CN105978373A - Three-phase inverter backstepping sliding mode control method and system for achieving stabilization of micro-grid - Google Patents

Abstract

The invention discloses a three-phase inverter backstepping sliding mode control method and system for achieving the stabilization of a micro-grid, and the method comprises the steps: firstly taking filter capacitor voltage and inductor current as control variables, and building a mathematic model of an inverter system; secondly combining a backstepping method and a sliding mode variable structure method, and building a feedback control model of the inverter system; finally enabling the feedback control model of the inverter system to act on pulse width modulation, and carrying out the control of a three-phase inverter, thereby achieving the three-phase inverter backstepping sliding mode control for achieving the stabilization of the micro-grid. The method gives comprehensive consideration to the reality of the engineering application, is used for the three-phase inverter, is good in steady and dynamic characteristics, is very robust for the parameter perturbation and load disturbance, is suitable for linear, nonlinear and unbalance loads, can be popularized to other different types of three-phase inverters, provides an idea for designing an inverter control system, and is good in prospect of engineering application.

Description

Three-phase inverter reverse-thrust sliding mode control method and system for realizing micro-grid stability

Technical Field

The invention belongs to the technical field of intelligent power grids, and particularly relates to a reverse-thrust sliding-mode control method and a system for a three-phase inverter, which are used for realizing the stability of a micro-grid.

Background

In recent years, a micro grid that integrates various distributed power systems and power electronics technologies has received increasing attention and research. The novel power supply system is formed by combining a mature distributed power supply technology, an advanced control device and various loads, is connected to a large power grid in a micro power grid mode, and can achieve the purpose of improving the power supply capacity and the power quality of the power grid by using a flexible control strategy.

The power electronic technology is of great importance for accessing the distributed power supply to the micro-grid, particularly the inversion link is the final interface for accessing a plurality of distributed power supplies to the micro-grid, the control method of the power electronic technology has important influence on the stable operation of the distributed power supply and the control strategy of the micro-grid, and the power electronic technology is an important basis for the operation control of the micro-grid. The basic idea of inverter control is that an inverter can stably output certain active power and reactive power according to setting when the inverter is in grid-connected operation; in island operation, the inverter is operated in a voltage source mode through control, and the frequency and the voltage of the micro-grid can be adjusted by taking the amplitude and the frequency of the output voltage of the inverter as control targets.

The inverter device is a typical switch type nonlinear system, and when the traditional linear control method is applied to the system, the rapidity and the accuracy of the traditional linear control method cannot meet ideal requirements. Therefore, the application of modern nonlinear control methods in power electronic systems has become one of the research hotspots of current power electronic control.

At present, nonlinear control of the inverter mainly comprises double closed loop PI control, dead beat control, repetitive control and the like, and the performance of the inverter is improved, but the nonlinear control also has the problems of different degrees. With the deep research of the nonlinear control theory, the precise linearization method based on the differential geometry theory is widely applied to the inverter, however, the method is established on the basis that the controlled object has a precise mathematical model, and the uncertainty problem of the actual system is not considered, so that the robustness is not strong, the calculation expression is complex, and the engineering realization is difficult. H_∞The performance of the control in the aspect of anti-interference capability is excellent, and the Chenbao remote and other people are based on H_∞H of single-phase voltage type inverter designed by control theory_∞The method comprises the steps that ① inverter mathematical models are built on the basis of an accurate model, the uncertainty problem existing in an actual system is not considered, and ② influence of external interference on the control performance is not considered.

From the analysis, the accuracy requirement of the prior art for controlling the three-phase inverter on the mathematical model of the inverter system is high, and the influence of the uncertainty of the actual system parameters and the external interference problem on the control performance is not considered, so that the robustness is not strong, and the requirement of practical application is not met; the technology with strong anti-interference performance is complex in solving and calculating process, repeated trial and error is needed, and engineering implementation is difficult.

Disclosure of Invention

The invention aims to provide a reverse thrust sliding mode control method and a system for a three-phase inverter, which are reasonable in design, have good steady-state and dynamic characteristics and realize the voltage and frequency stability of a microgrid.

The technical solution for realizing the purpose of the invention is as follows: a reverse thrust sliding mode control method for a three-phase inverter for realizing stabilization of a micro-grid comprises the following steps:

step A, establishing a mathematical model of an inverter system by taking filter capacitor voltage and inductor current as control variables;

b, combining a reverse pushing method with a sliding mode variable structure control method to construct a feedback control model of the inverter system;

and step C, acting the feedback control model of the inverter system on Pulse Width Modulation (PWM) to control the three-phase inverter, so as to realize stable reverse-thrust sliding-mode control of the three-phase inverter of the microgrid.

A system for realizing the three-phase inverter reverse-thrust sliding-mode control method comprises an information acquisition module, a virtual control module, a reverse-thrust sliding-mode control module, a pulse width modulation module and a three-phase inverter, wherein:

the information acquisition module acquires output signals of the inverter, wherein the signals comprise three-phase filter capacitor voltage values and three-phase filter inductor current values;

the virtual control module receives the inverter output signal acquired by the information acquisition module, compares the signal with a corresponding reference value, and sends a comparison result to the virtual control module and the reverse-thrust sliding-mode control module;

the virtual control module carries out reverse pushing processing on the comparison result and transmits the processing result to the reverse pushing sliding mode control module;

the backstepping and backstepping sliding mode control module performs backstepping and sliding mode control processing on the received signal and transmits a processing result to the pulse width modulation module;

the pulse width modulation module performs pulse width modulation on the received signals and then sends the signals to six switches of the three-phase inverter, so that reverse-thrust sliding-mode control of the three-phase inverter is realized.

