CN102324749A - STATCOM (Static Compensator) device based on switched system theory and robust control method for same - Google Patents

Abstract

The invention provides a STATCOM (Static Compensator) device based on a switched system theory. The STATCOM device comprises a reactor L, a voltage type inverter, a driving circuit, an outer ring control module and an inner ring control module. A control method for the STATCOM device comprises the following steps of modeling, signal acquisition, synchronous compensation, stability verification and feedback control. The control method has the following advantages that: (1) when a system is in failure, the stability of the system can be ensured, and interferences on performances of the system can be eliminated; (2) a confirmed voltage output function can reduce parameters which are taken into consideration in operation, and only parameters of resistance and inductance are required; (3) optimized indexes can be confirmed through a determined robust control model according to the definition of H (infinite) control of the control method; (4) the utilization of constraint conditions of an LMI (Linear Matrix Inequality) solving controller is the most convenient; and (5) the effectiveness and correctness of STATCOM compensation can be achieved by reasonably switching a turnoff device in a main circuit of the inverter based on switching rules, the utilization rate of the device is increased, and the service life of the device is prolonged.

Description

A kind of based on switched system theoretical STATCOM device and robust control method thereof

(1) technical field:

The invention belongs to power electronic technology and robust control technique field, especially a kind of based on switched system theoretical STATCOM STATCOM (Static Synchronous Compensator) device and H thereof _∞Robust control method.

(2) background technology:

At present the research of static var compensator STATCOM is mainly concentrated on main wiring mode and topological structure, system modelling, system control method and it aspects such as effect to stability of power system.First STATCOM commercial plant that adopts gate leve turn-off thyristor GTO (Gate Turn-Off Thyristor) in the world by US Westinghouse company's development; Use a plurality of inverters to be connected with the voltage electrical network through tortuous transformer or common transformer; Waveform phase shift stack with a plurality of inverter outputs; Obtain being similar to sine-shaped three symmetrical output voltages; The STATCOM commercial plant that puts into operation both at home and abroad later all adopts above-mentioned identical main circuit structure, is called as multiple inverter configuration.Multiple inverter configuration not only is issued to the purpose of aggrandizement apparatus capacity in the condition of the equal flow problem of having avoided the device parallel connection; While approaches sine wave by means of the method that the square-wave signal with several current transformers outputs is combined into staircase waveform; Can be issued to the purpose that suppresses harmonic wave in the condition that does not improve switching frequency again, therefore in high-power converter, be used widely.Though this structure very effectively, owing to need the tortuous transformer of particular design, had both improved cost, the complicacy that system is become, and each mutually between complicated electromagnetic coupled also make the phase-splitting control when asymmetric difficulty that becomes.

Continuous development along with power electronic technology; Big capacity device continues to bring out; Above-mentioned main circuit structure complicated problems should be not difficult to be resolved; Promptly might use single inverter to constitute the STATCOM of suitable capacity, utilize pulse-width modulation PWM (Pulse Width Modulation) technology to produce the sinusoidal output voltage of required power frequency simultaneously.At present; In the STATCOM main circuit; The main flow structure that is adopted is voltage source inverter VSI (Voltage source inverter); But also there is the researcher to carry out the application study in STATCOM, to having carried out Primary Study based on the dynamic model of the STATCOM of current source inverter, steady-state behaviour, Control System Design etc. to current source inverter CSI (Current source inverter).The STATCOM device can be regarded as and connects a controlled reactive power source with system.Set up one suitable, can reflect in detail that the Mathematical Modeling of STATCOM character is that device is control effectively, and then bring into play the basis that it should have effect.

(3) summary of the invention:

The object of the present invention is to provide a kind of based on switched system theoretical STATCOM device and H thereof _∞Robust control method; It can overcome the deficiency that prior art exists, be a kind of simple in structure, easy to operate, can satisfy effectively that the non-linear load or burden without work of electric power system increases rapidly and the user to the device and the control method thereof of the requirement that improves constantly with electricity quality.

