CN105375522A - Control method of photovoltaic grid-connected inverter - Google Patents

Abstract

The present invention discloses a control method of photovoltaic grid-connected inverter. The control method of photovoltaic grid-connected inverter comprises the following steps: the step 1, establishing an inverter mathematical model according to the circuit theorem and the state space average method; and the step 2, designing an inverter controller. According to the invention, the control method of a photovoltaic grid-connected inverter is able to satisfy the requirements of the robustness, the stability and the rapidity, and the control algorithm may reliably work when the system environment is sudden changed so as to allow the photovoltaic inverter to output a stable sinusoidal alternating current voltage.

Description

A kind of photovoltaic combining inverter control method

Technical field

The present invention relates to a kind of photovoltaic combining inverter control method, be specifically related to a kind of photovoltaic combining inverter control method adopting model reference adaptive and inverting overall situation fast terminal sliding formwork hybrid algorithm, belong to control system technical field.

Background technology

Low profile photovoltaic grid-connected system adopts the circuit topological structure of two-stage type high frequency not with isolating transformer usually.Namely prime adopts Boost circuit to realize DC-DC conversion, and rear class adopts high-frequency inverter to realize DC-AC conversion.Controlled by MPPT maximum power point tracking MaximunPowerPointTracking (MPPT) in Boost circuit, improve generating capacity.

In recent years, photovoltaic system generates electricity by way of merging two or more grid systems and is rapidly developed.But photovoltaic generation itself has instable feature, the quality of its grid-connected electric energy and generating efficiency are subject to the impact of the many factors such as ambient temperature, intensity of illumination, system structure parameter uncertainty and external interference, and thus effective inverter control algorithm is the key solving the grid-connected problem of photovoltaic system.

Traditional stagnant chain rate comparatively inverter control method can not the effective uncertain and perturbed problem for the treatment of system, and from control mechanism, just there is chattering phenomenon, when system environments is suddenlyd change, automatic tracking performance is poor; And common sliding-mode control cannot ensure system at Finite-time convergence to sliding-mode surface, the speed of asymptotic convergence is slower.

Summary of the invention

In order to solve the problems of the technologies described above, the invention provides a kind of photovoltaic combining inverter control method.

In order to achieve the above object, the technical solution adopted in the present invention is:

A kind of photovoltaic combining inverter control method, comprises the following steps,

Step one, sets up inverter Mathematical Modeling according to Circuit Theorem and State-space Averaging Principle;

$\left\{\begin{array}{c}\frac{{\mathrm{dx}}_1}{dt}=x_2\\ \frac{{\mathrm{dx}}_2}{dt}=-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\φ}\left(t\right)\end{array}\right.$

Wherein, state variable $\left\{\begin{array}{c}{x}_1=v_{ac}\\ x_2={\stackrel{\·}{v}}_{ac}\end{array}\right.,$ V _acfor inverter ac side voltage, v _dcdC side voltage of converter, C _acand L _acbe respectively inverter ac lateral capacitance and inductance, R _lfor network load, D is inverter duty cycle, for distracter, t () is external interference, Δ ₁and Δ ₂be respectively the error term caused by the parameter of electric capacity and inductance;

Step 2, design circuit control device;

A1) constructing virtual control function;

Definition control objectives is inverter ac side output voltage v _ac, reference voltage is electrical network power frequency sinusoidal voltage v _ac*, make tracing deviation e ₁=v _ac-v _ac*, then

Then virtual master function is,

$e_2=x_2+c_1{e}_1-{\stackrel{\·}{v}}_{ac*}$

Wherein, c ₁it is a real number being greater than zero;

A2) Lyapunov function is chosen,

$V_1=\frac{1}{2}{e}_1^2$

V ₁derivative be,

${\stackrel{\·}{V}}_1=-c_1{e}_1^2+e_1{e}_2$

If e ₂=0, so so need to design new Lyapunov function;

A3) defining sliding-mode surface is,

$s_c=e_2+{\mathrm{\αe}}_1+{{\mathrm{\βe}}_1}^{p_2/p_1}$

Wherein, α, β are sliding-mode surface constants, p ₁, p ₂for positive odd number, and p ₁> p ₂;

Virtual master function and tracing deviation are substituted into and can obtain,

$s_c={\stackrel{\·}{e}}_1+(c_1+\mathrm{\α})e_1+{{\mathrm{\βe}}_1}^{p_2/p_1}$

Then

${\stackrel{\·}{s}}_c=-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\φ}\left(t\right)-{\stackrel{\·\·}{v}}_{ac*}+(c_1+\mathrm{\α}){\stackrel{\·}{e}}_1+\frac{p_2}{p_1}{{\mathrm{\βe}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\·}{e}}_1;$

A4) add model reference self-adapting control, design new Lyapunov function;

