt triangular modulation, duty ratio d _j(j=A, B, C) meets following formula:

$d_j=\frac{1}{2}(1+\frac{v_{rj}}{V_{tri}}),j=A,B,C---\left(6\right)$

In formula (6), v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude, formula (6) substituted into formula (5), obtains formula (7):

$\stackrel{\‾}{i_j}=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j-\frac{U_{dc}}{2{\mathrm{LV}}_{tri}}{v}_{rj}---\left(7\right)$

In formula (7), represent the differential value of three-phase current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, b _jw _jrepresent that switching loss, metrical error and external factor are to the interference of system, U _dcfor DC voltage,

Formula (7) is reduced to:

$\stackrel{\‾}{i_j}=f_j+b_0{u}_j---\left(8\right)$

In formula (8): $f_j=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j,$

$b_0=-\frac{U_c}{2{\mathrm{LV}}_{tri}},$

u _j＝v _rj，

B in formula (8) ₀for the disturbance compensation factor, be determine to compensate the strong and weak factor, use as adjustable parameter in the controls, find out from formula (7), f _jnot only comprise switching loss, metrical error external disturbance information, also comprise the information of the characterization system internal dynamics relevant with output information;

Step 2, after step 1 pair parallel connection mixed type active filter system modeling terminates, set up linear active disturbance rejection control mathematical model:

Adopt linear extended state observer (Linear Extended State Observer-LESO) and linear state error feedback control rule (Linear State Error Feedback-LSEF) as single order automatic disturbance rejection controller, the linear extended state observer of governing equation (LESO) equation of single order automatic disturbance rejection controller and linear state error feedback control rule (LSEF) equation, linear extended state observer (LESO) equation is specifically expressed as:

$\left\{\begin{array}{c}\mathrm{\ϵ}=Z_{21}-I_{cx}\\ Z_{21}=Z_{22}-B_1\mathrm{\ϵ}+u\left(t\right)\\ Z_{22}=-B_2\mathrm{\ϵ}\end{array}\right.---\left(9\right)$

In formula (9), Z ₂₁, Z ₂₂for two output variables of linear extended state observer (LESO) equation, ε is error, I _cxfor compensating current signal, be system feedback, B ₁, B ₂for proportionality coefficient, known by formula (9), Z ₂₁tracking system feedback I _cx, and as the current feedback signal of controller, Z ₂₂be referred to as disturbance compensation, total disturbance a (t) of tracking system, and be introduced directly into the output of linear active disturbance rejection controller, feedforward compensation is carried out to the disturbance of system,

Linear state error feedback control rule (LSEF) is expressed as:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1=Z_{11}-Z_{21}\\ u_0=k_p{\mathrm{\ϵ}}_1\end{array}\right.---\left(10\right)$

In formula (10), Z ₁₁for instruction current signal, ε ₁for error, as the input of linear state error feedback control rule (LSEF), k _pfor proportionality coefficient, u ₀for initial controlled quentity controlled variable,

Convolution (9) and formula (10), obtain automatic disturbance rejection controller and always export u, and the expression formula of u is:

u＝(u ₀-Z ₂₂)/b (11)

In formula (11), u ₀for initial controlled quentity controlled variable, b is the disturbance compensation factor,

Known by formula (9), formula (10), formula (11), in the control procedure of linear active disturbance rejection controller, adjustable parameter is: the proportionality coefficient k in LSEF _p, the proportionality coefficient B in LESO ₁, B ₂, disturbance compensation factor b, controlled quentity controlled variable u finally acts on controlled device;

In step 3, the basis of linear active disturbance rejection controller that established in step 2, set up Repetitive control compensation linear active disturbance rejection Controlling model according to internal model principle, be specially: given input instruction current signal I _c ^*x, by more given I _c ^*x and actual output offset current I _cxthe deviation ε drawn _k, deviation ε _kthrough having the low pass filter Q of delay link ₁(s) e ^-Tsafter obtaining the deviation ε (k-T) in a sampling period, regulate through PID, finally obtain being that the Repetitive controller in cycle exports compensating signal U with T _rC, the expression formula of Repetitive control compensation linear active disturbance rejection Controlling model is specific as follows:

$\{\begin{array}{c}{\mathrm{\ϵ}}_1=I_{cx}^{*}-I_{cx}\\ \mathrm{\ϵ}(k-T)={\mathrm{\ϵ}}_1{e}^{-Ts}\\ U_{RC}=k_c\mathrm{\ϵ}(k-T)+{\mathrm{\ϵ}}_1\end{array}---\left(15\right)$

In formula (15), ε ₁for error, as instruction current signal I _c ^*x and actual offset current I _cxdifference, ε (k-T) was the error in a upper cycle, U _rCfor taking T as the compensating signal that the Repetitive controller in cycle exports,

Repetitive control compensation linear active disturbance rejection control in step 4, integrating step 3 and the linear active disturbance rejection in step 2 control two kinds of algorithms, and the control signal finally acting on system is

τ＝U _ADRC+U _RC(16)

In formula (16), U _aDRCfor the output signal of linear active disturbance rejection controller, U _aDRCfor automatic disturbance rejection controller always exports u, U _rCfor the output compensating signal of Repetitive controller;

Step 5, the control signal τ of the system that finally acts on drawn above to be inputted in controlled device, controls:

To finally act on the control signal τ of system, after triangular modulation, obtain six road pulse signals, by 6 switching tubes of the three-phase brachium pontis in six roads pulse signal input active filter (2), draw actual offset current I by the control of switch tube _cx, finally realize the control of parallel connection mixed type active filter system.

The feature of the present invention second technical scheme is also,

High switching frequency f span is f≤f _c, f _crepresent switching frequency.

The invention has the beneficial effects as follows, a kind of control method of parallel connection mixed type active power filtering, the comprehensive disturbance of system is observed while adopting linear active disturbance rejection control method can observe the state variable of system by extended state observer, obtain generalized state error and feedforward compensation is carried out to disturbance term, offset, therefore control system is made all to increase significantly in stability and robustness, the repetitive control adopted inputs the deviation of a upper periodic duty and existing deviation jointly as system, not only can improve the tracking accuracy of system, robustness can also be improved and improve Systematical control quality.

Accompanying drawing explanation

Fig. 1 is the structural representation of a kind of parallel connection mixed type active filter system of the present invention;

Fig. 2 is the control method neutral line Active Disturbance Rejection Control block diagram of a kind of parallel connection mixed type active filter system of the present invention;

Fig. 3 is based on the Shunt Hybrid Active Power Filter control block diagram that the linear active disturbance rejection repeating to compensate controls in the control method of a kind of parallel connection mixed type active filter system of the present invention.

In figure, 1. passive filter, 2. active filter, 3. nonlinear load, 4. AC network.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

A kind of parallel connection mixed type active filter system of the present invention, using voltage source inverter as its active part, using single tuned filter as its passive part, active part and single tuned filter form hybrid active filter, structure as shown in Figure 1, concrete structure is: comprise three components and be not connected to passive filter 1 in AC network 4 triple line, three groups of passive filters 1 are all connected to active filter 2 again, AC network 4 triple line is also connected with nonlinear load 3, passive filter 1 comprises the electric capacity C and inductance L that are sequentially connected in series in AC network 4 triple line.

Voltage source inverter regards a desirable voltage U as _c, harmonic source is equivalent to ideal current source I _l, assuming that the switch of inverter is desirable switching device, Parallel Hybrid Active Power Filter circuit structure can be reduced to construction of switch according to following formula, wherein u _j ^*(the three-phase power grid voltage equivalence reduced value that j=a, b, c) expression enter viewed from transformer side.

