Nonlinear control method for micro-grid inverter with anti-disturbance

Abstract

Nonlinear control method for the micro-grid inverter with anti-disturbance. By generating reference currents that satisfy specific active and reactive power command under various working conditions, and introducing a nonlinear control method based on Lyapunov function to control the inverter, fast and accurate tracking of the generated reference signals is realized. The method realizes effective decoupling control of active power and reactive power. The system has high dynamic response and good robustness. Besides, the control structure of the method is simple and easy to implement, and the synchronous control link and the additional voltage and current regulator are omitted. The method realizes fast and accurate power exchange and stable power transmission between the inverter and the grid in the micro-grid under various working conditions, and provides a guarantee for improving the energy management efficiency within the micro-grid.

Claims

1. A method for controlling power transmission between a micro-grid system and a power grid, comprising providing a micro-grid system and a nonlinear controller for the micro-grid system, wherein the micro-grid system comprises a distributed electric generation element that is connected to a power grid through a grid-connected point switch, a three-phase AC bus, a three-phase AC load, and a central controller; the distributed electric generation element comprises a DC voltage source, three-phase voltage source full-bridge inverter having six switch tubes corresponding to six channels, and an LCL-type filter circuit; and the LCL-type filter circuit comprises an inverter-side filter circuit, a grid-side filter circuit, and a filter capacitor, collecting voltage v.sub.c of the filter capacitor and current i.sub.0 of the grid-side inductance from the LCL-type filter circuit and establishing a mathematical model of a two-phase stationary coordinate system based on coordinate transformation of the voltage v.sub.c to v.sub.c and the grid-side inductance current i.sub.0 to i.sub.0 by the nonlinear controller, collecting voltage v.sub.g of the three-phase AC bus and local load current i.sub.load, generating a grid-side inductance current reference signal i.sub.o_ref in the two-phase stationary coordinate system based on the voltage v.sub.g and local load current i.sub.load according to instantaneous reactive power theory, and calculating grid-connected current i.sub.g based on the grid-side inductance current reference signal i.sub.o_ref, active power command P.sub.set, and reactive power command Q.sub.set from the central controller of the micro-grid, obtaining a first derivative {dot over (i)}.sub.o_ref (t) and a second derivative .sub.o_ref (t) of the grid-side inductance reference current signal i.sub.o_ref (t) by an observer, and using the first derivative and the second derivative as input signal values of the nonlinear controller, setting an original tracking error e.sub. and a filter tracking error E.sub. of a control variable i.sub.0, and building a grid-connected inverter nonlinear control model based on the original tracking error and the filter error by the nonlinear controller, obtaining a three-phase modulated wave signal according to the mathematical model of the LCL type grid-connected inverter and the grid-connected inverter nonlinear control model in a three-phase stationary coordinate system after coordinate transformation by the nonlinear controller, obtaining modulated pulse signals of six channels S1 to S6 from the three-phase modulated wave signal by the sine wave vector modulation module, inputting the modulated pulse signals of the six channels S1 to S6 and applying Lyapunov function to the three-phase voltage source full-bridge inverter, and transmitting power applied with the modulated pulse signals and the Lyapunov function between the three-phase voltage source full-bridge inverter of the micro-grid system and the power grid through the grid-connected point switch and maintaining stability of the power voltage therebetween.

2. The method for controlling power transmission between the micro-grid system and the power grid of claim 1, wherein the mathematical model of the two-phase stationary coordinate system based on the coordinate transformation of the voltage v.sub.c to v.sub.c and the grid-side inductance current i.sub.0 to i.sub.0 in the nonlinear controller is as follows: $\begin{array}{cc}\frac{{\mathrm{di}}_o}{\mathrm{dt}}=x_{}-d;\frac{{\mathrm{dx}}_{}}{\mathrm{dt}}=u_{},& \left(17\right)\end{array}$ wherein i.sub.o is the grid-side inductance current, u.sub. is a nonlinear control law in the two-phase stationary coordinate system; x.sub. is a state variable as follows:
x.sub.=v.sub.c/L.sub.o(18), d is a disturbance that comprises error caused by system disturbance and model uncertainty as follows: $\begin{array}{cc}d=\frac{1}{L_o}\left(v_g+v_g\right)+\frac{i_o}{L_o}\left(R_o+R_o\right)+\frac{1}{L_o}\left(L_o{\stackrel{.}{i}}_o-v_c\right),& \left(19\right)\end{array}$ L.sub.o is an estimate of a sum L.sub.o of the grid-side filter inductance and a line inductance, v.sub.g is a disturbance caused by a grid voltage, R.sub.o is a value of a line resistance, R.sub.o and L.sub.o are deviations between an actual applied value and a theoretical value due to uncertainty of line parameters, respectively, v.sub.c is an effect of the grid voltage disturbance on a capacitor voltage, i.sub.load is a load current in the two-phase stationary coordinate system, and v.sub.g is the grid voltage in the two-phase stationary coordinate system.