According to the character of distracter, suppose $\left|\mathrm{\&phi;}\left(t\right)\right|<b_2\left|x_2\right|+b_1\left|x_1\right|+b_0=b_0+b_1\left|v_{ac}\right|+b_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|,$ Adaptive control laws design is carried out according to the following formula,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{b}}}_0=m_0\left|s_c\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_1=m_1\left|s_c\right|\left|v_{ac}\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_2=m_2\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\end{array}\right.$

Wherein, normal number m ₀, m ₁and m ₂for adaptive gain, with b respectively ₀, b ₁and b ₂estimated value, b ₀, b ₁, b ₂for positive unknown parameter;

New Lyapunov function is,

$V_2^{\&prime;}=V_1+\frac{1}{2}{s_c}^2+\frac{1}{2}\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{{\tilde{b}}_i}^2$

Wherein, i=0,1,2, b ₀, b ₁, b ₂evaluated error;

New Lyapunov function differentiate can obtain,

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2^{\&prime;}={\stackrel{\&CenterDot;}{V}}_1+s_c{\stackrel{\&CenterDot;}{s}}_c-\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{\tilde{b}}_i{\stackrel{\&CenterDot;}{\hat{b}}}_i\\ =-c_1{e_1}^2+e_1{e}_2+s_c\&lsqb;-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{ac}+\mathrm{\&phi;}\left(t\right)+\left(c_1+\mathrm{\&alpha;}\right){\stackrel{\&CenterDot;}{e}}_1-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\\ -{m_0}^{-1}{\tilde{b}}_0{\stackrel{\&CenterDot;}{\hat{b}}}_0-{m_1}^{-1}{\tilde{b}}_1{\stackrel{\&CenterDot;}{\hat{b}}}_1-{m_2}^{-1}{\tilde{b}}_2{\stackrel{\&CenterDot;}{\hat{b}}}_2\end{array};$

A5) control law of employing model reference adaptive and inverting overall situation fast terminal sliding formwork hybrid algorithm is,

$D=\frac{1}{2}\{1+\frac{L_{ac}{C}_{ac}}{u_{dc}}\&lsqb;\frac{1}{R_L{C}_{ac}}{x}_2+\frac{1}{L_{ac}{C}_{ac}}{x}_1+D_1-(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1+{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}-c_2{s}_2-\frac{s_c}{{\left|s_c\right|}^2}{e}_1{e}_2-\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\}$

Wherein, $D_1=-\mathrm{sgn}\left(s_c\right)({\hat{b}}_0+{\hat{b}}_1|v_{ac}|+{\hat{b}}_2|{\stackrel{\&CenterDot;}{v}}_{ac}\left|\right)=-\frac{s_c}{\left|s_c\right|}\left({\hat{b}}_0+{\hat{b}}_1\left|v_{ac}\right|+{\hat{b}}_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\right).$

The single-phase grid-connected photovoltaic power generation system structure at described inverter place is the not isolated grid-connected circuit of two-stage type high frequency.

Described inverter structure is full-bridge voltage type inverter.

By plan boundary layer in circuit control device, reduce the chattering phenomenon that sliding formwork controls.

By arranging p ₁, p ₂scope meet the nonsingular requirement of overall fast terminal sliding formwork.

The beneficial effect that the present invention reaches: 1, inverter control method of the present invention can meet the requirement of robustness, stability and rapidity, when system environments is undergone mutation, control algolithm energy reliably working, makes the sinusoidal voltage of photovoltaic DC-to-AC converter stable output; 2, the present invention adopts model reference self-adapting control to carry out control rate design, reaches the object from motion tracking disturbance; 3, the present invention meets the requirement of inverter dynamic response, makes control have robustness; 4, back stepping control of the present invention is the subsystem of depression of order system decomposition, for subsystem design Lyapunov function and virtual master function ensure control stability; 5, overall fast terminal sliding formwork of the present invention controls to improve system convergence speed, is avoided by parameter designing the singular problem that may occur.

Accompanying drawing explanation

Fig. 1 is single-phase grid-connected photovoltaic power generation system structure chart.

Fig. 2 is S ₁, S ₄circuit during conducting.

Fig. 3 is circuit control device design structure diagram.

Fig. 4 be under standard operating conditions inverter output voltage with reference to grid-connected voltage-contrast figure.

Fig. 5 is light and temperature variation diagram.

Fig. 6 is the inverter output waveforms figure under light and temperature change.

Wherein, C in Fig. 1 _pVand L _pVbe respectively photovoltaic cell lateral capacitance and inductance, v _pVand i _pVphotovoltaic cell side voltage and current respectively, S is the switching tube of Boost circuit, C _dcfor Boost circuit boosting outlet side electric capacity, v _dcand i _dcbe respectively DC side voltage of converter and electric current, S ₁~ S ₄for inverter switching device pipe, C _acand L _acbe respectively inverter ac lateral capacitance and inductance, v _acfor inverter ac side output voltage, i _lfor network load electric current, R _lfor network load, v _ac*for grid-connected reference voltage.