Technical scheme of the present invention: a kind of based on the theoretical STATCOM device of switched system, comprise and contain system power supply U _sWith the electric power system of reactive load, it is characterized in that it is made up of reactor L, voltage source inverter, drive circuit, outer shroud control module and interior ring control module; Wherein, The ring control module is made up of generator in said; The outer shroud control module is made up of offset current detection algorithm and control algolithm module; The current signal of mains side and reactive load side in the input collection electric power system of said offset current detection algorithm, its output is connected with the input of control algolithm module; The input of said control algolithm module is connected with the input of generator; The output of said generator is connected with the input of drive circuit; The input of said voltage source inverter is connected with the output of drive circuit, and its output is connected with electric power system with reactor L.

Said outer shroud control module adopts the TMS320F2810 dsp chip.

A kind of H based on the theoretical STATCOM device of switched system _∞Robust control method is characterized in that it may further comprise the steps:

1, set up the equivalent circuit of single-phase STATCOM hybrid system according to the characteristic of STATCOM hybrid system, confirm that the single-phase STATCOM hybrid system robust control model of switching function is:

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_c}{\mathrm{dt}}=-\frac{r}{L}{i}_c-\frac{U_{\mathrm{con}}}{L}+\frac{U_S}{L}\\ -{\mathrm{si}}_c=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}\\ i_L=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}+i_s\end{array}\right.\⇒$

$\mathrm{dx}=\left[\begin{array}{c}{\mathrm{di}}_c\\ {\mathrm{dU}}_{\mathrm{dc}}\end{array}\right]=\left[\begin{array}{cc}-r/L& -s/L\\ -s/C& 0\end{array}\right]\left[\begin{array}{c}{i}_c\\ U_{\mathrm{dc}}\end{array}\right]+\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right]+w$

$=(A_0+A_{1}s)x+b+w$

Wherein $A_0=\left[\begin{array}{cc}-r/L& 0\\ 0& 0\end{array}\right],$ $A_1=\left[\begin{array}{cc}0& -1/L\\ -1/C& 0\end{array}\right],$ $b=\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right],$ U in the formula _sBe system side voltage; R is the inductance substitutional resistance; S is the PWM switch function;

2, confirm that according to the work purpose of synchronous compensator bucking-out system voltage output function is:

y＝C ₀i _cR

Make C here ₀Be constant;

3, can draw the non-linear and linearizing robust system model of the discrete switching of STATCOM equivalence by step 1 is:

$\left[\begin{array}{c}{i}_{C(k+1)}\\ U_{\mathrm{dc}(k+1)}\end{array}\right]=F\left(d_k\right)\left[\begin{array}{c}{i}_{\mathrm{Ck}}\\ U_{\mathrm{dck}}\end{array}\right]+g\left(d_k\right)+w_k,$ y _k＝C ₀i _CkR＝C ₁i _Ck

Wherein, C ₀Be constant; $F\left(d_k\right)={\mathrm{\Φ}}_{-1}^{1-d_k}{\mathrm{\Φ}}_1^{d_k};$ $g\left(d_k\right)={\mathrm{\Φ}}_{-1}^{1-d_k}{\mathrm{\γ}}_1^{d_k}+{\mathrm{\γ}}_{-1}^{1-d_k}$

The linear robust system of the discrete switching of its linear equivalence can be expressed as:

Δx _k+1＝F(d(t _k))Δx _k+h(d(t _k))Δd _k+w _k

Δy _k＝C ₁(y _k-y′ _k)

Wherein: $F\left(d\left(t_k\right)\right)={\mathrm{\Φ}}_{-1}^{1-d\left(t_k\right)}{\mathrm{\Φ}}_1^{d\left(t_k\right)}$ $h\left(d\left(t_k\right)\right)={\mathrm{\Φ}}_{-1}^{1-d\left(t_k\right)}{A}_1{x}^{d\left(t_k\right)}T$

$x^{d\left(t_k\right)}={\mathrm{\Φ}}_1^{1-d\left(t_k\right)}x+{\mathrm{\γ}}_1^{d\left(t_k\right)}$

Δ x _K+1=F (d (t _k)) Δ x _k+ h (d (t _k)) Δ d _k+ w _k, Δ y _k=C ₁(y _k-y ' _k) and $z_k=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\mathrm{\&Delta;}{x}_{1\mathrm{<figure-callout\; id="2"\; label="k\; c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ c_{}{}_2\mathrm{\&Delta;}{x}_{2k}\end{array}\right]={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\mathrm{\&Delta;}{x}_k$ For based on H _∞The state space of the augmentation controlled device of control theory is realized;