The control method of parallel connection mixed type active filter system of the present invention, based on parallel connection mixed type active filter system, specifically implement according to following steps:

Step 1, set up the Mathematical Modeling of parallel connection mixed type active filter system:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[s_A-\frac{1}{3}(s_A+s_B+s_C)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[s_B-\frac{1}{3}(s_A+s_B+s_C)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[s_C-\frac{1}{3}(s_A+s_B+s_C)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(1\right)$

In formula (1): ω is the angular frequency of circuital current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, i _a, i _b, i _cbe respectively three-phase current on line side value, u _dcfor DC voltage value, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, s _a, s _b, s _crepresent on off state, s _j(j=A, B, C) value is as follows:

S _jthe switch function of (j=A, B, C), under symmetric regular-sampled SPWM controls, is separately expressed as:

In formula (3): t represents the sampling time, T _cfor PWM switch periods, d is duty ratio, and m represents sampled point, m=1,2,3 ... ..,

Formula (3) is obtained by Fourier expansion:

$s_j=d_j+{\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(-1)}^n\frac{2}{n\mathrm{\π}}sin\left({\mathrm{nd}}_j\mathrm{\π}\right)cos\left(\frac{2n\mathrm{\π}t}{T_c}\right),j=A,B,C---\left(4\right)$

In formula (4), d _jrepresent duty ratio, T _cfor PWM switch periods,

Under high switching frequency f, high switching frequency f span is f≤f _c, f _crepresent switching frequency, ignore s _jthe high-frequency harmonic composition of (j=A, B, C) switch function, obtaining low frequency model by Fourier expansion expression formula is:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[d_A-\frac{1}{3}(d_A+d_B+d_C)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[d_B-\frac{1}{3}(d_A+d_B+d_C)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[d_C-\frac{1}{3}(d_A+d_B+d_C)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(5\right)$

In formula (5), r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter (1) capacitance, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, s _a, s _b, s _crepresent on off state, d _j(j=A, B, C) represents duty ratio,

Adopt triangular modulation, duty ratio d _j(j=A, B, C) meets following formula:

$d_j=\frac{1}{2}(1+\frac{v_{rj}}{V_{tri}}),j=A,B,C---\left(6\right)$

In formula (6), v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude,

The object of current follow-up control is the change of the offset current trace command current signal fast and accurately that Active Power Filter-APF is exported, and is the key factor determining Active Power Filter-APF stable state and dynamic property.Curren tracing control method directly determines accuracy and the rapidity of system,

Formula (6) is substituted into formula (5), obtains formula (7):

$\stackrel{\‾}{i_j}=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j-\frac{U_{dc}}{2{\mathrm{LV}}_{tri}}{v}_{rj}---\left(7\right)$

In formula (7), represent the differential value of three-phase current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, b _jw _jrepresent that switching loss, metrical error and external factor are to the interference of system, U _dcfor DC voltage,

Formula (7) is reduced to:

$\stackrel{\‾}{i_j}=f_j+b_0{u}_j---\left(8\right)$

In formula (8): $f_j=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j,$

$b_0=-\frac{U_c}{2{\mathrm{LV}}_{tri}},$

u _j＝v _rj，

B in formula (8) ₀for the disturbance compensation factor, be determine to compensate the strong and weak factor, use as adjustable parameter in the controls, find out from formula (7), f _jnot only comprise switching loss, metrical error external disturbance information, also comprise the information of the characterization system internal dynamics relevant with output information;

Step 2, after step 1 pair parallel connection mixed type active filter system modeling terminates, set up linear active disturbance rejection control mathematical model:

Adopt linear extended state observer (Linear Extended State Observer-LESO) and linear state error feedback control rule (Linear State Error Feedback-LSEF) as single order automatic disturbance rejection controller, the linear extended state observer of governing equation (LESO) equation of single order automatic disturbance rejection controller and linear state error feedback control rule (LSEF) equation, linear extended state observer (LESO) equation is specifically expressed as:

$\left\{\begin{array}{c}\mathrm{\ϵ}=Z_{21}-I_{cx}\\ Z_{21}=Z_{22}-B_1\mathrm{\ϵ}+u\left(t\right)\\ Z_{22}=-B_2\mathrm{\ϵ}\end{array}\right.---\left(9\right)$

