CN106300426A - The self adaptation passivity PI control method of grid-connected inverting system based on MMC - Google Patents

Abstract

The present invention relates to the self adaptation passivity PI control method of a kind of grid-connected inverting system based on MMC, described grid-connected inverting system includes three-phase alternating current potential source, uncontrollable commutator, dc bus link, three-phase modular multilevel inverter and electrical network, the every of described three-phase modular multilevel inverter the most all includes brachium pontis and lower brachium pontis, described method comprises the following steps:, under a b c rest frame, to set up bilinearity Lagrangian model；According to bilinearity Lagrangian model, obtain passivity PI control method；In passivity PI control method, add Automatic adjusument gain coefficient, it is achieved self adaptation passivity PI of high-power grid-connected inverting system based on MMC controls.Compared with prior art, the present invention have simple in construction, stablize field width, constraints is few, robust performance is excellent and the advantage such as applied widely.

Description

The self adaptation passivity PI control method of grid-connected inverting system based on MMC

Technical field

The present invention relates to modular multi-level converter stability contorting field, especially relate to a kind of based on MMC grid-connected The self adaptation passivity PI control method of inversion system.

Background technology

In recent years, along with MW class wind turbine group, the grid-connected power plant of large-scale photovoltaic, flexible high pressure DC transmission system Fast development, tradition two-level inverter is no longer able to meet application demand, mould due to the pressure performance of device and control performance Massing multi-level converter (Modular Multilevel Converter, MMC) obtains in high-power grid-connected inverting system Increasingly extensive application and popularization.The feature that MMC has that structural extended is strong, submodule is pressure demand is little and switching frequency is low, Controlling needed for just meeting the access power system of high-power power of alterating and direct current flexibility is flexible, the quality of power supply is high, fault freedom is excellent Requirement, but when the multivariate of MMC itself, strong nonlinearity characteristic and actual application there is the problem of time-varying unknown disturbance in system, makes Its stability contorting becomes high-power modular many level grid-connected inverting system and realizes the bottleneck place of further genralrlization application.

High-power grid-connected inverting system based on MMC, since within 2009, realizing engineer applied, has mainly used vector controlled Method, from system performance perspective, passes through coordinate transform, it is achieved uneoupled control, but in changed power wide ranges, systematic parameter Perturbing, exist under unknown time-varying interference cases, vector control method often cannot keep excellent dynamic and static performance, very To system unstability occurring, controlling failed situation.For the multivariate of MMC, close coupling, nonlinear characteristic, multiple non-linear control Method processed is from stability angle, and design vulnerability to jamming is excellent, the control system of strong robustness, achieves and preferably applies effect. For the stability contorting of high-power modular many level grid-connected inverting system, the theoretical result of the nonlinear Control of early stage mainly collects In guaranteeing that system is followed the tracks of while desired trajectory, it is achieved the control algorithm design that stable region is wider, anti-interference is higher, with biography System vector controlled is compared, and nonlinear control method design complexity, computationally intensive, engineer applied real-time is the best.

Passive coherent locating (Passivity-Based Control, PBC) relatively other nonlinear methods, have simple in construction, The advantage being easily achieved, PBC method, from energy point of view, uses suitably damping to inject or the mode of energy function planning, if Meter global stability control device, makes system exist under external disturbance or inner parameter perturbation situation, and still stable operation is in expectation work Make a little, it is achieved the tracking zero error of desired trajectory.Existing PBC method is most based on coordinate transform, designs Eular- Lagrangian equation, it is achieved decoupling stability contorting, but can coordinate transform can increase the complexity of controller design, save change Ring change saves, and simplifies PBC design further, promotes Parameter Perturbation adaptive ability, it is achieved be prone to application, function admirable, stable region The PBC method wide, robustness is good, for the stingy problem to be solved of Nonlinearity Control.

Summary of the invention

It is an object of the invention to provide the self adaptation passivity of a kind of grid-connected inverting system based on MMC for the problems referred to above PI control method.

The purpose of the present invention can be achieved through the following technical solutions:

A kind of self adaptation passivity PI control method of grid-connected inverting system based on MMC, described grid-connected inverting system bag Include three-phase alternating current potential source, uncontrollable commutator, dc bus link, three-phase modular multilevel inverter and electrical network, described The every of three-phase modular multilevel inverter the most all includes brachium pontis and lower brachium pontis, and described method comprises the following steps:

1) under a-b-c rest frame, bilinearity Lagrangian model is set up；

2) according to step 1) the bilinearity Lagrangian model set up, design Lagrangian dynamic reversible planning rail Mark, controls to combine with PI, obtains passivity PI control method；

3) in step 2) in the passivity PI control method that obtains, add Automatic adjusument gain coefficient, it is achieved based on MMC High-power grid-connected inverting system self adaptation passivity PI control.

Described step 1) particularly as follows:

11) MMC mission nonlinear differential state equation is set up；

12) under a-b-c rest frame, MMC mission nonlinear differential state equation is carried out coordinate transform, obtain double Linear Lagrangian model.

