CN106229979A - Control Method of Active Power Filter based on fractional order sliding formwork - Google Patents

Abstract

The invention discloses a kind of Control Method of Active Power Filter based on fractional order sliding formwork, including: (1) sets up the mathematical model of Active Power Filter-APF；(2) the control law equation of fractional order sliding mode controller based on Active Power Filter-APF is set up；(3) output utilizing fractional order sliding mode controller controls Active Power Filter-APF.The present invention is able to ensure that the real-time tracking to harmonic current, and the dynamic property of strengthening system, improves system robustness, applied load changes when, still can keep being well energy；Become controller by design sliding formwork and ensure that Active Power Filter-APF runs along sliding formwork track；In the middle of sliding mode controller, introduce fractional order module, add adjustable item compared with integer rank, improve the overall performance of system.

Description

Control Method of Active Power Filter based on fractional order sliding formwork

Technical field

The invention belongs to Active Power Filter-APF technical field, be specifically related to a kind of active electric power based on fractional order sliding formwork Filter control method.

Background technology

The capacitor of compensating reactive power is widely used in electrical network, under certain frequency, serial or parallel connection resonance may be met Condition, when this subharmonic is sufficiently large, will result in overvoltage or the overcurrent of danger, and this often leads to electrical equipment and equipment Damage, have a strong impact on the safe operation of power system.Additionally, the flowing that harmonic current is in electrical network can have on the line Merit power attenuation.The extension wire loss ratio that the kelvin effect of wire causes is bigger；Serious harmonic distortion makes opening of chopper Cutting capacity reduces, and may damage chopper, and in civil buildings, owing to the neutral conductor is general, relatively carefully (new standard has increased N line and led Line cross section), when substantial amounts of harmonic wave (generally triple-frequency harmonics) flows therethrough, wire can be made overheated, destroy insulation, and then occur Short circuit, causes fire.

At present, the conventional approach administering harmonic pollution can be divided into two kinds: one, improves power electronic equipment itself, Making it reduce harmonic wave during transformation of electrical energy to produce, hoisting power factor the most as far as possible, this method is applicable to electric power electricity Subset is the occasion in major harmonic source.Its two, use power filter device absorb harmonic wave produced by harmonic source nearby, it is Harmonics restraint is most effective at present is also most widely used measure.At present, domestic mainly employing passive filter processes electricity Harmonic wave in net.But the compensation characteristic of passive filter is single, and it is vulnerable to system impedance impact, causes resonance phenomena, put Big harmonic wave, and then burn compensation device, and be only capable of particular harmonic is effectively treated, the center of gravity of research is gradually turned by people To Active Power Filter-APF.It is the standard configuration product that intelligent grid is built that APF etc. purify electrical network product, can realize harmonic wave and idle dynamic State compensates, and response is fast, is affected by electric network impedance little, is difficult to and electric network impedance generation resonance；Each harmonic can be compensated, also can press down Flickering processed, compensating reactive power, compensation performance is not changed by mains frequency to be affected, and can effectively suppress harmonic pollution, therefore become humorous The important means that ripple is administered.

At present, the most not yet form the advanced control theory system of the Active Power Filter-APF of system, face many urgently The problem of solution to be studied.The modeling method of Active Power Filter-APF varies with each individual, and the control method of employing is varied, lacks The stability of system proves, the most first-class problem of system performance evaluation standard generally exists.So, the research of Active Power Filter-APF There is important significance of scientific research and wide market prospect.

Summary of the invention

For the problems referred to above, the present invention proposes a kind of Control Method of Active Power Filter based on fractional order sliding formwork.

Realizing above-mentioned technical purpose, reach above-mentioned technique effect, the present invention is achieved through the following technical solutions:

A kind of Control Method of Active Power Filter based on fractional order sliding formwork, comprises the following steps:

Step one, set up the mathematical model of Active Power Filter-APF；

Step 2, the control law equation of foundation fractional order sliding mode controller based on Active Power Filter-APF；

Step 3, utilize fractional order sliding mode controller output control Active Power Filter-APF.

In described step one, Active Power Filter-APF mathematical model is:

$\stackrel{\·}{x}=f\left(x\right)+bu+d$

Wherein, x is the compensation electric current of Active Power Filter-APF output,It is the first derivative of x, K=1,2,3, v₁,v₂,v₃It is respectively three-phase active power filter terminal voltage, i₁,i₂,i₃It is respectively three-phase and compensates electric current, R_cFor electricity Resistance, L_cFor inductance,v_dcFor capacitance voltage, u is the control law of fractional order sliding mode controller output, and d is system interference Amount, t is the time.