In formula (9), Z ₂₁, Z ₂₂for two output variables of linear extended state observer (LESO) equation, ε is error, I _cxfor compensating current signal, be system feedback, B ₁, B ₂for proportionality coefficient, known by formula (9), Z ₂₁tracking system feedback I _cx, and as the current feedback signal of controller, Z ₂₂be referred to as disturbance compensation, total disturbance a (t) of tracking system, and be introduced directly into the output of linear active disturbance rejection controller, feedforward compensation is carried out to the disturbance of system,

Linear state error feedback control rule (LSEF) is expressed as:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1=Z_{11}-Z_{21}\\ u_0=k_p{\mathrm{\ϵ}}_1\end{array}\right.---\left(10\right)$

In formula (10), Z ₁₁for instruction current signal, ε ₁for error, as the input of linear state error feedback control rule (LSEF), k _pfor proportionality coefficient, u ₀for initial controlled quentity controlled variable,

Convolution (9) and formula (10), obtain automatic disturbance rejection controller and always export u, and the expression formula of u is:

u＝(u ₀-Z ₂₂)/b (11)

In formula (11), u ₀for initial controlled quentity controlled variable, b is the disturbance compensation factor,

Known by formula (9), formula (10), formula (11), in the control procedure of linear active disturbance rejection controller, adjustable parameter is: the proportionality coefficient k in LSEF _p, the proportionality coefficient B in LESO ₁, B ₂, disturbance compensation factor b, controlled quentity controlled variable u finally acts on controlled device;

Linear active disturbance rejection control block diagram as shown in Figure 2, v (k) for system given, x ₁k () is the transient process that Nonlinear Tracking Differentiator arranges.Z ₁(k), z ₂k () is for expanding observer to the estimator of system mode, z ₁k () is that extended state observer is to x ₁the observed quantity of (k), z ₂k () is the observed quantity of extended state observer to " total disturbance ".Nonlinear state Error Feedback control law exports " compensation " after being disturbed, controlled quentity controlled variable u (k) finally acts on controlled device, y (k) is the actual output of system, d (k) is the summation to various in system " disturbance ", Nonlinear Tracking Differentiator can fast be followed the tracks of input signal and also provides good differential signal in non-overshoot ground, avoids because set point is suddenlyd change the acute variation of controlled quentity controlled variable and the overshoot of output variable caused; Extended state observer is the core of automatic disturbance rejection controller, utilizes it can not only estimate each state variable, can also estimate disturbance and give corresponding compensation; Export from the output of Nonlinear Tracking Differentiator and extended state observer and get error and just obtain system state variables error, these state variable errors are after the computing of nonlinear state Error Feedback control law, add the compensation rate that extended state observer is estimated unknown disturbance, finally as the controlled quentity controlled variable of controlled device.Active Disturbance Rejection Control CONTROLLER DESIGN has very large flexibility, Controller gain variations does not rely on the mathematical models of system, challenge is simplified, in addition, owing to adopting nonlinear feedback, even if do not use integrator also can realize basic floating, avoid the side effect of integral feedback;

Step 3, in actual applications, linear active disturbance rejection control can only the part of bucking-out system non-linear, therefore cannot realize high accuracy to control, in order to improve the tracking accuracy of system, introduce repetitive control to compensate output, on the basis of the linear active disturbance rejection controller namely established in step 2, Repetitive control compensation linear active disturbance rejection Controlling model is set up according to internal model principle, the basic thought of Repetitive controller comes from the internal model principle in control theory, internal model principle is pointed out, system can stable state indifference ground trace command signal or suppress the necessary and sufficient condition of interference signal to be the internal mold comprising this command signal or interference signal in stable closed loop, the complete internal mold M of external excitation signal is met for the cycle signal configuration that is T _f, M _fexpression formula be:

$M_f=\frac{1}{1-e^{-Ts}}---\left(12\right)$

In order to reduce the gain of control action at high band, improving the stability of system, introducing low pass filter Q (s) in systems in which, complete internal mold M _fseparately be written as:

$M_f=\frac{1}{1-Q\left(s\right)e^{-Ts}}---\left(13\right)$

In formula (13),

$Q\left(s\right)=\frac{1}{1+T_{q}s}---\left(14\right)$

T _qfor filter time constant, introduced in the Active Disturbance Rejection Control improved by repetitive control, compensate output signal, as shown in Figure 3, wherein Repetitive control compensation loop is as shown in RC part in accompanying drawing 3 for the structure of designed Repetitive control compensation ADRC,

Set up Repetitive control compensation linear active disturbance rejection Controlling model to be specially: given input instruction current signal I _c ^*x, by more given I _c ^*x and actual output offset current I _cxthe deviation ε drawn _k, deviation ε _kthrough having the low pass filter Q of delay link ₁(s) e ^-Tsafter obtaining the deviation ε (k-T) in a sampling period, regulate through PID, finally obtain being that the Repetitive controller in cycle exports compensating signal U with T _rC, the expression formula of Repetitive control compensation linear active disturbance rejection Controlling model is specific as follows:

$\{\begin{array}{c}{\mathrm{\ϵ}}_1=I_{cx}^{*}-I_{cx}\\ \mathrm{\ϵ}(k-T)={\mathrm{\ϵ}}_1{e}^{-Ts}\\ U_{RC}=k_c\mathrm{\ϵ}(k-T)+{\mathrm{\ϵ}}_1\end{array}---\left(15\right)$

In formula (15), ε ₁for error, as instruction current signal I _c ^*x and actual offset current I _cxdifference, ε (k-T) was the error in a upper cycle, U _rCfor taking T as the compensating signal that the Repetitive controller in cycle exports,

It is given that step 4, Repetitive controller can ensure to export accurate tracking, but elimination interference at least needs one-period to the impact exported; Automatic disturbance rejection controller can produce regulating action immediately to tracking error, response speed is very fast, feature acting in conjunction in conjunction with two kinds of algorithms can ensure that system has dynamic responding speed and higher tracking accuracy faster, namely the Repetitive control compensation linear active disturbance rejection control in integrating step 3 and the linear active disturbance rejection in step 2 control two kinds of algorithms, and the control signal finally acting on system is

τ＝U _ADRC+U _RC(16)

In formula (16), U _aDRCfor the output signal of linear active disturbance rejection controller, U _aDRCfor automatic disturbance rejection controller always exports u, U _rCfor the output compensating signal of Repetitive controller;

Step 5, the control signal τ of the system that finally acts on drawn above to be inputted in controlled device, controls:

To finally act on the control signal τ of system, after triangular modulation, obtain six road pulse signals, by 6 switching tubes of the three-phase brachium pontis in six roads pulse signal input active filter (2), draw actual offset current I by the control of switch tube _cx, finally realize the control of parallel connection mixed type active filter system.

The high accuracy that the servo system that is mainly used in repetitive control repeats track controls, this method inputs the deviation of a upper periodic duty and existing deviation jointly as system, not only can improve the tracking accuracy of system, robustness can also be improved and improve Systematical control quality.

In order to verify that the linear active disturbance rejection control method of parallel connection mixed type active filter system is compared to the superiority of triangular wave in disturbance rejection, and added after Repetitive controller compared to the superiority of independent linear active disturbance rejection in precision, MATLAB/Simulink emulates, with parallel connection mixed type active filter system for controlled device, the tuning number of times of single tuned filter elects 7 times as, and system parameters is: net side line voltage U _s: 380V; Mains frequency f _s: 50Hz; Electrical network distributed inductance L _s: 0.23mH; Rectifier bridge AC inductance L _aC: 2mH; Passive filter electric capacity C _f: 10.86uF; Passive filter inductance L _f: 19.1mH; Active filter DC bus capacitor C _dc: 3300uF; Active filter DC voltage U _dc: 150V.