Described MMC mission nonlinear differential state equation particularly as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_{CU}^{\Σ}}{dt}=\frac{n_U}{C^{arm}}{i}_{diff}+\frac{n_U}{2C^{arm}}{i}_V\\ \frac{{\mathrm{du}}_{CL}^{\Σ}}{dt}=\frac{n_L}{C^{arm}}{i}_{diff}+\frac{n_L}{2C^{arm}}{i}_V\\ \frac{{\mathrm{di}}_{diff}}{dt}=-\frac{R}{L}{i}_{diff}-\frac{n_U}{2L}{u}_{CU}^{\Σ}-\frac{n_L}{2L}{u}_{CL}^{\Σ}+\frac{u_D}{2L}\\ \frac{{\mathrm{di}}_V}{dt}=-\frac{R^{\′}}{L^{\′}}{i}_V-\frac{n_U}{2L^{\′}}{u}_{CU}^{\Σ}+\frac{n_L}{2L^{\′}}{u}_{CL}^{\Σ}-\frac{u_g}{L^{\′}}\end{array}\right.$

R '=R/2+R_Load

L '=L/2+L_Load

Wherein,WithIt is respectively the variable voltage of upper and lower brachium pontis, C^armFor brachium pontis series capacitance, n_UAnd n_LIt is respectively The insertion coefficient of upper and lower brachium pontis, R and L is respectively arm resistance and inductance, i_diffFor every phase circulation, i_VFor output electric current, u_DFor DC voltage, u_gFor grid side voltage, R ' is equivalent resistance, and L ' is equivalent inductance, R_LoadAnd L_LoadIt is respectively and is connected with electrical network Sets of lines all-in resistance and lumped inductance.

Described bilinearity Lagrangian model particularly as follows:

$\left\{\begin{array}{c}x=A_d\left(u\right)x+E\\ A_d\left(u\right)=A+u_1{B}_1+u_2{B}_2\end{array}\right.$

$A=\left[\begin{array}{cccc}-\frac{R}{L}& 0& 0& 0\\ 0& -\frac{R^{\′}}{L^{\′}}& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],E=\left[\begin{array}{c}\frac{u_D}{2L}\\ -\frac{u_g}{L^{\′}}\\ 0\\ 0\end{array}\right],B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\′}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],$

$B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\′}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

Wherein,For state variable, u=[u₁,u₂]^T=[n_u,n_L]^TFor control variable, C^armFor Brachium pontis series capacitance, n_UAnd n_LBeing respectively the insertion coefficient of upper and lower brachium pontis, R and L is respectively arm resistance and inductance, u_DFor direct current Side voltage, u_gFor grid side voltage, R ' is equivalent resistance, and L ' is equivalent inductance.

Described Lagrangian dynamic reversible planned trajectory particularly as follows:

$\tilde{x}=A_d\left(u\right)\tilde{x}+(\widetilde{u_1}{B}_1+\widetilde{u_2}{B}_2)x^{*}$

$\tilde{x}=x-x^{*}$

A_d(u)=A+u₁B₁+u₂B₂

Wherein,

$B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\′}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\′}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

U=[u₁,u₂]^T=[n_u,n_L]^TFor control variable,For the residual quantity signal of x, x^*For the desired trajectory of x,It is respectively u₁、u₂Residual quantity signal,It is respectively u₁、u₂Desired trajectory, C^armFor bridge Arm series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance.

The passive coherent locating expression formula of described passivity PI control method is:

$y=\left[\begin{array}{cc}{x}^{*T}& {B_1}^T\\ x^{*T}& {B_2}^T\end{array}\right]Px$

Wherein,

$P=\left[\begin{array}{cccc}2L& 0& 0& 0\\ 0& L^{\′}& 0& 0\\ 0& 0& C^{arm}& 0\\ 0& 0& 0& C^{arm}\end{array}\right]$

$B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\′}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\′}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

The passivity PI controller expression formula of described passivity PI control method is:

Z=y

$\tilde{u}=u-u^{*}=-K_{p}y-K_{i}z$

Wherein, x is state variable, and y is the output of high-power grid-connected inverting system based on MMC, and P is observer matrix, x^*For the desired trajectory of x, C^armFor brachium pontis series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance, and z is the integrated signal of y,For The residual quantity signal of u, u^*For the desired trajectory of u, K_pFor proportionality coefficient, K_iFor integral coefficient.

Described Automatic adjusument gain coefficient is control variable u₁And u₂Compensation dosage Δ u₁With Δ u₂, particularly as follows:

${\mathrm{\Δu}}_1={\mathrm{\α}}_1{\tilde{x}}^T{\mathrm{PB}}_1{x}^{*}$

${\mathrm{\Δu}}_2={\mathrm{\α}}_2{\tilde{x}}^T{\mathrm{PB}}_2{x}^{*}$

Wherein,

$B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\′}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\′}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

α₁And α₂Controlling gain for system, x is state variable, and P is observer matrix,For the residual quantity signal of x, x^*For x's Desired trajectory, C^armFor brachium pontis series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance.

Compared with prior art, the method have the advantages that

(1) under a-b-c rest frame, directly set up bilinearity Lagrangian model, analyze the strict nothing of system Source characteristic, saves the complicated step of coordinate transform, simplifies the design of PBC method, simple in construction.

(2) based on bilinear model, design Lagrangian dynamic reversible planned trajectory, control organic knot with simple PI Closing, passivity PI proposing more brief and practical controls new method, it is achieved while system desired trajectory is quickly followed the tracks of, and meets complete Office's asymptotically stability demand.

(3), during the energy function in passivity PI control method designs, Automatic adjusument gain coefficient is added, it is possible to according to The impedance parameter change of MMC system, it is achieved meet parameter self-optimization Front feedback control stable for Lyapunov, solve application The middle easy perturbed problem of MMC parameter.

(4) method of the present invention can realize complexity, dynamic, multivariate, the overall situation of strong nonlinearity MMC grid-connected inverting system Stability contorting and the quick tracking of desired trajectory, change and exist the situation of time-varying unknown disturbance, still can for state parameter Enough keeping good quiet, dynamic property, stable region is wider, and constraints is few, and robust performance is excellent.