4, utilize the LMI method to find the solution the stability of access control device and the constraints of validity is:

$\left[\begin{array}{cc}X& I\\ I& Y\end{array}\right]\&GreaterEqual;0$

$\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]\left[\begin{array}{ccc}{A}^{T}X+\mathrm{XA}& {\mathrm{XB}}_1& C_1^T\\ B_1^{T}X& -\mathrm{\&gamma;I}& 0\\ {\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1& 0& -\mathrm{\&gamma;<figure-callout\; id="1"\; label="I\; C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">I</figure-callout>}& \\ \end{array},\right]\left[\begin{array}{c}{C}^{}\end{array}\right]\left[\begin{array}{cc}{}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]<0$

${\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]}^T\left[\begin{array}{ccc}{\mathrm{YA}}^T+\mathrm{AY}& {\mathrm{YC}}_1^T& B_1\\ C_{1}Y& -\mathrm{\&gamma;I}& 0\\ B_1^T& 0& -\mathrm{\&gamma;I}\end{array}\right]\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]<0$

In the formula: $A=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{A}_i,{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{11},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{12},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{1N})$

${\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_2=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{21},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{22},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{2N})$

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1={(\sqrt{{\mathrm{\&alpha;}}_1}{C}_{11}^T,\sqrt{{\mathrm{\&alpha;}}_2}{C}_{12}^T,...,\sqrt{{\mathrm{\&alpha;}}_N}{C}_{1N}^T)}^T$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2={(C_{21}^T,C_{22}^T,...,C_{2N}^T)}^T$

$D=\mathrm{diag}\{\sqrt{{\mathrm{\&alpha;}}_1}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">D</figure-callout>}}_1,\sqrt{{\mathrm{\&alpha;}}_2}{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">D</figure-callout>}}_2,...,\sqrt{{\mathrm{\&alpha;}}_N}{D}_N\}$

In this case, switching law can be taken as:

$\mathrm{\&sigma;}\left(t\right)=\arg \min \left\{{\mathrm{\&xi;}}^T\right[{(A_i+B_{2i}{K}_i{C}_{2i})}^T{P}_c+P_c(A_i+B_{2i}{K}_i{C}_{2i})$

$+{\mathrm{\&gamma;}}^{-2}{P}_c{B}_{1i}{B}_{1i}^T{P}_c+{(C_i+D_i{K}_i{C}_{2i})}^T(C_i+D_i{K}_i{C}_{2i})\left]\mathrm{\&xi;}\right\}$

P in the formula _c=γ X _c

5, switching law can be obtained by the ctrb function among the Matlab automatically in the step 4, if σ (t) full rank, then switching law is controlled; Empirical tests is to d (t arbitrarily _kAll there is rank (L)≤1 _k)=2 are so switching law is controlled.Discuss how to suppress to disturb the influence of w to systematic function below, introduce expression for this reason and disturb scalar γ＞0 that suppresses level, the definition evaluation function is:

$z_k=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\mathrm{\&Delta;}{x}_{1\mathrm{<figure-callout\; id="2"\; label="k\; c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ c_{}{}_2\mathrm{\&Delta;}{x}_{2k}\end{array}\right]={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\mathrm{\&Delta;}{x}_k$

C wherein ₁, c ₂And C ₂Be respectively constant and coefficient matrix;

6, definition

T wherein _Zw(s) be closed loop transfer function, by w to z;

7, through regulating FEEDBACK CONTROL rule K, make the closed-loop system internal stability and || T _Zw(s) || _∞＜γ;

8, according to linear system H _∞Control theory is through using the solver mincx in the LMI tool box among the MTLAB, the matrix parameter A in the calculation procedure 1 ₀, A ₁, b, w carry out the reasonable compensation to system;

9, after system voltage, electric current change, detect electric current through detection module, through calculating, signal is delivered to the pulsed drive module feed back at last and realize in the inverter switching to reach the control effect;

Wherein, L _R, R series connection is inductive load, L is a filter inductance; C is a dc capacitor; U _sBe system power supply; U _ConBe the STATCOM output voltage; U _DcBe dc capacitor voltage; K ₁, K ₂, K ₃, K ₄4 switch elements; i _cBe offset current; i _LFor following the tracks of load current.