Compared with the prior art, the invention has the following remarkable advantages: 1) the method fully considers the influence of multiple factors such as uncertainty of filter parameters, external interference and the like on a three-phase inverter system, utilizes the characteristics that the sliding mode of a sliding mode variable structure has invariance, the dependence degree on a system mathematical model is low, and the robustness on system parameter perturbation and external interference is strong, combines a reverse method with a sliding mode control method, establishes the mathematical model of the inverter system by taking filter capacitor voltage and inductance current as control variables, uses the tracking error of the control variables as the input of a controller, and deduces that a feedback control law of the inverter system acts on pulse width modulation to control the three-phase inverter. The invention has reasonable design, comprehensively considers the practical engineering application, has good steady-state and dynamic characteristics, has strong robustness to parameter perturbation and load disturbance, is not only suitable for linear, nonlinear and unbalanced loads, but also can be popularized in other three-phase inverters of different types, provides an idea for the design of inverter control systems, and has good engineering application prospect. 2) The control method ensures that after the control system reaches a stable state under a rated pure resistance load, the load voltage and the load current have high starting speed and no waveform distortion, are both power frequency sine waves and are smooth, the voltage output has no static difference, and the frequency has no static difference. 3) The control method of the invention ensures that the load voltage of the control system has basically no change and the waveform distortion is very small under the condition of sudden change of the linear load, the current change is smooth, and the anti-interference capability of the system is improved. 4) The control method of the invention ensures that the control system responds transiently under the condition of sudden change of the input direct-current voltage, and the load voltage and the current are not influenced by the input direct-current voltage, thereby improving the anti-jamming capability of the three-phase inverter on the input direct-current voltage. 5) The control method of the invention enables the load voltage and current of the control system to be basically unaffected under the condition of perturbation of LC filtering parameters, thereby improving the anti-interference capability of the three-phase inverter on parameter uncertainty. 6) The control method of the invention ensures that the load voltage basically has no change and the waveform distortion is very small under the condition that the control system is provided with nonlinear load and unbalanced load, the unbalance degree of the three-phase voltage is very small, and the frequency fluctuation also meets the specified system frequency safety fluctuation range, thereby improving the power supply quality of the microgrid and ensuring the safe operation of the equipment in the microgrid.

The invention is described in further detail below with reference to the figures and the detailed description.

Drawings

Fig. 1 is a schematic structural diagram of a conventional master-slave microgrid.

Fig. 2 is a connection schematic diagram of a conventional three-phase photovoltaic full-bridge inverter system.

Fig. 3 is a block diagram of a reverse drive control of the three-phase inverter of the present invention.

Fig. 4 is a response waveform of the present invention when the load suddenly changes, wherein (a) is a load voltage diagram, (b) is a load current diagram, and (c) is a frequency diagram.

Fig. 5 is a response waveform obtained by the present invention when the illumination intensity is changed, in which (a) is an illumination intensity graph, (b) is a dc-side voltage graph, (c) is a load voltage graph, (d) is a load current graph, and (e) is a frequency graph.

Fig. 6 is a response waveform of the present invention when the ambient temperature changes, wherein (a) is an ambient temperature graph, (b) is a dc-side voltage graph, (c) is a load voltage graph, (d) is a load current graph, and (e) is a frequency graph.

Fig. 7 shows response waveforms obtained when L is 6.4mH and C is 470 μ F, where (a) is a load voltage diagram, (b) is a load current diagram, and (C) is a frequency diagram.

Fig. 8 is a response waveform with a non-linear load according to the present invention, wherein (a) is a load voltage diagram, (b) is a load current diagram, and (c) is a frequency diagram.

Fig. 9 is a response waveform with unbalanced load obtained by the present invention, in which (a) is a load voltage diagram, (b) is a load current diagram, and (c) is a frequency diagram.

Detailed Description

The invention discloses a reverse thrust sliding mode control method of a three-phase inverter for realizing the stability of a micro-grid, which comprises the following steps of:

step A, establishing a mathematical model of an inverter system by taking filter capacitor voltage and inductor current as control variables; the mathematical model of the inverter system is as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_c}{dt}=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+d_1\left(t\right)\\ \frac{{\mathrm{di}}_L}{dt}=-\frac{1}{L}{u}_c+\frac{1}{L}{u}_{inv}+d_2\left(t\right)\end{array}\right.$

in the formula u_c＝[u_cau_cbu_cc]^TThe collected three-phase filter capacitor voltage; i.e. i_L＝[i_Lai_Lbi_Lc]^TThe collected three-phase filtering inductance current; u-u_inv＝[u_invau_invbu_invc]^TThe output voltage of the three-phase inverter is L, C, the filter inductance value and the filter capacitance value are R, and the local load resistance value is R; d₁(t) is the total perturbation term matrix of voltage parameter uncertainty terms and external interference, d₂And (t) is a total perturbation term matrix of the current parameter uncertainty term and the external interference.

The voltage parameter uncertainty item and the total perturbation item matrix d of the external interference₁(t) is:

d₁(t)＝i_LΔ₁-U_cΔ₂+Δw₁(t)

in the formula,. DELTA.₁、Δ₂The uncertainty part of the system filter parameters (considered consistently according to the deviation of the three-phase parameters); Δ w₁(t), which is external interference and is caused by unstable voltage on the direct current side of the inverter or load fluctuation;

total perturbation term matrix d of current parameter uncertainty term and external interference₂(t) is:

d₂(t)＝u_invΔ₃-U_cΔ₃+Δw₂(t)

in the formula,. DELTA.₃The uncertainty part of the system filter parameters (considered consistently according to the deviation of the three-phase parameters); Δ w₂And (t) is external interference, which is mainly caused by unstable voltage on the direct current side of the inverter or load fluctuation.

B, combining a reverse pushing method with a sliding mode variable structure control method to construct a feedback control model of the inverter system; the feedback control model of the inverter system is as follows:

$u=G_2^{-1}(y,x)\[-F_2^{\′}(y,x)+{\stackrel{\·}{x}}_{ref}+k_{2}s+G_1^T\left(y\right)E_1+\mathrm{\η}\mathrm{sgn}\left(s\right)\]$

wherein, E₁＝[e_u1e_u2e_u3]^Tfor the input of the tracking error variable matrix,is E₁Virtual control quantity matrix x of subsystem_ref＝[i_Larefi_Lbrefi_Lcref]^TS is a sliding mode surface matrix selected by the sliding mode variable structure control, sgn(s) is a corresponding sign function, k₂＝diag(k₂₁,k₂₂,k₂₃)、η＝diag(η₁,η₂,η₃) Is an adjustable control parameter matrix.