(5) method of the present invention be applicable to electric power, aviation, metallurgical contour performance, in high precision, powerful power converter work Cheng Zhong, applied widely, Practical Performance is strong.

Accompanying drawing explanation

Fig. 1 is three-phase MMC circuit structure and the schematic diagram of submodule；

Fig. 2 is MMC one phase equivalent circuit figure；

β when Fig. 3 is system stability₁Value figure；

Fig. 4 is MMC self adaptation passivity PI control method overall structure block diagram；

Fig. 5 is the dSPACE integrated structure figure of MMC control system；

Fig. 6 is MMC self adaptation passivity PI control method experimental waveform figure, system under wherein (6a) is even running state Output voltage and current waveform figure, (6b) is system circulation and upper and lower bridge arm current oscillogram under even running state, and (6c) is System output voltage and current waveform figure under AC load inductance and sudden change of resistivity state, (6d) is AC load inductance and resistance System circulation and upper and lower bridge arm current oscillogram under mutation status；

Fig. 7 is the method flow diagram of the present invention.

Detailed description of the invention

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implement, give detailed embodiment and concrete operating process, but protection scope of the present invention be not limited to Following embodiment.

Three-phase MMC circuit structure and submodule schematic diagram as it is shown in figure 1, every mutually upper and lower brachium pontis has N number of submodule respectively, Each submodule is made up of a half-bridge circuit parallel connection direct electric capacity.Put into for suppression submodule and exit the voltage injustice caused Weighing apparatus, each brachium pontis one small inductor of series connection.

If setting by inserting coefficient n (t) control brachium pontis break-make, then define when all submodules of brachium pontis are bypassed, n (t)= 0；When all submodules of brachium pontis all access, n (t)=1.

Define each brachium pontis submodule capacitance be C, brachium pontis series electrical capacitance be C^arm, then have

$C^{arm}=\frac{C}{N}---\left(1\right)$

The effective capacitance value inserted is:

$C^m=\frac{C^{arm}}{n\left(t\right)}---\left(2\right)$

In formula: subscript m represents that brachium pontis is numbered.

Under a-b-c rest frame, balancing energy minimum with circulation between brachium pontis sets up the dynamic mathematical modulo of MMC for target Type.DefinitionBe the variable voltage of a brachium pontis, then the insertion voltage of brachium pontis m is:

$u_C^m=n\left(t\right)u_C^{\Σ}\left(t\right)---\left(3\right)$

Definition brachium pontis charging current is i (t), brachium pontis effective capacitance value is C^arm, then brachium pontis total capacitance voltage is represented by:

$\frac{{\mathrm{du}}_C^{\Σ}\left(t\right)}{dt}=\frac{i\left(t\right)}{C^m}---\left(4\right)$

Define upper and lower bridge arm current and be respectively i_UAnd i_L, output electric current be i_V, every phase circulation be i_diff, then meet:

$\begin{array}{c}{i}_U=\frac{i_V}{2}+i_{diff}\\ i_L=\frac{i_V}{2}-i_{diff}\end{array}---\left(5\right)$

Can push away:

$\begin{array}{c}{i}_V=i_U+i_L\\ i_{diff}=\frac{i_U-i_L}{2}\end{array}---\left(6\right)$

Definition n_U、n_LIt is respectively the insertion coefficient of upper and lower brachium pontis, then can be obtained by formula (2) and formula (4):

$\frac{{\mathrm{du}}_{CU}^{\Σ}\left(t\right)}{dt}=\frac{n_U{i}_U}{C^{arm}}---\left(7\right)$

$\frac{u_{CL}^{\Σ}\left(t\right)}{dt}=-\frac{n_L{i}_L}{C^{arm}}---\left(8\right)$

MMC one phase equivalent circuit is as in figure 2 it is shown, defining each arm resistance is R and inductance is the line that L is connected with electrical network Road lumped resistance is R_Load, lumped inductance be L_Load, then can be obtained by Kirchhoff's second law:

$\frac{u_D}{2}-{\mathrm{Ri}}_U-L\frac{{\mathrm{di}}_U}{dt}-n_U{u}_{CU}^{\Σ}=u_V---\left(9\right)$

$-\frac{u_D}{2}-{\mathrm{Ri}}_L-L\frac{{\mathrm{di}}_L}{dt}+n_L{u}_{CL}^{\Σ}=u_V---\left(10\right)$

$R_{Load}{i}_V+L_{Load}\frac{{\mathrm{di}}_V}{dt}+u_g=u_V---\left(11\right)$

Electric current i is obtained by formula (6), formula (9) and formula (10)_VAnd i_diffThe differential equation:

$\left\{\begin{array}{c}\frac{diff}{dt}=-\frac{R}{L}{i}_{diff}-\frac{n_U}{2L}{u}_{CU}^{\Σ}-\frac{n_L}{2L}{u}_{CL}^{\Σ}+\frac{u_D}{2L}\\ \frac{{\mathrm{di}}_V}{dt}=-\frac{R^{\′}}{L^{\′}}{i}_V-\frac{n_U}{2L^{\′}}{u}_{CU}^{\Σ}+\frac{n_L}{2L^{\′}}{u}_{CL}^{\Σ}-\frac{u_g}{L^{\′}}\end{array}\right.---\left(12\right)$

Formula (5) is substituted into formula (7) and formula (8) can go up brachium pontis total voltage and the lower brachium pontis total voltage differential equation:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_{CU}^{\Σ}}{dt}=\frac{n_U}{C^{arm}}{i}_{diff}+\frac{n_U}{2C^{arm}}{i}_V\\ \frac{{\mathrm{du}}_{CL}^{\Σ}}{dt}=\frac{n_L}{C^{arm}}{i}_{diff}-\frac{n_L}{2C^{arm}}{i}_V\end{array}\right.---\left(13\right)$

In formula: R '=R/2+R_LoadRepresent equivalent resistance, L '=L/2+L_LoadRepresent equivalent inductance.