3. The method for controlling power transmission between the micro-grid system and the power grid of claim 1, wherein the grid-side inductance current reference signal i.sub.o_ref in the two-phase stationary coordinate system is generated according to the instantaneous reactive power theory after coordinate transformation as follows: $\begin{array}{cc}{i}_{o\_\mathrm{ref}}=\left[\begin{array}{c}{i}_{o\_\mathrm{ref}}\\ i_{o\_\mathrm{ref}}\end{array}\right]=\left[\begin{array}{c}{i}_{\mathrm{load}}\\ i_{\mathrm{load}}\end{array}\right]-\left[\begin{array}{c}{i}_g\\ i_g\end{array}\right].& \left(20\right)\end{array}$

4. The method for controlling power transmission between the micro-grid system and the power grid of claim 3, wherein the original tracking error e.sub. and the filter tracking error E.sub. are set as follows:
e.sub.=i.sub.oi.sub.o_ref; E=E.sub.=ke.sub.+.sub.(22), wherein k is a custom constant greater than zero; .sub. is a first derivative of the original tracking error e.sub., and a tracking error is defined as
r=r.sub.=E.sub.+.sub.(23).

5. The method for controlling power transmission between the micro-grid system and the power grid of claim 1, wherein the grid-connected current i.sub.g is calculated as follows: $\begin{array}{cc}{i}_g=\left[\begin{array}{c}{i}_g\\ i_g\end{array}\right]=\frac{2}{3}.Math.\frac{1}{v_g^2+v_g^2}\left[\begin{array}{cc}{v}_g& v_g\\ v_g& -v_g\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{set}}\\ Q_{\mathrm{set}}\end{array}\right].& \left(21\right)\end{array}$ P.sub.set and Q.sub.set are the active power and reactive power commands from the central controller, respectively.

6. The method for controlling power transmission between the micro-grid system and the power grid of claim 1, wherein the grid-connected inverter nonlinear control model is built as follows: $\begin{array}{cc}{u}_{}\left(t\right)=-{\mathrm{kx}}_{}\left(t\right)-\left(+k_s\right)E_{}\left(t\right)+k{\stackrel{.}{i}}_{o\_\mathrm{ref}}\left(t\right)+{\stackrel{\mathrm{.Math.}}{i}}_{o\_\mathrm{ref}}\left(t\right)-{}_0^t\left(k_s+\frac{1}{}\right)E_{}\left(\right)d,& \left(24\right)\end{array}$ wherein i.sub.load is a load current in the two-phase stationary coordinate system, and k, , k.sub.s, are custom constants greater than zero, respectively.

7. The method for controlling power transmission between the micro-grid system and the power grid of claim 1, wherein the three-phase modulated wave signal v.sub.s is obtained in the three-phase stationary coordinate system as follows: $\begin{array}{cc}{v}_s=\frac{1}{K_d}.Math.v_i=\frac{1}{K_d}.Math.\left\{\frac{d}{\mathrm{dt}}\left({\stackrel{\_}{L}}_o\stackrel{\_}{C}.Math.u_{}+i_o\right){\stackrel{\_}{L}}_i+v_c\right\},& \left(25\right)\end{array}$ wherein v.sub.i is an inverter input voltage in the two-phase stationary coordinate system; K.sub.d is a scaling factor that is greater than zero and a DC voltage value of an inverter side; L.sub.i, C, L.sub.o are are estimates of the inverter-side filter inductance L.sub.i,the filter capacitor C, and sum L.sub.i of the grid-side filter inductance and the line parameter; v.sub.c is capacitor voltage in the two-phase stationary coordinate system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of a micro-grid system including an LCL type grid-connected inverter of the present invention.

(2) FIG. 2 is a schematic diagram showing the control method of the present invention.

(3) FIGS. 3(a) to 3(c) show the voltage waveform and the system active/reactive waveforms when the grid-connected point is interfered according to the present invention, among which, FIG. 3(a) shows the voltage waveform and the system active/reactive waveforms when harmonic is contained in the voltage of the grid-connected point; FIG. 3(b) shows the voltage waveform and the system active/reactive waveforms when voltage amplitude of the grid connection increases/decreases; and FIG. 3(c) shows the voltage waveform and the system active/reactive waveforms when frequency hopping of the grid-connected point occurs.