The sliding mode surface matrix selected by the sliding mode variable structure control is as follows: s ═ E₂The corresponding sliding mode approach law is

Wherein E is₂＝x_ref-i_L＝[e_i1e_i2e_i3]^T，sgn(s)＝[sgn(e_i1) sgn(e_i2) sgn(e_i3)]^T；

The virtual control quantity matrix x_refComprises the following steps:

wherein,k₁＝diag(k₁₁,k₁₂,k₁₃) Is a matrix of control parameters that can be adjusted,

in the formula, the derivative of a reference value, reference value y, of the filter capacitor voltage_ref＝[u_carefu_cbrefu_ccref]^TThe power frequency sine wave is three-phase symmetrical and has the amplitude of 310V.

And step C, acting the feedback control model of the inverter system on Pulse Width Modulation (PWM) to control the three-phase inverter, so as to realize stable reverse-thrust sliding-mode control of the three-phase inverter of the microgrid.

A system for realizing the three-phase inverter reverse-thrust sliding-mode control method comprises an information acquisition module, a virtual control module, a reverse-thrust sliding-mode control module, a pulse width modulation module and a three-phase inverter, wherein:

the information acquisition module acquires output signals of the inverter, wherein the signals comprise three-phase filter capacitor voltage values and three-phase filter inductor current values;

the virtual control module receives the inverter output signal acquired by the information acquisition module, compares the signal with a corresponding reference value, and sends a comparison result to the virtual control module and the reverse-thrust sliding-mode control module;

the virtual control module carries out reverse pushing processing on the comparison result and transmits the processing result to the reverse pushing sliding mode control module;

the backstepping and backstepping sliding mode control module performs backstepping and sliding mode control processing on the received signal and transmits a processing result to the pulse width modulation module;

the pulse width modulation module performs pulse width modulation on the received signals and then sends the signals to six switches of the three-phase inverter, so that reverse-thrust sliding-mode control of the three-phase inverter is realized.

The virtual control module performs reverse backward pushing processing on the comparison result by using a formula as follows:

$\mathrm{\β}({\stackrel{\·}{y}}_{ref},y)=F_1^{\′}\left(y\right)-{\stackrel{\·}{y}}_{ref}={\[-\frac{u_{ca}}{RC}-{\stackrel{\·}{u}}_{caref}-\frac{u_{cb}}{RC}-{\stackrel{\·}{u}}_{cbref}-\frac{u_{cc}}{RC}-{\stackrel{\·}{u}}_{ccref}\]}^T,$

$x_{ref}=G_1^{-1}\left(y\right)\[-\mathrm{\β}({\stackrel{\·}{y}}_{ref},y)+k_1{E}_1\]=\left[\begin{array}{c}\frac{u_{ca}}{R}+C{\stackrel{\·}{u}}_{caref}+k_{11}{e}_{u1}\\ \frac{u_{cb}}{R}+C{\stackrel{\·}{u}}_{cbref}+k_{12}{e}_{u2}\\ \frac{u_{cc}}{R}+C{\stackrel{\·}{u}}_{ccref}+k_{13}{e}_{u3}\end{array}\right].$

the backstepping and sliding mode control processing of the received signal by the backstepping and sliding mode control module adopts the following formula:

$\begin{array}{c}u=G_2^{-1}\[-F_2(y,x)+d_2\left(t\right)+{\stackrel{\·}{x}}_{ref}+k_{2}s+G_1^T\left(y\right)E_1+\mathrm{\η}\mathrm{sgn}\left(s\right)\]\\ =\left[\begin{array}{c}L{u}_{ca}+L{\stackrel{\·}{i}}_{Laref}+L{k}_{21}{e}_{i1}+\frac{L}{C}{e}_{u1}+L{\mathrm{\η}}_1\mathrm{sgn}\left(e_{i1}\right)\\ L{u}_{cb}+L{\stackrel{\·}{i}}_{Lbref}+L{k}_{22}{e}_{i2}+\frac{L}{C}{e}_{u2}+L{\mathrm{\η}}_2\mathrm{sgn}\left(e_{i2}\right)\\ L{u}_{cc}+L{\stackrel{\·}{i}}_{Lcref}+L{k}_{23}{e}_{i3}+\frac{L}{C}{e}_{u3}+L{\mathrm{\η}}_3\mathrm{sgn}\left(e_{i3}\right)\end{array}\right]\end{array}.$

as described in more detail below:

a three-phase inverter reverse-thrust sliding mode control method for realizing micro-grid voltage and frequency stability is realized on a master-slave micro-grid shown in figure 1 and a three-phase photovoltaic inverter system shown in figure 2, and mainly comprises a photovoltaic array, a DC/DC boost converter and a three-phase voltage type full-bridge inverter, wherein the DC/DC boost converter circuit comprises a capacitor C_pvInductor L_pvSwitch tube S₀And a diode D₀And acquiring the maximum power of the photovoltaic array by adopting an MPPT controller. The three-phase voltage type full-bridge inverter circuit consists of a DC/AC inverter and a control loop, and comprises six switching tubes S1-S6 and a filter inductor L_a、L_b、L_cFilter capacitor C_a、C_b、C_cThe local load is composed of a pure resistance load R. i.e. i_pv、u_pvOutput current, voltage, i for the photovoltaic array_dc、u_dcThe photovoltaic side outputs direct current and voltage, and the current of the inductor and the voltage of the capacitor are i_LAnd U_cThe load current is i_Load。

The invention relates to a reverse-thrust sliding-mode control method for a three-phase inverter, which realizes the voltage and frequency stability of a micro-grid. Firstly, according to the working principle of a three-phase full-bridge inverter, the filter capacitor voltage and the inductive current of the inverter are used as state variables, a non-precise mathematical model form conforming to the backstepping and backstepping design is established, in the last step of the backstepping and backstepping design, a sliding mode surface and an index approach law are selected by using a sliding mode variable structure method, an actual feedback control law expression of an inverter system is designed, and asymptotic stability of the whole system in the global sense is realized. The backward-thrust sliding mode controller designed by the method can effectively improve the robustness of the inverter system, resist perturbation of filter parameters and external interference, and improve the steady state and dynamic performance of the system.