Operation principle power electronic device of the present invention produces the trigger impulse of certain rule;, gate drive circuit goes to control conducting and the shutoff of IGBT after amplifying; Make STATCOM produce correct output voltage, the lock-out pulse according to obtaining from the electrical network sampling produces the pulse signal synchronous with line voltage; Output voltage and line voltage that STATCOM is produced keep synchronously; Thereby STATCOM can be incorporated into the power networks exactly, and control STATCOM output voltage makes with line voltage and keeps certain phase angle and control modulation degree, thereby accurately controls the reactive power output of STATCOM.Simultaneously, carry out high-rise defencive function, when STATCOM operates in overload or other abnormal state; And electric current surpasses when protecting the setting value that moves, and controller makes STATCOM get back to normal operating conditions through defencive function, avoids STATCOM low layer protection action; Make its operate as normal continuously, in case mistake appears in some element of controller itself, controller can be found and report to the police; Simultaneously do not make device out of service fully, after the fault restoration, can resume operation at an easy rate.

Along with the raising of carrier frequency, the harmonic content in the output voltage is more and more littler, is increased to after the certain value but work as carrier frequency, and it is not obvious to the effect that reduces the harmonic content in the output voltage to increase carrier frequency again.Can increase the switching loss of device owing to carrier frequency is too high on the contrary.Simultaneously, load reactance increases, and makes the increase of load reactive power cause load bus voltage to descend, and STATCOM and control system thereof are through detecting this variation, and control STATCOM self compensating system is idle, and voltage is recovered.Because the influence of impact load; Make the voltage on the motor bus that bigger decline arranged, but STATCOM and control system thereof can be carried out dynamic passive compensation immediately, busbar voltage is recovered very soon; Guarantee that motor speed is unlikely down with too much, and it is returned near the rated speed very soon.

Superiority of the present invention is: 1. when system breaks down, can make system stability on the one hand, can eliminate the influence of interference to systematic function on the other hand; 2. the voltage output function of confirming can reduce the parameter of consideration in service, only need know that the parameter of resistance and inductance gets final product; 3. can know according to the definition of its H ∞ control that through the robust control model of confirming, can confirming to optimize index, 4. to utilize LMI to find the solution the constraints of controller the most convenient; 5. reasonably switch the turn-off device in the converter main circuit according to switching law, can reach the validity accuracy of STATCOM compensation, improved devices use rate and useful life simultaneously.

(4) description of drawings:

Fig. 1 is the related a kind of structured flowchart based on the theoretical STATCOM device of switched system of the present invention.

Fig. 2 is the related a kind of H based on the theoretical STATCOM of switched system of the present invention _∞H ∞ standard control sketch map in the robust control method.

Fig. 3 is related a kind of based on TMS320F2810 architectural schematic in the STATCOM device of switched system theory for the present invention.

Fig. 4 is related a kind of based on TMS320F2810 module diagram in the STATCOM device of switched system theory for the present invention.

(5) embodiment:

Embodiment: a kind of based on the theoretical STATCOM device (see figure 1) of switched system, comprise and contain system power supply U _sWith the electric power system of reactive load, it is characterized in that it is made up of reactor L, voltage source inverter, drive circuit, outer shroud control module and interior ring control module; Wherein, The ring control module is made up of generator in said; The outer shroud control module is made up of offset current detection algorithm and control algolithm module; The current signal of mains side and reactive load side in the input collection electric power system of said offset current detection algorithm, its output is connected with the input of control algolithm module; The input of said control algolithm module is connected with the input of generator; The output of said generator is connected with the input of drive circuit; The input of said voltage source inverter is connected with the output of drive circuit, and its output is connected with electric power system with reactor L.

Said outer shroud control module adopts TMS320F2810 dsp chip (seeing Fig. 3, Fig. 4).