In order to compare the Performance comparision that linear active disturbance rejection (LADRC) and triangular wave control in disturbance rejection, recording two kinds of control methods in simulations respectively and placing an order when the value of inductance and electric capacity changes in tuning passive filter and net the THD value surveying electric current.The com-parison and analysis of two kinds of control method current on line side THD when table 1 is LC Parameters variation, can be drawn by table 1, when L Parameters variation, the THD change of LADRC control method is only 0.18%, and when triangular wave is changed to 0.53%, C Parameters variation, the THD change of LADRC control method is only 0.06%, and triangular wave is changed to 0.47%, therefore can reach a conclusion, LADRC control method serves good anti-jamming effectiveness when system parameter variations.

During table 1LC Parameters variation, two kinds of control method current on line side THD analyze and compare

In order to compare linear active disturbance rejection and repeat the compensation precision of linear active disturbance rejection, emulate two kinds of methods, table 2 be LADRC and the THD com-parison and analysis of current on line side under repeating linear Active Disturbance Rejection Control mode.As can be seen from Table 2, at the same conditions, repeating linear Auto-disturbance-rejection Control has higher tracking altitude compared to linear active disturbance rejection, after compensating, the THD of current on line side is lower, the superiority of the control method that the present invention proposes by simulating, verifying.

The THD of table 2 two kinds of control mode current on line side analyzes

Control method	Current on line side THD/ (%)
		LADRC	2.23
Repeat linear active disturbance rejection	2.09

The present invention distinguishes the deviation of compare instruction electric currents and offset current at three linear active disturbance rejection controllers; the deviation in a upper sampling period was obtained through delay link; process through PID controller and internal mold link; finally obtain periodic Repetitive controller and export compensating signal; be added to this compensating signal the output of linear active disturbance rejection controller; common input controlled device; not only to inside exist uncertainty and external disturbance estimate and compensate, can also improve systematic tracking accuracy, robustness and improvement system Control platform.

The present invention is applied to Parallel Hybrid Active Power Filter, has stronger robustness to the Parameter uncertainties on nonlinear load and circuit and change, has good dynamic property, very applicable to the current follow-up control problem solving active filter.

Claims (4)

1. a parallel connection mixed type active filter system, it is characterized in that, comprise three components and be not connected to passive filter (1) in AC network (4) triple line, three groups of passive filters (1) are all connected to again active filter (2), described AC network (4) triple line are also connected with nonlinear load (3).

2. a kind of parallel connection mixed type active filter system according to claim 1, it is characterized in that, described passive filter (1) comprises the electric capacity (C) and inductance (L) that are sequentially connected in series in AC network (4) triple line.

3. a control method for parallel connection mixed type active filter system, based on parallel connection mixed type active filter system, is characterized in that, specifically implements according to following steps:

Step 1, set up the Mathematical Modeling of parallel connection mixed type active filter system:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[s_A-\frac{1}{3}\left(s_A+s_B+s_C\right)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[s_B-\frac{1}{3}\left(s_A+s_B+s_C\right)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[s_C-\frac{1}{3}\left(s_A+s_B+s_C\right)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(1\right)$

In formula (1): ω is the angular frequency of circuital current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, i _a, i _b, i _cbe respectively three-phase current on line side value, u _dcfor DC voltage value, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, s _a, s _b, s _crepresent on off state, s _j(j=A, B, C) value is as follows:

S _jthe switch function of (j=A, B, C), under symmetric regular-sampled SPWM controls, is separately expressed as:

In formula (3): t represents the sampling time, T _cfor PWM switch periods, d is duty ratio, and m represents sampled point, m=1,2,3 ... ..,

Formula (3) is obtained by Fourier expansion:

$s_j=d_j+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}{(-1)}^n\frac{2}{n\mathrm{\π}}sin\left({\mathrm{nd}}_j\mathrm{\π}\right)cos\left(\frac{2n\mathrm{\π}t}{T_c}\right),j=A,B,C---\left(4\right)$