The control method of the invention comprises the following steps:

step 1, the DC/AC inverter receives the DC voltage u of the photovoltaic side bus_dcAnd controlling the conduction of the 6 switching tubes. Suppose S₁-S₆Ideal switches and their switching frequency is high enough to ignore their dead time, parasitic resistance across inductance and capacitance, as derived from kirchhoff's law:

in the abc coordinate system, the mathematical model of the inverter is

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_c}{dt}=-\frac{1}{CR}{u}_c+\frac{1}{C}{i}_L\\ \frac{{\mathrm{di}}_L}{dt}=\frac{1}{L}(u_{inv}-u_c)\end{array}\right.---\left(1\right)$

In the formula: u. of_c＝[u_cau_cbu_cc]^T-three-phase filter capacitor voltage;

i_L＝[i_Lai_Lbi_Lc]^T-three-phase filtered inductor current;

u_inv＝[u_invau_invbu_invc]^T-the inverter outputs a three-phase voltage.

The inverter has a plurality of uncertain factors, such as deviation between actual parameters and theoretical parameters of the filter inductor and the capacitor, inaccurate measurement of equivalent resistance of the filter inductor and the capacitor, aging of the filter inductor and the capacitor in the system operation process, time-varying load and the like. In view of the above uncertainties and making them compatible with the principles of back-stepping design, equation (1) is rewritten as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_c}{dt}=\left(\frac{1}{C}+{\mathrm{\Δ}}_1\right)i_L-\left(\frac{1}{CR}+{\mathrm{\Δ}}_2\right)u_c+{\mathrm{\Δw}}_1\left(t\right)\\ \frac{{\mathrm{di}}_L}{dt}=\left(\frac{1}{L}+{\mathrm{\Δ}}_3\right)(u_{inv}-u_c)+{\mathrm{\Δw}}_2\left(t\right)\end{array}\right.---\left(2\right)$

in the formula,. DELTA.₁、Δ₂、Δ₃The uncertainty part of the system parameters (considered according to the deviation of the three-phase filter parameters); Δ w₁(t),Δw₂(t) is external interference. Let the total uncertainty of the uncertainty term and the external disturbance be

d₁(t)＝i_LΔ₁-u_cΔ₂+Δw₁(t) (3)

d₂(t)＝u_invΔ₃-u_cΔ₃+Δw₂(t) (4)

The non-precise mathematical model of the three-phase full-bridge inverter obtained by the formulas (2-4) is

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_c}{dt}=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+d_1\left(t\right)\\ \frac{{\mathrm{di}}_L}{dt}=-\frac{1}{L}{u}_c+\frac{1}{L}{u}_{inv}+d_2\left(t\right)\end{array}\right.---\left(5\right)$

As can be seen from the mathematical model of the system, equation (1) is a multi-input multi-output nonlinear system, which is subordinate to the unified expression of equation (6):

$\left\{\begin{array}{c}\stackrel{\·}{y}=F_1\left(y\right)+G_1\left(y\right)x\\ \stackrel{\·}{x}=F_2(y,x)+G_2(y,x)u\end{array}\right.---\left(6\right)$

in the formula: y ═ u_c＝[u_cau_cbu_cc]^T

(7)

x＝i_L＝[i_Lai_Lbi_Lc]^T(8)

u＝u_inv＝[u_invau_invbu_invc]^T(9)

F₁(y)＝F₁'(y)+d₁(t) (10)

Wherein:d₁(t)＝[d₁₁(t) d₁₂(t) d₁₃(t)]^T

$G_1\left(y\right)=diag(\frac{1}{C},\frac{1}{C},\frac{1}{C})---\left(11\right)$

F₂(y,x)＝F₂'(y,x)+d₂(t) (12)

wherein,d₂(t)＝[d₂₁(t) d₂₂(t) d₂₃(t)]^T

$G_2(y,x)=diag(\frac{1}{L},\frac{1}{L},\frac{1}{L})---\left(13\right)$

and 2, aiming at a system meeting a strict feedback control structure, when a reverse recursion method is applied to design, a basic idea is to decompose a complex system into subsystems with the order not exceeding the system order, and design of the whole controller is completed by designing a part of Lyapunov function and a middle virtual control quantity through reverse recursion. The backstepping sliding mode control method is characterized in that in the last step of backstepping design, a sliding mode variable structure method is utilized, a sliding mode surface and index approach law is selected, and a backstepping sliding mode feedback control law of a system is designed.

As can be seen from equation (6), the order of the system is 2, so the whole design can be divided into two steps.

Step 2-1: designing a virtual control quantity x_ref

Defining a tracking error matrix E according to the system principal output₁Is composed of

E₁＝[e_u1e_u2e_u3]^T＝y_ref-y (14)

In the formula y_ref＝[u_carefu_cbrefu_ccref]^TFor outputting the desired value, the formula (14) is derived and arranged to obtain

${\stackrel{\·}{E}}_1={\stackrel{\·}{y}}_{ref}-\stackrel{\·}{y}={\stackrel{\·}{y}}_{ref}-F_1\left(y\right)-G_1\left(y\right)x---\left(15\right)$

Definition ofMatrix function and auxiliary error quantity E₂The matrix function is

$\mathrm{\β}({\stackrel{\·}{y}}_{ref},y)=F_1^{\′}\left(y\right)-{\stackrel{\·}{y}}_{ref}---\left(16\right)$

E₂＝[e_i1e_i2e_i3]^T＝x_ref-x (17)

x_ref＝[i_Larefi_Lbrefi_Lcref]^TIs a virtual control quantity.