In Fig. 3 for grid-connected reference voltage first derivative, for inverter ac side voltage first derivative, e ₁for tracing deviation, e ₂for virtual master function, c ₁, c ₂for being greater than the real number of zero, α, β are sliding-mode surface constant, p ₁, p ₂for positive odd number, s _cfor sliding-mode surface, δ is border thickness, for unknown parameter estimated value, m ₀, m ₁, m ₂for adaptive gain, D ₁for inverter duty cycle Stage Value, D is inverter duty cycle.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.Following examples only for technical scheme of the present invention is clearly described, and can not limit the scope of the invention with this.

As shown in Figure 1, a kind of photovoltaic combining inverter control method, comprises the following steps:

Step one, sets up inverter Mathematical Modeling according to Circuit Theorem and State-space Averaging Principle.

The single-phase grid-connected photovoltaic power generation system structure at inverter place is the not isolated grid-connected circuit of two-stage type high frequency, specifically as shown in Figure 1, be made up of photovoltaic array, Boost circuit (i.e. DC-DC circuit), inverter circuit (DC-AC circuit) and load.

Prime Boost circuit, by PWM (pulse width modulation) control realization MPPT and DC-DC boosting inverter; Rear class is inverter, by the conducting of PWM control switch pipe with block, realizes DC-AC conversion, provides standard compliant AC energy grid-connected.The Industrial Frequency Transformer that this circuit eliminates in inverter structure, thus has high, the lightweight advantage of efficiency, is used widely in small-power distributed photovoltaic power generation system.

Inverter structure is full-bridge voltage type inverter, as shown in DC-AC part in Fig. 1, if S ₁~ S ₄for perfect switch pipe, S in one-period ₁, S ₄it is D, S that the time of conducting accounts for the ratio in cycle ₂, S ₃it is 1-D that the time of conducting accounts for the ratio in cycle.

S ₁, S ₄circuit during conducting as shown in Figure 2, according to Circuit Theorem,

$\left\{\begin{array}{c}{L}_{ac}\frac{{\mathrm{di}}_{ac}}{dt}=v_{dc}-v_{ac}\\ C_{ac}\frac{{\mathrm{dv}}_{ac}}{dt}=i_{ac}-\frac{1}{R_L}{v}_{ac}\end{array}\right.---\left(1\right)$

Wherein, i _acinverter ac side output current;

In like manner knownly work as S ₂, S ₃have during conducting,

$\left\{\begin{array}{c}{L}_{ac}\frac{{\mathrm{di}}_{ac}}{dt}=-v_{dc}-v_{ac}\\ C_{ac}\frac{{\mathrm{dv}}_{ac}}{dt}=i_{ac}-\frac{1}{R_L}{v}_{ac}\end{array}\right.---\left(2\right)$

According to State-space Averaging Principle, then in one-period, the Mathematical Modeling of inverter can be described as

(1) formula × D+ (2) formula × 1-D, that is,

$\left\{\begin{array}{c}{L}_{ac}\frac{{\mathrm{di}}_{ac}}{dt}=(2D-1)v_{dc}-v_{ac}\\ C_{ac}\frac{{\mathrm{dv}}_{ac}}{dt}=i_{ac}-\frac{1}{R_L}{v}_{ac}\end{array}\right.---\left(3\right)$

Right $C_{ac}\frac{{\mathrm{dv}}_{ac}}{dt}=i_{ac}-\frac{1}{R_L}{v}_{ac}$ Differentiate can obtain,

$\frac{d^2{v}_{ac}}{{\mathrm{dt}}^2}=\frac{1}{C_{ac}}\frac{{\mathrm{di}}_{ac}}{dt}-\frac{1}{R_L{C}_{ac}}\frac{{\mathrm{dv}}_{ac}}{dt}---\left(4\right)$

? $L_{ac}\frac{{\mathrm{di}}_{ac}}{dt}=(2D-1)v_{dc}-v_{ac}$ Obtain after bringing (4) into,

$\frac{d^2{v}_{ac}}{{\mathrm{dt}}^2}=-\frac{1}{R_L{C}_{ac}}\frac{{\mathrm{dv}}_{ac}}{dt}-\frac{1}{L_{ac}{C}_{ac}}{v}_{ac}+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}---\left(5\right)$

Writ state variable $\left\{\begin{array}{c}{x}_1=v_{ac}\\ x_2={\stackrel{\&CenterDot;}{v}}_{ac}\end{array}\right.,$ State equation is set up to inverter as follows,

$\left\{\begin{array}{c}\frac{{\mathrm{dx}}_1}{dt}=x_2\\ \frac{{\mathrm{dx}}_2}{dt}=-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}\end{array}\right.---\left(6\right)$

Consider that in practical application, inverter can be subject to the interference of parameter uncertainty, extraneous factor, the equation adding distracter is,

In formula, Δ ₁and Δ ₂be respectively the error term caused by the parameter of electric capacity and inductance, for distracter, for external interference,

Then (7) formula becomes

$\left\{\begin{array}{c}\frac{{\mathrm{dx}}_1}{dt}=x_2\\ \frac{{\mathrm{dx}}_2}{dt}=-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)\end{array}\right.---\left(8\right)$

(8) formula is the inverter Mathematical Modeling considering system structure parameter uncertainty and external interference item.