In described step 2, the control law equation of fractional order sliding mode controller is:

$u=\frac{1}{{\mathrm{b\λ}}_1}\[-{\mathrm{\λ}}_{1}f\left(x\right)-{\mathrm{\λ}}_1\mathrm{\ρ}sgn\left(s\right)+{\mathrm{\λ}}_1{\stackrel{\·}{x}}_d+{\mathrm{\λ}}_{2}e+{\mathrm{\λ}}_3{D}^{\mathrm{\α}}e\]$

Wherein, λ₁、λ₂、λ₃For customized parameter and be positive number, x_dFor detecting signal code,For detection signal code Derivative, D^αe、D^α-1E is the Fractional Derivative of tracking error, and α takes arbitrarily for rational number；ρ is the interference upper bound, and interference upper bound ρ is Positive number, system interference amount d and interference upper bound ρ meet inequality ρ-| d | > σ₁, wherein, σ₁For positive number；S is switching function, s=-λ₁e-λ₂∫e-λ₃D^α-1E, the target of controller makes compensation electric current x tracing detection signal code x exactly_d, wherein, tracking error e= x_d-x。

Described step 3, particularly as follows: Active Power Filter-APF gathers the simulated load current in main circuit, passes through fractional order Controller processes and exports corresponding control law, controls the compensation electricity compensating the output of electric current generation module of Active Power Filter-APF Flow contrary with the amplitude same phase in detection signal code, finally give desired source current.

Beneficial effects of the present invention:

The control method of the Active Power Filter-APF based on fractional order sliding formwork of the present invention, it can be ensured that to harmonic current Real-time tracking, and the dynamic property of strengthening system, improve system robustness, applied load changes when, still can Keeping is well energy；Become controller by design sliding formwork and ensure that Active Power Filter-APF runs along sliding formwork track；At sliding formwork Introduce fractional order module in the middle of controller, add adjustable item compared with integer rank, improve the overall performance of system.

Accompanying drawing explanation

Fig. 1 be the present invention specific embodiment in the model schematic of Active Power Filter-APF.

Fig. 2 is Active Power Filter-APF fractional order sliding-mode control fundamental diagram of the present invention.

Fig. 3 be the present invention specific embodiment in actual output follow the trail of the time-domain response curve figure of expectation curve.

Fig. 4 be the present invention specific embodiment in staged add load after DC voltage response curve.

Detailed description of the invention

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, to the present invention It is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not used to Limit the present invention.

Below in conjunction with the accompanying drawings the application principle of the present invention is explained in detail.

A kind of Control Method of Active Power Filter based on fractional order sliding formwork, comprises the following steps:

Step one, set up the mathematical model of Active Power Filter-APF；

Step 2, the control law equation of foundation fractional order sliding mode controller based on Active Power Filter-APF；

Step 3, utilize fractional order sliding mode controller output control Active Power Filter-APF.

Present invention research is to apply relatively wide shunt voltage type Active Power Filter-APF, and in life, three intersect The application of stream electricity occupies the majority, so main research is for the situation of three-phase three-line system, as it is shown in figure 1, which show active The model of electric-power filter.

Active Power Filter-APF is mainly made up of three parts, is Harmonic currents detection module, current follow-up control mould respectively Block and compensation electric current generation module.Harmonic currents detection module generally uses harmonic current based on instantaneous reactive power theory Quickly detection.The compensation electric current of Three-phase Three-wire Active Power Filter (Active power filter, APF) generally uses PWM controls to occur.Compensating electric current should be contrary with the harmonic current amplitude same phase detected to reach harmonic carcellation component Purpose.

The basic functional principle of Active Power Filter-APF is, detects the voltage and current of object to be compensated, through instruction current Computing circuit calculates the command signal compensating electric current, and the compensated current occuring circuit of this signal amplifies, and draws compensation electric current (i.e. x in the present invention), compensate harmonic wave to be compensated in electric current and load current (i.e. detection signal code in the present invention) and Idle current canceling such as grade, finally gives desired source current.

Step one, set up the mathematical model of Active Power Filter-APF:

Equation below is can get according to Circuit theory and Kirchhoff's theorem:

$\left\{\begin{array}{c}{v}_1=L_c\frac{{\mathrm{di}}_1}{dt}+R_c{i}_1+v_{1M}+v_{MN}\\ v_2=L_c\frac{{\mathrm{di}}_2}{dt}+R_c{i}_2+v_{2M}+v_{MN}\\ v_3=L_c\frac{{\mathrm{di}}_3}{dt}+R_c{i}_3+v_{3M}+v_{MN}\end{array}\right.---\left(1\right)$

Wherein, v_1M、v_2M、v_3MIt is respectively the M end voltage to a, b, c end, v_MNVoltage for M end to N end；v₁,v₂,v₃Respectively For three phase active electric power filter terminal voltage, i₁,i₂,i₃It is respectively three-phase and compensates electric current, R_cFor resistance, L_cFor inductance；

Assume that AC supply voltage is stable, can obtain:

${\mathrm{\ν}}_{MN}=-\frac{1}{3}\underset{m=1}{\overset{3}{\Σ}}{v}_{mM}---\left(2\right)$

Wherein, v_mMThe voltage of a, b, c end is arrived respectively for M end, m=1,2,3；

Definition switch function c_k, the duty of instruction IGBT, it is defined as follows:

Wherein, k=1,2,3.