Substitution of formulae (16) and (17) for formula (15) can give:

${\stackrel{\·}{E}}_1=-\mathrm{\β}({\stackrel{\·}{y}}_{ref},y)-G_1\left(y\right)x_{ref}+G_1\left(y\right)E_2---\left(18\right)$

designing a virtual control quantity x according to an error system_refIs composed of

$x_{ref}=G_1^{-1}\left(y\right)\[-\mathrm{\β}({\stackrel{\·}{y}}_{ref},y)+k_1{E}_1\]---\left(19\right)$

WhereinIn order to feed back the gain matrix,and G₁And (y) is a nonlinear singular square matrix.

By substituting formula (19) for formula (18)

${\stackrel{\·}{E}}_1=-k_1{E}_1+G_1\left(y\right)E_2---\left(20\right)$

For formula (20), if E₂→ 0, then E₁→0。

Choosing Lyapunov function as

$V_1=\frac{1}{2}{E}_1^T{E}_1---\left(21\right)$

Derived from formula (21)

${\stackrel{\·}{V}}_1=\frac{1}{2}({\stackrel{\·}{E}}_1^T{E}_1+E_1^T{\stackrel{\·}{E}}_1)=\frac{1}{2}(-E_1^T{k}_1^T{E}_1+E_2^T{G}_1^T{E}_1-E_1^T{k}_1{E}_1+E_1^T{G}_1{E}_2)---\left(22\right)$

Due to k₁Is a diagonal matrix, E₁,E₂Is a column matrix having

$E_1^T{k}_1^T{E}_1=E_1^T{k}_1{E}_1---\left(23\right)$

$E_2^T{G}_1^T{E}_1=E_1^T{G}_1{E}_2---\left(24\right)$

By substituting the formulae (23) and (24) for the formula (22)) to obtain

${\stackrel{\·}{V}}_1=-E_1^T{k}_1{E}_1+E_2^T{G}_1^T{E}_1---\left(25\right)$

Step 2-2: designing a control quantity matrix u

Derived from formula (17)

${\stackrel{\·}{E}}_2={\stackrel{\·}{x}}_{ref}-\stackrel{\·}{x}={\stackrel{\·}{x}}_{ref}-F_2(y,x)-G_2(y,x)u---\left(26\right)$

Choosing Lyapunov function as

$V_2=V_1+\frac{1}{2}{E}_2^T{E}_2---\left(27\right)$

To V₂Is derived by

$\begin{array}{c}{\stackrel{\·}{V}}_2={\stackrel{\·}{V}}_1+\frac{1}{2}({\stackrel{\·}{E}}_2^T{E}_2+E_2^T{\stackrel{\·}{E}}_2)\\ ={\stackrel{\·}{V}}_1+\frac{1}{2}\left(\right({\stackrel{\·}{x}}_{ref}^T-F_2^T\left(y,x\right)-u^T{G}_2^T)E_2+E_2^T({\stackrel{\·}{x}}_{ref}-F_2\left(y,x\right)-G_2\left(y,x\right)u\left)\right)\\ =-E_1^T{k}_1{E}_1+E_2^T{G}_1^T{E}_1+\frac{1}{2}({\stackrel{\·}{x}}_{ref}^T{E}_2-F_2^T(y,x)E_2-u^T{G}_2^T(y,x)E_2+E_2^T{\stackrel{\·}{x}}_{ref}-E_2^T{F}_2\left(y,x\right)-E_2^T{G}_2\left(y,x\right)u)\end{array}$

Due to the fact thatE₂,F₂(y, x), u is the column momentArray, G₂For diagonal matrix, then

${\stackrel{\·}{x}}_{ref}^T{E}_2=E_2^T{\stackrel{\·}{x}}_{ref}---\left(28\right)$

$F_2^T(y,x)E_2=E_2^T{F}_2(y,x)---\left(29\right)$

$u^T{G}_2^T(y,x)E_2=E_2^T{G}_2(y,x)u---\left(30\right)$

$E_2^T{G}_1^T{E}_1=E_1^T{G}_1{E}_2---\left(31\right)$

${\stackrel{\·}{V}}_2=-E_1^T{k}_1{E}_1+E_2^T{G}_1^T{E}_1+E_2^T{\stackrel{\·}{x}}_{ref}-E_2^T{F}_2(y,x)-E_2^T{G}_2(y,x)u---\left(32\right)$

Selecting a sliding mode surface according to a sliding mode control theory

s＝E₂(33)

The approximation rule of sliding mode is selected as

$\stackrel{\·}{s}=-\mathrm{\η}\mathrm{sgn}\left(s\right)-k_{2}s---\left(34\right)$

Wherein η is > 0, whereinIn order to feed back the gain matrix,

using the above three formulas, the following control law can be obtained

$u=G_2^{-1}(y,x)\[-F_2^{\′}(y,x)+{\stackrel{\·}{x}}_{ref}+k_{2}s+G_1^T\left(y\right)E_1+\mathrm{\η}\mathrm{sgn}\left(s\right)\]---\left(35\right)$

Substituted into

${\stackrel{\·}{V}}_2=-E_1^T{k}_1{E}_1-E_2^T{k}_2{E}_2-E_2^T\mathrm{\η}\mathrm{sgn}\left(s\right)+E_2^T{d}_2\left(t\right)---\left(36\right)$

In the formula, there is an uncertainty term d₂(t), it is difficult to determine the stability of the system by the equation (36).