A kind of H based on the theoretical STATCOM device of switched system _∞The robust control method (see figure 2) is characterized in that it may further comprise the steps:

1, set up the equivalent circuit of single-phase STATCOM hybrid system according to the characteristic of STATCOM hybrid system, confirm that the single-phase STATCOM hybrid system robust control model of switching function is a (see figure 2):

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_c}{\mathrm{dt}}=-\frac{r}{L}{i}_c-\frac{U_{\mathrm{con}}}{L}+\frac{U_S}{L}\\ -{\mathrm{si}}_c=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}\\ i_L=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}+i_s\end{array}\right.\&DoubleRightArrow;$

$\mathrm{dx}=\left[\begin{array}{c}{\mathrm{di}}_c\\ {\mathrm{dU}}_{\mathrm{dc}}\end{array}\right]=\left[\begin{array}{cc}-r/L& -s/L\\ -s/C& 0\end{array}\right]\left[\begin{array}{c}{i}_c\\ U_{\mathrm{dc}}\end{array}\right]+\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right]+w$

$=(A_0+A_{1}s)x+b+w$

Wherein $A_0=\left[\begin{array}{cc}-r/L& 0\\ 0& 0\end{array}\right],$ $A_1=\left[\begin{array}{cc}0& -1/L\\ -1/C& 0\end{array}\right],$ $b=\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right],$ U in the formula _sBe system side voltage; R is the inductance substitutional resistance; S is the PWM switch function;

2, confirm that according to the work purpose of synchronous compensator bucking-out system voltage output function is:

y＝C ₀i _cR

Make C here ₀Be constant;

3, can draw the non-linear and linearizing robust system model of the discrete switching of STATCOM equivalence by step 1 is:

$\left[\begin{array}{c}{i}_{C(k+1)}\\ U_{\mathrm{dc}(k+1)}\end{array}\right]=F\left(d_k\right)\left[\begin{array}{c}{i}_{\mathrm{Ck}}\\ U_{\mathrm{dck}}\end{array}\right]+g\left(d_k\right)+w_k,$ y _k＝C ₀i _CkR＝C ₁i _Ck

Wherein, C ₀Be constant; $F\left(d_k\right)={\mathrm{\&Phi;}}_{-1}^{1-d_k}{\mathrm{\&Phi;}}_1^{d_k};$ $g\left(d_k\right)={\mathrm{\&Phi;}}_{-1}^{1-d_k}{\mathrm{\&gamma;}}_1^{d_k}+{\mathrm{\&gamma;}}_{-1}^{1-d_k}$

The linear robust system of the discrete switching of its linear equivalence can be expressed as:

Δx _k+1＝F(d(t _k))Δx _k+h(d(t _k))Δd _k+w _k

Δy _k＝C ₁(y _k-y′ _k)

Wherein: $F\left(d\left(t_k\right)\right)={\mathrm{\&Phi;}}_{-1}^{1-d\left(t_k\right)}{\mathrm{\&Phi;}}_1^{d\left(t_k\right)}$ $h\left(d\left(t_k\right)\right)={\mathrm{\&Phi;}}_{-1}^{1-d\left(t_k\right)}{A}_1{x}^{d\left(t_k\right)}T$

$x^{d\left(t_k\right)}={\mathrm{\&Phi;}}_1^{1-d\left(t_k\right)}x+{\mathrm{\&gamma;}}_1^{d\left(t_k\right)}$

Δ x _K+1=F (d (t _k)) Δ x _k+ h (d (t _k)) Δ d _k+ w _k, Δ y _k=C ₁(y _k-y ' _k) and $z_k=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\mathrm{\&Delta;}{x}_{1\mathrm{<figure-callout\; id="2"\; label="k\; c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ c_{}{}_2\mathrm{\&Delta;}{x}_{2k}\end{array}\right]={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\mathrm{\&Delta;}{x}_k$ For based on H _∞The state space of the augmentation controlled device of control theory is realized;

4, utilize the LMI method to find the solution the stability of access control device and the constraints of validity is:

$\left[\begin{array}{cc}X& I\\ I& Y\end{array}\right]\&GreaterEqual;0$

$\left[\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]\left[\begin{array}{ccc}{A}^{T}X+\mathrm{XA}& {\mathrm{XB}}_1& C_1^T\\ B_1^{T}X& -\mathrm{\&gamma;I}& 0\\ {\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1& 0& -\mathrm{\&gamma;<figure-callout\; id="1"\; label="I\; C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">I</figure-callout>}& \\ \end{array},\right]\left[\begin{array}{c}{C}^{}\end{array}\right]\left[\begin{array}{cc}{}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]<0$