Formula (12) and formula (13) constitute MMC system dynamics mathematical model state space equation.

Definition status variableIt is respectively circulation value, total current and upper and lower bridge arm voltage value； Control variable u=[u₁,u₂]^T=[n_u,n_L]^TIt is respectively the insertion coefficient of upper and lower brachium pontis.According to bilinearity Lagrangian equation Control characteristic, under a-b-c rest frame, MMC system dynamics mathematical model state space equation formula (12), formula (13) can Equivalent transformation is:

$\left\{\begin{array}{c}x=A_d\left(u\right)x+E\\ A_d\left(u\right)=A+u_1{B}_1+u_2{B}_2\end{array}\right.---\left(14\right)$

In formula:

$A=\left[\begin{array}{cccc}-\frac{R}{L}& 0& 0& 0\\ 0& -\frac{R^{\′}}{L^{\′}}& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],E=\left[\begin{array}{c}\frac{u_D}{2L}\\ -\frac{u_g}{L^{\′}}\\ 0\\ 0\end{array}\right],B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\′}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],$

$B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\′}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

It is satisfied

PA_d(u)+A_d(u) P=-2diag{2R, R', 0,0}≤0 (15)

Taking observer matrix P is:

$P=\left[\begin{array}{cccc}2L& 0& 0& 0\\ 0& L^{\′}& 0& 0\\ 0& 0& C^{arm}& 0\\ 0& 0& 0& C^{arm}\end{array}\right]---\left(16\right)$

By formula (15) definition positive semidefinite matrix Q it is:

$Q=-\frac{1}{2}\[{\mathrm{PA}}_d\left(u\right)+A_d\left(u\right)P\]=diag\{2R,R^{\′},0,0\}---\left(17\right)$

Design positive definite quadratic form energy function H (x) is:

$H\left(x\right)=\frac{1}{2}{x}^{T}Px---\left(18\right)$

Can be obtained by bilinearity Lagrangian equation (14) and energy function formula (18):

x^TPx=x^TPA_d(u)x+x^TPE=-x^TQx+x^TPE (19)

Formula (18) both members integration can obtain:

$H\left(x\right(t\left)\right)-H\left(x\right(0\left)\right)=-{\&Integral;}_0^t{x}^{T}Qxd\mathrm{\&tau;}+{\&Integral;}_0^t{x}^{T}PEd\mathrm{\&tau;}<{\&Integral;}_0^t{x}^{T}PEd\mathrm{\&tau;}---\left(20\right)$

Formula (20) left side expression formula is the increment of MMC system capacity, the energy supply that right-hand side expression provides for outside.By Passivity definition understands, if E regards as the input of MMC system, x regards the output of MMC system as, then mapFor defeated Go out Strictly passive control.

Definition desired trajectory is x^*, then can obtain according to MMC bilinearity Lagrangian equation (13):

$\left\{\begin{array}{c}{x}^{*}=A_d\left(u^{*}\right)x^{*}+E\\ A_d\left(u^{*}\right)=A+{u_1}^{*}{B}_1+{u_2}^{*}{B}_2\end{array}\right.---\left(21\right)$

System controls target and need to meet:

$\underset{t\&RightArrow;\mathrm{\&infin;}}{\lim }\&lsqb;x\left(t\right)-x^{*}\left(t\right)\&rsqb;=0---\left(22\right)$

If definition residual quantity signal is:

$\tilde{x}=x-x^{*}---\left(23\right)$

$\tilde{u}=u-u^{*}---\left(24\right)$

Then being designed Lagrangian dynamic reversible planned trajectory by formula (13) and formula (21) is:

$\tilde{x}=A_d\left(u\right)\tilde{x}+(\widetilde{u_1}+B_1+\widetilde{u_2}{B}_2)x^{*}---\left(24\right)$

Choose Lyapunov energy equation:

$V\left(\tilde{x}\right)=\frac{1}{2}{\tilde{x}}^{T}P\tilde{x}---\left(25\right)$

Derivation obtains system dissipation inequality:

$\begin{array}{c}V\left(\tilde{x}\right)={\tilde{x}}^{T}P\&lsqb;A_d\left(u\right)\tilde{x}+(\widetilde{u_1}{B}_1+\widetilde{u_2}{B}_2)x^{*}\&rsqb;\\ =-{\tilde{x}}^{T}Q\tilde{x}+{\tilde{x}}^T{\mathrm{PB}}_1{x}^{*}\widetilde{u_1}+{\tilde{x}}^T{\mathrm{PB}}_2{x}^{*}\widetilde{u_2}\\ \&le;{\tilde{x}}^T{\mathrm{PB}}_1{x}^{*}\widetilde{u_1}+{\tilde{x}}^T{\mathrm{PB}}_2{x}^{*}\widetilde{u_2}\\ =y^T\tilde{u}\end{array}---\left(26\right)$

In formula:

$y=\left[\begin{array}{cc}{x}^{*T}& {B_1}^T\\ x^{*T}& {B_2}^T\end{array}\right]Px=\left[\begin{array}{c}-{x_3}^{*}{x}_1-\frac{1}{2}{x_3}^{*}{x}_2+{x_1}^{*}{x}_3+\frac{1}{2}{x_2}^{*}{x}_3\\ -{x_4}^{*}{x}_1+\frac{1}{2}{x_4}^{*}{x}_2+{x_1}^{*}{x}_4+\frac{1}{2}{x_2}^{*}{x}_4\end{array}\right]$

By dissipation inequality (26) it can be seen that system Lyapunov stability is closely related with output y, therefore select shape The simple PI of formula controls, and organically combines with passive coherent locating, while making system meet control target, along Lagrangian integration Minimize track to move, quickly follow the tracks of desired trajectory, it is achieved Globally asymptotic controls.