According to the working principle of a three-phase voltage type inverter, the fluctuation of the capacitor voltage, the inductive current and the photovoltaic direct-current supply voltage of the inverter in one switching period is limited, and d is set_2i(t)≤d_imax,i＝1,2,3，d_imaxFor the upper limit of each phase disturbance, a control parameter η is selected_i≥d_imaxThen there is

$\begin{array}{c}-E_2^T\mathrm{\&eta;}\mathrm{sgn}\left(s\right)+E_2^T{d}_2\left(t\right)=-\&lsqb;\begin{array}{ccc}{e}_{i1}& e_{i2}& e_{i3}\end{array}\&rsqb;\&CenterDot;\left[\begin{array}{c}{\mathrm{\&eta;}}_1\mathrm{sgn}\left(e_{i1}\right)\\ {\mathrm{\&eta;}}_2\mathrm{sgn}\left(e_{i2}\right)\\ {\mathrm{\&eta;}}_3\mathrm{sgn}\left(e_{i3}\right)\end{array}\right]+\&lsqb;\begin{array}{ccc}{e}_{i1}& e_{i2}& e_{i3}\end{array}\&rsqb;\left[\begin{array}{c}{d}_{21}\left(t\right)\\ d_{22}\left(t\right)\\ d_{23}\left(t\right)\end{array}\right]\\ =-\left({\mathrm{\&eta;}}_1\right|e_{i1}|-e_{i1}{d}_{21}(t)+{\mathrm{\&eta;}}_2|e_{i2}|-e_{i2}{d}_{22}(t)+{\mathrm{\&eta;}}_3|e_{i3}|-e_{i3}{d}_{23}(t\left)\right)<0\end{array}$

From formula (36)

${\stackrel{\&CenterDot;}{V}}_2\&le;-E_1^T{k}_1{E}_1-E_2^T{k}_2{E}_2<0$

The system is asymptotically stable in a global sense according to the Lyapunov stability theorem.

Substituting the formulas (16) and (19) into (35) to obtain

$u=\left[\begin{array}{c}{\mathrm{LU}}_{ca}+L{\stackrel{\&CenterDot;}{x}}_{refa}+{\mathrm{Lk}}_{21}{e}_{i1}+\frac{L}{C}{e}_{u1}+{\mathrm{L\&eta;}}_1\mathrm{sgn}\left(e_{i1}\right)\\ {\mathrm{LU}}_{cb}+L{\stackrel{\&CenterDot;}{x}}_{refb}+{\mathrm{Lk}}_{22}{e}_{i2}+\frac{L}{C}{e}_{u2}+{\mathrm{L\&eta;}}_1\mathrm{sgn}\left(e_{i2}\right)\\ {\mathrm{LU}}_{cc}+L{\stackrel{\&CenterDot;}{x}}_{refc}+{\mathrm{Lk}}_{23}{e}_{i3}+\frac{L}{C}{e}_{u3}+{\mathrm{L\&eta;}}_1\mathrm{sgn}\left(e_{i3}\right)\end{array}\right]---\left(37\right)$

And 3, acting the feedback control model of the inverter system on Pulse Width Modulation (PWM) to control the three-phase inverter, thereby realizing the stable reverse-thrust sliding-mode control of the three-phase inverter of the microgrid.

In summary, a reverse sliding mode control block diagram of the three-phase inverter can be obtained as shown in fig. 3.

The following is described in more detail with reference to the examples:

examples

Simulation model is built based on PSCAD/EMTDC software to simulate controllerAnd (5) true verification. The simulation parameters are as follows: photovoltaic power generation system parameters: the illumination intensity is 1000lm/m²At an ambient temperature of 20 ℃ L_pv＝1mH，C_pv＝500μF，C_dc1000 μ F; inverter parameters: the output filter inductance L is 5mH, the capacitance C is 470 muF, and the local load is a rated pure resistive load R_a＝R_b＝R_c100 Ω; feedback control law parameters: k is a radical of₁₁＝k₁₂＝k₁₃＝3000，k₂₁＝k₂₂＝k₂₃＝25000，n₁＝n₂＝n₃＝100,₀46 and h₁100; the output voltage reference value is a three-phase symmetrical power frequency sine wave (with the same power grid voltage) with the amplitude of 310V, and the PWM switching frequency is f_s＝10kHz。

And carrying out simulation verification on the anti-disturbance capacity of the load of the photovoltaic inverter. The load jumps from R100 Ω to R50 Ω at 0.2s, and the waveforms of the output voltage and current are as shown in fig. 4. Therefore, when the load is suddenly changed, the transient transition time of the system is about 30ms, the output voltage waveform is basically free of disturbance, the current waveform is smoothly transited to a stable state, the frequency fluctuates between 50.01 Hz and 49.99Hz, and the disturbance is very small, so that the control strategy provided by the invention has a rapid dynamic characteristic and has good disturbance resistance on the load current.

And carrying out simulation verification on the external disturbance resistance of the photovoltaic inverter. The temperature is constant at 20 ℃, and the illumination intensity is controlled to be 1000lm/m at the time of 0.4s²The mutation is 1500lm/m². The 0.43s moment is 1500lm/m²Becomes 1000lm/m²The output voltage, current waveform and frequency response waveform are shown in fig. 5. From the simulation waveforms it can be seen that: when the illumination intensity changes, the voltage on the photovoltaic direct-current side fluctuates, but the output voltage and the current of the inverter are constant and are not interfered, the frequency disturbance is extremely small, and the disturbance resistance of the backstepping sliding mode control strategy to the illumination intensity change is very strong.

Illumination intensity is constant 1000lm/m²The temperature is changed from 20 deg.C to 25 deg.C at 0.4s, and from 25 deg.C to 20 deg.C at 0.43s, and voltage, current and frequency response waveforms such asAs shown in fig. 6. From the output voltage and current waveforms it can be seen that: when the ambient temperature changes, the voltage at the photovoltaic direct-current side has corresponding disturbance, the output voltage and the current of the inverter are constant, and the frequency disturbance is extremely small, which shows that the disturbance resistance of the backstepping sliding mode control strategy to the illumination intensity change is very strong.