${\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]}^T\left[\begin{array}{ccc}{\mathrm{YA}}^T+\mathrm{AY}& {\mathrm{YC}}_1^T& B_1\\ C_{1}Y& -\mathrm{\&gamma;I}& 0\\ B_1^T& 0& -\mathrm{\&gamma;I}\end{array}\right]\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]<0$

In the formula: $A=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{A}_i,{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_1=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{11},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{12},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{1N})$

${\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">B</figure-callout>}}_2=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{21},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{22},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{2N})$

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1={(\sqrt{{\mathrm{\&alpha;}}_1}{C}_{11}^T,\sqrt{{\mathrm{\&alpha;}}_2}{C}_{12}^T,...,\sqrt{{\mathrm{\&alpha;}}_N}{C}_{1N}^T)}^T$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2={(C_{21}^T,C_{22}^T,...,C_{2N}^T)}^T$

$D=\mathrm{diag}\{\sqrt{{\mathrm{\&alpha;}}_1}{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">D</figure-callout>}}_1,\sqrt{{\mathrm{\&alpha;}}_2}{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">D</figure-callout>}}_2,...,\sqrt{{\mathrm{\&alpha;}}_N}{D}_N\}$

In this case, switching law can be taken as:

$\mathrm{\&sigma;}\left(t\right)=\arg \min \left\{{\mathrm{\&xi;}}^T\right[{(A_i+B_{2i}{K}_i{C}_{2i})}^T{P}_c+P_c(A_i+B_{2i}{K}_i{C}_{2i})$

$+{\mathrm{\&gamma;}}^{-2}{P}_c{B}_{1i}{B}_{1i}^T{P}_c+{(C_i+D_i{K}_i{C}_{2i})}^T(C_i+D_i{K}_i{C}_{2i})\left]\mathrm{\&xi;}\right\}$

P in the formula _c=γ X _c；

5, switching law can be obtained by the ctrb function among the Matlab automatically in the step 4, if σ (t) full rank, then switching law is controlled; Empirical tests is to d (t arbitrarily _kAll there is rank (L)≤1 _k)=2 so switching law is controlled, discuss how to suppress to disturb the influence of w to systematic function below, introduce expression for this reason and disturb scalar γ＞0 that suppresses level, and the definition evaluation function is:

$z_k=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\mathrm{\&Delta;}{x}_{1\mathrm{<figure-callout\; id="2"\; label="k\; c"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">k</figure-callout>}}& \\ c_{}{}_2\mathrm{\&Delta;}{x}_{2k}\end{array}\right]={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000090071140000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\mathrm{\&Delta;}{x}_k$

C wherein ₁, c ₂And C ₂Be respectively constant and coefficient matrix;

6, definition T wherein _Zw(s) be closed loop transfer function, by w to z;

7, through regulating FEEDBACK CONTROL rule K, make the closed-loop system internal stability and || T _Zw(s) || _∞＜γ;

8, according to linear system H _∞Control theory is through using the solver mincx in the LMI tool box among the MTLAB, the matrix parameter A in the calculation procedure 1 ₀, A ₁, b, w carry out the reasonable compensation to system;

9, after system voltage, electric current change, detect electric current through detection module, through calculating, signal is delivered to the pulsed drive module feed back at last and realize in the inverter switching to reach the control effect.

Wherein, L _R, R series connection is inductive load, L is a filter inductance; C is a dc capacitor; U _sBe system power supply; U _ConBe the STATCOM output voltage; U _DcBe dc capacitor voltage; K ₁, K ₂, K ₃, K ₄4 switch elements; i _cBe offset current; i _LFor following the tracks of load current.

Claims (3)

1. the STATCOM device based on the switched system theory comprises and contains system power supply U _sWith the electric power system of reactive load, it is characterized in that it comprises reactor L, voltage source inverter, drive circuit, outer shroud control module and interior ring control module; Wherein, The ring control module is made up of generator in said; The outer shroud control module is made up of offset current detection algorithm and control algolithm module; The current signal of mains side and reactive load side in the input collection electric power system of said offset current detection algorithm, its output is connected with the input of control algolithm module; The input of said control algolithm module is connected with the input of generator; The output of said generator is connected with the input of drive circuit; The input of said voltage source inverter is connected with the output of drive circuit, and its output is connected with electric power system with reactor L.