Choose the simple architecture that PI controls, design passivity PI feedback control closed loop:

$\begin{array}{c}z=y\\ u=u^{*}-K_{p}y-K_{i}z\end{array}---\left(27\right)$

In formula: K_p=K_p ^T＞ 0, K_i=K_i ^T＞ 0 is respectively PI and controls proportionality coefficient, integral coefficient.

Residual quantity signal formula (23) is substituted into passivity PI controller formula (27), can obtain:

$\begin{array}{c}z=y\\ u=u-u^{*}=-K_{p}y-K_{i}z\end{array}---\left(28\right)$

Design energy function:

$W(\tilde{x},z)=V\left(\tilde{x}\right)+\frac{1}{2}{z}^T{K}_{i}z---\left(29\right)$

Derivation obtains:

$W=-{\tilde{x}}^{T}Q\tilde{x}+y^T\tilde{u}+z^T{K}_{i}y=-{\tilde{x}}^{T}Q\tilde{x}-y^T{K}_{p}y\&le;0---\left(30\right)$

Consider that desired signal exists time-varying unknown disturbance situation, definitionThen controller output y can be written as:

$\stackrel{\&OverBar;}{y}={(x^{*}+\mathrm{\&xi;})}^T{B}^{T}Px=y+{\mathrm{\&xi;}}^T{B}^{T}Px---\left(31\right)$

Formula (28) is derived as:

$\begin{array}{c}z=y+{\mathrm{\&xi;}}^T{B}^{T}Px\\ \tilde{u}=-K_{p}y-K_{i}z-K_p{\mathrm{\&xi;}}^T{B}^{T}Px\end{array}---\left(32\right)$

Then can be obtained by formula (30):

$W=-{\tilde{x}}^{T}Q\tilde{x}-y^T{K}_{p}y-K_p{\mathrm{\&xi;}}^T{B}^{T}Px\&le;0---\left(33\right)$

From the relation between passivity and Lyapunov stability, it is considered to passivity PI of time-varying unknown disturbance controls Method can not only realize effective tracking of desired trajectory, and can ensure that the system progressive Exponential Stability of the overall situation.

During high-power modular many level grid-connected inverters actual motion, systematic parameter often can change, as with temperature Raising, line resistance, filter inductance can increase therewith.Due to systematic parameter perturb, the steady-state conditions of Lyapunov function also with Change, thus affect the control effect of passivity PI method, even affect system stability.It is proposed that parameter self-optimization is mended Compensation method, improve system robustness, it is ensured that systematic parameter also can realize in the case of there is uncertainty desired trajectory accurate with Track and stable operation.

Definition control variable u₁、u₂Compensation dosage be Δ u₁、Δu₂, it is considered in system dissipation inequality (26)Negative Fixed, for making energy equation perseverance be negative, design:

$\begin{array}{c}{\mathrm{\&Delta;u}}_1={\mathrm{\&alpha;}}_1{\tilde{x}}^T{\mathrm{PB}}_1{x}^{*}\\ {\mathrm{\&Delta;u}}_2={\mathrm{\&alpha;}}_2{\tilde{x}}^T{\mathrm{PB}}_2{x}^{*}\end{array}---\left(34\right)$

In formula: α₁、α₂It is negative value, controls gain for system.Regulation α₁、α₂Grid-connected voltage, electric current can be made quickly to follow the tracks of ginseng Examine value, realize controlling desired dynamic and static performance under systematic parameter perturbation situation.Consider quantity of state change, can by formula (34) :

$\begin{array}{c}{\mathrm{\&Delta;u}}_1={\mathrm{\&alpha;}}_1(\widetilde{x_3}{x_1}^{*}+\frac{1}{2}\widetilde{x_3}{x_2}^{*}-\widetilde{x_1}{x_3}^{*}-\frac{1}{2}\widetilde{x_2}{x_3}^{*})\\ {\mathrm{\&Delta;u}}_2={\mathrm{\&alpha;}}_2(\widetilde{x_4}{x_1}^{*}+\frac{1}{2}\widetilde{x_4}{x_2}^{*}-\widetilde{x_1}{x_4}^{*}-\frac{1}{2}\widetilde{x_2}{x_4}^{*})\end{array}---\left(35\right)$

DefinitionSubstitution formula (35) can :

$\begin{array}{c}{\mathrm{\&Delta;u}}_1={\mathrm{\&alpha;}}_1(u_{CU}^{\&Sigma;}{i_{diff}}^{*}-\frac{1}{2}{i}_{diff}{u_{CU}^{\&Sigma;}}^{*}+\frac{1}{2}{u}_{CU}^{\&Sigma;}{i_V}^{*}-\frac{1}{2}{i}_V{u_{CU}^{\&Sigma;}}^{*})\\ {\mathrm{\&Delta;u}}_2={\mathrm{\&alpha;}}_2(u_{CU}^{\&Sigma;}{i_{diff}}^{*}-i_{diff}{u_{CL}^{\&Sigma;}}^{*}-\frac{1}{2}{i}_V{u_{Cl}^{\&Sigma;}}^{*}+{u_{CL}^{\&Sigma;}}^{*}{i_V}^{*})\end{array}---\left(36\right)$