Simulation verification is carried out on the perturbation resistance of the filter parameters of the photovoltaic inverter under the condition of pure resistive rated load, and the illumination intensity is selected to be 1000lm/m²The temperature is 20 ℃, and the load resistance is 50 omega. Fig. 7 shows simulation waveforms of load voltage, load current, and frequency response when L is 6.4mH and C is 470 μ F, where the voltage THD is 0.027%; simulation tests are carried out on other filter parameter combinations, and when the test result is that L is 6.4mH and C is 500 mu F, the voltage THD is 0.022%; when L is 5mH and C is 470 μ F, the voltage THD is 0.032%; when L is 5mH and C is 450 μ F, the voltage THD is 0.052%; when L is 7.5mH and C is 500 μ F, the voltage THD is 0.03%. The above results show that the control strategy provided by the invention is insensitive to the variation of the inverter LC filter parameters, has small steady-state error and distortion of the output voltage and no static difference in frequency, and can ensure that the output voltage accurately and quickly tracks the reference signal.

The nonlinear load adopts a three-phase uncontrolled rectifier bridge load, the filter capacitance of the rectifier is 1500 muF, the load resistance is 100 omega, and fig. 8 is a simulation waveform of the inverter when the inverter is in the nonlinear load. It can be known that the voltage waveform distortion is small under the condition of the nonlinear load, the output voltage THD is 0.42%, and the frequency is not affected; under the same condition, a control method of an inverse system sliding mode is adopted, and the THD in a simulation result is 1.07 percent; through comparison of control effects, the control strategy can effectively resist harmonic interference caused by nonlinear loads.

Unbalanced load can increase the unbalance degree and harmonic distortion rate of system operation voltage, influences little electric wire netting power quality. The unbalanced load is a linear unbalanced load, and Ra is 30 Ω, 20 Ω, and 20 Ω. The micro-source inverter controlled by PQ is affected by unbalanced load, the output voltage is seriously unbalanced, and the three-phase voltage waveform is irregular. The voltage unbalance is about 6.9%, which is seriously beyond the voltage unbalance requirement range specified by the safe operation of the power system. The simulation result of the unbalanced load with the sliding mode variable structure is shown in fig. 9. It can be seen that when the backstepping sliding mode control is adopted, the system voltage unbalance degree is reduced from 6.9% to 0.37%, and the THD is 0.78%. The system frequency fluctuates between 49.95 Hz and 50.10Hz, and the specified safe fluctuation range of the system frequency is met. Therefore, the sliding mode controller is connected to eliminate the influence of unbalanced load on the micro-grid and the power quality, optimize the power supply quality of the micro-grid and ensure the safe operation of equipment in the micro-grid.

The method fully considers the influence of multiple factors such as uncertainty of filter parameters, external interference and the like on a three-phase inverter system, utilizes the characteristics that the sliding mode of a sliding mode variable structure has invariance, the dependence degree on a system mathematical model is low, and the robustness on system parameter perturbation and external interference is strong, combines a reverse method with a sliding mode control method, establishes the mathematical model of the inverter system by taking filter capacitor voltage and inductance current as control variables, uses the tracking error of the control variables as the input of a controller, and deduces that a feedback control law of the inverter system acts on pulse width modulation to control the three-phase inverter. The invention has reasonable design, comprehensively considers the practical engineering application, has good steady-state and dynamic characteristics, has strong robustness to parameter perturbation and load disturbance, is not only suitable for linear, nonlinear and unbalanced loads, but also can be popularized in other three-phase inverters of different types, provides an idea for the design of inverter control systems, and has good engineering application prospect.

Claims (8)

1. A three-phase inverter reverse thrust sliding mode control method for realizing micro-grid stability is characterized by comprising the following steps:

step A, establishing a mathematical model of an inverter system by taking filter capacitor voltage and inductor current as control variables;

b, combining a reverse pushing method with a sliding mode variable structure control method to construct a feedback control model of the inverter system;

and step C, acting the feedback control model of the inverter system on Pulse Width Modulation (PWM) to control the three-phase inverter, so as to realize stable reverse-thrust sliding-mode control of the three-phase inverter of the microgrid.

2. The method for realizing the reverse-thrust sliding-mode control of the three-phase inverter for stabilizing the microgrid according to claim 1, wherein the mathematical model of the inverter system in the step A is as follows:

$\left\{\begin{array}{c}\frac{{\mathrm{du}}_c}{dt}=-\frac{1}{RC}{u}_c+\frac{1}{C}{i}_L+d_1\left(t\right)\\ \frac{{\mathrm{di}}_L}{dt}=-\frac{1}{L}{u}_c+\frac{1}{L}{u}_{inv}+d_2\left(t\right)\end{array}\right.$

in the formula u_c＝[u_cau_cbu_cc]^TThe collected three-phase filter capacitor voltage; i.e. i_L＝[i_Lai_Lbi_Lc]^TThe collected three-phase filtering inductance current; u-u_inv＝[u_invau_invbu_invc]^TThe output voltage of the three-phase inverter is L, C, the filter inductance value and the filter capacitance value are R, and the local load resistance value is R; d₁(t) is the total perturbation term matrix of voltage parameter uncertainty terms and external interference, d₂And (t) is a total perturbation term matrix of the current parameter uncertainty term and the external interference.

3. The method for realizing the reverse-thrust sliding-mode control of the three-phase inverter for stabilizing the microgrid according to claim 1, wherein the feedback control model of the inverter system in the step B is as follows:

$u=G_2^{-1}(y,x)\&lsqb;-F_2^{\&prime;}(y,x)+{\stackrel{\&CenterDot;}{x}}_{ref}+k_{2}s+G_1^T\left(y\right)E_1+\mathrm{\&eta;}sgn\left(s\right)\&rsqb;$

wherein, E₁＝[e_u1e_u2e_u3]^Tfor the input of the tracking error variable matrix,is E₁Virtual control quantity matrix x of subsystem_ref＝[i_Larefi_Lbrefi_Lcref]^TS is a sliding mode surface matrix selected by the sliding mode variable structure control, sgn(s) is a corresponding sign function, k₂＝diag(k₂₁,k₂₂,k₂₃)、η＝diag(η₁,η₂,η₃) Is an adjustable control parameter matrix.