2. according to a kind of described in the claim 1, it is characterized in that said outer shroud control module adopts the TMS320F2810 dsp chip based on the theoretical STATCOM device of switched system.

3. H based on the theoretical STATCOM device of switched system _∞Robust control method is characterized in that it may further comprise the steps:

1. set up the equivalent circuit of single-phase STATCOM hybrid system according to the characteristic of STATCOM hybrid system, confirm that the single-phase STATCOM hybrid system robust control model of switching function is (Fig. 2):

$\left\{\begin{array}{c}\frac{{\mathrm{di}}_c}{\mathrm{dt}}=-\frac{r}{L}{i}_c-\frac{U_{\mathrm{con}}}{L}+\frac{U_S}{L}\\ -{\mathrm{si}}_c=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}\\ i_L=C\frac{{\mathrm{dU}}_{\mathrm{dc}}}{\mathrm{dt}}+i_s\end{array}\right.\&DoubleRightArrow;$

$\mathrm{dx}=\left[\begin{array}{c}{\mathrm{di}}_c\\ {\mathrm{dU}}_{\mathrm{dc}}\end{array}\right]=\left[\begin{array}{cc}-r/L& -s/L\\ -s/C& 0\end{array}\right]\left[\begin{array}{c}{i}_c\\ U_{\mathrm{dc}}\end{array}\right]+\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right]+w$

$=(A_0+A_{1}s)x+b+w$

Wherein $A_0=\left[\begin{array}{cc}-r/L& 0\\ 0& 0\end{array}\right],$ $A_1=\left[\begin{array}{cc}0& -1/L\\ -1/C& 0\end{array}\right],$ $b=\left[\begin{array}{c}{U}_s/L\\ 0\end{array}\right],$ U in the formula _sBe system side voltage; R is the inductance substitutional resistance; S is the PWM switch function;

2. confirm that according to the work purpose of synchronous compensator bucking-out system voltage output function is:

y＝C ₀i _cR

Make C here ₀Be constant;

3. can draw the non-linear and linearizing robust system model of the discrete switching of STATCOM equivalence by step 1 is:

$\left[\begin{array}{c}{i}_{C(k+1)}\\ U_{\mathrm{dc}(k+1)}\end{array}\right]=F\left(d_k\right)\left[\begin{array}{c}{i}_{\mathrm{Ck}}\\ U_{\mathrm{dck}}\end{array}\right]+g\left(d_k\right)+w_k,$ y _k＝C ₀i _CKR＝C ₁i _CK

Wherein, C ₀Be constant; $F\left(d_k\right)={\mathrm{\&Phi;}}_{-1}^{1-d_k}{\mathrm{\&Phi;}}_1^{d_k};$ $g\left(d_k\right)={\mathrm{\&Phi;}}_{-1}^{1-d_k}{\mathrm{\&gamma;}}_1^{d_k}+{\mathrm{\&gamma;}}_{-1}^{1-d_k}$

The linear robust system of the discrete switching of its linear equivalence can be expressed as:

Δx _k+1＝F(d(t _k))Δx _k+h(d(t _k))Δd _k+w _k

Δy _k＝C ₁(y _k-y′ _k)

Wherein: $F\left(d\left(t_k\right)\right)={\mathrm{\&Phi;}}_{-1}^{1-d\left(t_k\right)}{\mathrm{\&Phi;}}_1^{d\left(t_k\right)}$ $h\left(d\left(t_k\right)\right)={\mathrm{\&Phi;}}_{-1}^{1-d\left(t_k\right)}{A}_1{x}^{d\left(t_k\right)}T$

$x^{d\left(t_k\right)}={\mathrm{\&Phi;}}_1^{1-d\left(t_k\right)}x+{\mathrm{\&gamma;}}_1^{d\left(t_k\right)}$

Δ x _K+1=F (d (t _k)) Δ x _k+ h (d (t _k)) Δ d _k+ w _k, Δ y _k=C ₁(y _k-y ' _k) and $z_k=\left[\begin{array}{c}{c}_1\mathrm{\&Delta;}{x}_{1k}\\ c_2\mathrm{\&Delta;}{x}_{2k}\end{array}\right]=C_2\mathrm{\&Delta;}{x}_k$ For based on H _∞The state space of the augmentation controlled device of control theory is realized;