In formula (4), d _jrepresent duty ratio, T _cfor PWM switch periods,

Under high switching frequency f, ignore s _jthe high-frequency harmonic composition of (j=A, B, C) switch function, obtaining low frequency model by Fourier expansion expression formula is:

$\left[\begin{array}{c}\frac{{\mathrm{di}}_a}{dt}\\ \frac{{\mathrm{di}}_b}{dt}\\ \frac{{\mathrm{di}}_c}{dt}\\ \frac{{\mathrm{du}}_{dc}}{dt}\end{array}\right]=\left[\begin{array}{cccc}-\frac{r}{L}& 0& 0& -\frac{1}{L}\[d_A-\frac{1}{3}\left(d_A+d_B+d_C\right)\]\\ 0& -\frac{r}{L}& 0& -\frac{1}{L}\[d_B-\frac{1}{3}\left(d_A+d_B+d_C\right)\]\\ 0& 0& -\frac{r}{L}& -\frac{1}{L}\[d_C-\frac{1}{3}\left(d_A+d_B+d_C\right)\]\\ \frac{s_A}{C}& \frac{s_B}{C}& \frac{s_C}{C}& 0\end{array}\right]\left[\begin{array}{c}{i}_a\\ i_b\\ i_c\\ u_{dc}\end{array}\right]+\left[\begin{array}{cccc}\frac{1}{L}& 0& 0& b_a{w}_a\\ 0& \frac{1}{L}& 0& b_b{w}_b\\ 0& 0& \frac{1}{L}& b_c{w}_c\\ 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}{u_a}^{*}\\ {u_b}^{*}\\ {u_c}^{*}\\ 1\end{array}\right]---\left(5\right)$

In formula (5), r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter (1) capacitance, b _aw _a, b _bw _b, b _cw _crepresent that switching loss, metrical error and external factor are to the interference of system, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, s _a, s _b, s _crepresent on off state, d _j(j=A, B, C) represents duty ratio,

Adopt triangular modulation, duty ratio d _j(j=A, B, C) meets following formula:

$d_j=\frac{1}{2}\left(1+\frac{v_{rj}}{V_{tri}}\right),j=A,B,C---\left(6\right)$

In formula (6), v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude, formula (6) substituted into formula (5), obtains formula (7):

$\stackrel{\‾}{i_j}=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j-\frac{U_{dc}}{2{\mathrm{LV}}_{tri}}{v}_{rj}---\left(7\right)$

In formula (7), represent the differential value of three-phase current, r is the equivalent resistance of system, and L is passive filter inductance value, and C is passive filter capacitance, v _rjrepresent modulating wave amplitude, V _trirepresent carrier amplitude, u _j ^*(j=a, b, c) represent three-phase power grid voltage equivalence reduced value, b _jw _jrepresent that switching loss, metrical error and external factor are to the interference of system, U _dcfor DC voltage,

Formula (7) is reduced to:

$\stackrel{\‾}{i_j}=f_j+b_0{u}_j---\left(8\right)$

In formula (8): $f_j=-\frac{r}{L}{i}_j+\frac{1}{L}{u_j}^{*}+b_j{w}_j,$

$b_0=-\frac{U_c}{2{\mathrm{LV}}_{tri}},$

u _j＝v _rj，

B in formula (8) ₀for the disturbance compensation factor, be determine to compensate the strong and weak factor, use as adjustable parameter in the controls, find out from formula (7), f _jnot only comprise switching loss, metrical error external disturbance information, also comprise the information of the characterization system internal dynamics relevant with output information;

Step 2, after pair parallel connection mixed type active filter system modeling of described step 1 terminates, set up linear active disturbance rejection control mathematical model:

Adopt linear extended state observer (Linear Extended State Observer-LESO) and linear state error feedback control rule (Linear State Error Feedback-LSEF) as single order automatic disturbance rejection controller, the linear extended state observer of governing equation (LESO) equation of single order automatic disturbance rejection controller and linear state error feedback control rule (LSEF) equation, linear extended state observer (LESO) equation is specifically expressed as:

$\left\{\begin{array}{c}\mathrm{\ϵ}=Z_{21}-I_{cx}\\ Z_{21}=Z_{22}-B_1\mathrm{\ϵ}+u\left(t\right)\\ Z_{22}=-B_2\mathrm{\ϵ}\end{array}\right.---\left(9\right)$

In formula (9), Z ₂₁, Z ₂₂for two output variables of linear extended state observer (LESO) equation, ε is error, I _cxfor compensating current signal, be system feedback, B ₁, B ₂for proportionality coefficient, known by formula (9), Z ₂₁tracking system feedback I _cx, and as the current feedback signal of controller, Z ₂₂be referred to as disturbance compensation, total disturbance a (t) of tracking system, and be introduced directly into the output of linear active disturbance rejection controller, feedforward compensation is carried out to the disturbance of system,

Linear state error feedback control rule (LSEF) is expressed as:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1=Z_{11}-Z_{21}\\ u_0=k_p{\mathrm{\ϵ}}_1\end{array}\right.---\left(10\right)$

In formula (10), Z ₁₁for instruction current signal, ε ₁for error, as the input of linear state error feedback control rule (LSEF), k _pfor proportionality coefficient, u ₀for initial controlled quentity controlled variable,

Convolution (9) and formula (10), obtain automatic disturbance rejection controller and always export u, and the expression formula of u is:

u＝(u ₀-Z ₂₂)/b (11)

In formula (11), u ₀for initial controlled quentity controlled variable, b is the disturbance compensation factor,

Known by formula (9), formula (10), formula (11), in the control procedure of linear active disturbance rejection controller, adjustable parameter is: the proportionality coefficient k in LSEF _p, the proportionality coefficient B in LESO ₁, B ₂, disturbance compensation factor b, controlled quentity controlled variable u finally acts on controlled device;

In step 3, the basis of linear active disturbance rejection controller that established in described step 2, set up Repetitive control compensation linear active disturbance rejection Controlling model according to internal model principle, be specially: given input instruction current signal I _c ^*x, by more given I _c ^*x and actual output offset current I _cxthe deviation ε drawn _k, deviation ε _kthrough having the low pass filter Q of delay link ₁(s) e ^-Tsafter obtaining the deviation ε (k-T) in a sampling period, regulate through PID, finally obtain being that the Repetitive controller in cycle exports compensating signal U with T _rC, the expression formula of Repetitive control compensation linear active disturbance rejection Controlling model is specific as follows:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1=I_c{{}^{*}}_x-I_{cx}\\ \mathrm{\ϵ}\left(k-T\right)={\mathrm{\ϵ}}_1{e}^{-Ts}\\ U_{RC}=k_c\mathrm{\ϵ}\left(k-T\right)+{\mathrm{\ϵ}}_1\end{array}\right.---\left(15\right)$

In formula (15), ε ₁for error, as instruction current signal I _c ^*x and actual offset current I _cxdifference, ε (k-T) was the error in a upper cycle, U _rCfor taking T as the compensating signal that the Repetitive controller in cycle exports,

Step 4, in conjunction with in described step 3 Repetitive control compensation linear active disturbance rejection control and described step 2 in linear active disturbance rejection control two kinds of algorithms, the control signal finally acting on system is

τ＝U _ADRC+U _RC(16)

In formula (16), U _aDRCfor the output signal of linear active disturbance rejection controller, U _aDRCfor automatic disturbance rejection controller always exports u, U _rCfor the output compensating signal of Repetitive controller;

Step 5, the control signal τ of the system that finally acts on drawn above to be inputted in controlled device, controls:

To finally act on the control signal τ of system, after triangular modulation, obtain six road pulse signals, by 6 switching tubes of the three-phase brachium pontis in six roads pulse signal input active filter (2), draw actual offset current I by the control of switch tube _cx, finally realize the control of parallel connection mixed type active filter system.

4. the control method of a kind of parallel connection mixed type active filter system according to claim 3, is characterized in that, described high switching frequency f span is f≤f _c, f _crepresent switching frequency.