Step 2, design circuit control device.

According to the physical characteristic of photovoltaic cell, the change of intensity of illumination and ambient temperature can export v to battery _pV, i _pVhave an impact, thus affect booster circuit v _dcoutput.From formula (8), v _dcwith change can cause state variable x ₁fluctuation.Therefore propose to adopt model reference self-adapting control and inverting overall situation fast terminal sliding formwork to control to photovoltaic DC-to-AC converter, reach inverter from motion tracking external disturbance, weaken the object of buffeting.As shown in Figure 3, mentality of designing is as follows for Controller gain variations structure chart: first according to the character of controlled device, and the reference model of a design controlled device, requires that this reference model can follow the tracks of the dynamic response of controlled device; Secondly, if object parameters is unknown or the unknown disturbances of existence, take the unknown parameter in estimates of parameters replacement system, wherein estimates of parameters is according to the adaptive control laws dynamic conditioning of design; Then, adopt inverting overall situation fast terminal sliding formwork to control, construct the Lyapunov equation comprising tracking error and parameter estimating error, then design the control law of controller based on Lyapunov Theory of Stability.When there is error between controlled device and reference model, adaptive law carrys out modifier controller parameter according to control information, and error is gone to zero gradually.

System decomposition is the subsystem being no more than systematic education by back stepping control, is each subsystem design Lyapunov function and intermediate virtual amount, always back to whole system, designs control rate with this.Because inverter is typical non linear system, inversion method is applicable to decomposing the non linear system of complexity, and retains all nonlinear transformations.For expanding the scope of application of control method, back stepping control and sliding formwork being controlled to combine, improving the robustness of controller.Overall situation fast terminal sliding formwork controls to be add nonlinear terms on the basis of normal linear sliding-mode surface, and make system Fast Convergent when far from equilibrium state, Guarantee Status tracking error can arrive zero in finite time.Inverting overall situation fast terminal sliding formwork controls on the basis ensureing control stability, to accelerate control rate.

Circuit control device comprises model reference self-adapting control design and inverting overall situation fast terminal sliding formwork control design case.

Design circuit control device concrete steps are as follows:

A1) constructing virtual control function.

Definition control objectives is inverter ac side output voltage v _ac, grid-connected reference voltage v _ac*for electrical network power frequency sinusoidal voltage, make tracing deviation e ₁=v _ac-v _ac*, then

${\stackrel{\&CenterDot;}{e}}_1={\stackrel{\&CenterDot;}{v}}_{ac}-{\stackrel{\&CenterDot;}{v}}_{ac*}={\stackrel{\&CenterDot;}{x}}_1-{\stackrel{\&CenterDot;}{v}}_{ac*}=x_2-{\stackrel{\&CenterDot;}{v}}_{ac*}---\left(9\right)$

Then virtual master function is,

$e_2=x_2+c_1{e}_1-{\stackrel{\&CenterDot;}{v}}_{ac*}---\left(10\right)$

Wherein, c ₁it is a real number being greater than zero.

A2) Lyapunov function is chosen,

$V_1=\frac{1}{2}{e}_1^2---\left(11\right)$

V ₁derivative be,

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_1=e_1{\stackrel{\&CenterDot;}{e}}_1=e_1\left(x_2-{\stackrel{\&CenterDot;}{v}}_{ac*}\right)\\ =e_1\left(e_2-c_1{e}_1+{\stackrel{\&CenterDot;}{v}}_{ac*}-{\stackrel{\&CenterDot;}{v}}_{ac*}\right)=-c_1{e}_1^2+e_1{e}_2\end{array}---\left(12\right)$

If e ₂=0, so so need to design new Lyapunov function.

A3) defining sliding-mode surface is,

$s_c=e_2+{\mathrm{\&alpha;e}}_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}---\left(13\right)$

Wherein, α, β are sliding-mode surface constants, p ₁, p ₂for positive odd number, and p ₁> p ₂;

According to formula (10) and (9) known,

$\begin{array}{c}{s}_c=x_2+c_1{e}_1-{\stackrel{\&CenterDot;}{v}}_{ac*}+{\mathrm{\&alpha;e}}_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}\\ =x_2-{\stackrel{\&CenterDot;}{v}}_{ac*}+c_1{e}_1+{\mathrm{\&alpha;e}}_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}\\ ={\stackrel{\&CenterDot;}{e}}_1+\left(c_1+\mathrm{\&alpha;}\right)e_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}\end{array}---\left(14\right)$