Meanwhile, definition v_kM=c_kv_dc, then formula (1) can be written as:

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_1}{dt}=-\frac{R_c}{L_c}{i}_1+\frac{v_1}{L_c}-\frac{v_{dc}}{L_c}(c_1-\frac{1}{3}\underset{m=1}{\overset{3}{\Σ}}{c}_m)\\ \frac{{\mathrm{di}}_2}{dt}=-\frac{R_c}{L_c}{i}_2+\frac{v_2}{L_c}-\frac{v_{dc}}{L_c}(c_2-\frac{1}{3}\underset{m=1}{\overset{3}{\Σ}}{c}_m)\\ \frac{{\mathrm{di}}_3}{dt}=-\frac{R_c}{L_c}{i}_3+\frac{v_3}{L_c}-\frac{v_{dc}}{L_c}(c_3-\frac{1}{3}\underset{m=1}{\overset{3}{\Σ}}{c}_m)\end{array}\right.---\left(4\right)$

Wherein, v_mM=c_mv_dc, c_mFor switch function, m=1,2,3；

In view of in real process, have interference and exist, then 3 equations of formula (4) can be write as following form:

$\stackrel{\·}{x}=f\left(x\right)+bu+d---\left(5\right)$

Wherein, x is the compensation electric current of Active Power Filter-APF output, x=[i₁,i₂,i₃],It is the first derivative of x,

K=1,2,3, v₁,v₂,v₃It is respectively three-phase active power filter terminal voltage, i₁,i₂,i₃Point Do not compensate electric current, R for three-phase_cFor resistance, L_cFor inductance,v_dcFor capacitance voltage, u, d are system interference amount, when t is Between.

Two, the control law equation of foundation fractional order sliding mode controller based on Active Power Filter-APF:

Setting the interference upper bound is a positive number as ρ, ρ, and system interference d and interference upper bound ρ meet inequality ρ-| d | > 0, control The target of device makes compensation electric current x tracing detection signal code x exactly_d, wherein, tracking error e=x_d-x。

Definition switching function s (i.e. fractional order Dynamic sliding mode face equation) is:

S=-λ₁e-λ₂∫e-λ₃D^α-1e (6)

In the present invention, the effect of switching function is after system reaches kinestate, it is possible to make tracking error gradually Close to 0.

OrderAvailable corresponding Equivalent control law equation is:

$u=\frac{1}{{\mathrm{b\λ}}_1}\[-{\mathrm{\λ}}_{1}f\left(x\right)-{\mathrm{\λ}}_{1}d+{\mathrm{\λ}}_1{\stackrel{\·}{x}}_d+{\mathrm{\λ}}_{2}e+{\mathrm{\λ}}_3{D}^{\mathrm{\α}}e\]$

Use switching function u_sw=λ₁ρ sgn (s) replaces λ₁D, can the control law equation of goals for rank sliding mode controller be:

$u=\frac{1}{{\mathrm{b\λ}}_1}\[-{\mathrm{\λ}}_{1}f\left(x\right)-{\mathrm{\λ}}_1\mathrm{\ρ}sgn\left(s\right)+{\mathrm{\λ}}_1{\stackrel{\·}{x}}_d+{\mathrm{\λ}}_{2}e+{\mathrm{\λ}}_3{D}^{\mathrm{\α}}e\]---\left(7\right)$

Three, utilize fractional order sliding mode controller output control Active Power Filter-APF:

Particularly as follows: Active Power Filter-APF gathers the simulated load current in main circuit, processed by fractional order control device And export corresponding control law, control the compensation electric current compensating the output of electric current generation module and the detection letter of Active Power Filter-APF Amplitude same phase in number electric current is contrary, finally gives desired source current.

Four, design Lyapunov function:

$V=\frac{1}{2}{s}^{T}s---\left(8\right)$

Then

$\begin{array}{c}\stackrel{\·}{V}=s^T\stackrel{\·}{s}\\ =s^T\{-{\mathrm{\λ}}_1\[{\stackrel{\·}{x}}_d-f\left(x\right)-b\frac{1}{{\mathrm{b\λ}}_1}(-{\mathrm{\λ}}_{1}f(x)-{\mathrm{\λ}}_1\mathrm{\ρ}\mathrm{sgn}(s)+{\mathrm{\λ}}_1{\stackrel{\·}{x}}_d+{\mathrm{\λ}}_2{D}^{\mathrm{\α}}e)-d\]-{\mathrm{\λ}}_{2}e-{\mathrm{\λ}}_3{D}^{\mathrm{\α}}e\}\\ =s^T{\mathrm{\λ}}_1(d-\mathrm{\ρ}\mathrm{sgn}(s\left)\right)\≤\left|s^T\right|{\mathrm{\λ}}_1\left(\right|d|-\mathrm{\ρ})\end{array}$

Because ρ-| d | > 0, λ₁> 0, thereforeSo system can be stablized.