4. utilize the LMI method to find the solution the stability of access control device and the constraints of validity is:

$\left[\begin{array}{cc}X& I\\ I& Y\end{array}\right]\&GreaterEqual;0$

$\left[\begin{array}{cc}{C}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]\left[\begin{array}{ccc}{A}^{T}X+\mathrm{XA}& {\mathrm{XB}}_1& C_1^T\\ B_1^{T}X& -\mathrm{\&gamma;I}& 0\\ C_1& 0& -\mathrm{\&gamma;I}\end{array}\right]\left[\begin{array}{cc}{C}^{1/2}& 0\\ 0& I\\ 0& I\end{array}\right]<0$

${\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]}^T\left[\begin{array}{ccc}{\mathrm{YA}}^T+\mathrm{AY}& {\mathrm{YC}}_1^T& B_1\\ C_{1}Y& -\mathrm{\&gamma;I}& 0\\ B_1^T& 0& -\mathrm{\&gamma;I}\end{array}\right]\left[\begin{array}{cc}{B}_2^{T\&perp;}& 0\\ D^{T\&perp;}& 0\\ 0& I\end{array}\right]<0$

In the formula: $A=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{A}_i,B_1=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{11},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{12},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{1N})$

$B_2=(\sqrt{{\mathrm{\&alpha;}}_1}{B}_{21},\sqrt{{\mathrm{\&alpha;}}_2}{B}_{22},...,\sqrt{{\mathrm{\&alpha;}}_N}{B}_{2N})$

$C_1={(\sqrt{{\mathrm{\&alpha;}}_1}{C}_{11}^T,\sqrt{{\mathrm{\&alpha;}}_2}{C}_{12}^T,...,\sqrt{{\mathrm{\&alpha;}}_N}{C}_{1N}^T)}^T$

$C_2={(C_{21}^T,C_{22}^T,...,C_{2N}^T)}^T$

$D=\mathrm{diag}\{\sqrt{{\mathrm{\&alpha;}}_1}{D}_1,\sqrt{{\mathrm{\&alpha;}}_2}{D}_2,...,\sqrt{{\mathrm{\&alpha;}}_N}{D}_N\}$

In this case, switching law can be taken as:

$\mathrm{\&sigma;}\left(t\right)=\arg \min \left\{{\mathrm{\&xi;}}^T\right[{(A_i+B_{2i}{K}_i{C}_{2i})}^T{P}_c+P_c(A_i+B_{2i}{K}_i{C}_{2i})$

$+{\mathrm{\&gamma;}}^{-2}{P}_c{B}_{1i}{B}_{1i}^T{P}_c+{(C_i+D_i{K}_i{C}_{2i})}^T(C_i+D_i{K}_i{C}_{2i})\left]\mathrm{\&xi;}\right\}$

P in the formula _c=γ X _c

5. switching law can be obtained by the ctrb function among the Matlab automatically in the step 4, if σ (t) full rank, then switching law is controlled; Empirical tests is to d (t arbitrarily _kAll there is rank (L)≤1 _k)=2 are so switching law is controlled;

6. definition

T wherein _Zw(s) be closed loop transfer function, by w to z;

7. through regulating FEEDBACK CONTROL rule K, make the closed-loop system internal stability and || T _Zw(s) || _∞＜γ;

8. according to linear system H _∞Control theory is through using the solver mincx in the LMI tool box among the MTLAB, the matrix parameter A in the calculation procedure 1 ₀, A ₁, b, w carry out the reasonable compensation to system;

9. after system voltage, electric current change, detect electric current, through calculating, signal is delivered to the pulsed drive module feed back at last and realize in the inverter switching to reach the control effect through detection module;

Wherein, L _R, R series connection is inductive load, L is a filter inductance; C is a dc capacitor; U _sBe system power supply; U _ConBe the STATCOM output voltage; U _DcBe dc capacitor voltage; K ₁, K ₂, K ₃, K ₄4 switch elements; i _cBe offset current; i _LFor following the tracks of load current.

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