Then ${\stackrel{\&CenterDot;}{s}}_c={\stackrel{\&CenterDot;\&CenterDot;}{e}}_1+(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1---\left(15\right)$

Can obtain according to formula (9) and (8),

$\begin{array}{c}{\stackrel{\&CenterDot;}{s}}_c={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+\left(c_1+\mathrm{\&alpha;}\right){\stackrel{\&CenterDot;}{e}}_1+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\\ =-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+\left(c_1+\mathrm{\&alpha;}\right){\stackrel{\&CenterDot;}{e}}_1+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\end{array}---\left(16\right)$

When system far from equilibrium state, non-linear partial system exponentially series convergence can be made, when system is close to linear segment α e during poised state ₁convergence rate faster than non-linear partial, make system the overall situation Fast Convergent.

A4) add model reference self-adapting control, design new Lyapunov function.

Model reference self-adapting control design is as follows:

According to the character of distracter, suppose $\left|\mathrm{\&phi;}\left(t\right)\right|<b_2\left|x_2\right|+b_1\left|x_1\right|+b_0=b_0+b_1\left|v_{ac}\right|+b_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|,$ Wherein, b ₀, b ₁, b ₂for positive unknown constant.

If with b respectively ₀, b ₁and b ₂estimated value, carry out adaptive control laws design according to the following formula, to realize unknown parameter b ₀, b ₁, b ₂estimation,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{b}}}_0=m_0\left|s_c\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_1=m_1\left|s_c\right|\left|v_{ac}\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_2=m_2\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\end{array}\right.---\left(17\right)$

Namely

$\left\{\begin{array}{c}{\hat{b}}_0=\&Integral;m_0\left|s_c\right|dt\\ {\hat{b}}_1=\&Integral;m_1\left|s_c\right|\left|v_{ac}\right|dt\\ {\hat{b}}_1=\&Integral;m_2\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|dt\end{array}\right.---\left(18\right)$

In formula, normal number m ₀, m ₁and m ₂for adaptive gain;

If ${\tilde{b}}_i=b_i-{\hat{b}}_i,(i=0,1,2)$

b ₀, b ₁, b ₂evaluated error because b ₀, b ₁, b ₂positive unknown constant, so there is derivative ${\stackrel{\&CenterDot;}{\tilde{b}}}_i=-{\stackrel{\&CenterDot;}{\hat{b}}}_i,\left(i=0,1,2\right).$

New Lyapunov function is,

$V_2^{\&prime;}=V_1+\frac{1}{2}{s_c}^2+\frac{1}{2}\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{{\tilde{b}}_i}^2---\left(19\right)$

New Lyapunov function differentiate, can obtain according to formula (12) and (16),

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2^{\&prime;}={\stackrel{\&CenterDot;}{V}}_1+s_c{\stackrel{\&CenterDot;}{s}}_c-\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{\tilde{b}}_i{\stackrel{\&CenterDot;}{\hat{b}}}_i\\ =-c_1{e_1}^2+e_1{e}_2+s_c\&lsqb;-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)+\left(c_1+\mathrm{\&alpha;}\right){\stackrel{\&CenterDot;}{e}}_1-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\\ -{m_0}^{-1}{\tilde{b}}_0{\stackrel{\&CenterDot;}{\hat{b}}}_0-{m_1}^{-1}{\tilde{b}}_1{\stackrel{\&CenterDot;}{\hat{b}}}_1-{m_2}^{-1}{\tilde{b}}_2{\stackrel{\&CenterDot;}{\hat{b}}}_2\end{array}---\left(20\right)$

A5) control law of employing model reference adaptive (MRAC) and inverting overall situation fast terminal sliding formwork (BGFTSMC) hybrid algorithm is,

$D=\frac{1}{2}\{1+\frac{L_{ac}{C}_{ac}}{u_{dc}}\&lsqb;\frac{1}{R_L{C}_{ac}}{x}_2+\frac{1}{L_{ac}{C}_{ac}}{x}_1+D_1-(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1+{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}-c_2{s}_2-\frac{s_c}{{\left|s_c\right|}^2}{e}_1{e}_2-\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\}---\left(21\right)$

Wherein, $D_1=-\mathrm{sgn}\left(s_c\right)({\hat{b}}_0+{\hat{b}}_1|v_{ac}|+{\hat{b}}_2|{\stackrel{\&CenterDot;}{v}}_{ac}\left|\right)=-\frac{s_c}{\left|s_c\right|}({\hat{b}}_0+{\hat{b}}_1|v_{ac}|+{\hat{b}}_2|{\stackrel{\&CenterDot;}{v}}_{ac}\left|\right).$