Assume that t system expected value is (X₁,X₂,X₃,X₄), controlling the value employed in target formula (22) is (X₁’, X₂’,X₃’,X₄'), for observation system Parameters variation situation, if

$\frac{{X_1}^{\&prime;}}{{X_3}^{\&prime;}}={\mathrm{\&beta;}}_1\frac{X_1}{X_3},\frac{{X_2}^{\&prime;}}{{X_3}^{\&prime;}}={\mathrm{\&beta;}}_2\frac{X_2}{X_3},\frac{{X_1}^{\&prime;}}{{X_4}^{\&prime;}}={\mathrm{\&beta;}}_3\frac{X_2}{X_4},\frac{{X_2}^{\&prime;}}{{X_4}^{\&prime;}}={\mathrm{\&beta;}}_4\frac{X_2}{X_4},z_1=\frac{\widetilde{x_1}}{X_1},z_2=\frac{\widetilde{x_2}}{X_2},z_3=\frac{\widetilde{x_3}}{X_3},z_4=\frac{\widetilde{x_4}}{X_4}---\left(37\right)$

Then system dissipative function derivative formula (26) can be written as:

$\begin{array}{c}V\left(\tilde{x}\right)={\mathrm{\&alpha;}}_1{X}_3{X_3}^{\&prime;}(z_3{X}_1-z_1{X}_1+\frac{1}{2}{z}_3{X}_2-\frac{1}{2}{z}_2{X}_2)(z_3{\mathrm{\&beta;}}_1{X}_1-z_1{X}_1+\frac{1}{2}{z}_3{\mathrm{\&beta;}}_2{X}_2-\frac{1}{2}{z}_2{X}_2)\\ +{\mathrm{\&alpha;}}_2{X}_4{X_4}^{\&prime;}(z_4{X}_1-z_1{X}_1-\frac{1}{2}{z}_4{X}_2-\frac{1}{2}{z}_2{X}_2)(z_4{\mathrm{\&beta;}}_3{X}_1-z_1{X}_1+\frac{1}{2}{z}_4{\mathrm{\&beta;}}_4{X}_2-\frac{1}{2}{z}_2{X}_2)\\ -2{{\mathrm{Rz}}_1}^2{X_1}^2-R^{\&prime;}{z_2}^2{X_2}^2\end{array}---\left(38\right)$

From controlling target, X₁=0, then formula (38) can abbreviation be:

$\begin{array}{c}V\left(\tilde{x}\right)=-\frac{1}{4}{X_2}^2(2R^{\&prime;}{z_2}^2-{\mathrm{\&alpha;}}_1{X}_3{X_3}^{\&prime;}(z_3-z_2\left)\right(z_3{\mathrm{\&beta;}}_2-z_2\left)\right)\\ -\frac{1}{4}{X_2}^2(2R^{\&prime;}{z_2}^2-{\mathrm{\&alpha;}}_2{X}_4{X_4}^{\&prime;}(z_4-z_2\left)\right(z_4{\mathrm{\&beta;}}_2-z_2\left)\right)\\ =-\frac{1}{4}{X_2}^2{f}_1(z_2,z_3)-\frac{1}{4}{X_2}^2{f}_1(z_2,z_4)\end{array}---\left(39\right)$

If meeting f₁(z₂,z₃) > 0 and f₂(z₂,z₄) > 0, thenNegative definite.

Make r₁=-α₁X₃X₃' > 0, r₂=-α₂X₄X₄' > 0, z₃=m₁z₂, z₄=m₂z₂, then have:

f₁(z₂,z₃)=z₂ ²[β₂r₁m₁ ²-r₁(1+β₂)m₁+(r₁+ 2R')]=z₂ ²λ₁(r₁,β₂,m₁) (40)

In formula: λ₁(r₁,β₂,m₁)=β₂r₁m₁ ²-r₁(1+β₂)m₁+(r₁+ 2R') for from becoming m₁Quadratic function, work as m₁=(1+ β₂)/2β₂Time take minima, then have:

${\mathrm{\&lambda;}}_{1\min }=2R^{\&prime;}+r_1-\frac{r_1{(1+{\mathrm{\&beta;}}_2)}^2}{4{\mathrm{\&beta;}}_2}---\left(41\right)$

If taking λ_1min> 0, then formula (40) positive definite, for making system asymptotically stability, designs β₂Span is β_a<β₂<β_b, β_a、β_b Meet:

$\begin{array}{c}{\mathrm{\&beta;}}_a=(1+\frac{4R^{\&prime;}}{r_1})-\sqrt{{(1+\frac{4R^{\&prime;}}{r_1})}^2-1}\\ {\mathrm{\&beta;}}_b=(1+\frac{4R^{\&prime;}}{r_1})-\sqrt{{(1+\frac{4R^{\&prime;}}{r_1})}^2-1}\end{array}---\left(42\right)$

From formula (42), λ_1minWith β₂Change as shown in Figure 3.During for making systematic parameter perturb, system still keeps steady Fixed, α₁Should level off to 0, and r as far as possible₁Level off to 0.