4. The method for realizing the reverse-thrust sliding-mode control of the three-phase inverter for stabilizing the micro-grid according to claim 2, wherein the voltage parameter isTotal perturbation term matrix d of number uncertainty term and external interference₁(t) is:

d₁(t)＝i_LΔ₁-U_cΔ₂+Δw₁(t)

in the formula,. DELTA.₁、Δ₂Is the uncertainty part of the system filter parameters; Δ w₁(t), which is external interference and is caused by unstable voltage on the direct current side of the inverter or load fluctuation;

total perturbation term matrix d of current parameter uncertainty term and external interference₂(t) is:

d₂(t)＝u_invΔ₃-U_cΔ₃+Δw₂(t)

in the formula,. DELTA.₃Is the uncertainty part of the system filter parameters; Δ w₂And (t) is external interference, which is mainly caused by unstable voltage on the direct current side of the inverter or load fluctuation.

5. The three-phase inverter reverse-thrust sliding-mode control method for realizing microgrid stabilization according to claim 3 is characterized in that: the sliding mode surface matrix selected by the sliding mode variable structure control is as follows: s ═ E₂The corresponding sliding mode approach law is

Wherein E is₂＝x_ref-i_L＝[e_i1e_i2e_i3]^T，sgn(s)＝[sgn(e_i1) sgn(e_i2) sgn(e_i3)]^T；

The virtual control quantity matrix x_refComprises the following steps:

wherein,k₁＝diag(k₁₁,k₁₂,k₁₃) To be adjustableThe control parameter matrix of (2) is,

$\mathrm{\&beta;}({\stackrel{\&CenterDot;}{y}}_{ref},y)=F_1^{\&prime;}\left(y\right)-{\stackrel{\&CenterDot;}{y}}_{ref}$

in the formula,the derivative of a reference value, reference value y, of the filter capacitor voltage_ref＝[u_carefu_cbrefu_ccref]^TThe power frequency sine wave is three-phase symmetrical and has the amplitude of 310V.

6. A system for realizing the reverse-thrust sliding-mode control method of the three-phase inverter according to claim 1 is characterized by comprising an information acquisition module, a virtual control module, a reverse-thrust sliding-mode control module, a pulse width modulation module and the three-phase inverter, wherein:

the information acquisition module acquires output signals of the inverter, wherein the signals comprise three-phase filter capacitor voltage values and three-phase filter inductor current values;

the virtual control module receives the inverter output signal acquired by the information acquisition module, compares the signal with a corresponding reference value, and sends a comparison result to the virtual control module and the reverse-thrust sliding-mode control module;

the virtual control module carries out reverse pushing processing on the comparison result and transmits the processing result to the reverse pushing sliding mode control module;

the backstepping and backstepping sliding mode control module performs backstepping and sliding mode control processing on the received signal and transmits a processing result to the pulse width modulation module;

the pulse width modulation module performs pulse width modulation on the received signals and then sends the signals to six switches of the three-phase inverter, so that reverse-thrust sliding-mode control of the three-phase inverter is realized.

7. The system of claim 6, wherein the virtual control module performs inverse transformation on the comparison result according to the following formula:

$\mathrm{\&beta;}({\stackrel{\&CenterDot;}{y}}_{ref},y)=F_1^{\&prime;}\left(y\right)-{\stackrel{\&CenterDot;}{y}}_{ref}={\&lsqb;-\frac{u_{ca}}{RC}-{\stackrel{\&CenterDot;}{u}}_{caref}-\frac{u_{cb}}{RC}-{\stackrel{\&CenterDot;}{u}}_{cbref}-\frac{u_{cc}}{RC}-{\stackrel{\&CenterDot;}{u}}_{ccref}\&rsqb;}^T,$

$x_{ref}=G_1^{-1}\left(y\right)\&lsqb;-\mathrm{\&beta;}({\stackrel{\&CenterDot;}{y}}_{ref},y)+k_1{E}_1\&rsqb;=\left[\begin{array}{c}\frac{u_{ca}}{R}+C{\stackrel{\&CenterDot;}{u}}_{caref}+k_{11}{e}_{u1}\\ \frac{u_{cb}}{R}+C{\stackrel{\&CenterDot;}{u}}_{cbref}+k_{12}{e}_{u2}\\ \frac{u_{cc}}{R}+C{\stackrel{\&CenterDot;}{u}}_{ccref}+k_{13}{e}_{u3}\end{array}\right].$

8. the system according to claim 6, wherein the backstepping and sliding mode control module performs backstepping and sliding mode control on the received signal according to the following formula:

$\begin{array}{c}u=G_2^{-1}\&lsqb;-F_2(y,x)+d_2\left(t\right)+{\stackrel{\&CenterDot;}{x}}_{ref}+k_{2}s+G_1^T\left(y\right)E_1+\mathrm{\&eta;}sgn\left(s\right)\&rsqb;\\ =\left[\begin{array}{c}L{u}_{ca}+L{\stackrel{\&CenterDot;}{i}}_{Laref}+L{k}_{21}{e}_{i1}+\frac{L}{C}{e}_{u1}+L{\mathrm{\&eta;}}_{1}sgn\left(e_{i1}\right)\\ L{u}_{cb}+L{\stackrel{\&CenterDot;}{i}}_{Lbref}+L{k}_{22}{e}_{i2}+\frac{L}{C}{e}_{u2}+L{\mathrm{\&eta;}}_{2}sgn\left(e_{i2}\right)\\ L{u}_{cc}+L{\stackrel{\&CenterDot;}{i}}_{Lcref}+L{k}_{23}{e}_{i3}+\frac{L}{C}{e}_{u3}+L{\mathrm{\&eta;}}_{3}sgn\left(e_{i3}\right)\end{array}\right]\end{array}.$