Bring formula (21) into formula (20), and convolution (15) can obtain,

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2^{\&prime;}=-c_1{e_1}^2-\frac{s_c}{\left|s_c\right|}\left({\hat{b}}_0+{\hat{b}}_1\left|v_{ac}\right|+{\hat{b}}_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\right)s_c+\mathrm{\&phi;}\left(t\right)s_c-c_2{s_c}^2-{m_0}^{-1}{\tilde{b}}_0{\stackrel{\&CenterDot;}{\hat{b}}}_0-{m_1}^{-1}{\tilde{b}}_1{\stackrel{\&CenterDot;}{\hat{b}}}_1-{m_2}^{-1}{\tilde{b}}_2{\stackrel{\&CenterDot;}{\hat{b}}}_2\\ =-c_1{e_1}^2-\left|s_c\right|\left({\hat{b}}_0+{\hat{b}}_1\left|v_{ac}\right|+{\hat{b}}_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\right)+\mathrm{\&phi;}\left(t\right)s_c-c_2{s_c}^2-{\tilde{b}}_0\left|s_c\right|-{\tilde{b}}_1\left|s_c\right|\left|v_{ac}\right|-{\tilde{b}}_2\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\\ =-c_1{e_1}^2-\left|s_c\right|\left({\hat{b}}_0+{\hat{b}}_0\right)-\left|s_c\right|\left|v_{ac}\right|\left({\hat{b}}_1+{\hat{b}}_1\right)-\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\left({\hat{b}}_2+{\hat{b}}_2\right)+\mathrm{\&phi;}\left(t\right)s_c-c_2{s_c}^2\\ =-c_1{e_1}^2-\left|s_c\right|b_0-\left|s_c\right|\left|v_{ac}\right|b_1-\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|b_2+\mathrm{\&phi;}\left(t\right)s_c-c_2{s_c}^2\\ \&le;-c_1{e_1}^2-c_2{s_2}^2\end{array}---\left(22\right)$

Work as c ₁and c ₂have during > 0 pursuit path reaches sliding-mode surface in finite time, and rests on sliding-mode surface, and system meets Liapunov second stability theorem condition.Illustrate that the duty ratio D designed according to formula (21) makes tracing deviation e ₁be zero, i.e. control inverter output AC voltage v _aclevel off to electrical network reference voltage, therefore the stability requirement of inverter system can be met according to the control law of auto-adaptive parameter design.

In order to reduce the chattering phenomenon that sliding formwork controls further, in circuit control device, plan boundary layer improves the tracking performance of system.

$D_1=\left\{\begin{array}{cc}-\frac{s_c}{\left|s_c\right|}\left({\hat{b}}_0+{\hat{b}}_1\left|v_{ac}\right|+{\hat{b}}_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\right)& \left|s_c\right|>\mathrm{\&delta;}\\ -\frac{s_c}{\mathrm{\&delta;}}\left({\hat{b}}_0+{\hat{b}}_1\left|v_{ac}\right|+{\hat{b}}_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\right)& \left|s_c\right|\&le;\mathrm{\&delta;}\end{array}\right.---\left(23\right)$

Wherein, δ > 0 is border thickness.

In the control law of design, contain in (21) , work as e ₁when=0 singular problem may be caused.Singular problem can be avoided by parameter designing, according to sliding-mode surface formula (14), when arriving sliding-mode surface, and s _c=0, so $\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1=\frac{p_2}{p_1}\mathrm{\&beta;}\&lsqb;-(c_1+\mathrm{\&alpha;}){e_1}^{\frac{p_2}{p_1}}-{{\mathrm{\&beta;e}}_1}^{\frac{2p_2-p_1}{p_1}}\&rsqb;,$ Design positive odd number p ₁, p ₂scope be p ₂< p ₁< 2p ₂, can ensure with not unusual, thus not unusual.Make p in the present invention ₁=5, p ₂=3 to meet the requirement of nonsingular design.

Overall situation fast terminal sliding formwork controls by optimum configurations, can prove arrive sliding-mode surface in finite time.

Proof procedure is as follows:

The s when arriving sliding-mode surface _c=0, according to formula (14), can obtain

${e_1}^{-p_2/p_1}\frac{{\mathrm{de}}_1}{dt}+(c_1+\mathrm{\&alpha;}){e_1}^{1-p_2/p_1}=-\mathrm{\&beta;}---\left(24\right)$

Definition $y={e_1}^{1-p_2/p_1},$ Then

$\frac{dy}{dt}=\frac{p_1-p_2}{p_1}{e_1}^{-p_2/p_1}\frac{{\mathrm{de}}_1}{dt}---\left(25\right)$

Then again rewriting (24) is

$\frac{dy}{dt}+\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})y=-\frac{p_1-p_2}{p_1}\mathrm{\&beta;}---\left(26\right)$

Separate this single order linear differential equation with constant coefficients, have

$y=e^{-{\&Integral;}_0^t\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})dt}({\&Integral;}_0^t-\frac{p_1-p_2}{p_1}{\mathrm{\&beta;e}}^{\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t}dt+C)---\left(27\right)$