(4) FIG. 4 shows waveforms of the system active/reactive power when the active/reactive power command changes suddenly in the present invention, indicating that the active/reactive power of the system has fast dynamic responses without any delay and transients to keep up with changes in power command.

(5) FIG. 5 shows the active/reactive power and current waveforms of the system under nonlinear loads in the present invention, indicating that the active/reactive power of the system has little affected by load changes even the loads are nonlinear.

DETAILED DESCRIPTION OF THE PRESENT INVENTION AND EMBODIMENTS

(6) In combination with figures, the embodiments of the present invention is further expounded.

(7) The nonlinear control method for the micro-grid inverter with anti-disturbance of the present invention is implemented on an LCL type grid-connected inverter in the micro-grid system shown in FIG. 1. The system mainly includes six parts: an external power grid 1, a grid-connected point switch 2, a three-phase AC bus 3, a three-phase load 4, a distributed electric generation element 5, and other distributed electric generation elements 6.

(8) The distributed electric generation element 5 includes a DC voltage source 7, a three-phase voltage source full-bridge inverter 8, an LCL-type filter circuit 9, and a line impedance 10. The DC voltage source 7 uses an ideal DC voltage source, and the voltage is expressed as V.sub.dc; the three-phase voltage source full-bridge inverter 8 includes six switch tubes S.sub.1S.sub.6; the LCL-type filter circuit 9 includes an inverter-side filter inductance L.sub.i 11, a filter capacitor C 12, and a grid-side filter inductance L.sub.g 13; the line impedance 10 includes the line resistance R.sub.o 14 and the line inductance L.sub.l 15. For the modeling's sake, the grid-side filter inductance L.sub.g and the equivalent line inductance L.sub.l are combined into L.sub.o 16. The no-load voltage of the three-phase voltage source full-bridge inverter 8 is v.sub.i; the voltage of the filter capacitor 12 is v.sub.c; the voltage at the grid-connected point is v.sub.g, the inductance current on the inverter side is i.sub.i; the inductance current on the grid side is i.sub.o; the load current is i.sub.load; the current flowing into the grid is i.sub.g.

(9) The control method of the present invention includes the following steps:

(10) Step 1: Collect the LCL type grid-connected inverter filter capacitor voltage v.sub.c and the grid-side inductance current i.sub.o, and the mathematical model of the two parameters in the two-phase stationary coordinate system are established through coordinate transformation;

(11) First, according to FIGS. 1 and 2, the mathematical model of the system in the two-phase stationary coordinate system is expressed as follows:

(12) $\begin{array}{cc}{L}_i\frac{{\mathrm{di}}_i}{\mathrm{dt}}=v_i-v_c{L}_o\frac{{\mathrm{di}}_o}{\mathrm{dt}}=v_c-v_g-R_o{i}_o.C\frac{{\mathrm{dv}}_c}{\mathrm{dt}}=i_i-i_o& \left(17\right)\end{array}$

(13) Considering the uncertainty of model parameters and the interference that the system may experience, equation (17) can be expressed as follows:

(14) $\begin{array}{cc}{\stackrel{.}{i}}_o=\frac{v_c}{L_o}-\frac{1}{L_o}\left(v_g+R_o{i}_o\right)-\frac{1}{L_o}\left(L_o{\stackrel{.}{i}}_o+v_g+R_o{i}_o-v_c\right)& \left(18\right)\end{array}$

(15) where L.sub.o, R.sub.o represents the deviation of system parameter estimation; v.sub.g represents the disturbance caused by the grid voltage, and v.sub.c represents the capacitor voltage disturbance caused by system parameter and grid voltage.

(16) The disturbance is expressed as follows:

(17) $\begin{array}{cc}{d}_1=\frac{1}{L_o}\left(v_g+v_g\right);d_2=\frac{i_o}{L_o}\left(R_o+R_o\right);d_3=\frac{1}{L_o}\left(L_o{\stackrel{.}{i}}_o-v_c\right).& \left(19\right)\end{array}$

(18) Define state variables:

(19) $x_{}=\frac{v_c}{{\stackrel{\_}{L}}_o},$
the control law is expressed as:

(20) 0$u_{}=\frac{1}{{\stackrel{\_}{L}}_o\stackrel{\_}{C}}\left(i_i-i_o\right),$
where L.sub.o, C are estimates of L.sub.o, C, respectively. Therefore, the simplified mathematical model of the grid-connected inverter is as follows:

(21) $\begin{array}{cc}\frac{{\mathrm{di}}_o}{\mathrm{dt}}=x_{}-d;\frac{{\mathrm{dx}}_{}}{\mathrm{dt}}=u_{}.& \left(20\right)\end{array}$

(22) where d is the disturbance and can be expressed as

(23) $d=\frac{d_1+d_2+d_3}{3},$
which is assumed to be unknown and finite.