Indeterminacy section β for systematic parameter₂∈[1-ε₁,1+ε₁], formula (42) α can be tried to achieve₁Minima is:

${\mathrm{\&alpha;}}_{1\min }=-\frac{2R^{\&prime;}}{X_2{X_3}^{\&prime;}}\frac{4(1-\mathrm{\&epsiv;})}{{\mathrm{\&epsiv;}}^2}---\left(43\right)$

In like manner can obtain α₂Minima is:

${\mathrm{\&alpha;}}_{2\min }=-\frac{2R^{\&prime;}}{X_4{X_4}^{\&prime;}}\frac{4(1-\mathrm{\&epsiv;})}{{\mathrm{\&epsiv;}}^2}$

In order to make tracking performance improve as far as possible, α₁And α₂Value should as far as possible little.Choose positive value delta as optimizing essence Degree, α₁And α₂Respectively at (α_1min,-Δ) and (α_2min,-Δ) and interval interior optimum option, target function is defined as:

$J({\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2)=\frac{1}{n}\underset{k=1}{\overset{n}{\&Sigma;}}(\sqrt{{\tilde{x}}_{1k}^2}+\sqrt{{\tilde{x}}_{2k}^2}+\sqrt{{\tilde{x}}_{3k}^2}+\sqrt{{\tilde{x}}_{4k}^2})---\left(45\right)$

When by state x₁、x₂、x₃、x₄During the target function value minimum that up-to-date n data determine, α₁And α₂Value is optimum.

In sum, MMC self adaptation passivity PI control method overall structure block diagram is as shown in Figure 4.Passivity PI controls Device realizes the quick tracking of desired trajectory, and Adaptive Compensation Control rule realizes the dysgenic effective suppression of system parameter disturbance, While guaranteeing that system quickly follows the tracks of desired control performance indications, there is Globally asymptotic characteristic.

By the rapid prototyping function of dSPACE system, set up 122V/750W MMC experiment porch as shown in Figure 5, can The correctness of fast verification self adaptation passivity PI control method and feasibility.MMC system every phase brachium pontis 4 submodules of series connection, Main circuit switch selects SKM50GB123D power model, controller with the DS1005PPC high speed processor of dSPACE as core, Self adaptation passivity PI control method is realized by MATLAB/Simulink modeling, completes Simulink mould by RTI real-time interface Type and the connection of dSPACE system, utilize RTW to be extended, it is achieved the automatic download of hardware identification code between the two, by Control Desk software carries out integrated management to debugging process, it is achieved adjust ginseng online, real-time inspection and control effect, to MMC even running and Under load changing situation, the asymptotic tracking of system mode parameter carries out validity test and checking.System experimentation parameter such as table 1 institute Show.The experimental waveform recorded is as shown in Figure 6.

Table 1

Figure (6a), figure (6b) are respectively system output voltage, output electric current, circulation and upper and lower under even running state Bridge arm current waveform, as seen from the figure, during system even running, output voltage is nine level, presents preferable sine, defeated Going out electric current the most smooth, electric current is consistent with voltage-phase, and power factor reaches 0.98, and circulation is preferably suppressed.Figure (6c), When figure (6d) respectively AC load inductance is sported 0.2mH by 0.5mH, AC load resistance is sported 2 Ω by 5 Ω, system is defeated Go out voltage, output electric current, circulation and upper and lower bridge arm current waveform, as seen from the figure, output voltage under load changing situation, Electric current maintains steadily, though fluctuation occurs in upper and lower bridge arm current, but self adaptation passivity PI control method makes bridge arm current the most extensive Multiple stable.

From experimental waveform analysis: self adaptation passivity PI control method is capable of MMC system even running, stable state Operation static difference is little, and circulation is little, and the quality of power supply is high, and the fast and stable that can realize MMC system in the case of load changing controls.Real Test result and demonstrate correctness and the effectiveness of proposed control method.

Claims (7)

1. a self adaptation passivity PI control method for grid-connected inverting system based on MMC, described grid-connected inverting system includes Three-phase alternating current potential source, uncontrollable commutator, dc bus link, three-phase modular multilevel inverter and electrical network, described three The every of phase module multi-electrical level inverter the most all includes brachium pontis and lower brachium pontis, it is characterised in that described method includes following step Rapid:

1) under a-b-c rest frame, bilinearity Lagrangian model is set up；

2) according to step 1) the bilinearity Lagrangian model set up, design Lagrangian dynamic reversible planned trajectory, with PI controls to combine, and obtains passivity PI control method；

3) in step 2) in the passivity PI control method that obtains, add Automatic adjusument gain coefficient, it is achieved based on MMC big Self adaptation passivity PI of power grid-connected inverting system controls.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 1, its feature It is, described step 1) particularly as follows:

11) MMC mission nonlinear differential state equation is set up；

12) under a-b-c rest frame, MMC mission nonlinear differential state equation is carried out coordinate transform, obtain bilinearity Lagrangian model.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 2, its feature Be, described MMC mission nonlinear differential state equation particularly as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_{CU}^{\&Sigma;}}{dt}=\frac{n_U}{C^{arm}}{i}_{diff}+\frac{n_U}{2C^{arm}}{i}_V\\ \frac{{\mathrm{du}}_{CL}^{\&Sigma;}}{dt}=\frac{n_L}{C^{arm}}{i}_{diff}-\frac{n_L}{2C^{arm}}{i}_V\\ \frac{{\mathrm{di}}_{diff}}{dt}=-\frac{R}{L}{i}_{diff}-\frac{n_U}{2L}{u}_{CU}^{\&Sigma;}-\frac{n_L}{2L}{u}_{CU}^{\&Sigma;}+\frac{u_D}{2L}\\ \frac{{\mathrm{di}}_V}{dt}=-\frac{R^{\&prime;}}{L^{\&prime;}}{i}_V-\frac{n_U}{2L^{\&prime;}}{u}_{CU}^{\&Sigma;}+\frac{n_L}{2L^{\&prime;}}{u}_{CU}^{\&Sigma;}-\frac{u_g}{L^{\&prime;}}\end{array}\right.$