As t=0, C=y (0),

Then (27) are

$y=-\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}+\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}{e}^{-\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t}+y\left(0\right)e^{-\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t}---\left(28\right)$

Be set to and reach balance point and (meet e ₁=0 and y=0) time be t _s, formula (28) becomes

$0=-\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}+\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}{e}^{-\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t_s}+y\left(0\right)e^{-\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t_s}$

Therefore, $\&lsqb;\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}+y\left(0\right)\&rsqb;e^{-\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t_s}=\frac{\mathrm{\&beta;}}{c_1+\mathrm{\&alpha;}}$

Namely

$e^{\frac{p_1-p_2}{p_1}(c_1+\mathrm{\&alpha;})t_s}=\frac{\&lsqb;\mathrm{\&beta;}+(c_1+\mathrm{\&alpha;})y\left(0\right)\&rsqb;}{\mathrm{\&beta;}}---\left(29\right)$

So prove out from initial condition e ₁(0) ≠ 0 to poised state e ₁(t _sthe time t of)=0 _smeet following formula

$t_s=\frac{p_1}{(c_1+\mathrm{\&alpha;})(p_1-p_2)}ln\frac{\mathrm{\&beta;}+(c_1+\mathrm{\&alpha;})e_1{\left(0\right)}^{(p_1-p_2)/p_1}}{\mathrm{\&beta;}}---\left(30\right)$

Illustrate by setting α, β, p ₁, p ₂, make system arrive poised state in finite time.

System parameter setting as shown in Table 1.

Table one system parameter table

When intensity of illumination is 1000W/m ², when ambient temperature is 25 DEG C, photovoltaic DC-to-AC converter exchanges result and exports as shown in Figure 4.As can be seen from the figure, inverter, after the transient process through 7 cycles, exports power frequency sinusoidal ac, and stable operation.Illustrate that the control algolithm of inverter is effective.

Consider that intensity of illumination in actual photovoltaic system operation and ambient temperature can change at any time, in the time that Fig. 5 simulates 0.6 second, Spline smoothing several times occurs, Fig. 6 records inverter ac voltage and exports and the output power from photovoltaic cells.Find that namely alternating voltage is stablized after 7 cycles, when light and temperature changes, alternating voltage exports substantially unaffected, and illustrates that inverter controller can steady operation, Algorithm robustness comparatively by force, can adapt to different operating states.

Said method adopts model reference self-adapting control to carry out control rate design, reaches the object from motion tracking disturbance; Said method meets the requirement of inverter dynamic response, makes control have robustness; The back stepping control of said method is the subsystem of depression of order system decomposition, for subsystem design Lyapunov function and virtual master function ensure control stability; The overall fast terminal sliding formwork of said method controls to improve system convergence speed, is avoided by parameter designing the singular problem that may occur.

In sum, inverter control method of the present invention can meet the requirement of robustness, stability and rapidity, and when system environments is undergone mutation, control algolithm energy reliably working, makes the sinusoidal voltage of photovoltaic DC-to-AC converter stable output.

The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from the technology of the present invention principle; can also make some improvement and distortion, these improve and distortion also should be considered as protection scope of the present invention.

Claims (5)

1. a photovoltaic combining inverter control method, is characterized in that: comprise the following steps,

Step one, sets up inverter Mathematical Modeling according to Circuit Theorem and State-space Averaging Principle;

$\left\{\begin{array}{c}\frac{{\mathrm{dx}}_1}{dt}=x_2\\ \frac{{\mathrm{dx}}_2}{dt}=-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)\end{array}\right.$

Wherein, state variable $\left\{\begin{array}{c}{x}_1=v_{ac}\\ x_2={\stackrel{\&CenterDot;}{v}}_{ac}\end{array}\right.,$ V _acfor inverter ac side voltage, v _dcdC side voltage of converter, C _acand L _acbe respectively inverter ac lateral capacitance and inductance, R _lfor network load, D is inverter duty cycle, for distracter, for external interference, Δ ₁and Δ ₂be respectively the error term caused by the parameter of electric capacity and inductance;

Step 2, design circuit control device;

A1) constructing virtual control function;

Definition control objectives is inverter ac side output voltage v _ac, grid-connected reference voltage v _ac*for electrical network power frequency sinusoidal voltage, make tracing deviation e ₁=v _ac-v _ac*, then

Then virtual master function is,

$e_2=x_2+c_1{e}_1-{\stackrel{\&CenterDot;}{v}}_{ac*}$

Wherein, c ₁it is a real number being greater than zero;

A2) Lyapunov function is chosen,

$V_1=\frac{1}{2}{e}_1^2$

V ₁derivative be,

${\stackrel{\&CenterDot;}{V}}_1=-c_1{e}_1^2+e_1{e}_2$

If e ₂=0, so so need to design new Lyapunov function;

A3) defining sliding-mode surface is,

$s_c=e_2+{\mathrm{\&alpha;e}}_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}$