(24) Step 2: Collect the AC bus voltage v.sub.g and the local load current i.sub.load. After coordinate transformation, the grid-side inductance current reference signal in the two-phase stationary coordinate system is generated according to the instantaneous reactive power theory. The derivative of the reference signal is taken by the observer to obtain the first and second derivative value of the reference signal as input signal values of the nonlinear controller;

(25) The collected signals v.sub.g and i.sub.load are coordinate transformed to obtain v.sub.g and i.sub.load, and the current reference value i.sub.o_ref of the grid-side filter inductance is obtained by the calculation formula (21) based on the instantaneous reactive power theory.

(26) $\begin{array}{cc}{i}_{o\_\mathrm{ref}}=\left[\begin{array}{c}{i}_{o\_\mathrm{ref}}\\ i_{o\_\mathrm{ref}}\end{array}\right]=\left[\begin{array}{c}{i}_{\mathrm{load}}\\ i_{\mathrm{load}}\end{array}\right]-\frac{2}{3}.Math.\frac{1}{v_g^2+v_g^2}\left[\begin{array}{cc}{v}_g& v_g\\ v_g& -v_g\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{set}}\\ Q_{\mathrm{set}}\end{array}\right].& \left(21\right)\end{array}$

(27) Then, accurate estimates of the first and second derivatives of the reference signal are obtained by the observer:
{dot over ()}.sub.o_ref=k.sub.o(i.sub.o_ref.sub.o_ref)(22),
where {dot over ()}.sub.o_ref and .sub.o_ref are the estimated values of {dot over (i)}.sub.o_ref and i.sub.o_ref, respectively, k.sub.o is the gain of the observer, and .sub.o_ref is updated in real time according to {circumflex over ({dot over (i)})}.sub.o_ref=k.sub.o(i.sub.o_ref.sub.o_ref).

(28) Define the output error of the observer as follows:
e.sub.1=i.sub.o_ref.sub.o_ref;e.sub.2={dot over (i)}.sub.o_ref{dot over ()}.sub.o_ref(23).

(29) By setting the gain of the observer k.sub.0 to a large enough value, the output error of the observer can be adjusted to within the range that the system allows. In the same way, the second derivative of the current reference signal is obtained on the basis of the first derivative.

(30) Step 3: Set the original tracking error and the filter tracking error of the control variable i.sub.o to establish a nonlinear control model of the grid-connected inverter. The original error signal and the filter tracking error signal are defined as:
e.sub.=i.sub.oi.sub.o_ref;E.sub.=ke.sub.+.sub.(24).

(31) Through the observer in step 2, the first derivative {dot over (i)}.sub.o of the grid-side filter inductance current is obtained. The filter tracking error E.sub. is obtained as an input signal of the nonlinear controller by the formula (24), and the nonlinear control law is as follows:

(32) $\begin{array}{cc}{u}_{}\left(t\right)=-{\mathrm{kx}}_{}\left(t\right)-\left(+k_s\right)E_{}\left(t\right)+k{\stackrel{.}{i}}_{o\_\mathrm{ref}}\left(t\right)+{\stackrel{\mathrm{.Math.}}{i}}_{o\_\mathrm{ref}}\left(t\right)-{}_0^t\left(k_s+\frac{1}{}\right)E_{}\left(\right)d,& \left(25\right)\end{array}$

(33) where k, , k.sub.s, and are custom constants greater than zero, respectively.

(34) Step 4: The modulated wave signal is obtained according to the LCL type grid-connected inverter mathematical model and the grid-connected inverter nonlinear control model. After coordinate transformation, the modulated wave signal in the three-phase stationary coordinate system is obtained. The grid-connected inverter is controlled by introducing a nonlinear control method based on Lyapunov function.

(35) According to equation (17), the modulation wave signal in the two-phase stationary coordinate system is as follows:

(36) $\begin{array}{cc}{v}_s=\frac{1}{K_d}.Math.v_i=\frac{1}{K_d}.Math.\left\{\frac{d}{\mathrm{dt}}\left({\stackrel{\_}{L}}_o\stackrel{\_}{C}.Math.u_{}+i_o\right){\stackrel{\_}{L}}_i+v_c\right\}.& \left(26\right)\end{array}$

(37) where L.sub.i is the estimated value of the inverter-side filter inductance; K.sub.d is the scaling factor greater than zero.