Five, Matlab emulation experiment

It is combined with dynamic model and the fractional order sliding-mode control of active power filter, passes through Matlab/Simulink Software design goes out mastery routine.

Supply voltage and frequency are V_s1=V_s2=V_s3=220V, f=50Hz, nonlinear load is R=10 Ω, L=2mH, The parameter of Active Power Filter-APF is L=100hH, R=100 Ω, C=100 μ F, λ₁=12, λ₂=3, λ₃=3, ρ=180000, α=0.9.

Compensating circuit during 0.04S and access switch Guan Bi, active filter is started working, and is connect respectively when 0.1S and 0.2S Enter an identical extra nonlinear load.

Experimental result is as shown in Figure 3, Figure 4.

The invention has the beneficial effects as follows:

The present invention designs fractional order sliding-mode control based on Active Power Filter-APF, it can be ensured that to harmonic current Real-time tracking, and the dynamic property of strengthening system, improve system robustness, applied load changes when, still can Keeping is well energy；Become controller by design sliding formwork and ensure that Active Power Filter-APF runs along sliding formwork track；At sliding formwork Introduce fractional order module in the middle of controller, add adjustable item compared with integer rank, improve the overall performance of system.

The ultimate principle of the present invention and principal character and advantages of the present invention have more than been shown and described.The technology of the industry Personnel, it should be appreciated that the present invention is not restricted to the described embodiments, simply illustrating this described in above-described embodiment and description The principle of invention, without departing from the spirit and scope of the present invention, the present invention also has various changes and modifications, and these become Change and improvement both falls within scope of the claimed invention.Claimed scope by appending claims and Equivalent defines.

Claims (4)

1. a Control Method of Active Power Filter based on fractional order sliding formwork, it is characterised in that comprise the following steps:

Step one, set up the mathematical model of Active Power Filter-APF；

Step 2, the control law equation of foundation fractional order sliding mode controller based on Active Power Filter-APF；

Step 3, utilize fractional order sliding mode controller output control Active Power Filter-APF.

A kind of Control Method of Active Power Filter based on fractional order sliding formwork the most according to claim 1, its feature exists In: in described step one, Active Power Filter-APF mathematical model is:

$\stackrel{\·}{x}=f\left(x\right)+bu+d$

Wherein, x is the compensation electric current of Active Power Filter-APF output,It is the first derivative of x,K=1, 2,3, v₁,v₂,v₃It is respectively three-phase active power filter terminal voltage, i₁,i₂,i₃It is respectively three-phase and compensates electric current, R_cFor resistance, L_cFor Inductance,v_dcFor capacitance voltage, u is the control law of fractional order sliding mode controller output, and d is system interference amount, and t is Time.

A kind of Control Method of Active Power Filter based on fractional order sliding formwork the most according to claim 2, its feature exists In: in described step 2, the control law equation of fractional order sliding mode controller is:

$u=\frac{1}{{\mathrm{b\λ}}_1}\[-{\mathrm{\λ}}_{1}f\left(x\right)-{\mathrm{\λ}}_1\mathrm{\ρ}sgn\left(s\right)+{\mathrm{\λ}}_1{\stackrel{\·}{x}}_d+{\mathrm{\λ}}_{2}e+{\mathrm{\λ}}_3{D}^{\mathrm{\α}}e\]$

Wherein, λ₁、λ₂、λ₃For customized parameter and be positive number, x_dFor detecting signal code,For leading of detection signal code Number, D^αe、D^α-1E is the Fractional Derivative of tracking error, and α takes arbitrarily for rational number；ρ is the interference upper bound, and interference upper bound ρ is just Number, system interference amount d and interference upper bound ρ meet inequality ρ-| d | > σ₁, wherein, σ₁For positive number；S is switching function, s=-λ₁e- λ₂∫e-λ₃D^α-1E, the target of controller makes compensation electric current x tracing detection signal code x exactly_d, wherein, tracking error e=x_d- x。

4. according to a kind of based on fractional order sliding formwork the Control Method of Active Power Filter described in claim 1 or 3, its feature It is: described step 3, particularly as follows: Active Power Filter-APF gathers the simulated load current in main circuit, passes through fractional order control Device processes and exports corresponding control law, control the compensation electric current compensating the output of electric current generation module of Active Power Filter-APF with Amplitude same phase in detection signal code is contrary, finally gives desired source current.