Wherein, α, β are sliding-mode surface constants, p ₁, p ₂for positive odd number, and p ₁> p ₂;

Virtual master function and tracing deviation are substituted into and can obtain,

$s_c={\stackrel{\&CenterDot;}{e}}_1+(c_1+\mathrm{\&alpha;})e_1+{{\mathrm{\&beta;e}}_1}^{p_2/p_1}$

Then

${\stackrel{\&CenterDot;}{s}}_c=-\frac{1}{R_L{C}_{ac}}{x}_2\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1;$

A4) add model reference self-adapting control, design new Lyapunov function;

According to the character of distracter, suppose $\left|\mathrm{\&phi;}\left(t\right)\right|<b_2\left|x_2\right|+b_1\left|x_1\right|+b_0=b_0+b_1\left|v_{ac}\right|+b_2\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|,$ Adaptive control laws design is carried out according to the following formula,

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\hat{b}}}_0=m_0\left|s_c\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_1=m_1\left|s_c\right|\left|v_{ac}\right|\\ {\stackrel{\&CenterDot;}{\hat{b}}}_2=m_2\left|s_c\right|\left|{\stackrel{\&CenterDot;}{v}}_{ac}\right|\end{array}\right.$

Wherein, normal number m ₀, m ₁and m ₂for adaptive gain, with b respectively ₀, b ₁and b ₂estimated value, b ₀, b ₁, b ₂for positive unknown parameter;

New Lyapunov function is,

$V_2^{\&prime;}=V_1+\frac{1}{2}{s_c}^2+\frac{1}{2}\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{{\tilde{b}}_i}^2$

Wherein, i=0,1,2, b ₀, b ₁, b ₂evaluated error;

New Lyapunov function differentiate can obtain,

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_2^{\&prime;}={\stackrel{\&CenterDot;}{V}}_1+s_c{\stackrel{\&CenterDot;}{s}}_c-\underset{i=0}{\overset{2}{\&Sigma;}}{m_i}^{-1}{\tilde{b}}_i{\stackrel{\&CenterDot;}{\hat{b}}}_1\\ =-c_1{e_1}^2+e_1{e}_2+s_c\&lsqb;-\frac{1}{R_L{C}_{ac}}{x}_2-\frac{1}{L_{ac}{C}_{ac}}{x}_1+\frac{2D-1}{L_{ac}{C}_{ac}}{v}_{dc}+\mathrm{\&phi;}\left(t\right)+(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1-{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}+\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\\ -{m_0}^{-1}{\tilde{b}}_0{\stackrel{\&CenterDot;}{\hat{b}}}_0-{m_1}^{-1}{\tilde{b}}_i{\stackrel{\&CenterDot;}{\hat{b}}}_1-{m_2}^{-1}{\tilde{b}}_2{\stackrel{\&CenterDot;}{\hat{b}}}_2\end{array};$

A5) control law of employing model reference adaptive and inverting overall situation fast terminal sliding formwork hybrid algorithm is,

$D=\frac{1}{2}\{1+\frac{L_{ac}{C}_{ac}}{u_{dc}}\&lsqb;\frac{1}{R_L{C}_{ac}}{x}_2+\frac{1}{L_{ac}{C}_{ac}}{x}_1+D_1-(c_1+\mathrm{\&alpha;}){\stackrel{\&CenterDot;}{e}}_1+{\stackrel{\&CenterDot;\&CenterDot;}{v}}_{ac*}-c_2{s}_c-\frac{s_c}{|s_c{|}^2}{e}_1{e}_2-\frac{p_2}{p_1}{{\mathrm{\&beta;e}}_1}^{\frac{p_2}{p_1}-1}{\stackrel{\&CenterDot;}{e}}_1\&rsqb;\}$

Wherein, $D_1=-\mathrm{sgn}\left(s_c\right)({\hat{b}}_0+{\hat{b}}_1|v_{ac}|+{\hat{b}}_2|{\stackrel{\&CenterDot;}{v}}_{ac}\left|\right)=-\frac{s_c}{\left|s_c\right|}({\hat{b}}_0+{\hat{b}}_1|v_{ac}|+{\hat{b}}_2|{\stackrel{\&CenterDot;}{v}}_{ac}\left|\right).$

2. a kind of photovoltaic combining inverter control method according to claim 1, is characterized in that: the single-phase grid-connected photovoltaic power generation system structure at described inverter place is the not isolated grid-connected circuit of two-stage type high frequency.

3. a kind of photovoltaic combining inverter control method according to claim 1 and 2, is characterized in that: described inverter structure is full-bridge voltage type inverter.

4. a kind of photovoltaic combining inverter control method according to claim 1, is characterized in that: by plan boundary layer in circuit control device, reduces the chattering phenomenon that sliding formwork controls.

5. a kind of photovoltaic combining inverter control method according to claim 1, is characterized in that: by arranging p ₁, p ₂scope meet the nonsingular requirement of overall fast terminal sliding formwork.