(38) The modulation wave signal is input into the sine wave vector modulation module to obtain pulse signals of six channels, S.sub.1S.sub.6, which are input into the three-phase voltage source full-bridge inverter circuit to control the said circuit.

(39) In conclusion, the nonlinear power control method of the LCL type grid-connected inverter can be obtained, as shown in FIG. 2.

(40) A simulation model of the LCL type grid-connected inverter system is built by Matlab/Simulink.

(41) Three working conditions are simulated to test the control method of the present invention, that is, the simulated inverter is affected by the voltage disturbance (containing harmonics, voltage amplitude fluctuation, and frequency hopping) at the grid-connected point, the power preset value is changed, and the nonlinear load is connected.

(42) Working condition 1: The grid voltage at the grid-connected point is disturbed. There are three main situations:

(43) 1. Background harmonics are contained;

(44) 2. Voltage amplitude fluctuation;

(45) 3. Frequency fluctuation.

(46) The power value is set to input 20 kW of active power to the grid and transmit 10 kVar of reactive power. The effects of the above three grid-side disturbances on the power input to the grid by the inverter are verified. The simulation results are shown in FIGS. 3(a) to 3(c). v.sub.ga, v.sub.gb, and v.sub.gc represent voltages of three phases at the grid-connected point abc respectively. P.sub.g and Q.sub.g represent the active and reactive power exchange between the inverter and the grid respectively. The simulation time of the system is 0.2 s. For the convenience of comparing, the voltage at the grid-connected point during 00.1 s is a ideal voltage waveform, and the voltage at the grid-connected point during 0.1 s0.2 s is disturbed, which is a non-ideal voltage waveform.

(47) Firstly, after 0.1 s, it is set that the voltage at the grid-connected point contains the third harmonic component of 15V and the fifth harmonic component of 15V, while the phase of the third harmonic component phase lags the phase of the fundamental component by 25 degrees, and the phase of the fifth harmonic component phase leads the phase of the fundamental component by 35 degrees. It can be seen from FIG. 3(a) that after 0.1 s, the active and reactive power input into the grid by the inverter can accurately track the preset power command, and the power transmission is kept stable when the voltage at the grid-connected point is distorted. No second harmonic pulsation is generated and no large fluctuation occurs at the moment when the voltage condition deteriorates.

(48) Then, after 0.1 s, it is set that the voltage amplitude at the grid-connected point begin to fluctuate. It can also be observed that the active and reactive power input into the grid are always maintained around the preset value and remains stable at all times.

(49) Finally, after 0.1 s, it is set that the voltage frequency at the grid-connected point jumps from 50 Hz to 49.5 Hz. It can be seen that the power transmission is not affected by the frequency change.

(50) Working condition 2: The preset power command changes over time. In 00.1 s, the active and reactive power input into the grid are set to zero; in 0.1 s0.2 s, the system transmits 10 kW of active power to the grid and receives 20 kVar of reactive power from the grid; in 0.2 s0.3 s, the system transmits 20 kW of active power to the grid and receives 10 kVar of reactive power from the grid; in 0.3 s0.4 s, the system transmits 10 kW of active power to the grid and receives 10 kVar of reactive power from the grid.

(51) It can be seen from the simulation results that the system realizes decoupling control of active and reactive power, and can track power commands quickly and accurately.

(52) Working condition 3: The system supplies power to the linear load from 0 to 0.1 s, and supplies power to the nonlinear load from 0.1 s to 0.2 s. And the power command is to transmit 20 kW of active power and 10 kVar of reactive power to the grid.

(53) From the waveforms of the system active/reactive power when the active/reactive power command changes suddenly in the present invention as shown in FIG. 4, the active/reactive power of the system has fast dynamic responses without any delay and transients to keep up with changes in power command. From the active/reactive power and current waveforms of the system under nonlinear loads in the present invention as shown in FIG. 5, the active/reactive power of the system has little affected by load changes even the loads are nonlinear.

(54) It can be seen from the simulation results that at the moment when the load sudden changes, the power has received a small impact and quickly converges to the command value, and ensures the smooth and accuracy quality of power transmission to the grid when the load is nonlinear.

(55) It can be seen that by using the said control method, the LCL type grid-connected inverter has good power transmission capability and the dynamic response of the system is rapid under conditions that the voltage point at the grid-connected is disturbed or the load is nonlinear.