R '=R/2+R_Load

L '=L/2+L_Load

Wherein,WithIt is respectively the variable voltage of upper and lower brachium pontis, C^armFor brachium pontis series capacitance, n_UAnd n_LThe most upper and lower The insertion coefficient of brachium pontis, R and L is respectively arm resistance and inductance, i_diffFor every phase circulation, i_VFor output electric current, u_DFor DC side Voltage, u_gFor grid side voltage, R ' is equivalent resistance, and L ' is equivalent inductance, R_LoadAnd L_LoadIt is respectively the circuit being connected with electrical network Lumped resistance and lumped inductance.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 2, its feature Be, described bilinearity Lagrangian model particularly as follows:

$\left\{\begin{array}{c}x=A_d\left(u\right)x+E\\ A_d\left(u\right)=A+u_1{B}_1+u_2{B}_2\end{array}\right.$

$\begin{array}{ccc}A=\left[\begin{array}{cccc}-\frac{R}{L}& 0& 0& 0\\ 0& -\frac{R^{\&prime;}}{L^{\&prime;}}& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right],& E=\left[\begin{array}{c}\frac{u_D}{2L}\\ -\frac{u_g}{L^{\&prime;}}\\ 0\\ 0\end{array}\right],& B_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\&prime;}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],\end{array}$

$B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\&prime;}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]$

Wherein,For state variable, u=[u₁,u₂]^T=[n_u,n_L]^TFor control variable, C^armFor brachium pontis Series capacitance, n_UAnd n_LBeing respectively the insertion coefficient of upper and lower brachium pontis, R and L is respectively arm resistance and inductance, u_DFor DC side electricity Pressure, u_gFor grid side voltage, R ' is equivalent resistance, and L ' is equivalent inductance.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 1, its feature Be, described Lagrangian dynamic reversible planned trajectory particularly as follows:

$\begin{array}{c}\tilde{x}=A_d\left(u\right)\tilde{x}+(\widetilde{u_1}{B}_1+\widetilde{u_2}{B}_2)x^{*}\\ \tilde{x}=x-x^{*}\end{array}$

A_d(u)=A+u₁B₁+u₂B₂

Wherein,

$\begin{array}{cc}{B}_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\&prime;}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],& B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\&prime;}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]\end{array}$

U=[u₁,u₂]^T=[n_u,n_L]^TFor control variable,For the residual quantity signal of x, x^*For the desired trajectory of x,It is respectively u₁、u₂Residual quantity signal,It is respectively u₁、u₂Desired trajectory, C^armFor bridge Arm series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 1, its feature Being, the passive coherent locating expression formula of described passivity PI control method is:

$y=\left[\begin{array}{cc}{x}^{*T}& B_1^T\\ x^{*T}& B_2^T\end{array}\right]Px$

Wherein,

$P=\left[\begin{array}{cccc}2L& 0& 0& 0\\ 0& L^{\&prime;}& 0& 0\\ 0& 0& C^{arm}& 0\\ 0& 0& 0& C^{arm}\end{array}\right]$

$\begin{array}{cc}{B}_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\&prime;}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],& B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\&prime;}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]\end{array}$

The passivity PI controller expression formula of described passivity PI control method is:

Z=y

$\tilde{u}=u-u^{*}=-K_{p}y-K_{i}z$

Wherein, x is state variable, and y is the output of high-power grid-connected inverting system based on MMC, and P is observer matrix, x^*For x Desired trajectory, C^armFor brachium pontis series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance, and z is the integrated signal of y,Difference for u Amount signal, u^*For the desired trajectory of u, K_pFor proportionality coefficient, K_iFor integral coefficient.

The self adaptation passivity PI control method of grid-connected inverting system based on MMC the most according to claim 1, its feature Being, described Automatic adjusument gain coefficient is control variable u₁And u₂Compensation dosage Δ u₁With Δ u₂, particularly as follows:

${\mathrm{\&Delta;u}}_1={\mathrm{\&alpha;}}_1{\tilde{x}}^T{\mathrm{PB}}_1{x}^{*}$

${\mathrm{\&Delta;u}}_2={\mathrm{\&alpha;}}_2{\tilde{x}}^T{\mathrm{PB}}_2{x}^{*}$

Wherein,

$\begin{array}{cc}{B}_1=\left[\begin{array}{cccc}0& 0& -\frac{1}{2L}& 0\\ 0& 0& -\frac{1}{2L^{\&prime;}}& 0\\ \frac{1}{C^{arm}}& \frac{1}{2C^{arm}}& 0& 0\\ 0& 0& 0& 0\end{array}\right],& B_2=\left[\begin{array}{cccc}0& 0& 0& -\frac{1}{2L}\\ 0& 0& 0& \frac{1}{2L^{\&prime;}}\\ 0& 0& 0& 0\\ \frac{1}{C^{arm}}& -\frac{1}{2C^{arm}}& 0& 0\end{array}\right]\end{array}$

α₁And α₂Controlling gain for system, x is state variable, and P is observer matrix,For the residual quantity signal of x, x^*Expectation for x Track, C^armFor brachium pontis series capacitance, L is brachium pontis inductance, and L ' is equivalent inductance.